[{"data":1,"prerenderedAt":24512},["ShallowReactive",2],{"blog-\u002Fblog\u002F001-backpropagation":3,"blog-all":24488},{"id":4,"title":5,"body":6,"date":24476,"description":24477,"draft":24478,"extension":24479,"image":24480,"meta":24481,"navigation":22996,"no":22976,"path":24482,"pinned":24478,"seo":24483,"stem":24484,"tags":24485,"updated":24480,"__hash__":24487},"blog\u002Fblog\u002F001-backpropagation.md","バックプロパゲーション（誤差逆伝播法）を数式から理解する",{"type":7,"value":8,"toc":24458},"minimark",[9,22,25,30,205,778,1492,1499,2119,2151,2520,2524,2924,3193,3197,3408,3882,3889,3893,3898,4303,4717,4752,5132,5136,5347,6302,6766,7275,7278,7789,8303,8773,8869,8873,9087,9595,9599,9899,10619,10762,10766,10769,11861,12833,13951,14096,14282,14286,14289,15859,16420,16949,16981,16985,16988,17895,18370,18374,19081,19085,19586,21289,21293,21791,21795,21802,22088,22415,22854,22955,22959,22962,24001,24004,24012,24111,24175,24179,24199,24206,24209,24454],[10,11,12,13,17,18,21],"p",{},"ニューラルネットワークの学習では、損失関数を小さくする方向へパラメータを少しずつ動かします。そのためには 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",[33,80,82,96],{"className":81},[36],[33,83,85],{"className":84},[40],[42,86,87],{"xmlns":44},[46,88,89,94],{},[49,90,91],{},[52,92,93],{},"l",[56,95,93],{"encoding":58},[33,97,99],{"className":98,"ariaHidden":63},[62],[33,100,102,106],{"className":101},[67],[33,103],{"className":104,"style":105},[71],"height:0.6944em;",[33,107,93],{"className":108,"style":109},[76,77],"margin-right:0.0197em;"," 層（",[33,112,114,146],{"className":113},[36],[33,115,117],{"className":116},[40],[42,118,119],{"xmlns":44},[46,120,121,143],{},[49,122,123,125,129,133,136,139,141],{},[52,124,93],{},[126,127,128],"mo",{},"=",[130,131,132],"mn",{},"1",[126,134,135],{"separator":63},",",[126,137,138],{},"…",[126,140,135],{"separator":63},[52,142,54],{},[56,144,145],{"encoding":58},"l = 1, \\dots, 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= 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層の重み行列とバイアス",[785,1075,1076,1152],{},[800,1077,1078],{},[33,1079,1081,1105],{"className":1080},[36],[33,1082,1084],{"className":1083},[40],[42,1085,1086],{"xmlns":44},[46,1087,1088,1102],{},[49,1089,1090],{},[237,1091,1092,1094],{},[52,1093,242],{"mathvariant":241},[49,1095,1096,1098,1100],{},[126,1097,248],{"stretchy":247},[52,1099,93],{},[126,1101,253],{"stretchy":247},[56,1103,1104],{"encoding":58},"\\mathbf{z}^{(l)}",[33,1106,1108],{"className":1107,"ariaHidden":63},[62],[33,1109,1111,1114],{"className":1110},[67],[33,1112],{"className":1113,"style":843},[71],[33,1115,1117,1120],{"className":1116},[76],[33,1118,242],{"className":1119},[76,414],[33,1121,1123],{"className":1122},[418],[33,1124,1126],{"className":1125},[386],[33,1127,1129],{"className":1128},[391],[33,1130,1132],{"className":1131,"style":843},[395],[33,1133,1134,1137],{"style":864},[33,1135],{"className":1136,"style":435},[403],[33,1138,1140],{"className":1139},[439,440,441,442],[33,1141,1143,1146,1149],{"className":1142},[76,442],[33,1144,248],{"className":1145},[449,442],[33,1147,93],{"className":1148,"style":109},[76,77,442],[33,1150,253],{"className":1151},[456,442],[800,1153,1154],{},"活性化関数に入る前の値（重み付き入力）",[785,1156,1157,1189],{},[800,1158,1159],{},[33,1160,1162,1176],{"className":1161},[36],[33,1163,1165],{"className":1164},[40],[42,1166,1167],{"xmlns":44},[46,1168,1169,1173],{},[49,1170,1171],{},[52,1172,341],{},[56,1174,1175],{"encoding":58},"\\sigma",[33,1177,1179],{"className":1178,"ariaHidden":63},[62],[33,1180,1182,1186],{"className":1181},[67],[33,1183],{"className":1184,"style":1185},[71],"height:0.4306em;",[33,1187,341],{"className":1188,"style":706},[76,77],[800,1190,1191],{},"活性化関数（成分ごとに適用）",[785,1193,1194,1348],{},[800,1195,1196],{},[33,1197,1199,1234],{"className":1198},[36],[33,1200,1202],{"className":1201},[40],[42,1203,1204],{"xmlns":44},[46,1205,1206,1231],{},[49,1207,1208,1220,1222],{},[237,1209,1210,1212],{},[52,1211,281],{"mathvariant":241},[49,1213,1214,1216,1218],{},[126,1215,248],{"stretchy":247},[52,1217,54],{},[126,1219,253],{"stretchy":247},[126,1221,128],{},[1223,1224,1225,1228],"mover",{"accent":63},[52,1226,1227],{"mathvariant":241},"y",[126,1229,1230],{},"^",[56,1232,1233],{"encoding":58},"\\mathbf{a}^{(L)} = \\hat{\\mathbf{y}}",[33,1235,1237,1290],{"className":1236,"ariaHidden":63},[62],[33,1238,1240,1243,1281,1284,1287],{"className":1239},[67],[33,1241],{"className":1242,"style":843},[71],[33,1244,1246,1249],{"className":1245},[76],[33,1247,281],{"className":1248},[76,414],[33,1250,1252],{"className":1251},[418],[33,1253,1255],{"className":1254},[386],[33,1256,1258],{"className":1257},[391],[33,1259,1261],{"className":1260,"style":843},[395],[33,1262,1263,1266],{"style":864},[33,1264],{"className":1265,"style":435},[403],[33,1267,1269],{"className":1268},[439,440,441,442],[33,1270,1272,1275,1278],{"className":1271},[76,442],[33,1273,248],{"className":1274},[449,442],[33,1276,54],{"className":1277},[76,77,442],[33,1279,253],{"className":1280},[456,442],[33,1282],{"className":1283,"style":162},[161],[33,1285,128],{"className":1286},[166],[33,1288],{"className":1289,"style":162},[161],[33,1291,1293,1297],{"className":1292},[67],[33,1294],{"className":1295,"style":1296},[71],"height:0.9023em;vertical-align:-0.1944em;",[33,1298,1301],{"className":1299},[76,1300],"katex-accent",[33,1302,1304,1339],{"className":1303},[386,387],[33,1305,1307,1336],{"className":1306},[391],[33,1308,1311,1322],{"className":1309,"style":1310},[395],"height:0.7079em;",[33,1312,1314,1318],{"style":1313},"top:-3em;",[33,1315],{"className":1316,"style":1317},[403],"height:3em;",[33,1319,1227],{"className":1320,"style":1321},[76,414],"margin-right:0.016em;",[33,1323,1325,1328],{"style":1324},"top:-3.0134em;",[33,1326],{"className":1327,"style":1317},[403],[33,1329,1333],{"className":1330,"style":1332},[1331],"accent-body","left:-0.25em;",[33,1334,1230],{"className":1335},[76],[33,1337,508],{"className":1338},[507],[33,1340,1342],{"className":1341},[391],[33,1343,1346],{"className":1344,"style":1345},[395],"height:0.1944em;",[33,1347],{},[800,1349,1350],{},"ネットワークの出力",[785,1352,1353,1458],{},[800,1354,1355],{},[33,1356,1358,1387],{"className":1357},[36],[33,1359,1361],{"className":1360},[40],[42,1362,1363],{"xmlns":44},[46,1364,1365,1384],{},[49,1366,1367,1370,1372,1378,1380,1382],{},[52,1368,54],{"mathvariant":1369},"script",[126,1371,248],{"stretchy":247},[1223,1373,1374,1376],{"accent":63},[52,1375,1227],{"mathvariant":241},[126,1377,1230],{},[126,1379,135],{"separator":63},[52,1381,1227],{"mathvariant":241},[126,1383,253],{"stretchy":247},[56,1385,1386],{"encoding":58},"\\mathcal{L}(\\hat{\\mathbf{y}}, \\mathbf{y})",[33,1388,1390],{"className":1389,"ariaHidden":63},[62],[33,1391,1393,1397,1401,1404,1446,1449,1452,1455],{"className":1392},[67],[33,1394],{"className":1395,"style":1396},[71],"height:1em;vertical-align:-0.25em;",[33,1398,54],{"className":1399},[76,1400],"mathcal",[33,1402,248],{"className":1403},[449],[33,1405,1407],{"className":1406},[76,1300],[33,1408,1410,1438],{"className":1409},[386,387],[33,1411,1413,1435],{"className":1412},[391],[33,1414,1416,1424],{"className":1415,"style":1310},[395],[33,1417,1418,1421],{"style":1313},[33,1419],{"className":1420,"style":1317},[403],[33,1422,1227],{"className":1423,"style":1321},[76,414],[33,1425,1426,1429],{"style":1324},[33,1427],{"className":1428,"style":1317},[403],[33,1430,1432],{"className":1431,"style":1332},[1331],[33,1433,1230],{"className":1434},[76],[33,1436,508],{"className":1437},[507],[33,1439,1441],{"className":1440},[391],[33,1442,1444],{"className":1443,"style":1345},[395],[33,1445],{},[33,1447,135],{"className":1448},[183],[33,1450],{"className":1451,"style":187},[161],[33,1453,1227],{"className":1454,"style":1321},[76,414],[33,1456,253],{"className":1457},[456],[800,1459,1460,1461,1491],{},"損失関数（",[33,1462,1464,1478],{"className":1463},[36],[33,1465,1467],{"className":1466},[40],[42,1468,1469],{"xmlns":44},[46,1470,1471,1475],{},[49,1472,1473],{},[52,1474,1227],{"mathvariant":241},[56,1476,1477],{"encoding":58},"\\mathbf{y}",[33,1479,1481],{"className":1480,"ariaHidden":63},[62],[33,1482,1484,1488],{"className":1483},[67],[33,1485],{"className":1486,"style":1487},[71],"height:0.6389em;vertical-align:-0.1944em;",[33,1489,1227],{"className":1490,"style":1321},[76,414]," は正解）",[10,1493,1494],{},[1495,1496],"img",{"alt":1497,"src":1498},"順伝播（実線）で信号を前へ送り、逆伝播（破線）で誤差 δ を後ろへ送る","\u002Fimages\u002Fblog\u002Fbackpropagation\u002Fnetwork.svg",[10,1500,1501,1502,21,1951,2059,2060,2088,2089,2118],{},"成分で書くと ",[33,1503,1505,1596],{"className":1504},[36],[33,1506,1508],{"className":1507},[40],[42,1509,1510],{"xmlns":44},[46,1511,1512,1593],{},[49,1513,1514,1530,1532,1541,1559,1577,1579],{},[1515,1516,1517,1519,1522],"msubsup",{},[52,1518,242],{},[52,1520,1521],{},"j",[49,1523,1524,1526,1528],{},[126,1525,248],{"stretchy":247},[52,1527,93],{},[126,1529,253],{"stretchy":247},[126,1531,128],{},[1533,1534,1535,1538],"msub",{},[126,1536,1537],{},"∑",[52,1539,1540],{},"k",[1515,1542,1543,1545,1551],{},[52,1544,268],{},[49,1546,1547,1549],{},[52,1548,1521],{},[52,1550,1540],{},[49,1552,1553,1555,1557],{},[126,1554,248],{"stretchy":247},[52,1556,93],{},[126,1558,253],{"stretchy":247},[1515,1560,1561,1563,1565],{},[52,1562,281],{},[52,1564,1540],{},[49,1566,1567,1569,1571,1573,1575],{},[126,1568,248],{"stretchy":247},[52,1570,93],{},[126,1572,290],{},[130,1574,132],{},[126,1576,253],{"stretchy":247},[126,1578,297],{},[1515,1580,1581,1583,1585],{},[52,1582,302],{},[52,1584,1521],{},[49,1586,1587,1589,1591],{},[126,1588,248],{"stretchy":247},[52,1590,93],{},[126,1592,253],{"stretchy":247},[56,1594,1595],{"encoding":58},"z^{(l)}_j = \\sum_k W^{(l)}_{jk} a^{(l-1)}_k + b^{(l)}_j",[33,1597,1599,1681,1884],{"className":1598,"ariaHidden":63},[62],[33,1600,1602,1606,1672,1675,1678],{"className":1601},[67],[33,1603],{"className":1604,"style":1605},[71],"height:1.4578em;vertical-align:-0.413em;",[33,1607,1609,1613],{"className":1608},[76],[33,1610,242],{"className":1611,"style":1612},[76,77],"margin-right:0.044em;",[33,1614,1616],{"className":1615},[418],[33,1617,1619,1663],{"className":1618},[386,387],[33,1620,1622,1660],{"className":1621},[391],[33,1623,1626,1639],{"className":1624,"style":1625},[395],"height:1.0448em;",[33,1627,1629,1632],{"style":1628},"top:-2.4231em;margin-left:-0.044em;margin-right:0.05em;",[33,1630],{"className":1631,"style":435},[403],[33,1633,1635],{"className":1634},[439,440,441,442],[33,1636,1521],{"className":1637,"style":1638},[76,77,442],"margin-right:0.0572em;",[33,1640,1642,1645],{"style":1641},"top:-3.2198em;margin-right:0.05em;",[33,1643],{"className":1644,"style":435},[403],[33,1646,1648],{"className":1647},[439,440,441,442],[33,1649,1651,1654,1657],{"className":1650},[76,442],[33,1652,248],{"className":1653},[449,442],[33,1655,93],{"className":1656,"style":109},[76,77,442],[33,1658,253],{"className":1659},[456,442],[33,1661,508],{"className":1662},[507],[33,1664,1666],{"className":1665},[391],[33,1667,1670],{"className":1668,"style":1669},[395],"height:0.413em;",[33,1671],{},[33,1673],{"className":1674,"style":162},[161],[33,1676,128],{"className":1677},[166],[33,1679],{"className":1680,"style":162},[161],[33,1682,1684,1688,1736,1739,1807,1875,1878,1881],{"className":1683},[67],[33,1685],{"className":1686,"style":1687},[71],"height:1.4822em;vertical-align:-0.4374em;",[33,1689,1692,1698],{"className":1690},[1691],"mop",[33,1693,1537],{"className":1694,"style":1697},[1691,1695,1696],"op-symbol","small-op","position:relative;top:0em;",[33,1699,1701],{"className":1700},[418],[33,1702,1704,1727],{"className":1703},[386,387],[33,1705,1707,1724],{"className":1706},[391],[33,1708,1711],{"className":1709,"style":1710},[395],"height:0.1864em;",[33,1712,1714,1717],{"style":1713},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[33,1715],{"className":1716,"style":435},[403],[33,1718,1720],{"className":1719},[439,440,441,442],[33,1721,1540],{"className":1722,"style":1723},[76,77,442],"margin-right:0.0315em;",[33,1725,508],{"className":1726},[507],[33,1728,1730],{"className":1729},[391],[33,1731,1734],{"className":1732,"style":1733},[395],"height:0.2997em;",[33,1735],{},[33,1737],{"className":1738,"style":187},[161],[33,1740,1742,1745],{"className":1741},[76],[33,1743,268],{"className":1744,"style":557},[76,77],[33,1746,1748],{"className":1747},[418],[33,1749,1751,1798],{"className":1750},[386,387],[33,1752,1754,1795],{"className":1753},[391],[33,1755,1757,1775],{"className":1756,"style":1625},[395],[33,1758,1760,1763],{"style":1759},"top:-2.3987em;margin-left:-0.1389em;margin-right:0.05em;",[33,1761],{"className":1762,"style":435},[403],[33,1764,1766],{"className":1765},[439,440,441,442],[33,1767,1769,1772],{"className":1768},[76,442],[33,1770,1521],{"className":1771,"style":1638},[76,77,442],[33,1773,1540],{"className":1774,"style":1723},[76,77,442],[33,1776,1777,1780],{"style":1641},[33,1778],{"className":1779,"style":435},[403],[33,1781,1783],{"className":1782},[439,440,441,442],[33,1784,1786,1789,1792],{"className":1785},[76,442],[33,1787,248],{"className":1788},[449,442],[33,1790,93],{"className":1791,"style":109},[76,77,442],[33,1793,253],{"className":1794},[456,442],[33,1796,508],{"className":1797},[507],[33,1799,1801],{"className":1800},[391],[33,1802,1805],{"className":1803,"style":1804},[395],"height:0.4374em;",[33,1806],{},[33,1808,1810,1813],{"className":1809},[76],[33,1811,281],{"className":1812},[76,77],[33,1814,1816],{"className":1815},[418],[33,1817,1819,1866],{"className":1818},[386,387],[33,1820,1822,1863],{"className":1821},[391],[33,1823,1825,1837],{"className":1824,"style":1625},[395],[33,1826,1828,1831],{"style":1827},"top:-2.3987em;margin-left:0em;margin-right:0.05em;",[33,1829],{"className":1830,"style":435},[403],[33,1832,1834],{"className":1833},[439,440,441,442],[33,1835,1540],{"className":1836,"style":1723},[76,77,442],[33,1838,1839,1842],{"style":1641},[33,1840],{"className":1841,"style":435},[403],[33,1843,1845],{"className":1844},[439,440,441,442],[33,1846,1848,1851,1854,1857,1860],{"className":1847},[76,442],[33,1849,248],{"className":1850},[449,442],[33,1852,93],{"className":1853,"style":109},[76,77,442],[33,1855,290],{"className":1856},[628,442],[33,1858,132],{"className":1859},[76,442],[33,1861,253],{"className":1862},[456,442],[33,1864,508],{"className":1865},[507],[33,1867,1869],{"className":1868},[391],[33,1870,1873],{"className":1871,"style":1872},[395],"height:0.3013em;",[33,1874],{},[33,1876],{"className":1877,"style":638},[161],[33,1879,297],{"className":1880},[628],[33,1882],{"className":1883,"style":638},[161],[33,1885,1887,1890],{"className":1886},[67],[33,1888],{"className":1889,"style":1605},[71],[33,1891,1893,1896],{"className":1892},[76],[33,1894,302],{"className":1895},[76,77],[33,1897,1899],{"className":1898},[418],[33,1900,1902,1943],{"className":1901},[386,387],[33,1903,1905,1940],{"className":1904},[391],[33,1906,1908,1920],{"className":1907,"style":1625},[395],[33,1909,1911,1914],{"style":1910},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[33,1912],{"className":1913,"style":435},[403],[33,1915,1917],{"className":1916},[439,440,441,442],[33,1918,1521],{"className":1919,"style":1638},[76,77,442],[33,1921,1922,1925],{"style":1641},[33,1923],{"className":1924,"style":435},[403],[33,1926,1928],{"className":1927},[439,440,441,442],[33,1929,1931,1934,1937],{"className":1930},[76,442],[33,1932,248],{"className":1933},[449,442],[33,1935,93],{"className":1936,"style":109},[76,77,442],[33,1938,253],{"className":1939},[456,442],[33,1941,508],{"className":1942},[507],[33,1944,1946],{"className":1945},[391],[33,1947,1949],{"className":1948,"style":1669},[395],[33,1950],{},[33,1952,1954,1984],{"className":1953},[36],[33,1955,1957],{"className":1956},[40],[42,1958,1959],{"xmlns":44},[46,1960,1961,1981],{},[49,1962,1963],{},[1515,1964,1965,1967,1973],{},[52,1966,268],{},[49,1968,1969,1971],{},[52,1970,1521],{},[52,1972,1540],{},[49,1974,1975,1977,1979],{},[126,1976,248],{"stretchy":247},[52,1978,93],{},[126,1980,253],{"stretchy":247},[56,1982,1983],{"encoding":58},"W^{(l)}_{jk}",[33,1985,1987],{"className":1986,"ariaHidden":63},[62],[33,1988,1990,1993],{"className":1989},[67],[33,1991],{"className":1992,"style":1687},[71],[33,1994,1996,1999],{"className":1995},[76],[33,1997,268],{"className":1998,"style":557},[76,77],[33,2000,2002],{"className":2001},[418],[33,2003,2005,2051],{"className":2004},[386,387],[33,2006,2008,2048],{"className":2007},[391],[33,2009,2011,2028],{"className":2010,"style":1625},[395],[33,2012,2013,2016],{"style":1759},[33,2014],{"className":2015,"style":435},[403],[33,2017,2019],{"className":2018},[439,440,441,442],[33,2020,2022,2025],{"className":2021},[76,442],[33,2023,1521],{"className":2024,"style":1638},[76,77,442],[33,2026,1540],{"className":2027,"style":1723},[76,77,442],[33,2029,2030,2033],{"style":1641},[33,2031],{"className":2032,"style":435},[403],[33,2034,2036],{"className":2035},[439,440,441,442],[33,2037,2039,2042,2045],{"className":2038},[76,442],[33,2040,248],{"className":2041},[449,442],[33,2043,93],{"className":2044,"style":109},[76,77,442],[33,2046,253],{"className":2047},[456,442],[33,2049,508],{"className":2050},[507],[33,2052,2054],{"className":2053},[391],[33,2055,2057],{"className":2056,"style":1804},[395],[33,2058],{}," は「前の層のユニット ",[33,2061,2063,2076],{"className":2062},[36],[33,2064,2066],{"className":2065},[40],[42,2067,2068],{"xmlns":44},[46,2069,2070,2074],{},[49,2071,2072],{},[52,2073,1540],{},[56,2075,1540],{"encoding":58},[33,2077,2079],{"className":2078,"ariaHidden":63},[62],[33,2080,2082,2085],{"className":2081},[67],[33,2083],{"className":2084,"style":105},[71],[33,2086,1540],{"className":2087,"style":1723},[76,77]," から、この層のユニット ",[33,2090,2092,2105],{"className":2091},[36],[33,2093,2095],{"className":2094},[40],[42,2096,2097],{"xmlns":44},[46,2098,2099,2103],{},[49,2100,2101],{},[52,2102,1521],{},[56,2104,1521],{"encoding":58},[33,2106,2108],{"className":2107,"ariaHidden":63},[62],[33,2109,2111,2115],{"className":2110},[67],[33,2112],{"className":2113,"style":2114},[71],"height:0.854em;vertical-align:-0.1944em;",[33,2116,1521],{"className":2117,"style":1638},[76,77]," への重み」を表します。",[10,2120,2121,2122,2150],{},"目標は、すべての ",[33,2123,2125,2138],{"className":2124},[36],[33,2126,2128],{"className":2127},[40],[42,2129,2130],{"xmlns":44},[46,2131,2132,2136],{},[49,2133,2134],{},[52,2135,93],{},[56,2137,93],{"encoding":58},[33,2139,2141],{"className":2140,"ariaHidden":63},[62],[33,2142,2144,2147],{"className":2143},[67],[33,2145],{"className":2146,"style":105},[71],[33,2148,93],{"className":2149,"style":109},[76,77]," について次の2つを求めることです。",[33,2152,2154],{"className":2153},[208],[33,2155,2157,2233],{"className":2156},[36],[33,2158,2160],{"className":2159},[40],[42,2161,2162],{"xmlns":44,"display":217},[46,2163,2164,2230],{},[49,2165,2166,2199,2201,2204],{},[2167,2168,2169,2177],"mfrac",{},[49,2170,2171,2175],{},[52,2172,2174],{"mathvariant":2173},"normal","∂",[52,2176,54],{"mathvariant":1369},[49,2178,2179,2181],{},[52,2180,2174],{"mathvariant":2173},[1515,2182,2183,2185,2191],{},[52,2184,268],{},[49,2186,2187,2189],{},[52,2188,1521],{},[52,2190,1540],{},[49,2192,2193,2195,2197],{},[126,2194,248],{"stretchy":247},[52,2196,93],{},[126,2198,253],{"stretchy":247},[126,2200,135],{"separator":63},[161,2202],{"width":2203},"2em",[2167,2205,2206,2212],{},[49,2207,2208,2210],{},[52,2209,2174],{"mathvariant":2173},[52,2211,54],{"mathvariant":1369},[49,2213,2214,2216],{},[52,2215,2174],{"mathvariant":2173},[1515,2217,2218,2220,2222],{},[52,2219,302],{},[52,2221,1521],{},[49,2223,2224,2226,2228],{},[126,2225,248],{"stretchy":247},[52,2227,93],{},[126,2229,253],{"stretchy":247},[56,2231,2232],{"encoding":58},"\\frac{\\partial \\mathcal{L}}{\\partial W^{(l)}_{jk}}, \\qquad \\frac{\\partial \\mathcal{L}}{\\partial b^{(l)}_j}",[33,2234,2236],{"className":2235,"ariaHidden":63},[62],[33,2237,2239,2243,2384,2387,2391,2394],{"className":2238},[67],[33,2240],{"className":2241,"style":2242},[71],"height:2.7437em;vertical-align:-1.3722em;",[33,2244,2246,2250,2381],{"className":2245},[76],[33,2247],{"className":2248},[449,2249],"nulldelimiter",[33,2251,2253],{"className":2252},[2167],[33,2254,2256,2372],{"className":2255},[386,387],[33,2257,2259,2369],{"className":2258},[391],[33,2260,2263,2343,2354],{"className":2261,"style":2262},[395],"height:1.3714em;",[33,2264,2266,2270],{"style":2265},"top:-2.11em;",[33,2267],{"className":2268,"style":2269},[403],"height:3.0448em;",[33,2271,2273,2277],{"className":2272},[76],[33,2274,2174],{"className":2275,"style":2276},[76],"margin-right:0.0556em;",[33,2278,2280,2283],{"className":2279},[76],[33,2281,268],{"className":2282,"style":557},[76,77],[33,2284,2286],{"className":2285},[418],[33,2287,2289,2335],{"className":2288},[386,387],[33,2290,2292,2332],{"className":2291},[391],[33,2293,2295,2312],{"className":2294,"style":1625},[395],[33,2296,2297,2300],{"style":1759},[33,2298],{"className":2299,"style":435},[403],[33,2301,2303],{"className":2302},[439,440,441,442],[33,2304,2306,2309],{"className":2305},[76,442],[33,2307,1521],{"className":2308,"style":1638},[76,77,442],[33,2310,1540],{"className":2311,"style":1723},[76,77,442],[33,2313,2314,2317],{"style":1641},[33,2315],{"className":2316,"style":435},[403],[33,2318,2320],{"className":2319},[439,440,441,442],[33,2321,2323,2326,2329],{"className":2322},[76,442],[33,2324,248],{"className":2325},[449,442],[33,2327,93],{"className":2328,"style":109},[76,77,442],[33,2330,253],{"className":2331},[456,442],[33,2333,508],{"className":2334},[507],[33,2336,2338],{"className":2337},[391],[33,2339,2341],{"className":2340,"style":1804},[395],[33,2342],{},[33,2344,2346,2349],{"style":2345},"top:-3.2748em;",[33,2347],{"className":2348,"style":2269},[403],[33,2350],{"className":2351,"style":2353},[2352],"frac-line","border-bottom-width:0.04em;",[33,2355,2357,2360],{"style":2356},"top:-3.7218em;",[33,2358],{"className":2359,"style":2269},[403],[33,2361,2363,2366],{"className":2362},[76],[33,2364,2174],{"className":2365,"style":2276},[76],[33,2367,54],{"className":2368},[76,1400],[33,2370,508],{"className":2371},[507],[33,2373,2375],{"className":2374},[391],[33,2376,2379],{"className":2377,"style":2378},[395],"height:1.3722em;",[33,2380],{},[33,2382],{"className":2383},[456,2249],[33,2385,135],{"className":2386},[183],[33,2388],{"className":2389,"style":2390},[161],"margin-right:2em;",[33,2392],{"className":2393,"style":187},[161],[33,2395,2397,2400,2517],{"className":2396},[76],[33,2398],{"className":2399},[449,2249],[33,2401,2403],{"className":2402},[2167],[33,2404,2406,2508],{"className":2405},[386,387],[33,2407,2409,2505],{"className":2408},[391],[33,2410,2412,2483,2491],{"className":2411,"style":2262},[395],[33,2413,2414,2417],{"style":2265},[33,2415],{"className":2416,"style":2269},[403],[33,2418,2420,2423],{"className":2419},[76],[33,2421,2174],{"className":2422,"style":2276},[76],[33,2424,2426,2429],{"className":2425},[76],[33,2427,302],{"className":2428},[76,77],[33,2430,2432],{"className":2431},[418],[33,2433,2435,2475],{"className":2434},[386,387],[33,2436,2438,2472],{"className":2437},[391],[33,2439,2441,2452],{"className":2440,"style":1625},[395],[33,2442,2443,2446],{"style":1910},[33,2444],{"className":2445,"style":435},[403],[33,2447,2449],{"className":2448},[439,440,441,442],[33,2450,1521],{"className":2451,"style":1638},[76,77,442],[33,2453,2454,2457],{"style":1641},[33,2455],{"className":2456,"style":435},[403],[33,2458,2460],{"className":2459},[439,440,441,442],[33,2461,2463,2466,2469],{"className":2462},[76,442],[33,2464,248],{"className":2465},[449,442],[33,2467,93],{"className":2468,"style":109},[76,77,442],[33,2470,253],{"className":2471},[456,442],[33,2473,508],{"className":2474},[507],[33,2476,2478],{"className":2477},[391],[33,2479,2481],{"className":2480,"style":1669},[395],[33,2482],{},[33,2484,2485,2488],{"style":2345},[33,2486],{"className":2487,"style":2269},[403],[33,2489],{"className":2490,"style":2353},[2352],[33,2492,2493,2496],{"style":2356},[33,2494],{"className":2495,"style":2269},[403],[33,2497,2499,2502],{"className":2498},[76],[33,2500,2174],{"className":2501,"style":2276},[76],[33,2503,54],{"className":2504},[76,1400],[33,2506,508],{"className":2507},[507],[33,2509,2511],{"className":2510},[391],[33,2512,2515],{"className":2513,"style":2514},[395],"height:1.3478em;",[33,2516],{},[33,2518],{"className":2519},[456,2249],[26,2521,2523],{"id":2522},"_2-鍵となる量誤差-δ","2. 鍵となる量：誤差 δ",[2525,2526,2528,2651],"definition",{"title":2527},"第 l 層の誤差",[10,2529,2530,2531,2559,2560,2563,2564,2650],{},"重み付き入力に対する損失の偏微分を、第 ",[33,2532,2534,2547],{"className":2533},[36],[33,2535,2537],{"className":2536},[40],[42,2538,2539],{"xmlns":44},[46,2540,2541,2545],{},[49,2542,2543],{},[52,2544,93],{},[56,2546,93],{"encoding":58},[33,2548,2550],{"className":2549,"ariaHidden":63},[62],[33,2551,2553,2556],{"className":2552},[67],[33,2554],{"className":2555,"style":105},[71],[33,2557,93],{"className":2558,"style":109},[76,77]," 層の ",[14,2561,2562],{},"誤差"," と呼び、",[33,2565,2567,2593],{"className":2566},[36],[33,2568,2570],{"className":2569},[40],[42,2571,2572],{"xmlns":44},[46,2573,2574,2590],{},[49,2575,2576],{},[237,2577,2578,2582],{},[52,2579,2581],{"mathvariant":2580},"bold-italic","δ",[49,2583,2584,2586,2588],{},[126,2585,248],{"stretchy":247},[52,2587,93],{},[126,2589,253],{"stretchy":247},[56,2591,2592],{"encoding":58},"\\boldsymbol{\\delta}^{(l)}",[33,2594,2596],{"className":2595,"ariaHidden":63},[62],[33,2597,2599,2603],{"className":2598},[67],[33,2600],{"className":2601,"style":2602},[71],"height:0.9723em;",[33,2604,2606,2617],{"className":2605},[76],[33,2607,2609],{"className":2608},[76],[33,2610,2612],{"className":2611},[76],[33,2613,2581],{"className":2614,"style":2616},[76,2615],"boldsymbol","margin-right:0.0382em;",[33,2618,2620],{"className":2619},[418],[33,2621,2623],{"className":2622},[386],[33,2624,2626],{"className":2625},[391],[33,2627,2629],{"className":2628,"style":2602},[395],[33,2630,2632,2635],{"style":2631},"top:-3.1473em;margin-right:0.05em;",[33,2633],{"className":2634,"style":435},[403],[33,2636,2638],{"className":2637},[439,440,441,442],[33,2639,2641,2644,2647],{"className":2640},[76,442],[33,2642,248],{"className":2643},[449,442],[33,2645,93],{"className":2646,"style":109},[76,77,442],[33,2648,253],{"className":2649},[456,442]," と書きます。",[33,2652,2654],{"className":2653},[208],[33,2655,2657,2712],{"className":2656},[36],[33,2658,2660],{"className":2659},[40],[42,2661,2662],{"xmlns":44,"display":217},[46,2663,2664,2709],{},[49,2665,2666,2680,2683],{},[1515,2667,2668,2670,2672],{},[52,2669,2581],{},[52,2671,1521],{},[49,2673,2674,2676,2678],{},[126,2675,248],{"stretchy":247},[52,2677,93],{},[126,2679,253],{"stretchy":247},[126,2681,2682],{},"≡",[2167,2684,2685,2691],{},[49,2686,2687,2689],{},[52,2688,2174],{"mathvariant":2173},[52,2690,54],{"mathvariant":1369},[49,2692,2693,2695],{},[52,2694,2174],{"mathvariant":2173},[1515,2696,2697,2699,2701],{},[52,2698,242],{},[52,2700,1521],{},[49,2702,2703,2705,2707],{},[126,2704,248],{"stretchy":247},[52,2706,93],{},[126,2708,253],{"stretchy":247},[56,2710,2711],{"encoding":58},"\\delta^{(l)}_j \\equiv \\frac{\\partial \\mathcal{L}}{\\partial z^{(l)}_j}",[33,2713,2715,2792],{"className":2714,"ariaHidden":63},[62],[33,2716,2718,2721,2783,2786,2789],{"className":2717},[67],[33,2719],{"className":2720,"style":1605},[71],[33,2722,2724,2728],{"className":2723},[76],[33,2725,2581],{"className":2726,"style":2727},[76,77],"margin-right:0.0379em;",[33,2729,2731],{"className":2730},[418],[33,2732,2734,2775],{"className":2733},[386,387],[33,2735,2737,2772],{"className":2736},[391],[33,2738,2740,2752],{"className":2739,"style":1625},[395],[33,2741,2743,2746],{"style":2742},"top:-2.4231em;margin-left:-0.0379em;margin-right:0.05em;",[33,2744],{"className":2745,"style":435},[403],[33,2747,2749],{"className":2748},[439,440,441,442],[33,2750,1521],{"className":2751,"style":1638},[76,77,442],[33,2753,2754,2757],{"style":1641},[33,2755],{"className":2756,"style":435},[403],[33,2758,2760],{"className":2759},[439,440,441,442],[33,2761,2763,2766,2769],{"className":2762},[76,442],[33,2764,248],{"className":2765},[449,442],[33,2767,93],{"className":2768,"style":109},[76,77,442],[33,2770,253],{"className":2771},[456,442],[33,2773,508],{"className":2774},[507],[33,2776,2778],{"className":2777},[391],[33,2779,2781],{"className":2780,"style":1669},[395],[33,2782],{},[33,2784],{"className":2785,"style":162},[161],[33,2787,2682],{"className":2788},[166],[33,2790],{"className":2791,"style":162},[161],[33,2793,2795,2799],{"className":2794},[67],[33,2796],{"className":2797,"style":2798},[71],"height:2.7192em;vertical-align:-1.3478em;",[33,2800,2802,2805,2921],{"className":2801},[76],[33,2803],{"className":2804},[449,2249],[33,2806,2808],{"className":2807},[2167],[33,2809,2811,2913],{"className":2810},[386,387],[33,2812,2814,2910],{"className":2813},[391],[33,2815,2817,2888,2896],{"className":2816,"style":2262},[395],[33,2818,2819,2822],{"style":2265},[33,2820],{"className":2821,"style":2269},[403],[33,2823,2825,2828],{"className":2824},[76],[33,2826,2174],{"className":2827,"style":2276},[76],[33,2829,2831,2834],{"className":2830},[76],[33,2832,242],{"className":2833,"style":1612},[76,77],[33,2835,2837],{"className":2836},[418],[33,2838,2840,2880],{"className":2839},[386,387],[33,2841,2843,2877],{"className":2842},[391],[33,2844,2846,2857],{"className":2845,"style":1625},[395],[33,2847,2848,2851],{"style":1628},[33,2849],{"className":2850,"style":435},[403],[33,2852,2854],{"className":2853},[439,440,441,442],[33,2855,1521],{"className":2856,"style":1638},[76,77,442],[33,2858,2859,2862],{"style":1641},[33,2860],{"className":2861,"style":435},[403],[33,2863,2865],{"className":2864},[439,440,441,442],[33,2866,2868,2871,2874],{"className":2867},[76,442],[33,2869,248],{"className":2870},[449,442],[33,2872,93],{"className":2873,"style":109},[76,77,442],[33,2875,253],{"className":2876},[456,442],[33,2878,508],{"className":2879},[507],[33,2881,2883],{"className":2882},[391],[33,2884,2886],{"className":2885,"style":1669},[395],[33,2887],{},[33,2889,2890,2893],{"style":2345},[33,2891],{"className":2892,"style":2269},[403],[33,2894],{"className":2895,"style":2353},[2352],[33,2897,2898,2901],{"style":2356},[33,2899],{"className":2900,"style":2269},[403],[33,2902,2904,2907],{"className":2903},[76],[33,2905,2174],{"className":2906,"style":2276},[76],[33,2908,54],{"className":2909},[76,1400],[33,2911,508],{"className":2912},[507],[33,2914,2916],{"className":2915},[391],[33,2917,2919],{"className":2918,"style":2514},[395],[33,2920],{},[33,2922],{"className":2923},[456,2249],[10,2925,2926,3024,3025,3053,3054,3152,3153,3188,3189,3192],{},[33,2927,2929,2955],{"className":2928},[36],[33,2930,2932],{"className":2931},[40],[42,2933,2934],{"xmlns":44},[46,2935,2936,2952],{},[49,2937,2938],{},[1515,2939,2940,2942,2944],{},[52,2941,2581],{},[52,2943,1521],{},[49,2945,2946,2948,2950],{},[126,2947,248],{"stretchy":247},[52,2949,93],{},[126,2951,253],{"stretchy":247},[56,2953,2954],{"encoding":58},"\\delta^{(l)}_j",[33,2956,2958],{"className":2957,"ariaHidden":63},[62],[33,2959,2961,2964],{"className":2960},[67],[33,2962],{"className":2963,"style":1605},[71],[33,2965,2967,2970],{"className":2966},[76],[33,2968,2581],{"className":2969,"style":2727},[76,77],[33,2971,2973],{"className":2972},[418],[33,2974,2976,3016],{"className":2975},[386,387],[33,2977,2979,3013],{"className":2978},[391],[33,2980,2982,2993],{"className":2981,"style":1625},[395],[33,2983,2984,2987],{"style":2742},[33,2985],{"className":2986,"style":435},[403],[33,2988,2990],{"className":2989},[439,440,441,442],[33,2991,1521],{"className":2992,"style":1638},[76,77,442],[33,2994,2995,2998],{"style":1641},[33,2996],{"className":2997,"style":435},[403],[33,2999,3001],{"className":3000},[439,440,441,442],[33,3002,3004,3007,3010],{"className":3003},[76,442],[33,3005,248],{"className":3006},[449,442],[33,3008,93],{"className":3009,"style":109},[76,77,442],[33,3011,253],{"className":3012},[456,442],[33,3014,508],{"className":3015},[507],[33,3017,3019],{"className":3018},[391],[33,3020,3022],{"className":3021,"style":1669},[395],[33,3023],{}," は「ユニット ",[33,3026,3028,3041],{"className":3027},[36],[33,3029,3031],{"className":3030},[40],[42,3032,3033],{"xmlns":44},[46,3034,3035,3039],{},[49,3036,3037],{},[52,3038,1521],{},[56,3040,1521],{"encoding":58},[33,3042,3044],{"className":3043,"ariaHidden":63},[62],[33,3045,3047,3050],{"className":3046},[67],[33,3048],{"className":3049,"style":2114},[71],[33,3051,1521],{"className":3052,"style":1638},[76,77]," の入力 ",[33,3055,3057,3083],{"className":3056},[36],[33,3058,3060],{"className":3059},[40],[42,3061,3062],{"xmlns":44},[46,3063,3064,3080],{},[49,3065,3066],{},[1515,3067,3068,3070,3072],{},[52,3069,242],{},[52,3071,1521],{},[49,3073,3074,3076,3078],{},[126,3075,248],{"stretchy":247},[52,3077,93],{},[126,3079,253],{"stretchy":247},[56,3081,3082],{"encoding":58},"z^{(l)}_j",[33,3084,3086],{"className":3085,"ariaHidden":63},[62],[33,3087,3089,3092],{"className":3088},[67],[33,3090],{"className":3091,"style":1605},[71],[33,3093,3095,3098],{"className":3094},[76],[33,3096,242],{"className":3097,"style":1612},[76,77],[33,3099,3101],{"className":3100},[418],[33,3102,3104,3144],{"className":3103},[386,387],[33,3105,3107,3141],{"className":3106},[391],[33,3108,3110,3121],{"className":3109,"style":1625},[395],[33,3111,3112,3115],{"style":1628},[33,3113],{"className":3114,"style":435},[403],[33,3116,3118],{"className":3117},[439,440,441,442],[33,3119,1521],{"className":3120,"style":1638},[76,77,442],[33,3122,3123,3126],{"style":1641},[33,3124],{"className":3125,"style":435},[403],[33,3127,3129],{"className":3128},[439,440,441,442],[33,3130,3132,3135,3138],{"className":3131},[76,442],[33,3133,248],{"className":3134},[449,442],[33,3136,93],{"className":3137,"style":109},[76,77,442],[33,3139,253],{"className":3140},[456,442],[33,3142,508],{"className":3143},[507],[33,3145,3147],{"className":3146},[391],[33,3148,3150],{"className":3149,"style":1669},[395],[33,3151],{}," を少し動かしたとき、損失がどれだけ変わるか」を表します。バックプロパゲーションは、この ",[33,3154,3156,3170],{"className":3155},[36],[33,3157,3159],{"className":3158},[40],[42,3160,3161],{"xmlns":44},[46,3162,3163,3167],{},[49,3164,3165],{},[52,3166,2581],{"mathvariant":2580},[56,3168,3169],{"encoding":58},"\\boldsymbol{\\delta}",[33,3171,3173],{"className":3172,"ariaHidden":63},[62],[33,3174,3176,3179],{"className":3175},[67],[33,3177],{"className":3178,"style":105},[71],[33,3180,3182],{"className":3181},[76],[33,3183,3185],{"className":3184},[76],[33,3186,2581],{"className":3187,"style":2616},[76,2615]," を ",[14,3190,3191],{},"出力層から入力層へ向かって順番に"," 計算していく手法です。",[26,3194,3196],{"id":3195},"_3-連鎖律","3. 連鎖律",[10,3198,3199,3200,3229,3230,3377,3378,3407],{},"多変数の連鎖律を思い出しておきます。",[33,3201,3203,3217],{"className":3202},[36],[33,3204,3206],{"className":3205},[40],[42,3207,3208],{"xmlns":44},[46,3209,3210,3214],{},[49,3211,3212],{},[52,3213,54],{"mathvariant":1369},[56,3215,3216],{"encoding":58},"\\mathcal{L}",[33,3218,3220],{"className":3219,"ariaHidden":63},[62],[33,3221,3223,3226],{"className":3222},[67],[33,3224],{"className":3225,"style":72},[71],[33,3227,54],{"className":3228},[76,1400]," が中間変数 ",[33,3231,3233,3265],{"className":3232},[36],[33,3234,3236],{"className":3235},[40],[42,3237,3238],{"xmlns":44},[46,3239,3240,3262],{},[49,3241,3242,3249,3251,3253,3255],{},[1533,3243,3244,3247],{},[52,3245,3246],{},"u",[130,3248,132],{},[126,3250,135],{"separator":63},[126,3252,138],{},[126,3254,135],{"separator":63},[1533,3256,3257,3259],{},[52,3258,3246],{},[52,3260,3261],{},"n",[56,3263,3264],{"encoding":58},"u_1, \\dots, u_n",[33,3266,3268],{"className":3267,"ariaHidden":63},[62],[33,3269,3271,3275,3318,3321,3324,3327,3330,3333,3336],{"className":3270},[67],[33,3272],{"className":3273,"style":3274},[71],"height:0.625em;vertical-align:-0.1944em;",[33,3276,3278,3281],{"className":3277},[76],[33,3279,3246],{"className":3280},[76,77],[33,3282,3284],{"className":3283},[418],[33,3285,3287,3309],{"className":3286},[386,387],[33,3288,3290,3306],{"className":3289},[391],[33,3291,3294],{"className":3292,"style":3293},[395],"height:0.3011em;",[33,3295,3297,3300],{"style":3296},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[33,3298],{"className":3299,"style":435},[403],[33,3301,3303],{"className":3302},[439,440,441,442],[33,3304,132],{"className":3305},[76,442],[33,3307,508],{"className":3308},[507],[33,3310,3312],{"className":3311},[391],[33,3313,3316],{"className":3314,"style":3315},[395],"height:0.15em;",[33,3317],{},[33,3319,135],{"className":3320},[183],[33,3322],{"className":3323,"style":187},[161],[33,3325,138],{"className":3326},[191],[33,3328],{"className":3329,"style":187},[161],[33,3331,135],{"className":3332},[183],[33,3334],{"className":3335,"style":187},[161],[33,3337,3339,3342],{"className":3338},[76],[33,3340,3246],{"className":3341},[76,77],[33,3343,3345],{"className":3344},[418],[33,3346,3348,3369],{"className":3347},[386,387],[33,3349,3351,3366],{"className":3350},[391],[33,3352,3355],{"className":3353,"style":3354},[395],"height:0.1514em;",[33,3356,3357,3360],{"style":3296},[33,3358],{"className":3359,"style":435},[403],[33,3361,3363],{"className":3362},[439,440,441,442],[33,3364,3261],{"className":3365},[76,77,442],[33,3367,508],{"className":3368},[507],[33,3370,3372],{"className":3371},[391],[33,3373,3375],{"className":3374,"style":3315},[395],[33,3376],{}," を通して ",[33,3379,3381,3395],{"className":3380},[36],[33,3382,3384],{"className":3383},[40],[42,3385,3386],{"xmlns":44},[46,3387,3388,3393],{},[49,3389,3390],{},[52,3391,3392],{},"v",[56,3394,3392],{"encoding":58},[33,3396,3398],{"className":3397,"ariaHidden":63},[62],[33,3399,3401,3404],{"className":3400},[67],[33,3402],{"className":3403,"style":1185},[71],[33,3405,3392],{"className":3406,"style":706},[76,77]," に依存しているとき、次が成り立ちます。",[33,3409,3411],{"className":3410},[208],[33,3412,3414,3494],{"className":3413},[36],[33,3415,3417],{"className":3416},[40],[42,3418,3419],{"xmlns":44,"display":217},[46,3420,3421,3491],{},[49,3422,3423,3437,3439,3455,3473],{},[2167,3424,3425,3431],{},[49,3426,3427,3429],{},[52,3428,2174],{"mathvariant":2173},[52,3430,54],{"mathvariant":1369},[49,3432,3433,3435],{},[52,3434,2174],{"mathvariant":2173},[52,3436,3392],{},[126,3438,128],{},[3440,3441,3442,3444,3453],"munderover",{},[126,3443,1537],{},[49,3445,3446,3449,3451],{},[52,3447,3448],{},"i",[126,3450,128],{},[130,3452,132],{},[52,3454,3261],{},[2167,3456,3457,3463],{},[49,3458,3459,3461],{},[52,3460,2174],{"mathvariant":2173},[52,3462,54],{"mathvariant":1369},[49,3464,3465,3467],{},[52,3466,2174],{"mathvariant":2173},[1533,3468,3469,3471],{},[52,3470,3246],{},[52,3472,3448],{},[2167,3474,3475,3485],{},[49,3476,3477,3479],{},[52,3478,2174],{"mathvariant":2173},[1533,3480,3481,3483],{},[52,3482,3246],{},[52,3484,3448],{},[49,3486,3487,3489],{},[52,3488,2174],{"mathvariant":2173},[52,3490,3392],{},[56,3492,3493],{"encoding":58},"\\frac{\\partial \\mathcal{L}}{\\partial v} = \\sum_{i=1}^{n} \\frac{\\partial \\mathcal{L}}{\\partial u_i} \\frac{\\partial u_i}{\\partial v}",[33,3495,3497,3585],{"className":3496,"ariaHidden":63},[62],[33,3498,3500,3504,3576,3579,3582],{"className":3499},[67],[33,3501],{"className":3502,"style":3503},[71],"height:2.0574em;vertical-align:-0.686em;",[33,3505,3507,3510,3573],{"className":3506},[76],[33,3508],{"className":3509},[449,2249],[33,3511,3513],{"className":3512},[2167],[33,3514,3516,3564],{"className":3515},[386,387],[33,3517,3519,3561],{"className":3518},[391],[33,3520,3522,3537,3546],{"className":3521,"style":2262},[395],[33,3523,3525,3528],{"style":3524},"top:-2.314em;",[33,3526],{"className":3527,"style":1317},[403],[33,3529,3531,3534],{"className":3530},[76],[33,3532,2174],{"className":3533,"style":2276},[76],[33,3535,3392],{"className":3536,"style":706},[76,77],[33,3538,3540,3543],{"style":3539},"top:-3.23em;",[33,3541],{"className":3542,"style":1317},[403],[33,3544],{"className":3545,"style":2353},[2352],[33,3547,3549,3552],{"style":3548},"top:-3.677em;",[33,3550],{"className":3551,"style":1317},[403],[33,3553,3555,3558],{"className":3554},[76],[33,3556,2174],{"className":3557,"style":2276},[76],[33,3559,54],{"className":3560},[76,1400],[33,3562,508],{"className":3563},[507],[33,3565,3567],{"className":3566},[391],[33,3568,3571],{"className":3569,"style":3570},[395],"height:0.686em;",[33,3572],{},[33,3574],{"className":3575},[456,2249],[33,3577],{"className":3578,"style":162},[161],[33,3580,128],{"className":3581},[166],[33,3583],{"className":3584,"style":162},[161],[33,3586,3588,3592,3667,3670,3777],{"className":3587},[67],[33,3589],{"className":3590,"style":3591},[71],"height:2.9291em;vertical-align:-1.2777em;",[33,3593,3596],{"className":3594},[1691,3595],"op-limits",[33,3597,3599,3658],{"className":3598},[386,387],[33,3600,3602,3655],{"className":3601},[391],[33,3603,3606,3628,3640],{"className":3604,"style":3605},[395],"height:1.6514em;",[33,3607,3609,3613],{"style":3608},"top:-1.8723em;margin-left:0em;",[33,3610],{"className":3611,"style":3612},[403],"height:3.05em;",[33,3614,3616],{"className":3615},[439,440,441,442],[33,3617,3619,3622,3625],{"className":3618},[76,442],[33,3620,3448],{"className":3621},[76,77,442],[33,3623,128],{"className":3624},[166,442],[33,3626,132],{"className":3627},[76,442],[33,3629,3631,3634],{"style":3630},"top:-3.05em;",[33,3632],{"className":3633,"style":3612},[403],[33,3635,3636],{},[33,3637,1537],{"className":3638},[1691,1695,3639],"large-op",[33,3641,3643,3646],{"style":3642},"top:-4.3em;margin-left:0em;",[33,3644],{"className":3645,"style":3612},[403],[33,3647,3649],{"className":3648},[439,440,441,442],[33,3650,3652],{"className":3651},[76,442],[33,3653,3261],{"className":3654},[76,77,442],[33,3656,508],{"className":3657},[507],[33,3659,3661],{"className":3660},[391],[33,3662,3665],{"className":3663,"style":3664},[395],"height:1.2777em;",[33,3666],{},[33,3668],{"className":3669,"style":187},[161],[33,3671,3673,3676,3774],{"className":3672},[76],[33,3674],{"className":3675},[449,2249],[33,3677,3679],{"className":3678},[2167],[33,3680,3682,3765],{"className":3681},[386,387],[33,3683,3685,3762],{"className":3684},[391],[33,3686,3688,3740,3748],{"className":3687,"style":2262},[395],[33,3689,3690,3693],{"style":3524},[33,3691],{"className":3692,"style":1317},[403],[33,3694,3696,3699],{"className":3695},[76],[33,3697,2174],{"className":3698,"style":2276},[76],[33,3700,3702,3705],{"className":3701},[76],[33,3703,3246],{"className":3704},[76,77],[33,3706,3708],{"className":3707},[418],[33,3709,3711,3732],{"className":3710},[386,387],[33,3712,3714,3729],{"className":3713},[391],[33,3715,3718],{"className":3716,"style":3717},[395],"height:0.3117em;",[33,3719,3720,3723],{"style":3296},[33,3721],{"className":3722,"style":435},[403],[33,3724,3726],{"className":3725},[439,440,441,442],[33,3727,3448],{"className":3728},[76,77,442],[33,3730,508],{"className":3731},[507],[33,3733,3735],{"className":3734},[391],[33,3736,3738],{"className":3737,"style":3315},[395],[33,3739],{},[33,3741,3742,3745],{"style":3539},[33,3743],{"className":3744,"style":1317},[403],[33,3746],{"className":3747,"style":2353},[2352],[33,3749,3750,3753],{"style":3548},[33,3751],{"className":3752,"style":1317},[403],[33,3754,3756,3759],{"className":3755},[76],[33,3757,2174],{"className":3758,"style":2276},[76],[33,3760,54],{"className":3761},[76,1400],[33,3763,508],{"className":3764},[507],[33,3766,3768],{"className":3767},[391],[33,3769,3772],{"className":3770,"style":3771},[395],"height:0.836em;",[33,3773],{},[33,3775],{"className":3776},[456,2249],[33,3778,3780,3783,3879],{"className":3779},[76],[33,3781],{"className":3782},[449,2249],[33,3784,3786],{"className":3785},[2167],[33,3787,3789,3871],{"className":3788},[386,387],[33,3790,3792,3868],{"className":3791},[391],[33,3793,3795,3809,3817],{"className":3794,"style":2262},[395],[33,3796,3797,3800],{"style":3524},[33,3798],{"className":3799,"style":1317},[403],[33,3801,3803,3806],{"className":3802},[76],[33,3804,2174],{"className":3805,"style":2276},[76],[33,3807,3392],{"className":3808,"style":706},[76,77],[33,3810,3811,3814],{"style":3539},[33,3812],{"className":3813,"style":1317},[403],[33,3815],{"className":3816,"style":2353},[2352],[33,3818,3819,3822],{"style":3548},[33,3820],{"className":3821,"style":1317},[403],[33,3823,3825,3828],{"className":3824},[76],[33,3826,2174],{"className":3827,"style":2276},[76],[33,3829,3831,3834],{"className":3830},[76],[33,3832,3246],{"className":3833},[76,77],[33,3835,3837],{"className":3836},[418],[33,3838,3840,3860],{"className":3839},[386,387],[33,3841,3843,3857],{"className":3842},[391],[33,3844,3846],{"className":3845,"style":3717},[395],[33,3847,3848,3851],{"style":3296},[33,3849],{"className":3850,"style":435},[403],[33,3852,3854],{"className":3853},[439,440,441,442],[33,3855,3448],{"className":3856},[76,77,442],[33,3858,508],{"className":3859},[507],[33,3861,3863],{"className":3862},[391],[33,3864,3866],{"className":3865,"style":3315},[395],[33,3867],{},[33,3869,508],{"className":3870},[507],[33,3872,3874],{"className":3873},[391],[33,3875,3877],{"className":3876,"style":3570},[395],[33,3878],{},[33,3880],{"className":3881},[456,2249],[10,3883,3884,3885,3888],{},"ニューラルネットワークでは、ある層の値は ",[14,3886,3887],{},"次の層のすべてのユニットを通して"," 損失に影響します。そのため、和の形の連鎖律が自然に現れます。",[26,3890,3892],{"id":3891},"_4-4つの基本式","4. 4つの基本式",[3894,3895,3897],"h3",{"id":3896},"bp1-出力層の誤差","(BP1) 出力層の誤差",[10,3899,3900,4104,4105,4203,4204,4302],{},[33,3901,3903,3951],{"className":3902},[36],[33,3904,3906],{"className":3905},[40],[42,3907,3908],{"xmlns":44},[46,3909,3910,3948],{},[49,3911,3912,3926,3928,3930,3932,3946],{},[1515,3913,3914,3916,3918],{},[52,3915,281],{},[52,3917,1521],{},[49,3919,3920,3922,3924],{},[126,3921,248],{"stretchy":247},[52,3923,54],{},[126,3925,253],{"stretchy":247},[126,3927,128],{},[52,3929,341],{},[126,3931,248],{"stretchy":247},[1515,3933,3934,3936,3938],{},[52,3935,242],{},[52,3937,1521],{},[49,3939,3940,3942,3944],{},[126,3941,248],{"stretchy":247},[52,3943,54],{},[126,3945,253],{"stretchy":247},[126,3947,253],{"stretchy":247},[56,3949,3950],{"encoding":58},"a^{(L)}_j = \\sigma(z^{(L)}_j)",[33,3952,3954,4029],{"className":3953,"ariaHidden":63},[62],[33,3955,3957,3960,4020,4023,4026],{"className":3956},[67],[33,3958],{"className":3959,"style":1605},[71],[33,3961,3963,3966],{"className":3962},[76],[33,3964,281],{"className":3965},[76,77],[33,3967,3969],{"className":3968},[418],[33,3970,3972,4012],{"className":3971},[386,387],[33,3973,3975,4009],{"className":3974},[391],[33,3976,3978,3989],{"className":3977,"style":1625},[395],[33,3979,3980,3983],{"style":1910},[33,3981],{"className":3982,"style":435},[403],[33,3984,3986],{"className":3985},[439,440,441,442],[33,3987,1521],{"className":3988,"style":1638},[76,77,442],[33,3990,3991,3994],{"style":1641},[33,3992],{"className":3993,"style":435},[403],[33,3995,3997],{"className":3996},[439,440,441,442],[33,3998,4000,4003,4006],{"className":3999},[76,442],[33,4001,248],{"className":4002},[449,442],[33,4004,54],{"className":4005},[76,77,442],[33,4007,253],{"className":4008},[456,442],[33,4010,508],{"className":4011},[507],[33,4013,4015],{"className":4014},[391],[33,4016,4018],{"className":4017,"style":1669},[395],[33,4019],{},[33,4021],{"className":4022,"style":162},[161],[33,4024,128],{"className":4025},[166],[33,4027],{"className":4028,"style":162},[161],[33,4030,4032,4035,4038,4041,4101],{"className":4031},[67],[33,4033],{"className":4034,"style":1605},[71],[33,4036,341],{"className":4037,"style":706},[76,77],[33,4039,248],{"className":4040},[449],[33,4042,4044,4047],{"className":4043},[76],[33,4045,242],{"className":4046,"style":1612},[76,77],[33,4048,4050],{"className":4049},[418],[33,4051,4053,4093],{"className":4052},[386,387],[33,4054,4056,4090],{"className":4055},[391],[33,4057,4059,4070],{"className":4058,"style":1625},[395],[33,4060,4061,4064],{"style":1628},[33,4062],{"className":4063,"style":435},[403],[33,4065,4067],{"className":4066},[439,440,441,442],[33,4068,1521],{"className":4069,"style":1638},[76,77,442],[33,4071,4072,4075],{"style":1641},[33,4073],{"className":4074,"style":435},[403],[33,4076,4078],{"className":4077},[439,440,441,442],[33,4079,4081,4084,4087],{"className":4080},[76,442],[33,4082,248],{"className":4083},[449,442],[33,4085,54],{"className":4086},[76,77,442],[33,4088,253],{"className":4089},[456,442],[33,4091,508],{"className":4092},[507],[33,4094,4096],{"className":4095},[391],[33,4097,4099],{"className":4098,"style":1669},[395],[33,4100],{},[33,4102,253],{"className":4103},[456]," なので、",[33,4106,4108,4134],{"className":4107},[36],[33,4109,4111],{"className":4110},[40],[42,4112,4113],{"xmlns":44},[46,4114,4115,4131],{},[49,4116,4117],{},[1515,4118,4119,4121,4123],{},[52,4120,242],{},[52,4122,1521],{},[49,4124,4125,4127,4129],{},[126,4126,248],{"stretchy":247},[52,4128,54],{},[126,4130,253],{"stretchy":247},[56,4132,4133],{"encoding":58},"z^{(L)}_j",[33,4135,4137],{"className":4136,"ariaHidden":63},[62],[33,4138,4140,4143],{"className":4139},[67],[33,4141],{"className":4142,"style":1605},[71],[33,4144,4146,4149],{"className":4145},[76],[33,4147,242],{"className":4148,"style":1612},[76,77],[33,4150,4152],{"className":4151},[418],[33,4153,4155,4195],{"className":4154},[386,387],[33,4156,4158,4192],{"className":4157},[391],[33,4159,4161,4172],{"className":4160,"style":1625},[395],[33,4162,4163,4166],{"style":1628},[33,4164],{"className":4165,"style":435},[403],[33,4167,4169],{"className":4168},[439,440,441,442],[33,4170,1521],{"className":4171,"style":1638},[76,77,442],[33,4173,4174,4177],{"style":1641},[33,4175],{"className":4176,"style":435},[403],[33,4178,4180],{"className":4179},[439,440,441,442],[33,4181,4183,4186,4189],{"className":4182},[76,442],[33,4184,248],{"className":4185},[449,442],[33,4187,54],{"className":4188},[76,77,442],[33,4190,253],{"className":4191},[456,442],[33,4193,508],{"className":4194},[507],[33,4196,4198],{"className":4197},[391],[33,4199,4201],{"className":4200,"style":1669},[395],[33,4202],{}," は ",[33,4205,4207,4233],{"className":4206},[36],[33,4208,4210],{"className":4209},[40],[42,4211,4212],{"xmlns":44},[46,4213,4214,4230],{},[49,4215,4216],{},[1515,4217,4218,4220,4222],{},[52,4219,281],{},[52,4221,1521],{},[49,4223,4224,4226,4228],{},[126,4225,248],{"stretchy":247},[52,4227,54],{},[126,4229,253],{"stretchy":247},[56,4231,4232],{"encoding":58},"a^{(L)}_j",[33,4234,4236],{"className":4235,"ariaHidden":63},[62],[33,4237,4239,4242],{"className":4238},[67],[33,4240],{"className":4241,"style":1605},[71],[33,4243,4245,4248],{"className":4244},[76],[33,4246,281],{"className":4247},[76,77],[33,4249,4251],{"className":4250},[418],[33,4252,4254,4294],{"className":4253},[386,387],[33,4255,4257,4291],{"className":4256},[391],[33,4258,4260,4271],{"className":4259,"style":1625},[395],[33,4261,4262,4265],{"style":1910},[33,4263],{"className":4264,"style":435},[403],[33,4266,4268],{"className":4267},[439,440,441,442],[33,4269,1521],{"className":4270,"style":1638},[76,77,442],[33,4272,4273,4276],{"style":1641},[33,4274],{"className":4275,"style":435},[403],[33,4277,4279],{"className":4278},[439,440,441,442],[33,4280,4282,4285,4288],{"className":4281},[76,442],[33,4283,248],{"className":4284},[449,442],[33,4286,54],{"className":4287},[76,77,442],[33,4289,253],{"className":4290},[456,442],[33,4292,508],{"className":4293},[507],[33,4295,4297],{"className":4296},[391],[33,4298,4300],{"className":4299,"style":1669},[395],[33,4301],{}," だけを通して損失に影響します。",[33,4304,4306],{"className":4305},[208],[33,4307,4309,4394],{"className":4308},[36],[33,4310,4312],{"className":4311},[40],[42,4313,4314],{"xmlns":44,"display":217},[46,4315,4316,4391],{},[49,4317,4318,4332,4334,4360,4364,4371],{},[1515,4319,4320,4322,4324],{},[52,4321,2581],{},[52,4323,1521],{},[49,4325,4326,4328,4330],{},[126,4327,248],{"stretchy":247},[52,4329,54],{},[126,4331,253],{"stretchy":247},[126,4333,128],{},[2167,4335,4336,4342],{},[49,4337,4338,4340],{},[52,4339,2174],{"mathvariant":2173},[52,4341,54],{"mathvariant":1369},[49,4343,4344,4346],{},[52,4345,2174],{"mathvariant":2173},[1515,4347,4348,4350,4352],{},[52,4349,281],{},[52,4351,1521],{},[49,4353,4354,4356,4358],{},[126,4355,248],{"stretchy":247},[52,4357,54],{},[126,4359,253],{"stretchy":247},[4361,4362,4363],"mtext",{}," ",[237,4365,4366,4368],{},[52,4367,341],{},[126,4369,4370],{"mathvariant":2173,"lspace":225,"rspace":225},"′",[49,4372,4373,4375,4389],{},[126,4374,248],{"fence":63},[1515,4376,4377,4379,4381],{},[52,4378,242],{},[52,4380,1521],{},[49,4382,4383,4385,4387],{},[126,4384,248],{"stretchy":247},[52,4386,54],{},[126,4388,253],{"stretchy":247},[126,4390,253],{"fence":63},[56,4392,4393],{"encoding":58},"\\delta^{(L)}_j = \\frac{\\partial \\mathcal{L}}{\\partial a^{(L)}_j} \\, \\sigma'\\left(z^{(L)}_j\\right)",[33,4395,4397,4472],{"className":4396,"ariaHidden":63},[62],[33,4398,4400,4403,4463,4466,4469],{"className":4399},[67],[33,4401],{"className":4402,"style":1605},[71],[33,4404,4406,4409],{"className":4405},[76],[33,4407,2581],{"className":4408,"style":2727},[76,77],[33,4410,4412],{"className":4411},[418],[33,4413,4415,4455],{"className":4414},[386,387],[33,4416,4418,4452],{"className":4417},[391],[33,4419,4421,4432],{"className":4420,"style":1625},[395],[33,4422,4423,4426],{"style":2742},[33,4424],{"className":4425,"style":435},[403],[33,4427,4429],{"className":4428},[439,440,441,442],[33,4430,1521],{"className":4431,"style":1638},[76,77,442],[33,4433,4434,4437],{"style":1641},[33,4435],{"className":4436,"style":435},[403],[33,4438,4440],{"className":4439},[439,440,441,442],[33,4441,4443,4446,4449],{"className":4442},[76,442],[33,4444,248],{"className":4445},[449,442],[33,4447,54],{"className":4448},[76,77,442],[33,4450,253],{"className":4451},[456,442],[33,4453,508],{"className":4454},[507],[33,4456,4458],{"className":4457},[391],[33,4459,4461],{"className":4460,"style":1669},[395],[33,4462],{},[33,4464],{"className":4465,"style":162},[161],[33,4467,128],{"className":4468},[166],[33,4470],{"className":4471,"style":162},[161],[33,4473,4475,4478,4603,4606,4639,4642],{"className":4474},[67],[33,4476],{"className":4477,"style":2798},[71],[33,4479,4481,4484,4600],{"className":4480},[76],[33,4482],{"className":4483},[449,2249],[33,4485,4487],{"className":4486},[2167],[33,4488,4490,4592],{"className":4489},[386,387],[33,4491,4493,4589],{"className":4492},[391],[33,4494,4496,4567,4575],{"className":4495,"style":2262},[395],[33,4497,4498,4501],{"style":2265},[33,4499],{"className":4500,"style":2269},[403],[33,4502,4504,4507],{"className":4503},[76],[33,4505,2174],{"className":4506,"style":2276},[76],[33,4508,4510,4513],{"className":4509},[76],[33,4511,281],{"className":4512},[76,77],[33,4514,4516],{"className":4515},[418],[33,4517,4519,4559],{"className":4518},[386,387],[33,4520,4522,4556],{"className":4521},[391],[33,4523,4525,4536],{"className":4524,"style":1625},[395],[33,4526,4527,4530],{"style":1910},[33,4528],{"className":4529,"style":435},[403],[33,4531,4533],{"className":4532},[439,440,441,442],[33,4534,1521],{"className":4535,"style":1638},[76,77,442],[33,4537,4538,4541],{"style":1641},[33,4539],{"className":4540,"style":435},[403],[33,4542,4544],{"className":4543},[439,440,441,442],[33,4545,4547,4550,4553],{"className":4546},[76,442],[33,4548,248],{"className":4549},[449,442],[33,4551,54],{"className":4552},[76,77,442],[33,4554,253],{"className":4555},[456,442],[33,4557,508],{"className":4558},[507],[33,4560,4562],{"className":4561},[391],[33,4563,4565],{"className":4564,"style":1669},[395],[33,4566],{},[33,4568,4569,4572],{"style":2345},[33,4570],{"className":4571,"style":2269},[403],[33,4573],{"className":4574,"style":2353},[2352],[33,4576,4577,4580],{"style":2356},[33,4578],{"className":4579,"style":2269},[403],[33,4581,4583,4586],{"className":4582},[76],[33,4584,2174],{"className":4585,"style":2276},[76],[33,4587,54],{"className":4588},[76,1400],[33,4590,508],{"className":4591},[507],[33,4593,4595],{"className":4594},[391],[33,4596,4598],{"className":4597,"style":2514},[395],[33,4599],{},[33,4601],{"className":4602},[456,2249],[33,4604],{"className":4605,"style":187},[161],[33,4607,4609,4612],{"className":4608},[76],[33,4610,341],{"className":4611,"style":706},[76,77],[33,4613,4615],{"className":4614},[418],[33,4616,4618],{"className":4617},[386],[33,4619,4621],{"className":4620},[391],[33,4622,4625],{"className":4623,"style":4624},[395],"height:0.8019em;",[33,4626,4627,4630],{"style":431},[33,4628],{"className":4629,"style":435},[403],[33,4631,4633],{"className":4632},[439,440,441,442],[33,4634,4636],{"className":4635},[76,442],[33,4637,4370],{"className":4638},[76,442],[33,4640],{"className":4641,"style":187},[161],[33,4643,4645,4651,4711],{"className":4644},[191],[33,4646,4648],{"className":4647,"style":717},[449,716],[33,4649,248],{"className":4650},[721,722],[33,4652,4654,4657],{"className":4653},[76],[33,4655,242],{"className":4656,"style":1612},[76,77],[33,4658,4660],{"className":4659},[418],[33,4661,4663,4703],{"className":4662},[386,387],[33,4664,4666,4700],{"className":4665},[391],[33,4667,4669,4680],{"className":4668,"style":1625},[395],[33,4670,4671,4674],{"style":1628},[33,4672],{"className":4673,"style":435},[403],[33,4675,4677],{"className":4676},[439,440,441,442],[33,4678,1521],{"className":4679,"style":1638},[76,77,442],[33,4681,4682,4685],{"style":1641},[33,4683],{"className":4684,"style":435},[403],[33,4686,4688],{"className":4687},[439,440,441,442],[33,4689,4691,4694,4697],{"className":4690},[76,442],[33,4692,248],{"className":4693},[449,442],[33,4695,54],{"className":4696},[76,77,442],[33,4698,253],{"className":4699},[456,442],[33,4701,508],{"className":4702},[507],[33,4704,4706],{"className":4705},[391],[33,4707,4709],{"className":4708,"style":1669},[395],[33,4710],{},[33,4712,4714],{"className":4713,"style":717},[456,716],[33,4715,253],{"className":4716},[721,722],[10,4718,4719,4720,4751],{},"ベクトルで書くと、",[33,4721,4723,4738],{"className":4722},[36],[33,4724,4726],{"className":4725},[40],[42,4727,4728],{"xmlns":44},[46,4729,4730,4735],{},[49,4731,4732],{},[126,4733,4734],{},"⊙",[56,4736,4737],{"encoding":58},"\\odot",[33,4739,4741],{"className":4740,"ariaHidden":63},[62],[33,4742,4744,4748],{"className":4743},[67],[33,4745],{"className":4746,"style":4747},[71],"height:0.6667em;vertical-align:-0.0833em;",[33,4749,4734],{"className":4750},[76]," を成分ごとの積（アダマール積）として次のようになります。",[33,4753,4755],{"className":4754},[208],[33,4756,4758,4846],{"className":4757},[36],[33,4759,4761],{"className":4760},[40],[42,4762,4763],{"xmlns":44,"display":217},[46,4764,4765,4843],{},[221,4766,4768],{"width":4767},"100%",[227,4769,4770,4773,4836,4838],{},[230,4771],{"width":4772},"50%",[230,4774,4775],{},[49,4776,4777,4789,4791,4808,4810,4812,4818],{},[237,4778,4779,4781],{},[52,4780,2581],{"mathvariant":2580},[49,4782,4783,4785,4787],{},[126,4784,248],{"stretchy":247},[52,4786,54],{},[126,4788,253],{"stretchy":247},[126,4790,128],{},[1533,4792,4793,4796],{},[52,4794,4795],{"mathvariant":2173},"∇",[237,4797,4798,4800],{},[52,4799,281],{"mathvariant":241},[49,4801,4802,4804,4806],{},[126,4803,248],{"stretchy":247},[52,4805,54],{},[126,4807,253],{"stretchy":247},[52,4809,54],{"mathvariant":1369},[126,4811,4734],{},[237,4813,4814,4816],{},[52,4815,341],{},[126,4817,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[49,4819,4820,4822,4834],{},[126,4821,248],{"fence":63},[237,4823,4824,4826],{},[52,4825,242],{"mathvariant":241},[49,4827,4828,4830,4832],{},[126,4829,248],{"stretchy":247},[52,4831,54],{},[126,4833,253],{"stretchy":247},[126,4835,253],{"fence":63},[230,4837],{"width":4772},[230,4839,4840],{},[4361,4841,4842],{},"(BP1)",[56,4844,4845],{"encoding":58},"\\boldsymbol{\\delta}^{(L)} = \\nabla_{\\mathbf{a}^{(L)}} \\mathcal{L} \\odot \\sigma'\\left(\\mathbf{z}^{(L)}\\right) \\tag{BP1}",[33,4847,4849,4908,5013,5108],{"className":4848,"ariaHidden":63},[62],[33,4850,4852,4855,4899,4902,4905],{"className":4851},[67],[33,4853],{"className":4854,"style":2602},[71],[33,4856,4858,4867],{"className":4857},[76],[33,4859,4861],{"className":4860},[76],[33,4862,4864],{"className":4863},[76],[33,4865,2581],{"className":4866,"style":2616},[76,2615],[33,4868,4870],{"className":4869},[418],[33,4871,4873],{"className":4872},[386],[33,4874,4876],{"className":4875},[391],[33,4877,4879],{"className":4878,"style":2602},[395],[33,4880,4881,4884],{"style":2631},[33,4882],{"className":4883,"style":435},[403],[33,4885,4887],{"className":4886},[439,440,441,442],[33,4888,4890,4893,4896],{"className":4889},[76,442],[33,4891,248],{"className":4892},[449,442],[33,4894,54],{"className":4895},[76,77,442],[33,4897,253],{"className":4898},[456,442],[33,4900],{"className":4901,"style":162},[161],[33,4903,128],{"className":4904},[166],[33,4906],{"className":4907,"style":162},[161],[33,4909,4911,4915,5001,5004,5007,5010],{"className":4910},[67],[33,4912],{"className":4913,"style":4914},[71],"height:0.914em;vertical-align:-0.2306em;",[33,4916,4918,4921],{"className":4917},[76],[33,4919,4795],{"className":4920},[76],[33,4922,4924],{"className":4923},[418],[33,4925,4927,4992],{"className":4926},[386,387],[33,4928,4930,4989],{"className":4929},[391],[33,4931,4934],{"className":4932,"style":4933},[395],"height:0.3448em;",[33,4935,4937,4940],{"style":4936},"top:-2.4694em;margin-left:0em;margin-right:0.05em;",[33,4938],{"className":4939,"style":435},[403],[33,4941,4943],{"className":4942},[439,440,441,442],[33,4944,4946],{"className":4945},[76,442],[33,4947,4949,4952],{"className":4948},[76,442],[33,4950,281],{"className":4951},[76,414,442],[33,4953,4955],{"className":4954},[418],[33,4956,4958],{"className":4957},[386],[33,4959,4961],{"className":4960},[391],[33,4962,4965],{"className":4963,"style":4964},[395],"height:0.822em;",[33,4966,4968,4972],{"style":4967},"top:-2.822em;margin-right:0.0714em;",[33,4969],{"className":4970,"style":4971},[403],"height:2.5357em;",[33,4973,4977],{"className":4974},[439,4975,4976,442],"reset-size3","size1",[33,4978,4980,4983,4986],{"className":4979},[76,442],[33,4981,248],{"className":4982},[449,442],[33,4984,54],{"className":4985},[76,77,442],[33,4987,253],{"className":4988},[456,442],[33,4990,508],{"className":4991},[507],[33,4993,4995],{"className":4994},[391],[33,4996,4999],{"className":4997,"style":4998},[395],"height:0.2306em;",[33,5000],{},[33,5002,54],{"className":5003},[76,1400],[33,5005],{"className":5006,"style":638},[161],[33,5008,4734],{"className":5009},[628],[33,5011],{"className":5012,"style":638},[161],[33,5014,5016,5020,5052,5055],{"className":5015},[67],[33,5017],{"className":5018,"style":5019},[71],"height:1.8em;vertical-align:-0.65em;",[33,5021,5023,5026],{"className":5022},[76],[33,5024,341],{"className":5025,"style":706},[76,77],[33,5027,5029],{"className":5028},[418],[33,5030,5032],{"className":5031},[386],[33,5033,5035],{"className":5034},[391],[33,5036,5038],{"className":5037,"style":4624},[395],[33,5039,5040,5043],{"style":431},[33,5041],{"className":5042,"style":435},[403],[33,5044,5046],{"className":5045},[439,440,441,442],[33,5047,5049],{"className":5048},[76,442],[33,5050,4370],{"className":5051},[76,442],[33,5053],{"className":5054,"style":187},[161],[33,5056,5058,5064,5102],{"className":5057},[191],[33,5059,5061],{"className":5060,"style":717},[449,716],[33,5062,248],{"className":5063},[721,722],[33,5065,5067,5070],{"className":5066},[76],[33,5068,242],{"className":5069},[76,414],[33,5071,5073],{"className":5072},[418],[33,5074,5076],{"className":5075},[386],[33,5077,5079],{"className":5078},[391],[33,5080,5082],{"className":5081,"style":428},[395],[33,5083,5084,5087],{"style":431},[33,5085],{"className":5086,"style":435},[403],[33,5088,5090],{"className":5089},[439,440,441,442],[33,5091,5093,5096,5099],{"className":5092},[76,442],[33,5094,248],{"className":5095},[449,442],[33,5097,54],{"className":5098},[76,77,442],[33,5100,253],{"className":5101},[456,442],[33,5103,5105],{"className":5104,"style":717},[456,716],[33,5106,253],{"className":5107},[721,722],[33,5109,5112,5115],{"className":5110},[5111],"katex-tag",[33,5113],{"className":5114,"style":5019},[71],[33,5116,5119,5122,5129],{"className":5117},[76,5118],"text",[33,5120,248],{"className":5121},[76],[33,5123,5125],{"className":5124},[76],[33,5126,5128],{"className":5127},[76],"BP1",[33,5130,253],{"className":5131},[76],[3894,5133,5135],{"id":5134},"bp2-誤差を1つ前の層へ伝える","(BP2) 誤差を1つ前の層へ伝える",[10,5137,5138,5235,5236,5346],{},[33,5139,5141,5166],{"className":5140},[36],[33,5142,5144],{"className":5143},[40],[42,5145,5146],{"xmlns":44},[46,5147,5148,5164],{},[49,5149,5150],{},[1515,5151,5152,5154,5156],{},[52,5153,242],{},[52,5155,1521],{},[49,5157,5158,5160,5162],{},[126,5159,248],{"stretchy":247},[52,5161,93],{},[126,5163,253],{"stretchy":247},[56,5165,3082],{"encoding":58},[33,5167,5169],{"className":5168,"ariaHidden":63},[62],[33,5170,5172,5175],{"className":5171},[67],[33,5173],{"className":5174,"style":1605},[71],[33,5176,5178,5181],{"className":5177},[76],[33,5179,242],{"className":5180,"style":1612},[76,77],[33,5182,5184],{"className":5183},[418],[33,5185,5187,5227],{"className":5186},[386,387],[33,5188,5190,5224],{"className":5189},[391],[33,5191,5193,5204],{"className":5192,"style":1625},[395],[33,5194,5195,5198],{"style":1628},[33,5196],{"className":5197,"style":435},[403],[33,5199,5201],{"className":5200},[439,440,441,442],[33,5202,1521],{"className":5203,"style":1638},[76,77,442],[33,5205,5206,5209],{"style":1641},[33,5207],{"className":5208,"style":435},[403],[33,5210,5212],{"className":5211},[439,440,441,442],[33,5213,5215,5218,5221],{"className":5214},[76,442],[33,5216,248],{"className":5217},[449,442],[33,5219,93],{"className":5220,"style":109},[76,77,442],[33,5222,253],{"className":5223},[456,442],[33,5225,508],{"className":5226},[507],[33,5228,5230],{"className":5229},[391],[33,5231,5233],{"className":5232,"style":1669},[395],[33,5234],{}," は、次の層のすべての 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を通して損失に影響します。連鎖律より、次が成り立ちます。",[33,5348,5350],{"className":5349},[208],[33,5351,5353,5528],{"className":5352},[36],[33,5354,5356],{"className":5355},[40],[42,5357,5358],{"xmlns":44,"display":217},[46,5359,5360,5525],{},[49,5361,5362,5376,5378,5385,5415,5457,5459,5465,5483],{},[1515,5363,5364,5366,5368],{},[52,5365,2581],{},[52,5367,1521],{},[49,5369,5370,5372,5374],{},[126,5371,248],{"stretchy":247},[52,5373,93],{},[126,5375,253],{"stretchy":247},[126,5377,128],{},[5379,5380,5381,5383],"munder",{},[126,5382,1537],{},[52,5384,1540],{},[2167,5386,5387,5393],{},[49,5388,5389,5391],{},[52,5390,2174],{"mathvariant":2173},[52,5392,54],{"mathvariant":1369},[49,5394,5395,5397],{},[52,5396,2174],{"mathvariant":2173},[1515,5398,5399,5401,5403],{},[52,5400,242],{},[52,5402,1540],{},[49,5404,5405,5407,5409,5411,5413],{},[126,5406,248],{"stretchy":247},[52,5408,93],{},[126,5410,297],{},[130,5412,132],{},[126,5414,253],{"stretchy":247},[2167,5416,5417,5439],{},[49,5418,5419,5421],{},[52,5420,2174],{"mathvariant":2173},[1515,5422,5423,5425,5427],{},[52,5424,242],{},[52,5426,1540],{},[49,5428,5429,5431,5433,5435,5437],{},[126,5430,248],{"stretchy":247},[52,5432,93],{},[126,5434,297],{},[130,5436,132],{},[126,5438,253],{"stretchy":247},[49,5440,5441,5443],{},[52,5442,2174],{"mathvariant":2173},[1515,5444,5445,5447,5449],{},[52,5446,242],{},[52,5448,1521],{},[49,5450,5451,5453,5455],{},[126,5452,248],{"stretchy":247},[52,5454,93],{},[126,5456,253],{"stretchy":247},[126,5458,128],{},[5379,5460,5461,5463],{},[126,5462,1537],{},[52,5464,1540],{},[1515,5466,5467,5469,5471],{},[52,5468,2581],{},[52,5470,1540],{},[49,5472,5473,5475,5477,5479,5481],{},[126,5474,248],{"stretchy":247},[52,5476,93],{},[126,5478,297],{},[130,5480,132],{},[126,5482,253],{"stretchy":247},[2167,5484,5485,5507],{},[49,5486,5487,5489],{},[52,5488,2174],{"mathvariant":2173},[1515,5490,5491,5493,5495],{},[52,5492,242],{},[52,5494,1540],{},[49,5496,5497,5499,5501,5503,5505],{},[126,5498,248],{"stretchy":247},[52,5500,93],{},[126,5502,297],{},[130,5504,132],{},[126,5506,253],{"stretchy":247},[49,5508,5509,5511],{},[52,5510,2174],{"mathvariant":2173},[1515,5512,5513,5515,5517],{},[52,5514,242],{},[52,5516,1521],{},[49,5518,5519,5521,5523],{},[126,5520,248],{"stretchy":247},[52,5522,93],{},[126,5524,253],{"stretchy":247},[56,5526,5527],{"encoding":58},"\\delta^{(l)}_j\n= \\sum_k \\frac{\\partial \\mathcal{L}}{\\partial z^{(l+1)}_k} \\frac{\\partial z^{(l+1)}_k}{\\partial z^{(l)}_j}\n= \\sum_k \\delta^{(l+1)}_k \\frac{\\partial z^{(l+1)}_k}{\\partial z^{(l)}_j}",[33,5529,5531,5606,5994],{"className":5530,"ariaHidden":63},[62],[33,5532,5534,5537,5597,5600,5603],{"className":5533},[67],[33,5535],{"className":5536,"style":1605},[71],[33,5538,5540,5543],{"className":5539},[76],[33,5541,2581],{"className":5542,"style":2727},[76,77],[33,5544,5546],{"className":5545},[418],[33,5547,5549,5589],{"className":5548},[386,387],[33,5550,5552,5586],{"className":5551},[391],[33,5553,5555,5566],{"className":5554,"style":1625},[395],[33,5556,5557,5560],{"style":2742},[33,5558],{"className":5559,"style":435},[403],[33,5561,5563],{"className":5562},[439,440,441,442],[33,5564,1521],{"className":5565,"style":1638},[76,77,442],[33,5567,5568,5571],{"style":1641},[33,5569],{"className":5570,"style":435},[403],[33,5572,5574],{"className":5573},[439,440,441,442],[33,5575,5577,5580,5583],{"className":5576},[76,442],[33,5578,248],{"className":5579},[449,442],[33,5581,93],{"className":5582,"style":109},[76,77,442],[33,5584,253],{"className":5585},[456,442],[33,5587,508],{"className":5588},[507],[33,5590,5592],{"className":5591},[391],[33,5593,5595],{"className":5594,"style":1669},[395],[33,5596],{},[33,5598],{"className":5599,"style":162},[161],[33,5601,128],{"className":5602},[166],[33,5604],{"className":5605,"style":162},[161],[33,5607,5609,5613,5660,5663,5795,5985,5988,5991],{"className":5608},[67],[33,5610],{"className":5611,"style":5612},[71],"height:3.0839em;vertical-align:-1.3478em;",[33,5614,5616],{"className":5615},[1691,3595],[33,5617,5619,5651],{"className":5618},[386,387],[33,5620,5622,5648],{"className":5621},[391],[33,5623,5626,5638],{"className":5624,"style":5625},[395],"height:1.05em;",[33,5627,5629,5632],{"style":5628},"top:-1.8479em;margin-left:0em;",[33,5630],{"className":5631,"style":3612},[403],[33,5633,5635],{"className":5634},[439,440,441,442],[33,5636,1540],{"className":5637,"style":1723},[76,77,442],[33,5639,5640,5643],{"style":3630},[33,5641],{"className":5642,"style":3612},[403],[33,5644,5645],{},[33,5646,1537],{"className":5647},[1691,1695,3639],[33,5649,508],{"className":5650},[507],[33,5652,5654],{"className":5653},[391],[33,5655,5658],{"className":5656,"style":5657},[395],"height:1.3021em;",[33,5659],{},[33,5661],{"className":5662,"style":187},[161],[33,5664,5666,5669,5792],{"className":5665},[76],[33,5667],{"className":5668},[449,2249],[33,5670,5672],{"className":5671},[2167],[33,5673,5675,5783],{"className":5674},[386,387],[33,5676,5678,5780],{"className":5677},[391],[33,5679,5681,5758,5766],{"className":5680,"style":2262},[395],[33,5682,5683,5686],{"style":2265},[33,5684],{"className":5685,"style":2269},[403],[33,5687,5689,5692],{"className":5688},[76],[33,5690,2174],{"className":5691,"style":2276},[76],[33,5693,5695,5698],{"className":5694},[76],[33,5696,242],{"className":5697,"style":1612},[76,77],[33,5699,5701],{"className":5700},[418],[33,5702,5704,5750],{"className":5703},[386,387],[33,5705,5707,5747],{"className":5706},[391],[33,5708,5710,5721],{"className":5709,"style":1625},[395],[33,5711,5712,5715],{"style":5299},[33,5713],{"className":5714,"style":435},[403],[33,5716,5718],{"className":5717},[439,440,441,442],[33,5719,1540],{"className":5720,"style":1723},[76,77,442],[33,5722,5723,5726],{"style":1641},[33,5724],{"className":5725,"style":435},[403],[33,5727,5729],{"className":5728},[439,440,441,442],[33,5730,5732,5735,5738,5741,5744],{"className":5731},[76,442],[33,5733,248],{"className":5734},[449,442],[33,5736,93],{"className":5737,"style":109},[76,77,442],[33,5739,297],{"className":5740},[628,442],[33,5742,132],{"className":5743},[76,442],[33,5745,253],{"className":5746},[456,442],[33,5748,508],{"className":5749},[507],[33,5751,5753],{"className":5752},[391],[33,5754,5756],{"className":5755,"style":1872},[395],[33,5757],{},[33,5759,5760,5763],{"style":2345},[33,5761],{"className":5762,"style":2269},[403],[33,5764],{"className":5765,"style":2353},[2352],[33,5767,5768,5771],{"style":2356},[33,5769],{"className":5770,"style":2269},[403],[33,5772,5774,5777],{"className":5773},[76],[33,5775,2174],{"className":5776,"style":2276},[76],[33,5778,54],{"className":5779},[76,1400],[33,5781,508],{"className":5782},[507],[33,5784,5786],{"className":5785},[391],[33,5787,5790],{"className":5788,"style":5789},[395],"height:1.2361em;",[33,5791],{},[33,5793],{"className":5794},[456,2249],[33,5796,5798,5801,5982],{"className":5797},[76],[33,5799],{"className":5800},[449,2249],[33,5802,5804],{"className":5803},[2167],[33,5805,5807,5974],{"className":5806},[386,387],[33,5808,5810,5971],{"className":5809},[391],[33,5811,5814,5885,5893],{"className":5812,"style":5813},[395],"height:1.7361em;",[33,5815,5816,5819],{"style":2265},[33,5817],{"className":5818,"style":2269},[403],[33,5820,5822,5825],{"className":5821},[76],[33,5823,2174],{"className":5824,"style":2276},[76],[33,5826,5828,5831],{"className":5827},[76],[33,5829,242],{"className":5830,"style":1612},[76,77],[33,5832,5834],{"className":5833},[418],[33,5835,5837,5877],{"className":5836},[386,387],[33,5838,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ame":6151},[418],[33,6153,6155,6195],{"className":6154},[386,387],[33,6156,6158,6192],{"className":6157},[391],[33,6159,6161,6172],{"className":6160,"style":1625},[395],[33,6162,6163,6166],{"style":1628},[33,6164],{"className":6165,"style":435},[403],[33,6167,6169],{"className":6168},[439,440,441,442],[33,6170,1521],{"className":6171,"style":1638},[76,77,442],[33,6173,6174,6177],{"style":1641},[33,6175],{"className":6176,"style":435},[403],[33,6178,6180],{"className":6179},[439,440,441,442],[33,6181,6183,6186,6189],{"className":6182},[76,442],[33,6184,248],{"className":6185},[449,442],[33,6187,93],{"className":6188,"style":109},[76,77,442],[33,6190,253],{"className":6191},[456,442],[33,6193,508],{"className":6194},[507],[33,6196,6198],{"className":6197},[391],[33,6199,6201],{"className":6200,"style":1669},[395],[33,6202],{},[33,6204,6205,6208],{"style":2345},[33,6206],{"className":6207,"style":2269},[403],[33,6209],{"className":6210,"style":2353},[2352],[33,6212,6213,6216],{"style":5895},[33,6214],{"className":6215,"style":2269},[403],[33,6217,6219,6222],{"className":6218},[76],[33,6220,2174],{"className":6221,"style":2276},[76],[33,6223,6225,6228],{"className":6224},[76],[33,6226,242],{"className":6227,"style":1612},[76,77],[33,6229,6231],{"className":6230},[418],[33,6232,6234,6280],{"className":6233},[386,387],[33,6235,6237,6277],{"className":6236},[391],[33,6238,6240,6251],{"className":6239,"style":1625},[395],[33,6241,6242,6245],{"style":5299},[33,6243],{"className":6244,"style":435},[403],[33,6246,6248],{"className":6247},[439,440,441,442],[33,6249,1540],{"className":6250,"style":1723},[76,77,442],[33,6252,6253,6256],{"style":1641},[33,6254],{"className":6255,"style":435},[403],[33,6257,6259],{"className":6258},[439,440,441,442],[33,6260,6262,6265,6268,6271,6274],{"className":6261},[76,442],[33,6263,248],{"className":6264},[449,442],[33,6266,93],{"className":6267,"style":109},[76,77,442],[33,6269,297],{"className":6270},[628,442],[33,6272,132],{"className":6273},[76,442],[33,6275,253],{"className":6276},[456,442],[33,6278,508],{"className":6279},[507],[33,6281,6283],{"className":6282},[391],[33,6284,6286],{"className":6285,"style":1872},[395],[33,6287],{},[33,6289,508],{"className":6290},[507],[33,6292,6294],{"className":6293},[391],[33,6295,6297],{"className":6296,"style":2514},[395],[33,6298],{},[33,6300],{"className":6301},[456,2249],[10,6303,6304,6305,6765],{},"ここで ",[33,6306,6308,6408],{"className":6307},[36],[33,6309,6311],{"className":6310},[40],[42,6312,6313],{"xmlns":44},[46,6314,6315,6405],{},[49,6316,6317,6335,6337,6343,6365,6367,6369,6383,6385,6387],{},[1515,6318,6319,6321,6323],{},[52,6320,242],{},[52,6322,1540],{},[49,6324,6325,6327,6329,6331,6333],{},[126,6326,248],{"stretchy":247},[52,6328,93],{},[126,6330,297],{},[130,6332,132],{},[126,6334,253],{"stretchy":247},[126,6336,128],{},[1533,6338,6339,6341],{},[126,6340,1537],{},[52,6342,1521],{},[1515,6344,6345,6347,6353],{},[52,6346,268],{},[49,6348,6349,6351],{},[52,6350,1540],{},[52,6352,1521],{},[49,6354,6355,6357,6359,6361,6363],{},[126,6356,248],{"stretchy":247},[52,6358,93],{},[126,6360,297],{},[130,6362,132],{},[126,6364,253],{"stretchy":247},[52,6366,341],{},[126,6368,248],{"stretchy":247},[1515,6370,6371,6373,6375],{},[52,6372,242],{},[52,6374,1521],{},[49,6376,6377,6379,6381],{},[126,6378,248],{"stretchy":247},[52,6380,93],{},[126,6382,253],{"stretchy":247},[126,6384,253],{"stretchy":247},[126,6386,297],{},[1515,6388,6389,6391,6393],{},[52,6390,302],{},[52,6392,1540],{},[49,6394,6395,6397,6399,6401,6403],{},[126,6396,248],{"stretchy":247},[52,6398,93],{},[126,6400,297],{},[130,6402,132],{},[126,6404,253],{"stretchy":247},[56,6406,6407],{"encoding":58},"z^{(l+1)}_k = \\sum_j W^{(l+1)}_{kj} \\sigma(z^{(l)}_j) + b^{(l+1)}_k",[33,6409,6411,6492,6693],{"className":6410,"ariaHidden":63},[62],[33,6412,6414,6417,6483,6486,6489],{"className":6413},[67],[33,6415],{"className":6416,"style":5278},[71],[33,6418,6420,6423],{"className":6419},[76],[33,6421,242],{"className":6422,"style":1612},[76,77],[33,6424,6426],{"className":6425},[418],[33,6427,6429,6475],{"className":6428},[386,387],[33,6430,6432,6472],{"className":6431},[391],[33,6433,6435,6446],{"className":6434,"style":1625},[395],[33,6436,6437,6440],{"style":5299},[33,6438],{"className":6439,"style":435},[403],[33,6441,6443],{"className":6442},[439,440,441,442],[33,6444,1540],{"className":6445,"style":1723},[76,77,442],[33,6447,6448,6451],{"style":1641},[33,6449],{"className":6450,"style":435},[403],[33,6452,6454],{"className":6453},[439,440,441,442],[33,6455,6457,6460,6463,6466,6469],{"className":6456},[76,442],[33,6458,248],{"className":6459},[449,442],[33,6461,93],{"className":6462,"style":109},[76,77,442],[33,6464,297],{"className":6465},[628,442],[33,6467,132],{"className":6468},[76,442],[33,6470,253],{"className":6471},[456,442],[33,6473,508],{"className":6474},[507],[33,6476,6478],{"className":6477},[391],[33,6479,6481],{"className":6480,"style":1872},[395],[33,6482],{},[33,6484],{"className":6485,"style":162},[161],[33,6487,128],{"className":6488},[166],[33,6490],{"className":6491,"style":162},[161],[33,6493,6495,6498,6540,6543,6615,6618,6621,6681,6684,6687,6690],{"className":6494},[67],[33,6496],{"className":6497,"style":1687},[71],[33,6499,6501,6504],{"className":6500},[1691],[33,6502,1537],{"className":6503,"style":1697},[1691,1695,1696],[33,6505,6507],{"className":6506},[418],[33,6508,6510,6531],{"className":6509},[386,387],[33,6511,6513,6528],{"className":6512},[391],[33,6514,6517],{"className":6515,"style":6516},[395],"height:0.162em;",[33,6518,6519,6522],{"style":1713},[33,6520],{"className":6521,"style":435},[403],[33,6523,6525],{"className":6524},[439,440,441,442],[33,6526,1521],{"className":6527,"style":1638},[76,77,442],[33,6529,508],{"className":6530},[507],[33,6532,6534],{"className":6533},[391],[33,6535,6538],{"className":6536,"style":6537},[395],"height:0.4358em;",[33,6539],{},[33,6541],{"className":6542,"style":187},[161],[33,6544,6546,6549],{"className":6545},[76],[33,6547,268],{"className":6548,"style":557},[76,77],[33,6550,6552],{"className":6551},[418],[33,6553,6555,6607],{"className":6554},[386,387],[33,6556,6558,6604],{"className":6557},[391],[33,6559,6561,6578],{"className":6560,"style":1625},[395],[33,6562,6563,6566],{"style":1759},[33,6564],{"className":6565,"style":435},[403],[33,6567,6569],{"className":6568},[439,440,441,442],[33,6570,6572,6575],{"className":6571},[76,442],[33,6573,1540],{"className":6574,"style":1723},[76,77,442],[33,6576,1521],{"className":6577,"style":1638},[76,77,442],[33,6579,6580,6583],{"style":1641},[33,6581],{"className":6582,"style":435},[403],[33,6584,6586],{"className":6585},[439,440,441,442],[33,6587,6589,6592,6595,6598,6601],{"className":6588},[76,442],[33,6590,248],{"className":6591},[449,442],[33,6593,93],{"className":6594,"style":109},[76,77,442],[33,6596,297],{"className":6597},[628,442],[33,6599,132],{"className":6600},[76,442],[33,6602,253],{"className":6603},[456,442],[33,6605,508],{"className":6606},[507],[33,6608,6610],{"className":6609},[391],[33,6611,6613],{"className":6612,"style":1804},[395],[33,6614],{},[33,6616,341],{"className":6617,"style":706},[76,77],[33,6619,248],{"className":6620},[449],[33,6622,6624,6627],{"className":6623},[76],[33,6625,242],{"className":6626,"style":1612},[76,77],[33,6628,6630],{"className":6629},[418],[33,6631,6633,6673],{"className":6632},[386,387],[33,6634,6636,6670],{"className":6635},[391],[33,6637,6639,6650],{"className":6638,"style":1625},[395],[33,6640,6641,6644],{"style":1628},[33,6642],{"className":6643,"style":435},[403],[33,6645,6647],{"className":6646},[439,440,441,442],[33,6648,1521],{"className":6649,"style":1638},[76,77,442],[33,6651,6652,6655],{"style":1641},[33,6653],{"className":6654,"style":435},[403],[33,6656,6658],{"className":6657},[439,440,441,442],[33,6659,6661,6664,6667],{"className":6660},[76,442],[33,6662,248],{"className":6663},[449,442],[33,6665,93],{"className":6666,"style":109},[76,77,442],[33,6668,253],{"className":6669},[456,442],[33,6671,508],{"className":6672},[507],[33,6674,6676],{"className":6675},[391],[33,6677,6679],{"className":6678,"style":1669},[395],[33,6680],{},[33,6682,253],{"className":6683},[456],[33,6685],{"className":6686,"style":638},[161],[33,6688,297],{"className":6689},[628],[33,6691],{"className":6692,"style":638},[161],[33,6694,6696,6699],{"className":6695},[67],[33,6697],{"className":6698,"style":5278},[71],[33,6700,6702,6705],{"className":6701},[76],[33,6703,302],{"className":6704},[76,77],[33,6706,6708],{"className":6707},[418],[33,6709,6711,6757],{"className":6710},[386,387],[33,6712,6714,6754],{"className":6713},[391],[33,6715,6717,6728],{"className":6716,"style":1625},[395],[33,6718,6719,6722],{"style":1827},[33,6720],{"className":6721,"style":435},[403],[33,6723,6725],{"className":6724},[439,440,441,442],[33,6726,1540],{"className":6727,"style":1723},[76,77,442],[33,6729,6730,6733],{"style":1641},[33,6731],{"className":6732,"style":435},[403],[33,6734,6736],{"className":6735},[439,440,441,442],[33,6737,6739,6742,6745,6748,6751],{"className":6738},[76,442],[33,6740,248],{"className":6741},[449,442],[33,6743,93],{"className":6744,"style":109},[76,77,442],[33,6746,297],{"className":6747},[628,442],[33,6749,132],{"className":6750},[76,442],[33,6752,253],{"className":6753},[456,442],[33,6755,508],{"className":6756},[507],[33,6758,6760],{"className":6759},[391],[33,6761,6763],{"className":6762,"style":1872},[395],[33,6764],{}," なので、次のようになります。",[33,6767,6769],{"className":6768},[208],[33,6770,6772,6878],{"className":6771},[36],[33,6773,6775],{"className":6774},[40],[42,6776,6777],{"xmlns":44,"display":217},[46,6778,6779,6875],{},[49,6780,6781,6823,6825,6847,6849,6855],{},[2167,6782,6783,6805],{},[49,6784,6785,6787],{},[52,6786,2174],{"mathvariant":2173},[1515,6788,6789,6791,6793],{},[52,6790,242],{},[52,6792,1540],{},[49,6794,6795,6797,6799,6801,6803],{},[126,6796,248],{"stretchy":247},[52,6798,93],{},[126,6800,297],{},[130,6802,132],{},[126,6804,253],{"stretchy":247},[49,6806,6807,6809],{},[52,6808,2174],{"mathvariant":2173},[1515,6810,6811,6813,6815],{},[52,6812,242],{},[52,6814,1521],{},[49,6816,6817,6819,6821],{},[126,6818,248],{"stretchy":247},[52,6820,93],{},[126,6822,253],{"stretchy":247},[126,6824,128],{},[1515,6826,6827,6829,6835],{},[52,6828,268],{},[49,6830,6831,6833],{},[52,6832,1540],{},[52,6834,1521],{},[49,6836,6837,6839,6841,6843,6845],{},[126,6838,248],{"stretchy":247},[52,6840,93],{},[126,6842,297],{},[130,6844,132],{},[126,6846,253],{"stretchy":247},[4361,6848,4363],{},[237,6850,6851,6853],{},[52,6852,341],{},[126,6854,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[49,6856,6857,6859,6873],{},[126,6858,248],{"fence":63},[1515,6860,6861,6863,6865],{},[52,6862,242],{},[52,6864,1521],{},[49,6866,6867,6869,6871],{},[126,6868,248],{"stretchy":247},[52,6870,93],{},[126,6872,253],{"stretchy":247},[126,6874,253],{"fence":63},[56,6876,6877],{"encoding":58},"\\frac{\\partial z^{(l+1)}_k}{\\partial z^{(l)}_j} = W^{(l+1)}_{kj} \\, \\sigma'\\left(z^{(l)}_j\\right)",[33,6879,6881,7084],{"className":6880,"ariaHidden":63},[62],[33,6882,6884,6887,7075,7078,7081],{"className":6883},[67],[33,6885],{"className":6886,"style":5612},[71],[33,6888,6890,6893,7072],{"className":6889},[76],[33,6891],{"className":6892},[449,2249],[33,6894,6896],{"className":6895},[2167],[33,6897,6899,7064],{"className":6898},[386,387],[33,6900,6902,7061],{"className":6901},[391],[33,6903,6905,6976,6984],{"className":6904,"style":5813},[395],[33,6906,6907,6910],{"style":2265},[33,6908],{"className":6909,"style":2269},[403],[33,6911,6913,6916],{"className":6912},[76],[33,6914,2174],{"className":6915,"style":2276},[76],[33,6917,6919,6922],{"className":6918},[76],[33,6920,242],{"className":6921,"style":1612},[76,77],[33,6923,6925],{"className":6924},[418],[33,6926,6928,6968],{"className":6927},[386,387],[33,6929,6931,6965],{"className":6930},[391],[33,6932,6934,6945],{"className":6933,"style":1625},[395],[33,6935,6936,6939],{"style":1628},[33,6937],{"className":6938,"style":435},[403],[33,6940,6942],{"className":6941},[439,440,441,442],[33,6943,1521],{"className":6944,"style":1638},[76,77,442],[33,6946,6947,6950],{"style":1641},[33,6948],{"className":6949,"style":435},[403],[33,6951,6953],{"className":6952},[439,440,441,442],[33,6954,6956,6959,6962],{"className":6955},[76,442],[33,6957,248],{"className":6958},[449,442],[33,6960,93],{"className":6961,"style":109},[76,77,442],[33,6963,253],{"className":6964},[456,442],[33,6966,508],{"className":6967},[507],[33,6969,6971],{"className":6970},[391],[33,6972,6974],{"className":6973,"style":1669},[395],[33,6975],{},[33,6977,6978,6981],{"style":2345},[33,6979],{"className":6980,"style":2269},[403],[33,6982],{"className":6983,"style":2353},[2352],[33,6985,6986,6989],{"style":5895},[33,6987],{"className":6988,"style":2269},[403],[33,6990,6992,6995],{"className":6991},[76],[33,6993,2174],{"className":6994,"style":2276},[76],[33,6996,6998,7001],{"className":6997},[76],[33,6999,242],{"className":7000,"style":1612},[76,77],[33,7002,7004],{"className":7003},[418],[33,7005,7007,7053],{"className":7006},[386,387],[33,7008,7010,7050],{"className":7009},[391],[33,7011,7013,7024],{"className":7012,"style":1625},[395],[33,7014,7015,7018],{"style":5299},[33,7016],{"className":7017,"style":435},[403],[33,7019,7021],{"className":7020},[439,440,441,442],[33,7022,1540],{"className":7023,"style":1723},[76,77,442],[33,7025,7026,7029],{"style":1641},[33,7027],{"className":7028,"style":435},[403],[33,7030,7032],{"className":7031},[439,440,441,442],[33,7033,7035,7038,7041,7044,7047],{"className":7034},[76,442],[33,7036,248],{"className":7037},[449,442],[33,7039,93],{"className":7040,"style":109},[76,77,442],[33,7042,297],{"className":7043},[628,442],[33,7045,132],{"className":7046},[76,442],[33,7048,253],{"className":7049},[456,442],[33,7051,508],{"className":7052},[507],[33,7054,7056],{"className":7055},[391],[33,7057,7059],{"className":7058,"style":1872},[395],[33,7060],{},[33,7062,508],{"className":7063},[507],[33,7065,7067],{"className":7066},[391],[33,7068,7070],{"className":7069,"style":2514},[395],[33,7071],{},[33,7073],{"className":7074},[456,2249],[33,7076],{"className":7077,"style":162},[161],[33,7079,128],{"className":7080},[166],[33,7082],{"className":7083,"style":162},[161],[33,7085,7087,7090,7162,7165,7197,7200],{"className":7086},[67],[33,7088],{"className":7089,"style":5019},[71],[33,7091,7093,7096],{"className":7092},[76],[33,7094,268],{"className":7095,"style":557},[76,77],[33,7097,7099],{"className":7098},[418],[33,7100,7102,7154],{"className":7101},[386,387],[33,7103,7105,7151],{"className":7104},[391],[33,7106,7108,7125],{"className":7107,"style":1625},[395],[33,7109,7110,7113],{"style":1759},[33,7111],{"className":7112,"style":435},[403],[33,7114,7116],{"className":7115},[439,440,441,442],[33,7117,7119,7122],{"className":7118},[76,442],[33,7120,1540],{"className":7121,"style":1723},[76,77,442],[33,7123,1521],{"className":7124,"style":1638},[76,77,442],[33,7126,7127,7130],{"style":1641},[33,7128],{"className":7129,"style":435},[403],[33,7131,7133],{"className":7132},[439,440,441,442],[33,7134,7136,7139,7142,7145,7148],{"className":7135},[76,442],[33,7137,248],{"className":7138},[449,442],[33,7140,93],{"className":7141,"style":109},[76,77,442],[33,7143,297],{"className":7144},[628,442],[33,7146,132],{"className":7147},[76,442],[33,7149,253],{"className":7150},[456,442],[33,7152,508],{"className":7153},[507],[33,7155,7157],{"className":7156},[391],[33,7158,7160],{"className":7159,"style":1804},[395],[33,7161],{},[33,7163],{"className":7164,"style":187},[161],[33,7166,7168,7171],{"className":7167},[76],[33,7169,341],{"className":7170,"style":706},[76,77],[33,7172,7174],{"className":7173},[418],[33,7175,7177],{"className":7176},[386],[33,7178,7180],{"className":7179},[391],[33,7181,7183],{"className":7182,"style":4624},[395],[33,7184,7185,7188],{"style":431},[33,7186],{"className":7187,"style":435},[403],[33,7189,7191],{"className":7190},[439,440,441,442],[33,7192,7194],{"className":7193},[76,442],[33,7195,4370],{"className":7196},[76,442],[33,7198],{"className":7199,"style":187},[161],[33,7201,7203,7209,7269],{"className":7202},[191],[33,7204,7206],{"className":7205,"style":717},[449,716],[33,7207,248],{"className":7208},[721,722],[33,7210,7212,7215],{"className":7211},[76],[33,7213,242],{"className":7214,"style":1612},[76,77],[33,7216,7218],{"className":7217},[418],[33,7219,7221,7261],{"className":7220},[386,387],[33,7222,7224,7258],{"className":7223},[391],[33,7225,7227,7238],{"className":7226,"style":1625},[395],[33,7228,7229,7232],{"style":1628},[33,7230],{"className":7231,"style":435},[403],[33,7233,7235],{"className":7234},[439,440,441,442],[33,7236,1521],{"className":7237,"style":1638},[76,77,442],[33,7239,7240,7243],{"style":1641},[33,7241],{"className":7242,"style":435},[403],[33,7244,7246],{"className":7245},[439,440,441,442],[33,7247,7249,7252,7255],{"className":7248},[76,442],[33,7250,248],{"className":7251},[449,442],[33,7253,93],{"className":7254,"style":109},[76,77,442],[33,7256,253],{"className":7257},[456,442],[33,7259,508],{"className":7260},[507],[33,7262,7264],{"className":7263},[391],[33,7265,7267],{"className":7266,"style":1669},[395],[33,7268],{},[33,7270,7272],{"className":7271,"style":717},[456,716],[33,7273,253],{"className":7274},[721,722],[10,7276,7277],{},"これを代入すると、次が得られます。",[33,7279,7281],{"className":7280},[208],[33,7282,7284,7390],{"className":7283},[36],[33,7285,7287],{"className":7286},[40],[42,7288,7289],{"xmlns":44,"display":217},[46,7290,7291,7387],{},[49,7292,7293,7307,7309,7361,7367],{},[1515,7294,7295,7297,7299],{},[52,7296,2581],{},[52,7298,1521],{},[49,7300,7301,7303,7305],{},[126,7302,248],{"stretchy":247},[52,7304,93],{},[126,7306,253],{"stretchy":247},[126,7308,128],{},[49,7310,7311,7313,7319,7341,7359],{},[126,7312,248],{"fence":63},[5379,7314,7315,7317],{},[126,7316,1537],{},[52,7318,1540],{},[1515,7320,7321,7323,7329],{},[52,7322,268],{},[49,7324,7325,7327],{},[52,7326,1540],{},[52,7328,1521],{},[49,7330,7331,7333,7335,7337,7339],{},[126,7332,248],{"stretchy":247},[52,7334,93],{},[126,7336,297],{},[130,7338,132],{},[126,7340,253],{"stretchy":247},[1515,7342,7343,7345,7347],{},[52,7344,2581],{},[52,7346,1540],{},[49,7348,7349,7351,7353,7355,7357],{},[126,7350,248],{"stretchy":247},[52,7352,93],{},[126,7354,297],{},[130,7356,132],{},[126,7358,253],{"stretchy":247},[126,7360,253],{"fence":63},[237,7362,7363,7365],{},[52,7364,341],{},[126,7366,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[49,7368,7369,7371,7385],{},[126,7370,248],{"fence":63},[1515,7372,7373,7375,7377],{},[52,7374,242],{},[52,7376,1521],{},[49,7378,7379,7381,7383],{},[126,7380,248],{"stretchy":247},[52,7382,93],{},[126,7384,253],{"stretchy":247},[126,7386,253],{"fence":63},[56,7388,7389],{"encoding":58},"\\delta^{(l)}_j = \\left( \\sum_k W^{(l+1)}_{kj} \\delta^{(l+1)}_k \\right) \\sigma'\\left(z^{(l)}_j\\right)",[33,7391,7393,7468],{"className":7392,"ariaHidden":63},[62],[33,7394,7396,7399,7459,7462,7465],{"className":7395},[67],[33,7397],{"className":7398,"style":1605},[71],[33,7400,7402,7405],{"className":7401},[76],[33,7403,2581],{"className":7404,"style":2727},[76,77],[33,7406,7408],{"className":7407},[418],[33,7409,7411,7451],{"className":7410},[386,387],[33,7412,7414,7448],{"className":7413},[391],[33,7415,7417,7428],{"className":7416,"style":1625},[395],[33,7418,7419,7422],{"style":2742},[33,7420],{"className":7421,"style":435},[403],[33,7423,7425],{"className":7424},[439,440,441,442],[33,7426,1521],{"className":7427,"style":1638},[76,77,442],[33,7429,7430,7433],{"style":1641},[33,7431],{"className":7432,"style":435},[403],[33,7434,7436],{"className":7435},[439,440,441,442],[33,7437,7439,7442,7445],{"className":7438},[76,442],[33,7440,248],{"className":7441},[449,442],[33,7443,93],{"className":7444,"style":109},[76,77,442],[33,7446,253],{"className":7447},[456,442],[33,7449,508],{"className":7450},[507],[33,7452,7454],{"className":7453},[391],[33,7455,7457],{"className":7456,"style":1669},[395],[33,7458],{},[33,7460],{"className":7461,"style":162},[161],[33,7463,128],{"className":7464},[166],[33,7466],{"className":7467,"style":162},[161],[33,7469,7471,7475,7676,7679,7711,7714],{"className":7470},[67],[33,7472],{"className":7473,"style":7474},[71],"height:3.0521em;vertical-align:-1.3021em;",[33,7476,7478,7485,7529,7532,7604,7670],{"className":7477},[191],[33,7479,7481],{"className":7480,"style":717},[449,716],[33,7482,248],{"className":7483},[721,7484],"size4",[33,7486,7488],{"className":7487},[1691,3595],[33,7489,7491,7521],{"className":7490},[386,387],[33,7492,7494,7518],{"className":7493},[391],[33,7495,7497,7508],{"className":7496,"style":5625},[395],[33,7498,7499,7502],{"style":5628},[33,7500],{"className":7501,"style":3612},[403],[33,7503,7505],{"className":7504},[439,440,441,442],[33,7506,1540],{"className":7507,"style":1723},[76,77,442],[33,7509,7510,7513],{"style":3630},[33,7511],{"className":7512,"style":3612},[403],[33,7514,7515],{},[33,7516,1537],{"className":7517},[1691,1695,3639],[33,7519,508],{"className":7520},[507],[33,7522,7524],{"className":7523},[391],[33,7525,7527],{"className":7526,"style":5657},[395],[33,7528],{},[33,7530],{"className":7531,"style":187},[161],[33,7533,7535,7538],{"className":7534},[76],[33,7536,268],{"className":7537,"style":557},[76,77],[33,7539,7541],{"className":7540},[418],[33,7542,7544,7596],{"className":7543},[386,387],[33,7545,7547,7593],{"className":7546},[391],[33,7548,7550,7567],{"className":7549,"style":1625},[395],[33,7551,7552,7555],{"style":1759},[33,7553],{"className":7554,"style":435},[403],[33,7556,7558],{"className":7557},[439,440,441,442],[33,7559,7561,7564],{"className":7560},[76,442],[33,7562,1540],{"className":7563,"style":1723},[76,77,442],[33,7565,1521],{"className":7566,"style":1638},[76,77,442],[33,7568,7569,7572],{"style":1641},[33,7570],{"className":7571,"style":435},[403],[33,7573,7575],{"className":7574},[439,440,441,442],[33,7576,7578,7581,7584,7587,7590],{"className":7577},[76,442],[33,7579,248],{"className":7580},[449,442],[33,7582,93],{"className":7583,"style":109},[76,77,442],[33,7585,297],{"className":7586},[628,442],[33,7588,132],{"className":7589},[76,442],[33,7591,253],{"className":7592},[456,442],[33,7594,508],{"className":7595},[507],[33,7597,7599],{"className":7598},[391],[33,7600,7602],{"className":7601,"style":1804},[395],[33,7603],{},[33,7605,7607,7610],{"className":7606},[76],[33,7608,2581],{"className":7609,"style":2727},[76,77],[33,7611,7613],{"className":7612},[418],[33,7614,7616,7662],{"className":7615},[386,387],[33,7617,7619,7659],{"className":7618},[391],[33,7620,7622,7633],{"className":7621,"style":1625},[395],[33,7623,7624,7627],{"style":6067},[33,7625],{"className":7626,"style":435},[403],[33,7628,7630],{"className":7629},[439,440,441,442],[33,7631,1540],{"className":7632,"style":1723},[76,77,442],[33,7634,7635,7638],{"style":1641},[33,7636],{"className":7637,"style":435},[403],[33,7639,7641],{"className":7640},[439,440,441,442],[33,7642,7644,7647,7650,7653,7656],{"className":7643},[76,442],[33,7645,248],{"className":7646},[449,442],[33,7648,93],{"className":7649,"style":109},[76,77,442],[33,7651,297],{"className":7652},[628,442],[33,7654,132],{"className":7655},[76,442],[33,7657,253],{"className":7658},[456,442],[33,7660,508],{"className":7661},[507],[33,7663,7665],{"className":7664},[391],[33,7666,7668],{"className":7667,"style":1872},[395],[33,7669],{},[33,7671,7673],{"className":7672,"style":717},[456,716],[33,7674,253],{"className":7675},[721,7484],[33,7677],{"className":7678,"style":187},[161],[33,7680,7682,7685],{"className":7681},[76],[33,7683,341],{"className":7684,"style":706},[76,77],[33,7686,7688],{"className":7687},[418],[33,7689,7691],{"className":7690},[386],[33,7692,7694],{"className":7693},[391],[33,7695,7697],{"className":7696,"style":4624},[395],[33,7698,7699,7702],{"style":431},[33,7700],{"className":7701,"style":435},[403],[33,7703,7705],{"className":7704},[439,440,441,442],[33,7706,7708],{"className":7707},[76,442],[33,7709,4370],{"className":7710},[76,442],[33,7712],{"className":7713,"style":187},[161],[33,7715,7717,7723,7783],{"className":7716},[191],[33,7718,7720],{"className":7719,"style":717},[449,716],[33,7721,248],{"className":7722},[721,722],[33,7724,7726,7729],{"className":7725},[76],[33,7727,242],{"className":7728,"style":1612},[76,77],[33,7730,7732],{"className":7731},[418],[33,7733,7735,7775],{"className":7734},[386,387],[33,7736,7738,7772],{"className":7737},[391],[33,7739,7741,7752],{"className":7740,"style":1625},[395],[33,7742,7743,7746],{"style":1628},[33,7744],{"className":7745,"style":435},[403],[33,7747,7749],{"className":7748},[439,440,441,442],[33,7750,1521],{"className":7751,"style":1638},[76,77,442],[33,7753,7754,7757],{"style":1641},[33,7755],{"className":7756,"style":435},[403],[33,7758,7760],{"className":7759},[439,440,441,442],[33,7761,7763,7766,7769],{"className":7762},[76,442],[33,7764,248],{"className":7765},[449,442],[33,7767,93],{"className":7768,"style":109},[76,77,442],[33,7770,253],{"className":7771},[456,442],[33,7773,508],{"className":7774},[507],[33,7776,7778],{"className":7777},[391],[33,7779,7781],{"className":7780,"style":1669},[395],[33,7782],{},[33,7784,7786],{"className":7785,"style":717},[456,716],[33,7787,253],{"className":7788},[721,722],[10,7790,7791,8042,8043,8182,8183,8273,8274,8302],{},[33,7792,7794,7852],{"className":7793},[36],[33,7795,7797],{"className":7796},[40],[42,7798,7799],{"xmlns":44},[46,7800,7801,7849],{},[49,7802,7803,7809,7831],{},[1533,7804,7805,7807],{},[126,7806,1537],{},[52,7808,1540],{},[1515,7810,7811,7813,7819],{},[52,7812,268],{},[49,7814,7815,7817],{},[52,7816,1540],{},[52,7818,1521],{},[49,7820,7821,7823,7825,7827,7829],{},[126,7822,248],{"stretchy":247},[52,7824,93],{},[126,7826,297],{},[130,7828,132],{},[126,7830,253],{"stretchy":247},[1515,7832,7833,7835,7837],{},[52,7834,2581],{},[52,7836,1540],{},[49,7838,7839,7841,7843,7845,7847],{},[126,7840,248],{"stretchy":247},[52,7842,93],{},[126,7844,297],{},[130,7846,132],{},[126,7848,253],{"stretchy":247},[56,7850,7851],{"encoding":58},"\\sum_k W^{(l+1)}_{kj} \\delta^{(l+1)}_k",[33,7853,7855],{"className":7854,"ariaHidden":63},[62],[33,7856,7858,7861,7901,7904,7976],{"className":7857},[67],[33,7859],{"className":7860,"style":1687},[71],[33,7862,7864,7867],{"className":7863},[1691],[33,7865,1537],{"className":7866,"style":1697},[1691,1695,1696],[33,7868,7870],{"className":7869},[418],[33,7871,7873,7893],{"className":7872},[386,387],[33,7874,7876,7890],{"className":7875},[391],[33,7877,7879],{"className":7878,"style":1710},[395],[33,7880,7881,7884],{"style":1713},[33,7882],{"className":7883,"style":435},[403],[33,7885,7887],{"className":7886},[439,440,441,442],[33,7888,1540],{"className":7889,"style":1723},[76,77,442],[33,7891,508],{"className":7892},[507],[33,7894,7896],{"className":7895},[391],[33,7897,7899],{"className":7898,"style":1733},[395],[33,7900],{},[33,7902],{"className":7903,"style":187},[161],[33,7905,7907,7910],{"className":7906},[76],[33,7908,268],{"className":7909,"style":557},[76,77],[33,7911,7913],{"className":7912},[418],[33,7914,7916,7968],{"className":7915},[386,387],[33,7917,7919,7965],{"className":7918},[391],[33,7920,7922,7939],{"className":7921,"style":1625},[395],[33,7923,7924,7927],{"style":1759},[33,7925],{"className":7926,"style":435},[403],[33,7928,7930],{"className":7929},[439,440,441,442],[33,7931,7933,7936],{"className":7932},[76,442],[33,7934,1540],{"className":7935,"style":1723},[76,77,442],[33,7937,1521],{"className":7938,"style":1638},[76,77,442],[33,7940,7941,7944],{"style":1641},[33,7942],{"className":7943,"style":435},[403],[33,7945,7947],{"className":7946},[439,440,441,442],[33,7948,7950,7953,7956,7959,7962],{"className":7949},[76,442],[33,7951,248],{"className":7952},[449,442],[33,7954,93],{"className":7955,"style":109},[76,77,442],[33,7957,297],{"className":7958},[628,442],[33,7960,132],{"className":7961},[76,442],[33,7963,253],{"className":7964},[456,442],[33,7966,508],{"className":7967},[507],[33,7969,7971],{"className":7970},[391],[33,7972,7974],{"className":7973,"style":1804},[395],[33,7975],{},[33,7977,7979,7982],{"className":7978},[76],[33,7980,2581],{"className":7981,"style":2727},[76,77],[33,7983,7985],{"className":7984},[418],[33,7986,7988,8034],{"className":7987},[386,387],[33,7989,7991,8031],{"className":7990},[391],[33,7992,7994,8005],{"className":7993,"style":1625},[395],[33,7995,7996,7999],{"style":6067},[33,7997],{"className":7998,"style":435},[403],[33,8000,8002],{"className":8001},[439,440,441,442],[33,8003,1540],{"className":8004,"style":1723},[76,77,442],[33,8006,8007,8010],{"style":1641},[33,8008],{"className":8009,"style":435},[403],[33,8011,8013],{"className":8012},[439,440,441,442],[33,8014,8016,8019,8022,8025,8028],{"className":8015},[76,442],[33,8017,248],{"className":8018},[449,442],[33,8020,93],{"className":8021,"style":109},[76,77,442],[33,8023,297],{"className":8024},[628,442],[33,8026,132],{"className":8027},[76,442],[33,8029,253],{"className":8030},[456,442],[33,8032,508],{"className":8033},[507],[33,8035,8037],{"className":8036},[391],[33,8038,8040],{"className":8039,"style":1872},[395],[33,8041],{}," は、転置行列 ",[33,8044,8046,8085],{"className":8045},[36],[33,8047,8049],{"className":8048},[40],[42,8050,8051],{"xmlns":44},[46,8052,8053,8082],{},[49,8054,8055],{},[237,8056,8057,8079],{},[49,8058,8059,8061,8077],{},[126,8060,248],{"fence":63},[237,8062,8063,8065],{},[52,8064,268],{},[49,8066,8067,8069,8071,8073,8075],{},[126,8068,248],{"stretchy":247},[52,8070,93],{},[126,8072,297],{},[130,8074,132],{},[126,8076,253],{"stretchy":247},[126,8078,253],{"fence":63},[52,8080,8081],{"mathvariant":2173},"⊤",[56,8083,8084],{"encoding":58},"\\left(W^{(l+1)}\\right)^\\top",[33,8086,8088],{"className":8087,"ariaHidden":63},[62],[33,8089,8091,8095],{"className":8090},[67],[33,8092],{"className":8093,"style":8094},[71],"height:1.477em;vertical-align:-0.35em;",[33,8096,8098,8157],{"className":8097},[191],[33,8099,8101,8107,8151],{"className":8100},[191],[33,8102,8104],{"className":8103,"style":717},[449,716],[33,8105,248],{"className":8106},[721,4976],[33,8108,8110,8113],{"className":8109},[76],[33,8111,268],{"className":8112,"style":557},[76,77],[33,8114,8116],{"className":8115},[418],[33,8117,8119],{"className":8118},[386],[33,8120,8122],{"className":8121},[391],[33,8123,8125],{"className":8124,"style":843},[395],[33,8126,8127,8130],{"style":864},[33,8128],{"className":8129,"style":435},[403],[33,8131,8133],{"className":8132},[439,440,441,442],[33,8134,8136,8139,8142,8145,8148],{"className":8135},[76,442],[33,8137,248],{"className":8138},[449,442],[33,8140,93],{"className":8141,"style":109},[76,77,442],[33,8143,297],{"className":8144},[628,442],[33,8146,132],{"className":8147},[76,442],[33,8149,253],{"className":8150},[456,442],[33,8152,8154],{"className":8153,"style":717},[456,716],[33,8155,253],{"className":8156},[721,4976],[33,8158,8160],{"className":8159},[418],[33,8161,8163],{"className":8162},[386],[33,8164,8166],{"className":8165},[391],[33,8167,8170],{"className":8168,"style":8169},[395],"height:1.127em;",[33,8171,8173,8176],{"style":8172},"top:-3.3409em;margin-right:0.05em;",[33,8174],{"className":8175,"style":435},[403],[33,8177,8179],{"className":8178},[439,440,441,442],[33,8180,8081],{"className":8181},[76,442]," とベクトル ",[33,8184,8186,8214],{"className":8185},[36],[33,8187,8189],{"className":8188},[40],[42,8190,8191],{"xmlns":44},[46,8192,8193,8211],{},[49,8194,8195],{},[237,8196,8197,8199],{},[52,8198,2581],{"mathvariant":2580},[49,8200,8201,8203,8205,8207,8209],{},[126,8202,248],{"stretchy":247},[52,8204,93],{},[126,8206,297],{},[130,8208,132],{},[126,8210,253],{"stretchy":247},[56,8212,8213],{"encoding":58},"\\boldsymbol{\\delta}^{(l+1)}",[33,8215,8217],{"className":8216,"ariaHidden":63},[62],[33,8218,8220,8223],{"className":8219},[67],[33,8221],{"className":8222,"style":2602},[71],[33,8224,8226,8235],{"className":8225},[76],[33,8227,8229],{"className":8228},[76],[33,8230,8232],{"className":8231},[76],[33,8233,2581],{"className":8234,"style":2616},[76,2615],[33,8236,8238],{"className":8237},[418],[33,8239,8241],{"className":8240},[386],[33,8242,8244],{"className":8243},[391],[33,8245,8247],{"className":8246,"style":2602},[395],[33,8248,8249,8252],{"style":2631},[33,8250],{"className":8251,"style":435},[403],[33,8253,8255],{"className":8254},[439,440,441,442],[33,8256,8258,8261,8264,8267,8270],{"className":8257},[76,442],[33,8259,248],{"className":8260},[449,442],[33,8262,93],{"className":8263,"style":109},[76,77,442],[33,8265,297],{"className":8266},[628,442],[33,8268,132],{"className":8269},[76,442],[33,8271,253],{"className":8272},[456,442]," の積の第 ",[33,8275,8277,8290],{"className":8276},[36],[33,8278,8280],{"className":8279},[40],[42,8281,8282],{"xmlns":44},[46,8283,8284,8288],{},[49,8285,8286],{},[52,8287,1521],{},[56,8289,1521],{"encoding":58},[33,8291,8293],{"className":8292,"ariaHidden":63},[62],[33,8294,8296,8299],{"className":8295},[67],[33,8297],{"className":8298,"style":2114},[71],[33,8300,1521],{"className":8301,"style":1638},[76,77]," 成分です。したがって、次のようにまとめられます。",[33,8304,8306],{"className":8305},[208],[33,8307,8309,8424],{"className":8308},[36],[33,8310,8312],{"className":8311},[40],[42,8313,8314],{"xmlns":44,"display":217},[46,8315,8316,8421],{},[221,8317,8318],{"width":4767},[227,8319,8320,8322,8414,8416],{},[230,8321],{"width":4772},[230,8323,8324],{},[49,8325,8326,8338,8340,8388,8390,8396],{},[237,8327,8328,8330],{},[52,8329,2581],{"mathvariant":2580},[49,8331,8332,8334,8336],{},[126,8333,248],{"stretchy":247},[52,8335,93],{},[126,8337,253],{"stretchy":247},[126,8339,128],{},[49,8341,8342,8344,8370,8386],{},[126,8343,248],{"fence":63},[237,8345,8346,8368],{},[49,8347,8348,8350,8366],{},[126,8349,248],{"fence":63},[237,8351,8352,8354],{},[52,8353,268],{},[49,8355,8356,8358,8360,8362,8364],{},[126,8357,248],{"stretchy":247},[52,8359,93],{},[126,8361,297],{},[130,8363,132],{},[126,8365,253],{"stretchy":247},[126,8367,253],{"fence":63},[52,8369,8081],{"mathvariant":2173},[237,8371,8372,8374],{},[52,8373,2581],{"mathvariant":2580},[49,8375,8376,8378,8380,8382,8384],{},[126,8377,248],{"stretchy":247},[52,8379,93],{},[126,8381,297],{},[130,8383,132],{},[126,8385,253],{"stretchy":247},[126,8387,253],{"fence":63},[126,8389,4734],{},[237,8391,8392,8394],{},[52,8393,341],{},[126,8395,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[49,8397,8398,8400,8412],{},[126,8399,248],{"fence":63},[237,8401,8402,8404],{},[52,8403,242],{"mathvariant":241},[49,8405,8406,8408,8410],{},[126,8407,248],{"stretchy":247},[52,8409,93],{},[126,8411,253],{"stretchy":247},[126,8413,253],{"fence":63},[230,8415],{"width":4772},[230,8417,8418],{},[4361,8419,8420],{},"(BP2)",[56,8422,8423],{"encoding":58},"\\boldsymbol{\\delta}^{(l)} = \\left( \\left(W^{(l+1)}\\right)^\\top \\boldsymbol{\\delta}^{(l+1)} \\right) \\odot \\sigma'\\left(\\mathbf{z}^{(l)}\\right) \\tag{BP2}",[33,8425,8427,8486,8657,8751],{"className":8426,"ariaHidden":63},[62],[33,8428,8430,8433,8477,8480,8483],{"className":8429},[67],[33,8431],{"className":8432,"style":2602},[71],[33,8434,8436,8445],{"className":8435},[76],[33,8437,8439],{"className":8438},[76],[33,8440,8442],{"className":8441},[76],[33,8443,2581],{"className":8444,"style":2616},[76,2615],[33,8446,8448],{"className":8447},[418],[33,8449,8451],{"className":8450},[386],[33,8452,8454],{"className":8453},[391],[33,8455,8457],{"className":8456,"style":2602},[395],[33,8458,8459,8462],{"style":2631},[33,8460],{"className":8461,"style":435},[403],[33,8463,8465],{"className":8464},[439,440,441,442],[33,8466,8468,8471,8474],{"className":8467},[76,442],[33,8469,248],{"className":8470},[449,442],[33,8472,93],{"className":8473,"style":109},[76,77,442],[33,8475,253],{"className":8476},[456,442],[33,8478],{"className":8479,"style":162},[161],[33,8481,128],{"className":8482},[166],[33,8484],{"className":8485,"style":162},[161],[33,8487,8489,8493,8648,8651,8654],{"className":8488},[67],[33,8490],{"className":8491,"style":8492},[71],"height:2.4em;vertical-align:-0.95em;",[33,8494,8496,8502,8589,8592,8642],{"className":8495},[191],[33,8497,8499],{"className":8498,"style":717},[449,716],[33,8500,248],{"className":8501},[721,441],[33,8503,8505,8564],{"className":8504},[191],[33,8506,8508,8514,8558],{"className":8507},[191],[33,8509,8511],{"className":8510,"style":717},[449,716],[33,8512,248],{"className":8513},[721,722],[33,8515,8517,8520],{"className":8516},[76],[33,8518,268],{"className":8519,"style":557},[76,77],[33,8521,8523],{"className":8522},[418],[33,8524,8526],{"className":8525},[386],[33,8527,8529],{"className":8528},[391],[33,8530,8532],{"className":8531,"style":428},[395],[33,8533,8534,8537],{"style":431},[33,8535],{"className":8536,"style":435},[403],[33,8538,8540],{"className":8539},[439,440,441,442],[33,8541,8543,8546,8549,8552,8555],{"className":8542},[76,442],[33,8544,248],{"className":8545},[449,442],[33,8547,93],{"className":8548,"style":109},[76,77,442],[33,8550,297],{"className":8551},[628,442],[33,8553,132],{"className":8554},[76,442],[33,8556,253],{"className":8557},[456,442],[33,8559,8561],{"className":8560,"style":717},[456,716],[33,8562,253],{"className":8563},[721,722],[33,8565,8567],{"className":8566},[418],[33,8568,8570],{"className":8569},[386],[33,8571,8573],{"className":8572},[391],[33,8574,8577],{"className":8575,"style":8576},[395],"height:1.389em;",[33,8578,8580,8583],{"style":8579},"top:-3.6029em;margin-right:0.05em;",[33,8581],{"className":8582,"style":435},[403],[33,8584,8586],{"className":8585},[439,440,441,442],[33,8587,8081],{"className":8588},[76,442],[33,8590],{"className":8591,"style":187},[161],[33,8593,8595,8604],{"className":8594},[76],[33,8596,8598],{"className":8597},[76],[33,8599,8601],{"className":8600},[76],[33,8602,2581],{"className":8603,"style":2616},[76,2615],[33,8605,8607],{"className":8606},[418],[33,8608,8610],{"className":8609},[386],[33,8611,8613],{"className":8612},[391],[33,8614,8616],{"className":8615,"style":2602},[395],[33,8617,8618,8621],{"style":2631},[33,8619],{"className":8620,"style":435},[403],[33,8622,8624],{"className":8623},[439,440,441,442],[33,8625,8627,8630,8633,8636,8639],{"className":8626},[76,442],[33,8628,248],{"className":8629},[449,442],[33,8631,93],{"className":8632,"style":109},[76,77,442],[33,8634,297],{"className":8635},[628,442],[33,8637,132],{"className":8638},[76,442],[33,8640,253],{"className":8641},[456,442],[33,8643,8645],{"className":8644,"style":717},[456,716],[33,8646,253],{"className":8647},[721,441],[33,8649],{"className":8650,"style":638},[161],[33,8652,4734],{"className":8653},[628],[33,8655],{"className":8656,"style":638},[161],[33,8658,8660,8663,8695,8698],{"className":8659},[67],[33,8661],{"className":8662,"style":5019},[71],[33,8664,8666,8669],{"className":8665},[76],[33,8667,341],{"className":8668,"style":706},[76,77],[33,8670,8672],{"className":8671},[418],[33,8673,8675],{"className":8674},[386],[33,8676,8678],{"className":8677},[391],[33,8679,8681],{"className":8680,"style":4624},[395],[33,8682,8683,8686],{"style":431},[33,8684],{"className":8685,"style":435},[403],[33,8687,8689],{"className":8688},[439,440,441,442],[33,8690,8692],{"className":8691},[76,442],[33,8693,4370],{"className":8694},[76,442],[33,8696],{"className":8697,"style":187},[161],[33,8699,8701,8707,8745],{"className":8700},[191],[33,8702,8704],{"className":8703,"style":717},[449,716],[33,8705,248],{"className":8706},[721,722],[33,8708,8710,8713],{"className":8709},[76],[33,8711,242],{"className":8712},[76,414],[33,8714,8716],{"className":8715},[418],[33,8717,8719],{"className":8718},[386],[33,8720,8722],{"className":8721},[391],[33,8723,8725],{"className":8724,"style":428},[395],[33,8726,8727,8730],{"style":431},[33,8728],{"className":8729,"style":435},[403],[33,8731,8733],{"className":8732},[439,440,441,442],[33,8734,8736,8739,8742],{"className":8735},[76,442],[33,8737,248],{"className":8738},[449,442],[33,8740,93],{"className":8741,"style":109},[76,77,442],[33,8743,253],{"className":8744},[456,442],[33,8746,8748],{"className":8747,"style":717},[456,716],[33,8749,253],{"className":8750},[721,722],[33,8752,8754,8757],{"className":8753},[5111],[33,8755],{"className":8756,"style":8492},[71],[33,8758,8760,8763,8770],{"className":8759},[76,5118],[33,8761,248],{"className":8762},[76],[33,8764,8766],{"className":8765},[76],[33,8767,8769],{"className":8768},[76],"BP2",[33,8771,253],{"className":8772},[76],[10,8774,8775,8776,8804,8805,8868],{},"順伝播では ",[33,8777,8779,8792],{"className":8778},[36],[33,8780,8782],{"className":8781},[40],[42,8783,8784],{"xmlns":44},[46,8785,8786,8790],{},[49,8787,8788],{},[52,8789,268],{},[56,8791,268],{"encoding":58},[33,8793,8795],{"className":8794,"ariaHidden":63},[62],[33,8796,8798,8801],{"className":8797},[67],[33,8799],{"className":8800,"style":72},[71],[33,8802,268],{"className":8803,"style":557},[76,77]," を掛けて信号を前へ送りました。逆伝播では ",[14,8806,8807,8867],{},[33,8808,8810,8828],{"className":8809},[36],[33,8811,8813],{"className":8812},[40],[42,8814,8815],{"xmlns":44},[46,8816,8817,8825],{},[49,8818,8819],{},[237,8820,8821,8823],{},[52,8822,268],{},[52,8824,8081],{"mathvariant":2173},[56,8826,8827],{"encoding":58},"W^\\top",[33,8829,8831],{"className":8830,"ariaHidden":63},[62],[33,8832,8834,8838],{"className":8833},[67],[33,8835],{"className":8836,"style":8837},[71],"height:0.8491em;",[33,8839,8841,8844],{"className":8840},[76],[33,8842,268],{"className":8843,"style":557},[76,77],[33,8845,8847],{"className":8846},[418],[33,8848,8850],{"className":8849},[386],[33,8851,8853],{"className":8852},[391],[33,8854,8856],{"className":8855,"style":8837},[395],[33,8857,8858,8861],{"style":864},[33,8859],{"className":8860,"style":435},[403],[33,8862,8864],{"className":8863},[439,440,441,442],[33,8865,8081],{"className":8866},[76,442]," を掛けて誤差を後ろへ送ります","。これが「逆伝播」という名前の由来です。",[3894,8870,8872],{"id":8871},"bp3-バイアスに関する勾配","(BP3) バイアスに関する勾配",[10,8874,8875,9086],{},[33,8876,8878,8929],{"className":8877},[36],[33,8879,8881],{"className":8880},[40],[42,8882,8883],{"xmlns":44},[46,8884,8885,8926],{},[49,8886,8887,8889,8903,8906,8908,8922,8924],{},[52,8888,2174],{"mathvariant":2173},[1515,8890,8891,8893,8895],{},[52,8892,242],{},[52,8894,1521],{},[49,8896,8897,8899,8901],{},[126,8898,248],{"stretchy":247},[52,8900,93],{},[126,8902,253],{"stretchy":247},[52,8904,8905],{"mathvariant":2173},"\u002F",[52,8907,2174],{"mathvariant":2173},[1515,8909,8910,8912,8914],{},[52,8911,302],{},[52,8913,1521],{},[49,8915,8916,8918,8920],{},[126,8917,248],{"stretchy":247},[52,8919,93],{},[126,8921,253],{"stretchy":247},[126,8923,128],{},[130,8925,132],{},[56,8927,8928],{"encoding":58},"\\partial z^{(l)}_j \u002F \\partial b^{(l)}_j = 1",[33,8930,8932,9076],{"className":8931,"ariaHidden":63},[62],[33,8933,8935,8938,8941,9001,9004,9007,9067,9070,9073],{"className":8934},[67],[33,8936],{"className":8937,"style":1605},[71],[33,8939,2174],{"className":8940,"style":2276},[76],[33,8942,8944,8947],{"className":8943},[76],[33,8945,242],{"className":8946,"style":1612},[76,77],[33,8948,8950],{"className":8949},[418],[33,8951,8953,8993],{"className":8952},[386,387],[33,8954,8956,8990],{"className":8955},[391],[33,8957,8959,8970],{"className":8958,"style":1625},[395],[33,8960,8961,8964],{"style":1628},[33,8962],{"className":8963,"style":435},[403],[33,8965,8967],{"className":8966},[439,440,441,442],[33,8968,1521],{"className":8969,"style":1638},[76,77,442],[33,8971,8972,8975],{"style":1641},[33,8973],{"className":8974,"style":435},[403],[33,8976,8978],{"className":8977},[439,440,441,442],[33,8979,8981,8984,8987],{"className":8980},[76,442],[33,8982,248],{"className":8983},[449,442],[33,8985,93],{"className":8986,"style":109},[76,77,442],[33,8988,253],{"className":8989},[456,442],[33,8991,508],{"className":8992},[507],[33,8994,8996],{"className":8995},[391],[33,8997,8999],{"className":8998,"style":1669},[395],[33,9000],{},[33,9002,8905],{"className":9003},[76],[33,9005,2174],{"className":9006,"style":2276},[76],[33,9008,9010,9013],{"className":9009},[76],[33,9011,302],{"className":9012},[76,77],[33,9014,9016],{"className":9015},[418],[33,9017,9019,9059],{"className":9018},[386,387],[33,9020,9022,9056],{"className":9021},[391],[33,9023,9025,9036],{"className":9024,"style":1625},[395],[33,9026,9027,9030],{"style":1910},[33,9028],{"className":9029,"style":435},[403],[33,9031,9033],{"className":9032},[439,440,441,442],[33,9034,1521],{"className":9035,"style":1638},[76,77,442],[33,9037,9038,9041],{"style":1641},[33,9039],{"className":9040,"style":435},[403],[33,9042,9044],{"className":9043},[439,440,441,442],[33,9045,9047,9050,9053],{"className":9046},[76,442],[33,9048,248],{"className":9049},[449,442],[33,9051,93],{"className":9052,"style":109},[76,77,442],[33,9054,253],{"className":9055},[456,442],[33,9057,508],{"className":9058},[507],[33,9060,9062],{"className":9061},[391],[33,9063,9065],{"className":9064,"style":1669},[395],[33,9066],{},[33,9068],{"className":9069,"style":162},[161],[33,9071,128],{"className":9072},[166],[33,9074],{"className":9075,"style":162},[161],[33,9077,9079,9083],{"className":9078},[67],[33,9080],{"className":9081,"style":9082},[71],"height:0.6444em;",[33,9084,132],{"className":9085},[76]," なので、次が成り立ちます。",[33,9088,9090],{"className":9089},[208],[33,9091,9093,9202],{"className":9092},[36],[33,9094,9096],{"className":9095},[40],[42,9097,9098],{"xmlns":44,"display":217},[46,9099,9100,9199],{},[221,9101,9102],{"width":4767},[227,9103,9104,9106,9192,9194],{},[230,9105],{"width":4772},[230,9107,9108],{},[49,9109,9110,9136,9138,9152,9155,9158,9160,9176,9178,9180],{},[2167,9111,9112,9118],{},[49,9113,9114,9116],{},[52,9115,2174],{"mathvariant":2173},[52,9117,54],{"mathvariant":1369},[49,9119,9120,9122],{},[52,9121,2174],{"mathvariant":2173},[1515,9123,9124,9126,9128],{},[52,9125,302],{},[52,9127,1521],{},[49,9129,9130,9132,9134],{},[126,9131,248],{"stretchy":247},[52,9133,93],{},[126,9135,253],{"stretchy":247},[126,9137,128],{},[1515,9139,9140,9142,9144],{},[52,9141,2581],{},[52,9143,1521],{},[49,9145,9146,9148,9150],{},[126,9147,248],{"stretchy":247},[52,9149,93],{},[126,9151,253],{"stretchy":247},[161,9153],{"width":9154},"1em",[126,9156,9157],{},"⟺",[161,9159],{"width":9154},[1533,9161,9162,9164],{},[52,9163,4795],{"mathvariant":2173},[237,9165,9166,9168],{},[52,9167,302],{"mathvariant":241},[49,9169,9170,9172,9174],{},[126,9171,248],{"stretchy":247},[52,9173,93],{},[126,9175,253],{"stretchy":247},[52,9177,54],{"mathvariant":1369},[126,9179,128],{},[237,9181,9182,9184],{},[52,9183,2581],{"mathvariant":2580},[49,9185,9186,9188,9190],{},[126,9187,248],{"stretchy":247},[52,9189,93],{},[126,9191,253],{"stretchy":247},[230,9193],{"width":4772},[230,9195,9196],{},[4361,9197,9198],{},"(BP3)",[56,9200,9201],{"encoding":58},"\\frac{\\partial \\mathcal{L}}{\\partial b^{(l)}_j} = \\delta^{(l)}_j\n\\quad\\Longleftrightarrow\\quad\n\\nabla_{\\mathbf{b}^{(l)}} \\mathcal{L} = \\boldsymbol{\\delta}^{(l)} \\tag{BP3}",[33,9203,9205,9345,9427,9523,9573],{"className":9204,"ariaHidden":63},[62],[33,9206,9208,9211,9336,9339,9342],{"className":9207},[67],[33,9209],{"className":9210,"style":2798},[71],[33,9212,9214,9217,9333],{"className":9213},[76],[33,9215],{"className":9216},[449,2249],[33,9218,9220],{"className":9219},[2167],[33,9221,9223,9325],{"className":9222},[386,387],[33,9224,9226,9322],{"className":9225},[391],[33,9227,9229,9300,9308],{"className":9228,"style":2262},[395],[33,9230,9231,9234],{"style":2265},[33,9232],{"className":9233,"style":2269},[403],[33,9235,9237,9240],{"className":9236},[76],[33,9238,2174],{"className":9239,"style":2276},[76],[33,9241,9243,9246],{"className":9242},[76],[33,9244,302],{"className":9245},[76,77],[33,9247,9249],{"className":9248},[418],[33,9250,9252,9292],{"className":9251},[386,387],[33,9253,9255,9289],{"className":9254},[391],[33,9256,9258,9269],{"className":9257,"style":1625},[395],[33,9259,9260,9263],{"style":1910},[33,9261],{"className":9262,"style":435},[403],[33,9264,9266],{"className":9265},[439,440,441,442],[33,9267,1521],{"className":9268,"style":1638},[76,77,442],[33,9270,9271,9274],{"style":1641},[33,9272],{"className":9273,"style":435},[403],[33,9275,9277],{"className":9276},[439,440,441,442],[33,9278,9280,9283,9286],{"className":9279},[76,442],[33,9281,248],{"className":9282},[449,442],[33,9284,93],{"className":9285,"style":109},[76,77,442],[33,9287,253],{"className":9288},[456,442],[33,9290,508],{"className":9291},[507],[33,9293,9295],{"className":9294},[391],[33,9296,9298],{"className":9297,"style":1669},[395],[33,9299],{},[33,9301,9302,9305],{"style":2345},[33,9303],{"className":9304,"style":2269},[403],[33,9306],{"className":9307,"style":2353},[2352],[33,9309,9310,9313],{"style":2356},[33,9311],{"className":9312,"style":2269},[403],[33,9314,9316,9319],{"className":9315},[76],[33,9317,2174],{"className":9318,"style":2276},[76],[33,9320,54],{"className":9321},[76,1400],[33,9323,508],{"className":9324},[507],[33,9326,9328],{"className":9327},[391],[33,9329,9331],{"className":9330,"style":2514},[395],[33,9332],{},[33,9334],{"className":9335},[456,2249],[33,9337],{"className":9338,"style":162},[161],[33,9340,128],{"className":9341},[166],[33,9343],{"className":9344,"style":162},[161],[33,9346,9348,9351,9411,9415,9418,9421,9424],{"className":9347},[67],[33,9349],{"className":9350,"style":1605},[71],[33,9352,9354,9357],{"className":9353},[76],[33,9355,2581],{"className":9356,"style":2727},[76,77],[33,9358,9360],{"className":9359},[418],[33,9361,9363,9403],{"className":9362},[386,387],[33,9364,9366,9400],{"className":9365},[391],[33,9367,9369,9380],{"className":9368,"style":1625},[395],[33,9370,9371,9374],{"style":2742},[33,9372],{"className":9373,"style":435},[403],[33,9375,9377],{"className":9376},[439,440,441,442],[33,9378,1521],{"className":9379,"style":1638},[76,77,442],[33,9381,9382,9385],{"style":1641},[33,9383],{"className":9384,"style":435},[403],[33,9386,9388],{"className":9387},[439,440,441,442],[33,9389,9391,9394,9397],{"className":9390},[76,442],[33,9392,248],{"className":9393},[449,442],[33,9395,93],{"className":9396,"style":109},[76,77,442],[33,9398,253],{"className":9399},[456,442],[33,9401,508],{"className":9402},[507],[33,9404,9406],{"className":9405},[391],[33,9407,9409],{"className":9408,"style":1669},[395],[33,9410],{},[33,9412],{"className":9413,"style":9414},[161],"margin-right:1em;",[33,9416],{"className":9417,"style":162},[161],[33,9419,9157],{"className":9420},[166],[33,9422],{"className":9423,"style":9414},[161],[33,9425],{"className":9426,"style":162},[161],[33,9428,9430,9433,9511,9514,9517,9520],{"className":9429},[67],[33,9431],{"className":9432,"style":4914},[71],[33,9434,9436,9439],{"className":9435},[76],[33,9437,4795],{"className":9438},[76],[33,9440,9442],{"className":9441},[418],[33,9443,9445,9503],{"className":9444},[386,387],[33,9446,9448,9500],{"className":9447},[391],[33,9449,9451],{"className":9450,"style":4933},[395],[33,9452,9453,9456],{"style":4936},[33,9454],{"className":9455,"style":435},[403],[33,9457,9459],{"className":9458},[439,440,441,442],[33,9460,9462],{"className":9461},[76,442],[33,9463,9465,9468],{"className":9464},[76,442],[33,9466,302],{"className":9467},[76,414,442],[33,9469,9471],{"className":9470},[418],[33,9472,9474],{"className":9473},[386],[33,9475,9477],{"className":9476},[391],[33,9478,9480],{"className":9479,"style":4964},[395],[33,9481,9482,9485],{"style":4967},[33,9483],{"className":9484,"style":4971},[403],[33,9486,9488],{"className":9487},[439,4975,4976,442],[33,9489,9491,9494,9497],{"className":9490},[76,442],[33,9492,248],{"className":9493},[449,442],[33,9495,93],{"className":9496,"style":109},[76,77,442],[33,9498,253],{"className":9499},[456,442],[33,9501,508],{"className":9502},[507],[33,9504,9506],{"className":9505},[391],[33,9507,9509],{"className":9508,"style":4998},[395],[33,9510],{},[33,9512,54],{"className":9513},[76,1400],[33,9515],{"className":9516,"style":162},[161],[33,9518,12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重みに関する勾配",[10,9600,9601,9086],{},[33,9602,9604,9674],{"className":9603},[36],[33,9605,9607],{"className":9606},[40],[42,9608,9609],{"xmlns":44},[46,9610,9611,9671],{},[49,9612,9613,9615,9629,9631,9633,9651,9653],{},[52,9614,2174],{"mathvariant":2173},[1515,9616,9617,9619,9621],{},[52,9618,242],{},[52,9620,1521],{},[49,9622,9623,9625,9627],{},[126,9624,248],{"stretchy":247},[52,9626,93],{},[126,9628,253],{"stretchy":247},[52,9630,8905],{"mathvariant":2173},[52,9632,2174],{"mathvariant":2173},[1515,9634,9635,9637,9643],{},[52,9636,268],{},[49,9638,9639,9641],{},[52,9640,1521],{},[52,9642,1540],{},[49,9644,9645,9647,9649],{},[126,9646,248],{"stretchy":247},[52,9648,93],{},[126,9650,253],{"stretchy":247},[126,9652,128],{},[1515,9654,9655,9657,9659],{},[52,9656,281],{},[52,9658,1540],{},[49,9660,9661,9663,9665,9667,9669],{},[126,9662,248],{"stretchy":247},[52,9664,93],{},[126,9666,290],{},[130,9668,132],{},[126,9670,253],{"stretchy":247},[56,9672,9673],{"encoding":58},"\\partial z^{(l)}_j \u002F \\partial W^{(l)}_{jk} = a^{(l-1)}_k",[33,9675,9677,9827],{"className":9676,"ariaHidden":63},[62],[33,9678,9680,9683,9686,9746,9749,9752,9818,9821,9824],{"className":9679},[67],[33,9681],{"className":9682,"style":1687},[71],[33,9684,2174],{"className":9685,"style":2276},[76],[33,9687,9689,9692],{"className":9688},[76],[33,9690,242],{"className":9691,"style":1612},[76,77],[33,9693,9695],{"className":9694},[418],[33,9696,9698,9738],{"className":9697},[386,387],[33,9699,9701,9735],{"className":9700},[391],[33,9702,9704,9715],{"className":9703,"style":1625},[395],[33,9705,9706,9709],{"style":1628},[33,9707],{"className":9708,"style":435},[403],[33,9710,9712],{"className":9711},[439,440,441,442],[33,9713,1521],{"className":9714,"style":1638},[76,77,442],[33,9716,9717,9720],{"style":1641},[33,9718],{"className":9719,"style":435},[403],[33,9721,9723],{"className":9722},[439,440,441,442],[33,9724,9726,9729,9732],{"className":9725},[76,442],[33,9727,248],{"className":9728},[449,442],[33,9730,93],{"className":9731,"style":109},[76,77,442],[33,9733,253],{"className":9734},[456,442],[33,9736,508],{"className":9737},[507],[33,9739,9741],{"className":9740},[391],[33,9742,9744],{"className":9743,"style":1669},[395],[33,9745],{},[33,9747,8905],{"className":9748},[76],[33,9750,2174],{"className":9751,"style":2276},[76],[33,9753,9755,9758],{"className":9754},[76],[33,9756,268],{"className":9757,"style":557},[76,77],[33,9759,9761],{"className":9760},[418],[33,9762,9764,9810],{"className":9763},[386,387],[33,9765,9767,9807],{"className":9766},[391],[33,9768,9770,9787],{"className":9769,"style":1625},[395],[33,9771,9772,9775],{"style":1759},[33,9773],{"className":9774,"style":435},[403],[33,9776,9778],{"className":9777},[439,440,441,442],[33,9779,9781,9784],{"className":9780},[76,442],[33,9782,1521],{"className":9783,"style":1638},[76,77,442],[33,9785,1540],{"className":9786,"style":1723},[76,77,442],[33,9788,9789,9792],{"style":1641},[33,9790],{"className":9791,"style":435},[403],[33,9793,9795],{"className":9794},[439,440,441,442],[33,9796,9798,9801,9804],{"className":9797},[76,442],[33,9799,248],{"className":9800},[449,442],[33,9802,93],{"className":9803,"style":109},[76,77,442],[33,9805,253],{"className":9806},[456,442],[33,9808,508],{"className":9809},[507],[33,9811,9813],{"className":9812},[391],[33,9814,9816],{"className":9815,"style":1804},[395],[33,9817],{},[33,9819],{"className":9820,"style":162},[161],[33,9822,128],{"className":9823},[166],[33,9825],{"className":9826,"style":162},[161],[33,9828,9830,9833],{"className":9829},[67],[33,9831],{"className":9832,"style":5278},[71],[33,9834,9836,9839],{"className":9835},[76],[33,9837,281],{"className":9838},[76,77],[33,9840,9842],{"className":9841},[418],[33,9843,9845,9891],{"className":9844},[386,387],[33,9846,9848,9888],{"className":9847},[391],[33,9849,9851,9862],{"className":9850,"style":1625},[395],[33,9852,9853,9856],{"style":1827},[33,9854],{"className":9855,"style":435},[403],[33,9857,9859],{"className":9858},[439,440,441,442],[33,9860,1540],{"className":9861,"style":1723},[76,77,442],[33,9863,9864,9867],{"style":1641},[33,9865],{"className":9866,"style":435},[403],[33,9868,9870],{"className":9869},[439,440,441,442],[33,9871,9873,9876,9879,9882,9885],{"className":9872},[76,442],[33,9874,248],{"className":9875},[449,442],[33,9877,93],{"className":9878,"style":109},[76,77,442],[33,9880,290],{"className":9881},[628,442],[33,9883,132],{"className":9884},[76,442],[33,9886,253],{"className":9887},[456,442],[33,9889,508],{"className":9890},[507],[33,9892,9894],{"className":9893},[391],[33,9895,9897],{"className":9896,"style":1872},[395],[33,9898],{},[33,9900,9902],{"className":9901},[208],[33,9903,9905,10062],{"className":9904},[36],[33,9906,9908],{"className":9907},[40],[42,9909,9910],{"xmlns":44,"display":217},[46,9911,9912,10059],{},[221,9913,9914],{"width":4767},[227,9915,9916,9918,10052,10054],{},[230,9917],{"width":4772},[230,9919,9920],{},[49,9921,9922,9952,9954,9968,9970,9988,9990,9992,9994,10010,10012,10014,10026],{},[2167,9923,9924,9930],{},[49,9925,9926,9928],{},[52,9927,2174],{"mathvariant":2173},[52,9929,54],{"mathvariant":1369},[49,9931,9932,9934],{},[52,9933,2174],{"mathvariant":2173},[1515,9935,9936,9938,9944],{},[52,9937,268],{},[49,9939,9940,9942],{},[52,9941,1521],{},[52,9943,1540],{},[49,9945,9946,9948,9950],{},[126,9947,248],{"stretchy":247},[52,9949,93],{},[126,9951,253],{"stretchy":247},[126,9953,128],{},[1515,9955,9956,9958,9960],{},[52,9957,2581],{},[52,9959,1521],{},[49,9961,9962,9964,9966],{},[126,9963,248],{"stretchy":247},[52,9965,93],{},[126,9967,253],{"stretchy":247},[4361,9969,4363],{},[1515,9971,9972,9974,9976],{},[52,9973,281],{},[52,9975,1540],{},[49,9977,9978,9980,9982,9984,9986],{},[126,9979,248],{"stretchy":247},[52,9981,93],{},[126,9983,290],{},[130,9985,132],{},[126,9987,253],{"stretchy":247},[161,9989],{"width":9154},[126,9991,9157],{},[161,9993],{"width":9154},[1533,9995,9996,9998],{},[52,9997,4795],{"mathvariant":2173},[237,9999,10000,10002],{},[52,10001,268],{},[49,10003,10004,10006,10008],{},[126,10005,248],{"stretchy":247},[52,10007,93],{},[126,10009,253],{"stretchy":247},[52,10011,54],{"mathvariant":1369},[126,10013,128],{},[237,10015,10016,10018],{},[52,10017,2581],{"mathvariant":2580},[49,10019,10020,10022,10024],{},[126,10021,248],{"stretchy":247},[52,10023,93],{},[126,10025,253],{"stretchy":247},[237,10027,10028,10050],{},[49,10029,10030,10032,10048],{},[126,10031,248],{"fence":63},[237,10033,10034,10036],{},[52,10035,281],{"mathvariant":241},[49,10037,10038,10040,10042,10044,10046],{},[126,10039,248],{"stretchy":247},[52,10041,93],{},[126,10043,290],{},[130,10045,132],{},[126,10047,253],{"stretchy":247},[126,10049,253],{"fence":63},[52,10051,8081],{"mathvariant":2173},[230,10053],{"width":4772},[230,10055,10056],{},[4361,10057,10058],{},"(BP4)",[56,10060,10061],{"encoding":58},"\\frac{\\partial \\mathcal{L}}{\\partial W^{(l)}_{jk}} = \\delta^{(l)}_j \\, a^{(l-1)}_k\n\\quad\\Longleftrightarrow\\quad\n\\nabla_{W^{(l)}} \\mathcal{L} = \\boldsymbol{\\delta}^{(l)} \\left(\\mathbf{a}^{(l-1)}\\right)^\\top \\tag{BP4}",[33,10063,10065,10211,10361,10457,10596],{"className":10064,"ariaHidden":63},[62],[33,10066,10068,10071,10202,10205,10208],{"className":10067},[67],[33,10069],{"className":10070,"style":2242},[71],[33,10072,10074,10077,10199],{"className":10073},[76],[33,10075],{"className":10076},[449,2249],[33,10078,10080],{"className":10079},[2167],[33,10081,10083,10191],{"className":10082},[386,387],[33,10084,10086,10188],{"className":10085},[391],[33,10087,10089,10166,10174],{"className":10088,"style":2262},[395],[33,10090,10091,10094],{"style":2265},[33,10092],{"className":10093,"style":2269},[403],[33,10095,10097,10100],{"className":10096},[76],[33,10098,2174],{"className":10099,"style":2276},[76],[33,10101,10103,10106],{"className":10102},[76],[33,10104,268],{"className":10105,"style":557},[76,77],[33,10107,10109],{"className":10108},[418],[33,10110,10112,10158],{"className":10111},[386,387],[33,10113,10115,10155],{"className":10114},[391],[33,10116,10118,10135],{"className":10117,"style":1625},[395],[33,10119,10120,10123],{"style":1759},[33,10121],{"className":10122,"style":435},[403],[33,10124,10126],{"className":10125},[439,440,441,442],[33,10127,10129,10132],{"className":10128},[76,442],[33,10130,1521],{"className":10131,"style":1638},[76,77,442],[33,10133,1540],{"className":10134,"style":1723},[76,77,442],[33,10136,10137,10140],{"style":1641},[33,10138],{"className":10139,"style":435},[403],[33,10141,10143],{"className":10142},[439,440,441,442],[33,10144,10146,10149,10152],{"className":10145},[76,442],[33,10147,248],{"className":10148},[449,442],[33,10150,93],{"className":10151,"style":109},[76,77,442],[33,10153,253],{"className":10154},[456,442],[33,10156,508],{"className":10157},[507],[33,10159,10161],{"className":10160},[391],[33,10162,10164],{"className":10163,"style":1804},[395],[33,10165],{},[33,10167,10168,10171],{"style":2345},[33,10169],{"className":10170,"style":2269},[403],[33,10172],{"className":10173,"style":2353},[2352],[33,10175,10176,10179],{"style":2356},[33,10177],{"className":10178,"style":2269},[403],[33,10180,10182,10185],{"className":10181},[76],[33,10183,2174],{"className":10184,"style":2276},[76],[33,10186,54],{"className":10187},[76,1400],[33,10189,508],{"className":10190},[507],[33,10192,10194],{"className":10193},[391],[33,10195,10197],{"className":10196,"style":2378},[395],[33,10198],{},[33,10200],{"className":10201},[456,2249],[33,10203],{"className":10204,"style":162},[161],[33,10206,128],{"className":10207},[166],[33,10209],{"className":10210,"style":162},[161],[33,10212,10214,10217,10277,10280,10346,10349,10352,10355,10358],{"className":10213},[67],[33,10215],{"className":10216,"style":1605},[71],[33,10218,10220,10223],{"className":10219},[76],[33,10221,2581],{"className":10222,"style":2727},[76,77],[33,10224,10226],{"className":10225},[418],[33,10227,10229,10269],{"className":10228},[386,387],[33,10230,10232,10266],{"className":10231},[391],[33,10233,10235,10246],{"className":10234,"style":1625},[395],[33,10236,10237,10240],{"style":2742},[33,10238],{"className":10239,"style":435},[403],[33,10241,10243],{"className":10242},[439,440,441,442],[33,10244,1521],{"className":10245,"style":1638},[76,77,442],[33,10247,10248,10251],{"style":1641},[33,10249],{"className":10250,"style":435},[403],[33,10252,10254],{"className":10253},[439,440,441,442],[33,10255,10257,10260,10263],{"className":10256},[76,442],[33,10258,248],{"className":10259},[449,442],[33,10261,93],{"className":10262,"style":109},[76,77,442],[33,10264,253],{"className":10265},[456,442],[33,10267,508],{"className":10268},[507],[33,10270,10272],{"className":10271},[391],[33,10273,10275],{"className":10274,"style":1669},[395],[33,10276],{},[33,10278],{"className":10279,"style":187},[161],[33,10281,10283,10286],{"className":10282},[76],[33,10284,281],{"className":10285},[76,77],[33,10287,10289],{"className":10288},[418],[33,10290,10292,10338],{"className":10291},[386,387],[33,10293,10295,10335],{"className":10294},[391],[33,10296,10298,10309],{"className":10297,"style":1625},[395],[33,10299,10300,10303],{"style":1827},[33,10301],{"className":10302,"style":435},[403],[33,10304,10306],{"className":10305},[439,440,441,442],[33,10307,1540],{"className":10308,"style":1723},[76,77,442],[33,10310,10311,10314],{"style":1641},[33,10312],{"className":10313,"style":435},[403],[33,10315,10317],{"className":10316},[439,440,441,442],[33,10318,10320,10323,10326,10329,10332],{"className":10319},[76,442],[33,10321,248],{"className":10322},[449,442],[33,10324,93],{"className":10325,"style":109},[76,77,442],[33,10327,290],{"className":10328},[628,442],[33,10330,132],{"className":10331},[76,442],[33,10333,253],{"className":10334},[456,442],[33,10336,508],{"className":10337},[507],[33,10339,10341],{"className":10340},[391],[33,10342,10344],{"className":10343,"style":1872},[395],[33,10345],{},[33,10347],{"className":10348,"style":9414},[161],[33,10350],{"className":10351,"style":162},[161],[33,10353,9157],{"className":10354},[166],[33,1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",[14,10623,10624],{},"出口側の誤差"," × ",[14,10627,10628],{},"入口側の活性","」です。入力側のユニットがほとんど発火していなければ（",[33,10631,10633,10668],{"className":10632},[36],[33,10634,10636],{"className":10635},[40],[42,10637,10638],{"xmlns":44},[46,10639,10640,10665],{},[49,10641,10642,10660,10663],{},[1515,10643,10644,10646,10648],{},[52,10645,281],{},[52,10647,1540],{},[49,10649,10650,10652,10654,10656,10658],{},[126,10651,248],{"stretchy":247},[52,10653,93],{},[126,10655,290],{},[130,10657,132],{},[126,10659,253],{"stretchy":247},[126,10661,10662],{},"≈",[130,10664,235],{},[56,10666,10667],{"encoding":58},"a^{(l-1)}_k \\approx 0",[33,10669,10671,10752],{"className":10670,"ariaHidden":63},[62],[33,10672,10674,10677,10743,10746,10749],{"className":10673},[67],[33,10675],{"className":10676,"style":5278},[71],[33,10678,10680,10683],{"className":10679},[76],[33,10681,281],{"className":10682},[76,77],[33,10684,10686],{"className":10685},[418],[33,10687,10689,10735],{"className":10688},[386,387],[33,10690,10692,10732],{"className":10691},[391],[33,10693,10695,10706],{"className":10694,"style":1625},[395],[33,10696,10697,10700],{"style":1827},[33,10698],{"className":10699,"style":435},[403],[33,10701,10703],{"className":10702},[439,440,441,442],[33,10704,1540],{"className":10705,"style":1723},[76,77,442],[33,10707,10708,10711],{"style":1641},[33,10709],{"className":10710,"style":435},[403],[33,10712,10714],{"className":10713},[439,440,441,442],[33,10715,10717,10720,10723,10726,10729],{"className":10716},[76,442],[33,10718,248],{"className":10719},[449,442],[33,10721,93],{"className":10722,"style":109},[76,77,442],[33,10724,290],{"className":10725},[628,442],[33,10727,132],{"className":10728},[76,442],[33,10730,253],{"className":10731},[456,442],[33,10733,508],{"className":10734},[507],[33,10736,10738],{"className":10737},[391],[33,10739,10741],{"className":10740,"style":1872},[395],[33,10742],{},[33,10744],{"className":10745,"style":162},[161],[33,10747,10662],{"className":10748},[166],[33,10750],{"className":10751,"style":162},[161],[33,10753,10755,10758],{"className":10754},[67],[33,10756],{"className":10757,"style":9082},[71],[33,10759,235],{"className":10760},[76],"）、その重みはほとんど学習されません。",[26,10763,10765],{"id":10764},"_5-よく使う組み合わせでの出力層の誤差","5. よく使う組み合わせでの出力層の誤差",[10,10767,10768],{},"(BP1) は、出力層の活性化関数と損失関数の組み合わせによって簡単な形になります。",[779,10770,10771,10863],{},[782,10772,10773],{},[785,10774,10775,10778,10781],{},[788,10776,10777],{},"出力層",[788,10779,10780],{},"損失関数",[788,10782,10783],{},[33,10784,10786,10810],{"className":10785},[36],[33,10787,10789],{"className":10788},[40],[42,10790,10791],{"xmlns":44},[46,10792,10793,10807],{},[49,10794,10795],{},[237,10796,10797,10799],{},[52,10798,2581],{"mathvariant":2580},[49,10800,10801,10803,10805],{},[126,10802,248],{"stretchy":247},[52,10804,54],{},[126,10806,253],{"stretchy":247},[56,10808,10809],{"encoding":58},"\\boldsymbol{\\delta}^{(L)}",[33,10811,10813],{"className":10812,"ariaHidden":63},[62],[33,10814,10816,10819],{"className":10815},[67],[33,10817],{"className":10818,"style":2602},[71],[33,10820,10822,10831],{"className":10821},[76],[33,10823,10825],{"className":10824},[76],[33,10826,10828],{"className":10827},[76],[33,10829,2581],{"className":10830,"style":2616},[76,2615],[33,10832,10834],{"className":10833},[418],[33,10835,10837],{"className":10836},[386],[33,10838,10840],{"className":10839},[391],[33,10841,10843],{"className":10842,"style":2602},[395],[33,10844,10845,10848],{"style":2631},[33,10846],{"className":10847,"style":435},[403],[33,10849,10851],{"className":10850},[439,440,441,442],[33,10852,10854,10857,10860],{"className":10853},[76,442],[33,10855,248],{"className":10856},[449,442],[33,10858,54],{"className":10859},[76,77,442],[33,10861,253],{"className":10862},[456,442],[795,10864,10865,11186,11289,11631],{},[785,10866,10867,10870,11090],{},[800,10868,10869],{},"恒等関数",[800,10871,10872,10873],{},"二乗誤差 ",[33,10874,10876,10914],{"className":10875},[36],[33,10877,10879],{"className":10878},[40],[42,10880,10881],{"xmlns":44},[46,10882,10883,10911],{},[49,10884,10885,10892,10895,10901,10903,10905],{},[2167,10886,10887,10889],{},[130,10888,132],{},[130,10890,10891],{},"2",[126,10893,10894],{"stretchy":247},"∥",[1223,10896,10897,10899],{"accent":63},[52,10898,1227],{"mathvariant":241},[126,10900,1230],{},[126,10902,290],{},[52,10904,1227],{"mathvariant":241},[237,10906,10907,10909],{},[126,10908,10894],{"stretchy":247},[130,10910,10891],{},[56,10912,10913],{"encoding":58},"\\frac{1}{2}\\lVert \\hat{\\mathbf{y}} - \\mathbf{y} \\rVert^2",[33,10915,10917,11050],{"className":10916,"ariaHidden":63},[62],[33,10918,10920,10924,10996,10999,11041,11044,11047],{"className":10919},[67],[33,10921],{"className":10922,"style":10923},[71],"height:1.1901em;vertical-align:-0.345em;",[33,10925,10927,10930,10993],{"className":10926},[76],[33,10928],{"className":10929},[449,2249],[33,10931,10933],{"className":10932},[2167],[33,10934,10936,10984],{"className":10935},[386,387],[33,10937,10939,10981],{"className":10938},[391],[33,10940,10943,10958,10966],{"className":10941,"style":10942},[395],"height:0.8451em;",[33,10944,10946,10949],{"style":10945},"top:-2.655em;",[33,10947],{"className":10948,"style":1317},[403],[33,10950,10952],{"className":10951},[439,440,441,442],[33,10953,10955],{"className":10954},[76,442],[33,10956,10891],{"className":10957},[76,442],[33,10959,10960,10963],{"style":3539},[33,10961],{"className":10962,"style":1317},[403],[33,10964],{"className":10965,"style":2353},[2352],[33,10967,10969,10972],{"style":10968},"top:-3.394em;",[33,10970],{"className":10971,"style":1317},[403],[33,10973,10975],{"className":10974},[439,440,441,442],[33,10976,10978],{"className":10977},[76,442],[33,10979,132],{"className":10980},[76,442],[33,10982,508],{"className":10983},[507],[33,10985,10987],{"className":10986},[391],[33,10988,10991],{"className":10989,"style":10990},[395],"height:0.345em;",[33,10992],{},[33,10994],{"className":10995},[456,2249],[33,10997,10894],{"className":10998},[449],[33,11000,11002],{"className":11001},[76,1300],[33,11003,11005,11033],{"className":11004},[386,387],[33,11006,11008,11030],{"className":11007},[391],[33,11009,11011,11019],{"className":11010,"style":1310},[395],[33,11012,11013,11016],{"style":1313},[33,11014],{"className":11015,"style":1317},[403],[33,11017,1227],{"className":11018,"style":1321},[76,414],[33,11020,11021,11024],{"style":1324},[33,11022],{"className":11023,"style":1317},[403],[33,11025,11027],{"className":11026,"style":1332},[1331],[33,11028,1230],{"className":11029},[76],[33,11031,508],{"className":11032},[507],[33,11034,11036],{"className":11035},[391],[33,11037,11039],{"className":11038,"style":1345},[395],[33,11040],{},[33,11042],{"className":11043,"style":638},[161],[33,11045,290],{"className":11046},[628],[33,11048],{"className":11049,"style":638},[161],[33,11051,11053,11057,11060],{"className":11052},[67],[33,11054],{"className":11055,"style":11056},[71],"height:1.0641em;vertical-align:-0.25em;",[33,11058,1227],{"className":11059,"style":1321},[76,414],[33,11061,11063,11066],{"className":11062},[456],[33,11064,10894],{"className":11065},[456],[33,11067,11069],{"className":11068},[418],[33,11070,11072],{"className":11071},[386],[33,11073,11075],{"className":11074},[391],[33,11076,11079],{"className":11077,"style":11078},[395],"height:0.8141em;",[33,11080,11081,11084],{"style":864},[33,11082],{"className":11083,"style":435},[403],[33,11085,11087],{"className":11086},[439,440,441,442],[33,11088,10891],{"className":11089},[76,442],[800,11091,11092],{},[33,11093,11095,11117],{"className":11094},[36],[33,11096,11098],{"className":11097},[40],[42,11099,11100],{"xmlns":44},[46,11101,11102,11114],{},[49,11103,11104,11110,11112],{},[1223,11105,11106,11108],{"accent":63},[52,11107,1227],{"mathvariant":241},[126,11109,1230],{},[126,11111,290],{},[52,11113,1227],{"mathvariant":241},[56,11115,11116],{"encoding":58},"\\hat{\\mathbf{y}} - \\mathbf{y}",[33,11118,11120,11177],{"className":11119,"ariaHidden":63},[62],[33,11121,11123,11126,11168,11171,11174],{"className":11122},[67],[33,11124],{"className":11125,"style":1296},[71],[33,11127,11129],{"className":11128},[76,1300],[33,11130,11132,11160],{"className":11131},[386,387],[33,11133,11135,11157],{"className":11134},[391],[33,11136,11138,11146],{"className":11137,"style":1310},[395],[33,11139,11140,11143],{"style":1313},[33,11141],{"className":11142,"style":1317},[403],[33,11144,1227],{"className":11145,"style":1321},[76,414],[33,11147,11148,11151],{"style":1324},[33,11149],{"className":11150,"style":1317},[403],[33,11152,11154],{"className":11153,"style":1332},[1331],[33,11155,1230],{"className":11156},[76],[33,11158,508],{"className":11159},[507],[33,11161,11163],{"className":11162},[391],[33,11164,11166],{"className":11165,"style":1345},[395],[33,11167],{},[33,11169],{"className":11170,"style":638},[161],[33,11172,290],{"className":11173},[628],[33,11175],{"className":11176,"style":638},[161],[33,11178,11180,11183],{"className":11179},[67],[33,11181],{"className":11182,"style":1487},[71],[33,11184,1227],{"className":11185,"style":1321},[76,414],[785,11187,11188,11191,11194],{},[800,11189,11190],{},"シグモイド",[800,11192,11193],{},"二値交差エントロピー",[800,11195,11196],{},[33,11197,11199,11220],{"className":11198},[36],[33,11200,11202],{"className":11201},[40],[42,11203,11204],{"xmlns":44},[46,11205,11206,11218],{},[49,11207,11208,11214,11216],{},[1223,11209,11210,11212],{"accent":63},[52,11211,1227],{"mathvariant":241},[126,11213,1230],{},[126,11215,290],{},[52,11217,1227],{"mathvariant":241},[56,11219,11116],{"encoding":58},[33,11221,11223,11280],{"className":11222,"ariaHidden":63},[62],[33,11224,11226,11229,11271,11274,11277],{"className":11225},[67],[33,11227],{"className":11228,"style":1296},[71],[33,11230,11232],{"className":11231},[76,1300],[33,11233,11235,11263],{"className":11234},[386,387],[33,11236,11238,11260],{"className":11237},[391],[33,11239,11241,11249],{"className":11240,"style":1310},[395],[33,11242,11243,11246],{"style":1313},[33,11244],{"className":11245,"style":1317},[403],[33,11247,1227],{"className":11248,"style":1321},[76,414],[33,11250,11251,11254],{"style":1324},[33,11252],{"className":11253,"style":1317},[403],[33,11255,11257],{"className":11256,"style":1332},[1331],[33,11258,1230],{"className":11259},[76],[33,11261,508],{"className":11262},[507],[33,11264,11266],{"className":11265},[391],[33,11267,11269],{"className":11268,"style":1345},[395],[33,11270],{},[33,11272],{"className":11273,"style":638},[161],[33,11275,290],{"className":11276},[628],[33,11278],{"className":11279,"style":638},[161],[33,11281,11283,11286],{"className":11282},[67],[33,11284],{"className":11285,"style":1487},[71],[33,11287,1227],{"className":11288,"style":1321},[76,414],[785,11290,11291,11294,11536],{},[800,11292,11293],{},"ソフトマックス",[800,11295,11296,11297],{},"交差エントロピー ",[33,11298,11300,11342],{"className":11299},[36],[33,11301,11303],{"className":11302},[40],[42,11304,11305],{"xmlns":44},[46,11306,11307,11339],{},[49,11308,11309,11311,11317,11323,11326,11329],{},[126,11310,290],{},[1533,11312,11313,11315],{},[126,11314,1537],{},[52,11316,3448],{},[1533,11318,11319,11321],{},[52,11320,1227],{},[52,11322,3448],{},[52,11324,11325],{},"log",[126,11327,11328],{},"⁡",[1533,11330,11331,11337],{},[1223,11332,11333,11335],{"accent":63},[52,11334,1227],{},[126,11336,1230],{},[52,11338,3448],{},[56,11340,11341],{"encoding":58},"-\\sum_i y_i \\log \\hat{y}_i",[33,11343,11345],{"className":11344,"ariaHidden":63},[62],[33,11346,11348,11352,11355,11358,11398,11401,11442,11445,11453,11456],{"className":11347},[67],[33,11349],{"className":11350,"style":11351},[71],"height:1.0497em;vertical-align:-0.2997em;",[33,11353,290],{"className":11354},[76],[33,11356],{"className":11357,"style":187},[161],[33,11359,11361,11364],{"className":11360},[1691],[33,11362,1537],{"className":11363,"style":1697},[1691,1695,1696],[33,11365,11367],{"className":11366},[418],[33,11368,11370,11390],{"className":11369},[386,387],[33,11371,11373,11387],{"className":11372},[391],[33,11374,11376],{"className":11375,"style":6516},[395],[33,11377,11378,11381],{"style":1713},[33,11379],{"className":11380,"style":435},[403],[33,11382,11384],{"className":11383},[439,440,441,442],[33,11385,3448],{"className":11386},[76,77,442],[33,11388,508],{"className":11389},[507],[33,11391,11393],{"className":11392},[391],[33,11394,11396],{"className":11395,"style":1733},[395],[33,11397],{},[33,11399],{"className":11400,"style":187},[161],[33,11402,11404,11407],{"className":11403},[76],[33,11405,1227],{"className":11406,"style":706},[76,77],[33,11408,11410],{"className":11409},[418],[33,11411,11413,11434],{"className":11412},[386,387],[33,11414,11416,11431],{"className":11415},[391],[33,11417,11419],{"className":11418,"style":3717},[395],[33,11420,11422,11425],{"style":11421},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[33,11423],{"className":11424,"style":435},[403],[33,11426,11428],{"className":11427},[439,440,441,442],[33,11429,3448],{"className":11430},[76,77,442],[33,11432,508],{"className":11433},[507],[33,11435,11437],{"className":11436},[391],[33,11438,11440],{"className":11439,"style":3315},[395],[33,11441],{},[33,11443],{"className":11444,"style":187},[161],[33,11446,11448,11449],{"className":11447},[1691],"lo",[33,11450,11452],{"style":11451},"margin-right:0.0139em;","g",[33,11454],{"className":11455,"style":187},[161],[33,11457,11459,11502],{"className":11458},[76],[33,11460,11462],{"className":11461},[76,1300],[33,11463,11465,11494],{"className":11464},[386,387],[33,11466,11468,11491],{"className":11467},[391],[33,11469,11471,11479],{"className":11470,"style":105},[395],[33,11472,11473,11476],{"style":1313},[33,11474],{"className":11475,"style":1317},[403],[33,11477,1227],{"className":11478,"style":706},[76,77],[33,11480,11481,11484],{"style":1313},[33,11482],{"className":11483,"style":1317},[403],[33,11485,11488],{"className":11486,"style":11487},[1331],"left:-0.1944em;",[33,11489,1230],{"className":11490},[76],[33,11492,508],{"className":11493},[507],[33,11495,11497],{"className":11496},[391],[33,11498,11500],{"className":11499,"style":1345},[395],[33,11501],{},[33,11503,11505],{"className":11504},[418],[33,11506,11508,11528],{"className":11507},[386,387],[33,11509,11511,11525],{"className":11510},[391],[33,11512,11514],{"className":11513,"style":3717},[395],[33,11515,11516,11519],{"style":11421},[33,11517],{"className":11518,"style":435},[403],[33,11520,11522],{"className":11521},[439,440,441,442],[33,11523,3448],{"className":11524},[76,77,442],[33,11526,508],{"className":11527},[507],[33,11529,11531],{"className":11530},[391],[33,11532,11534],{"className":11533,"style":3315},[395],[33,11535],{},[800,11537,11538],{},[33,11539,11541,11562],{"className":11540},[36],[33,11542,11544],{"className":11543},[40],[42,11545,11546],{"xmlns":44},[46,11547,11548,11560],{},[49,11549,11550,11556,11558],{},[1223,11551,11552,11554],{"accent":63},[52,11553,1227],{"mathvariant":241},[126,11555,1230],{},[126,11557,290],{},[52,11559,1227],{"mathvariant":241},[56,11561,11116],{"encoding":58},[33,11563,11565,11622],{"className":11564,"ariaHidden":63},[62],[33,11566,11568,11571,11613,11616,11619],{"className":11567},[67],[33,11569],{"className":11570,"style":1296},[71],[33,11572,11574],{"className":11573},[76,1300],[33,11575,11577,11605],{"className":11576},[386,387],[33,11578,11580,11602],{"className":11579},[391],[33,11581,11583,11591],{"className":11582,"style":1310},[395],[33,11584,11585,11588],{"style":1313},[33,11586],{"className":11587,"style":1317},[403],[33,11589,1227],{"className":11590,"style":1321},[76,414],[33,11592,11593,11596],{"style":1324},[33,11594],{"className":11595,"style":1317},[403],[33,11597,11599],{"className":11598,"style":1332},[1331],[33,11600,1230],{"className":11601},[76],[33,11603,508],{"className":11604},[507],[33,11606,11608],{"className":11607},[391],[33,11609,11611],{"className":11610,"style":1345},[395],[33,11612],{},[33,11614],{"className":11615,"style":638},[161],[33,11617,290],{"className":11618},[628],[33,11620],{"className":11621,"style":638},[161],[33,11623,11625,11628],{"className":11624},[67],[33,11626],{"className":11627,"style":1487},[71],[33,11629,1227],{"className":11630,"style":1321},[76,414],[785,11632,11633,11635,11638],{},[800,11634,11190],{},[800,11636,11637],{},"二乗誤差",[800,11639,11640],{},[33,11641,11643,11693],{"className":11642},[36],[33,11644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- \\mathbf{y}) \\odot \\sigma'(\\mathbf{z}^{(L)})",[33,11694,11696,11756,11777],{"className":11695,"ariaHidden":63},[62],[33,11697,11699,11702,11705,11747,11750,11753],{"className":11698},[67],[33,11700],{"className":11701,"style":1396},[71],[33,11703,248],{"className":11704},[449],[33,11706,11708],{"className":11707},[76,1300],[33,11709,11711,11739],{"className":11710},[386,387],[33,11712,11714,11736],{"className":11713},[391],[33,11715,11717,11725],{"className":11716,"style":1310},[395],[33,11718,11719,11722],{"style":1313},[33,11720],{"className":11721,"style":1317},[403],[33,11723,1227],{"className":11724,"style":1321},[76,414],[33,11726,11727,11730],{"style":1324},[33,11728],{"className":11729,"style":1317},[403],[33,11731,11733],{"className":11732,"style":1332},[1331],[33,11734,1230],{"className":11735},[76],[33,11737,508],{"className":11738},[507],[33,11740,11742],{"className":11741},[391],[33,11743,11745],{"className":11744,"style":1345},[395],[33,11746],{},[33,11748],{"className":11749,"style":638},[161],[33,11751,290],{"className":11752},[628],[33,11754],{"className":11755,"style":638},[161],[33,11757,11759,11762,11765,11768,11771,11774],{"className":11758},[67],[33,11760],{"className":11761,"style":1396},[71],[33,11763,1227],{"className":11764,"style":1321},[76,414],[33,11766,253],{"className":11767},[456],[33,11769],{"className":11770,"style":638},[161],[33,11772,4734],{"className":11773},[628],[33,11775],{"className":11776,"style":638},[161],[33,11778,11780,11784,11817,11820,11858],{"className":11779},[67],[33,11781],{"className":11782,"style":11783},[71],"height:1.138em;vertical-align:-0.25em;",[33,11785,11787,11790],{"className":11786},[76],[33,11788,341],{"className":11789,"style":706},[76,77],[33,11791,11793],{"className":11792},[418],[33,11794,11796],{"className":11795},[386],[33,11797,11799],{"className":11798},[391],[33,11800,11803],{"className":11801,"style":11802},[395],"height:0.7519em;",[33,11804,11805,11808],{"style":864},[33,11806],{"className":11807,"style":435},[403],[33,11809,11811],{"className":11810},[439,440,441,442],[33,11812,11814],{"className":11813},[76,442],[33,11815,4370],{"className":11816},[76,442],[33,11818,248],{"className":11819},[449],[33,11821,11823,11826],{"className":11822},[76],[33,11824,242],{"className":11825},[76,414],[33,11827,11829],{"className":11828},[418],[33,11830,11832],{"className":11831},[386],[33,11833,11835],{"className":11834},[391],[33,11836,11838],{"className":11837,"style":843},[395],[33,11839,11840,11843],{"style":864},[33,11841],{"className":11842,"style":435},[403],[33,11844,11846],{"className":11845},[439,440,441,442],[33,11847,11849,11852,11855],{"className":11848},[76,442],[33,11850,248],{"className":11851},[449,442],[33,11853,54],{"className":11854},[76,77,442],[33,11856,253],{"className":11857},[456,442],[33,11859,253],{"className":11860},[456],[10,11862,11863,11864,12031,12032,12387,12388,12832],{},"ソフトマックスと交差エントロピーの組み合わせは、ソフトマックスが成分ごとの関数ではないので (BP1) をそのままは使えません。それでも、直接計算すると ",[33,11865,11867,11903],{"className":11866},[36],[33,11868,11870],{"className":11869},[40],[42,11871,11872],{"xmlns":44},[46,11873,11874,11900],{},[49,11875,11876,11888,11890,11896,11898],{},[237,11877,11878,11880],{},[52,11879,2581],{"mathvariant":2580},[49,11881,11882,11884,11886],{},[126,11883,248],{"stretchy":247},[52,11885,54],{},[126,11887,253],{"stretchy":247},[126,11889,128],{},[1223,11891,11892,11894],{"accent":63},[52,11893,1227],{"mathvariant":241},[126,11895,1230],{},[126,11897,290],{},[52,11899,1227],{"mathvariant":241},[56,11901,11902],{"encoding":58},"\\boldsymbol{\\delta}^{(L)} = \\hat{\\mathbf{y}} - \\mathbf{y}",[33,11904,11906,11965,12022],{"className":11905,"ariaHidden":63},[62],[33,11907,11909,11912,11956,11959,11962],{"className":11908},[67],[33,11910],{"className":11911,"style":2602},[71],[33,11913,11915,11924],{"className":11914},[76],[33,11916,11918],{"className":11917},[76],[33,11919,11921],{"className":11920},[76],[33,11922,2581],{"className":11923,"style":2616},[76,2615],[33,11925,11927],{"className":11926},[418],[33,11928,11930],{"className":11929},[386],[33,11931,11933],{"className":11932},[391],[33,11934,11936],{"className":11935,"style":2602},[395],[33,11937,11938,11941],{"style":2631},[33,11939],{"className":11940,"style":435},[403],[33,11942,11944],{"className":11943},[439,440,441,442],[33,11945,11947,11950,11953],{"className":11946},[76,442],[33,11948,248],{"className":11949},[449,442],[33,11951,54],{"className":11952},[76,77,442],[33,11954,253],{"className":11955},[456,442],[33,11957],{"className":11958,"style":162},[161],[33,11960,128],{"className":11961},[166],[33,11963],{"className":11964,"style":162},[161],[33,11966,11968,11971,12013,12016,12019],{"className":11967},[67],[33,11969],{"className":11970,"style":1296},[71],[33,11972,11974],{"className":11973},[76,1300],[33,11975,11977,12005],{"className":11976},[386,387],[33,11978,11980,12002],{"className":11979},[391],[33,11981,11983,11991],{"className":11982,"style":1310},[395],[33,11984,11985,11988],{"style":1313},[33,11986],{"className":11987,"style":1317},[403],[33,11989,1227],{"className":11990,"style":1321},[76,414],[33,11992,11993,11996],{"style":1324},[33,11994],{"className":11995,"style":1317},[403],[33,11997,11999],{"className":11998,"style":1332},[1331],[33,12000,1230],{"className":12001},[76],[33,12003,508],{"className":12004},[507],[33,12006,12008],{"className":12007},[391],[33,12009,12011],{"className":12010,"style":1345},[395],[33,12012],{},[33,12014],{"className":12015,"style":638},[161],[33,12017,290],{"className":12018},[628],[33,12020],{"className":12021,"style":638},[161],[33,12023,12025,12028],{"className":12024},[67],[33,12026],{"className":12027,"style":1487},[71],[33,12029,1227],{"className":12030,"style":1321},[76,414]," という非常に簡単な形になります。",[33,12033,12035,12089],{"className":12034},[36],[33,12036,12038],{"className":12037},[40],[42,12039,12040],{"xmlns":44},[46,12041,12042,12086],{},[49,12043,12044,12054,12056,12067,12069,12076],{},[1533,12045,12046,12052],{},[1223,12047,12048,12050],{"accent":63},[52,12049,1227],{},[126,12051,1230],{},[52,12053,3448],{},[126,12055,128],{},[237,12057,12058,12061],{},[52,12059,12060],{},"e",[1533,12062,12063,12065],{},[52,12064,242],{},[52,12066,3448],{},[52,12068,8905],{"mathvariant":2173},[1533,12070,12071,12073],{},[126,12072,1537],{},[52,12074,12075],{},"m",[237,12077,12078,12080],{},[52,12079,12060],{},[1533,12081,12082,12084],{},[52,12083,242],{},[52,12085,12075],{},[56,12087,12088],{"encoding":58},"\\hat{y}_i = e^{z_i} \u002F \\sum_m e^{z_m}",[33,12090,12092,12187],{"className":12091,"ariaHidden":63},[62],[33,12093,12095,12099,12178,12181,12184],{"className":12094},[67],[33,12096],{"className":12097,"style":12098},[71],"height:0.8889em;vertical-align:-0.1944em;",[33,12100,12102,12144],{"className":12101},[76],[33,12103,12105],{"className":12104},[76,1300],[33,12106,12108,12136],{"className":12107},[386,387],[33,12109,12111,12133],{"className":12110},[391],[33,12112,12114,12122],{"className":12113,"style":105},[395],[33,12115,12116,12119],{"style":1313},[33,12117],{"className":12118,"style":1317},[403],[33,12120,1227],{"className":12121,"style":706},[76,77],[33,12123,12124,12127],{"style":1313},[33,12125],{"className":12126,"style":1317},[403],[33,12128,12130],{"className":12129,"style":11487},[1331],[33,12131,1230],{"className":12132},[76],[33,12134,508],{"className":12135},[507],[33,12137,12139],{"className":12138},[391],[33,12140,12142],{"className":12141,"style":1345},[395],[33,12143],{},[33,12145,12147],{"className":12146},[418],[33,12148,12150,12170],{"className":12149},[386,387],[33,12151,12153,12167],{"className":12152},[391],[33,12154,12156],{"className":12155,"style":3717},[395],[33,12157,12158,12161],{"style":11421},[33,12159],{"className":12160,"style":435},[403],[33,12162,12164],{"className":12163},[439,440,441,442],[33,12165,3448],{"className":12166},[76,77,442],[33,12168,508],{"className":12169},[507],[33,12171,12173],{"className":12172},[391],[33,12174,12176],{"className":12175,"style":3315},[395],[33,12177],{},[33,12179],{"className":12180,"style":162},[161],[33,12182,128],{"className":12183},[166],[33,12185],{"className":12186,"style":162},[161],[33,12188,12190,12193,12267,12270,12273,12314,12317],{"className":12189},[67],[33,12191],{"className":12192,"style":11351},[71],[33,12194,12196,12199],{"className":12195},[76],[33,12197,12060],{"className":12198},[76,77],[33,12200,12202],{"className":12201},[418],[33,12203,12205],{"className":12204},[386],[33,12206,12208],{"className":12207},[391],[33,12209,12212],{"className":12210,"style":12211},[395],"height:0.6644em;",[33,12213,12214,12217],{"style":864},[33,12215],{"className":12216,"style":435},[403],[33,12218,12220],{"className":12219},[439,440,441,442],[33,12221,12223],{"className":12222},[76,442],[33,12224,12226,12229],{"className":12225},[76,442],[33,12227,242],{"className":12228,"style":1612},[76,77,442],[33,12230,12232],{"className":12231},[418],[33,12233,12235,12258],{"className":12234},[386,387],[33,12236,12238,12255],{"className":12237},[391],[33,12239,12242],{"className":12240,"style":12241},[395],"height:0.3281em;",[33,12243,12245,12249],{"style":12244},"top:-2.357em;margin-left:-0.044em;margin-right:0.0714em;",[33,12246],{"className":12247,"style":12248},[403],"height:2.5em;",[33,12250,12252],{"className":12251},[439,4975,4976,442],[33,12253,3448],{"className":12254},[76,77,442],[33,12256,508],{"className":12257},[507],[33,12259,12261],{"className":12260},[391],[33,12262,12265],{"className":12263,"style":12264},[395],"height:0.143em;",[33,12266],{},[33,12268,8905],{"className":12269},[76],[33,12271],{"className":12272,"style":187},[161],[33,12274,12276,12279],{"className":12275},[1691],[33,12277,1537],{"className":12278,"style":1697},[1691,1695,1696],[33,12280,12282],{"className":12281},[418],[33,12283,12285,12306],{"className":12284},[386,387],[33,12286,12288,12303],{"className":12287},[391],[33,12289,12292],{"className":12290,"style":12291},[395],"height:0.0017em;",[33,12293,12294,12297],{"style":1713},[33,12295],{"className":12296,"style":435},[403],[33,12298,12300],{"className":12299},[439,440,441,442],[33,12301,12075],{"className":12302},[76,77,442],[33,12304,508],{"className":12305},[507],[33,12307,12309],{"className":12308},[391],[33,12310,12312],{"className":12311,"style":1733},[395],[33,12313],{},[33,12315],{"className":12316,"style":187},[161],[33,12318,12320,12323],{"className":12319},[76],[33,12321,12060],{"className":12322},[76,77],[33,12324,12326],{"className":12325},[418],[33,12327,12329],{"className":12328},[386],[33,12330,12332],{"className":12331},[391],[33,12333,12335],{"className":12334,"style":12211},[395],[33,12336,12337,12340],{"style":864},[33,12338],{"className":12339,"style":435},[403],[33,12341,12343],{"className":12342},[439,440,441,442],[33,12344,12346],{"className":12345},[76,442],[33,12347,12349,12352],{"className":12348},[76,442],[33,12350,242],{"className":12351,"style":1612},[76,77,442],[33,12353,12355],{"className":12354},[418],[33,12356,12358,12379],{"className":12357},[386,387],[33,12359,12361,12376],{"className":12360},[391],[33,12362,12365],{"className":12363,"style":12364},[395],"height:0.1645em;",[33,12366,12367,12370],{"style":12244},[33,12368],{"className":12369,"style":12248},[403],[33,12371,12373],{"className":12372},[439,4975,4976,442],[33,12374,12075],{"className":12375},[76,77,442],[33,12377,508],{"className":12378},[507],[33,12380,12382],{"className":12381},[391],[33,12383,12385],{"className":12384,"style":12264},[395],[33,12386],{}," より ",[33,12389,12391,12468],{"className":12390},[36],[33,12392,12394],{"className":12393},[40],[42,12395,12396],{"xmlns":44},[46,12397,12398,12465],{},[49,12399,12400,12402,12412,12414,12416,12422,12424,12434,12436,12439,12442,12444,12446,12448,12451,12453,12463],{},[52,12401,2174],{"mathvariant":2173},[1533,12403,12404,12410],{},[1223,12405,12406,12408],{"accent":63},[52,12407,1227],{},[126,12409,1230],{},[52,12411,3448],{},[52,12413,8905],{"mathvariant":2173},[52,12415,2174],{"mathvariant":2173},[1533,12417,12418,12420],{},[52,12419,242],{},[52,12421,1521],{},[126,12423,128],{},[1533,12425,12426,12432],{},[1223,12427,12428,12430],{"accent":63},[52,12429,1227],{},[126,12431,1230],{},[52,12433,3448],{},[126,12435,248],{"stretchy":247},[130,12437,132],{"mathvariant":12438},"double-struck",[126,12440,12441],{"stretchy":247},"[",[52,12443,3448],{},[126,12445,128],{},[52,12447,1521],{},[126,12449,12450],{"stretchy":247},"]",[126,12452,290],{},[1533,12454,12455,12461],{},[1223,12456,12457,12459],{"accent":63},[52,12458,1227],{},[126,12460,1230],{},[52,12462,1521],{},[126,12464,253],{"stretchy":247},[56,12466,12467],{"encoding":58},"\\partial \\hat{y}_i \u002F \\partial z_j = \\hat{y}_i (\\mathbb{1}[i=j] - \\hat{y}_j)",[33,12469,12471,12617,12723,12744],{"className":12470,"ariaHidden":63},[62],[33,12472,12474,12478,12481,12560,12563,12566,12608,12611,12614],{"className":12473},[67],[33,12475],{"className":12476,"style":12477},[71],"height:1.0361em;vertical-align:-0.2861em;",[33,12479,2174],{"className":12480,"style":2276},[76],[33,12482,12484,12526],{"className":12483},[76],[33,12485,12487],{"className":12486},[76,1300],[33,12488,12490,12518],{"className":12489},[386,387],[33,12491,12493,12515],{"className":12492},[391],[33,12494,12496,12504],{"className":12495,"style":105},[395],[33,12497,12498,12501],{"style":1313},[33,12499],{"className":12500,"style":1317},[403],[33,12502,1227],{"className":12503,"style":706},[76,77],[33,12505,12506,12509],{"style":1313},[33,12507],{"className":12508,"style":1317},[403],[33,12510,12512],{"className":12511,"style":11487},[1331],[33,12513,1230],{"className":12514},[76],[33,12516,508],{"className":12517},[507],[33,12519,12521],{"className":12520},[391],[33,12522,12524],{"className":12523,"style":1345},[395],[33,12525],{},[33,12527,12529],{"className":12528},[418],[33,12530,12532,12552],{"className":12531},[386,387],[33,12533,12535,12549],{"className":12534},[391],[33,12536,12538],{"className":12537,"style":3717},[395],[33,12539,12540,12543],{"style":11421},[33,12541],{"className":12542,"style":435},[403],[33,12544,12546],{"className":12545},[439,440,441,442],[33,12547,3448],{"className":12548},[76,77,442],[33,12550,508],{"className":12551},[507],[33,12553,12555],{"className":12554},[391],[33,12556,12558],{"className":12557,"style":3315},[395],[33,12559],{},[33,12561,8905],{"className":12562},[76],[33,12564,2174],{"className":12565,"style":2276},[76],[33,12567,12569,12572],{"className":12568},[76],[33,12570,242],{"className":12571,"style":1612},[76,77],[33,12573,12575],{"className":12574},[418],[33,12576,12578,12599],{"className":12577},[386,387],[33,12579,12581,12596],{"className":12580},[391],[33,12582,12584],{"className":12583,"style":3717},[395],[33,12585,12587,12590],{"style":12586},"top:-2.55em;margin-left:-0.044em;margin-right:0.05em;",[33,12588],{"className":12589,"style":435},[403],[33,12591,12593],{"className":12592},[439,440,441,442],[33,12594,1521],{"className":12595,"style":1638},[76,77,442],[33,12597,508],{"className":12598},[507],[33,12600,12602],{"className":12601},[391],[33,12603,12606],{"className":12604,"style":12605},[395],"height:0.2861em;",[33,12607],{},[33,12609],{"className":12610,"style":162},[161],[33,12612,128],{"className":12613},[166],[33,12615],{"className":12616,"style":162},[161],[33,12618,12620,12623,12702,12705,12708,12711,12714,12717,12720],{"className":12619},[67],[33,12621],{"className":12622,"style":1396},[71],[33,12624,12626,12668],{"className":12625},[76],[33,12627,12629],{"className":12628},[76,1300],[33,12630,12632,12660],{"className":12631},[386,387],[33,12633,12635,12657],{"className":12634},[391],[33,12636,12638,12646],{"className":12637,"style":105},[395],[33,12639,12640,12643],{"style":1313},[33,12641],{"className":12642,"style":1317},[403],[33,12644,1227],{"className":12645,"style":706},[76,77],[33,12647,12648,12651],{"style":1313},[33,12649],{"className":12650,"style":1317},[403],[33,12652,12654],{"className":12653,"style":11487},[1331],[33,12655,1230],{"className":12656},[76],[33,12658,508],{"className":12659},[507],[33,12661,12663],{"className":12662},[391],[33,12664,12666],{"className":12665,"style":1345},[395],[33,12667],{},[33,12669,12671],{"className":12670},[418],[33,12672,12674,12694],{"className":12673},[386,387],[33,12675,12677,12691],{"className":12676},[391],[33,12678,12680],{"className":12679,"style":3717},[395],[33,12681,12682,12685],{"style":11421},[33,12683],{"className":12684,"style":435},[403],[33,12686,12688],{"className":12687},[439,440,441,442],[33,12689,3448],{"className":12690},[76,77,442],[33,12692,508],{"className":12693},[507],[33,12695,12697],{"className":12696},[391],[33,12698,12700],{"className":12699,"style":3315},[395],[33,12701],{},[33,12703,248],{"className":12704},[449],[33,12706,132],{"className":12707},[76],[33,12709,12441],{"className":12710},[449],[33,12712,3448],{"className":12713},[76,77],[33,12715],{"className":12716,"style":162},[161],[33,12718,128],{"className":12719},[166],[33,12721],{"className":12722,"style":162},[161],[33,12724,12726,12729,12732,12735,12738,12741],{"className":12725},[67],[33,12727],{"className":12728,"style":1396},[71],[33,12730,1521],{"className":12731,"style":1638},[76,77],[33,12733,12450],{"className":12734},[456],[33,12736],{"className":12737,"style":638},[161],[33,12739,290],{"className":12740},[628],[33,12742],{"className":12743,"style":638},[161],[33,12745,12747,12750,12829],{"className":12746},[67],[33,12748],{"className":12749,"style":12477},[71],[33,12751,12753,12795],{"className":12752},[76],[33,12754,12756],{"className":12755},[76,1300],[33,12757,12759,12787],{"className":12758},[386,387],[33,12760,12762,12784],{"className":12761},[391],[33,12763,12765,12773],{"className":12764,"style":105},[395],[33,12766,12767,12770],{"style":1313},[33,12768],{"className":12769,"style":1317},[403],[33,12771,1227],{"className":12772,"style":706},[76,77],[33,12774,12775,12778],{"style":1313},[33,12776],{"className":12777,"style":1317},[403],[33,12779,12781],{"className":12780,"style":11487},[1331],[33,12782,1230],{"className":12783},[76],[33,12785,508],{"className":12786},[507],[33,12788,12790],{"className":12789},[391],[33,12791,12793],{"className":12792,"style":1345},[395],[33,12794],{},[33,12796,12798],{"className":12797},[418],[33,12799,12801,12821],{"className":12800},[386,387],[33,12802,12804,12818],{"className":12803},[391],[33,12805,12807],{"className":12806,"style":3717},[395],[33,12808,12809,12812],{"style":11421},[33,12810],{"className":12811,"style":435},[403],[33,12813,12815],{"className":12814},[439,440,441,442],[33,12816,1521],{"className":12817,"style":1638},[76,77,442],[33,12819,508],{"className":12820},[507],[33,12822,12824],{"className":12823},[391],[33,12825,12827],{"className":12826,"style":12605},[395],[33,12828],{},[33,12830,253],{"className":12831},[456]," なので、次のように計算できます。",[33,12834,12836],{"className":12835},[208],[33,12837,12839,12991],{"className":12838},[36],[33,12840,12842],{"className":12841},[40],[42,12843,12844],{"xmlns":44,"display":217},[46,12845,12846,12988],{},[49,12847,12848,12866,12868,12870,12876,12894,12904,12934,12936,12938,12944,12946,12956,12962,12968,12970,12980,12982],{},[2167,12849,12850,12856],{},[49,12851,12852,12854],{},[52,12853,2174],{"mathvariant":2173},[52,12855,54],{"mathvariant":1369},[49,12857,12858,12860],{},[52,12859,2174],{"mathvariant":2173},[1533,12861,12862,12864],{},[52,12863,242],{},[52,12865,1521],{},[126,12867,128],{},[126,12869,290],{},[5379,12871,12872,12874],{},[126,12873,1537],{},[52,12875,3448],{},[2167,12877,12878,12884],{},[1533,12879,12880,12882],{},[52,12881,1227],{},[52,12883,3448],{},[1533,12885,12886,12892],{},[1223,12887,12888,12890],{"accent":63},[52,12889,1227],{},[126,12891,1230],{},[52,12893,3448],{},[1533,12895,12896,12902],{},[1223,12897,12898,12900],{"accent":63},[52,12899,1227],{},[126,12901,1230],{},[52,12903,3448],{},[49,12905,12906,12908,12910,12912,12914,12916,12918,12920,12922,12932],{},[126,12907,248],{"fence":63},[130,12909,132],{"mathvariant":12438},[126,12911,12441],{"stretchy":247},[52,12913,3448],{},[126,12915,128],{},[52,12917,1521],{},[126,12919,12450],{"stretchy":247},[126,12921,290],{},[1533,12923,12924,12930],{},[1223,12925,12926,12928],{"accent":63},[52,12927,1227],{},[126,12929,1230],{},[52,12931,1521],{},[126,12933,253],{"fence":63},[126,12935,128],{},[126,12937,290],{},[1533,12939,12940,12942],{},[52,12941,1227],{},[52,12943,1521],{},[126,12945,297],{},[1533,12947,12948,12954],{},[1223,12949,12950,12952],{"accent":63},[52,12951,1227],{},[126,12953,1230],{},[52,12955,1521],{},[5379,12957,12958,12960],{},[126,12959,1537],{},[52,12961,3448],{},[1533,12963,12964,12966],{},[52,12965,1227],{},[52,12967,3448],{},[126,12969,128],{},[1533,12971,12972,12978],{},[1223,12973,12974,12976],{"accent":63},[52,12975,1227],{},[126,12977,1230],{},[52,12979,1521],{},[126,12981,290],{},[1533,12983,12984,12986],{},[52,12985,1227],{},[52,12987,1521],{},[56,12989,12990],{"encoding":58},"\\frac{\\partial \\mathcal{L}}{\\partial z_j}\n= -\\sum_i \\frac{y_i}{\\hat{y}_i} \\hat{y}_i \\left(\\mathbb{1}[i=j] - \\hat{y}_j\\right)\n= -y_j + \\hat{y}_j \\sum_i y_i\n= \\hat{y}_j - y_j",[33,12992,12994,13116,13565,13624,13809,13904],{"className":12993,"ariaHidden":63},[62],[33,12995,12997,13001,13107,13110,13113],{"className":12996},[67],[33,12998],{"className":12999,"style":13000},[71],"height:2.3435em;vertical-align:-0.9721em;",[33,13002,13004,13007,13104],{"className":13003},[76],[33,13005],{"className":13006},[449,2249],[33,13008,13010],{"className":13009},[2167],[33,13011,13013,13095],{"className":13012},[386,387],[33,13014,13016,13092],{"className":13015},[391],[33,13017,13019,13070,13078],{"className":13018,"style":2262},[395],[33,13020,13021,13024],{"style":3524},[33,13022],{"className":13023,"style":1317},[403],[33,13025,13027,13030],{"className":13026},[76],[33,13028,2174],{"className":13029,"style":2276},[76],[33,13031,13033,13036],{"className":13032},[76],[33,13034,242],{"className":13035,"style":1612},[76,77],[33,13037,13039],{"className":13038},[418],[33,13040,13042,13062],{"className":13041},[386,387],[33,13043,13045,13059],{"className":13044},[391],[33,13046,13048],{"className":13047,"style":3717},[395],[33,13049,13050,13053],{"style":12586},[33,13051],{"className":13052,"style":435},[403],[33,13054,13056],{"className":13055},[439,440,441,442],[33,13057,1521],{"className":13058,"style":1638},[76,77,442],[33,13060,508],{"className":13061},[507],[33,13063,13065],{"className":13064},[391],[33,13066,13068],{"className":13067,"style":12605},[395],[33,13069],{},[33,13071,13072,13075],{"style":3539},[33,13073],{"className":13074,"style":1317},[403],[33,13076],{"className":13077,"style":2353},[2352],[33,13079,13080,13083],{"style":3548},[33,13081],{"className":13082,"style":1317},[403],[33,13084,13086,13089],{"className":13085},[76],[33,13087,2174],{"className":13088,"style":2276},[76],[33,13090,54],{"className":13091},[76,1400],[33,13093,508],{"className":13094},[507],[33,13096,13098],{"className":13097},[391],[33,13099,13102],{"className":13100,"style":13101},[395],"height:0.9721em;",[33,13103],{},[33,13105],{"className":13106},[456,2249],[33,13108],{"className":13109,"style":162},[161],[33,13111,128],{"className":13112},[166],[33,13114],{"className":13115,"style":162},[161],[33,13117,13119,13123,13126,13129,13173,13176,13353,13432,13435,13556,13559,13562],{"className":13118},[67],[33,13120],{"className":13121,"style":13122},[71],"height:2.3852em;vertical-align:-1.2777em;",[33,13124,290],{"className":13125},[76],[33,13127],{"className":13128,"style":187},[161],[33,13130,13132],{"className":13131},[1691,3595],[33,13133,13135,13165],{"className":13134},[386,387],[33,13136,13138,13162],{"className":13137},[391],[33,13139,13141,13152],{"className":13140,"style":5625},[395],[33,13142,13143,13146],{"style":3608},[33,13144],{"className":13145,"style":3612},[403],[33,13147,13149],{"className":13148},[439,440,441,442],[33,13150,3448],{"className":13151},[76,77,442],[33,13153,13154,13157],{"style":3630},[33,13155],{"className":13156,"style":3612},[403],[33,13158,13159],{},[33,13160,1537],{"className":13161},[1691,1695,3639],[33,13163,508],{"className":13164},[507],[33,13166,13168],{"className":13167},[391],[33,13169,13171],{"className":13170,"style":3664},[395],[33,13172],{},[33,13174],{"className":13175,"style":187},[161],[33,13177,13179,13182,13350],{"className":13178},[76],[33,13180],{"className":13181},[449,2249],[33,13183,13185],{"className":13184},[2167],[33,13186,13188,13341],{"className":13187},[386,387],[33,13189,13191,13338],{"className":13190},[391],[33,13192,13195,13282,13290],{"className":13193,"style":13194},[395],"height:1.1076em;",[33,13196,13197,13200],{"style":3524},[33,13198],{"className":13199,"style":1317},[403],[33,13201,13203],{"className":13202},[76],[33,13204,13206,13248],{"className":13205},[76],[33,13207,13209],{"className":13208},[76,1300],[33,13210,13212,13240],{"className":13211},[386,387],[33,13213,13215,13237],{"className":13214},[391],[33,13216,13218,13226],{"className":13217,"style":105},[395],[33,13219,13220,13223],{"style":1313},[33,13221],{"className":13222,"style":1317},[403],[33,13224,1227],{"className":13225,"style":706},[76,77],[33,13227,13228,13231],{"style":1313},[33,13229],{"className":13230,"style":1317},[403],[33,13232,13234],{"className":13233,"style":11487},[1331],[33,13235,1230],{"className":13236},[76],[33,13238,508],{"className":13239},[507],[33,13241,13243],{"className":13242},[391],[33,13244,13246],{"className":13245,"style":1345},[395],[33,13247],{},[33,13249,13251],{"className":13250},[418],[33,13252,13254,13274],{"className":13253},[386,387],[33,13255,13257,13271],{"className":13256},[391],[33,13258,13260],{"className":13259,"style":3717},[395],[33,13261,13262,13265],{"style":11421},[33,13263],{"className":13264,"style":435},[403],[33,13266,13268],{"className":13267},[439,440,441,442],[33,13269,3448],{"className":13270},[76,77,442],[33,13272,508],{"className":13273},[507],[33,13275,13277],{"className":13276},[391],[33,13278,13280],{"className":13279,"style":3315},[395],[33,13281],{},[33,13283,13284,13287],{"style":3539},[33,13285],{"className":13286,"style":1317},[403],[33,13288],{"className":13289,"style":2353},[2352],[33,13291,13292,13295],{"style":3548},[33,13293],{"className":13294,"style":1317},[403],[33,13296,13298],{"className":13297},[76],[33,13299,13301,13304],{"className":13300},[76],[33,13302,1227],{"className":13303,"style":706},[76,77],[33,13305,13307],{"className":13306},[418],[33,13308,13310,13330],{"className":13309},[386,387],[33,13311,13313,13327],{"className":13312},[391],[33,13314,13316],{"className":13315,"style":3717},[395],[33,13317,13318,13321],{"style":11421},[33,13319],{"className":13320,"style":435},[403],[33,13322,13324],{"className":13323},[439,440,441,442],[33,13325,3448],{"className":13326},[76,77,442],[33,13328,508],{"className":13329},[507],[33,13331,13333],{"className":13332},[391],[33,13334,13336],{"className":13335,"style":3315},[395],[33,13337],{},[33,13339,508],{"className":13340},[507],[33,13342,13344],{"className":13343},[391],[33,13345,13348],{"className":13346,"style":13347},[395],"height:0.8804em;",[33,13349],{},[33,13351],{"className":13352},[456,2249],[33,13354,13356,13398],{"className":13355},[76],[33,13357,13359],{"className":13358},[76,1300],[33,13360,13362,13390],{"className":13361},[386,387],[33,13363,13365,13387],{"className":13364},[391],[33,13366,13368,13376],{"className":13367,"style":105},[395],[33,13369,13370,13373],{"style":1313},[33,13371],{"className":13372,"style":1317},[403],[33,13374,1227],{"className":13375,"style":706},[76,77],[33,13377,13378,13381],{"style":1313},[33,13379],{"className":13380,"style":1317},[403],[33,13382,13384],{"className":13383,"style":11487},[1331],[33,13385,1230],{"className":13386},[76],[33,13388,508],{"className":13389},[507],[33,13391,13393],{"className":13392},[391],[33,13394,13396],{"className":13395,"style":1345},[395],[33,13397],{},[33,13399,13401],{"className":13400},[418],[33,13402,13404,13424],{"className":13403},[386,387],[33,13405,13407,13421],{"className":13406},[391],[33,13408,13410],{"className":13409,"style":3717},[395],[33,13411,13412,13415],{"style":11421},[33,13413],{"className":13414,"style":435},[403],[33,13416,13418],{"className":13417},[439,440,441,442],[33,13419,3448],{"className":13420},[76,77,442],[33,13422,508],{"className":13423},[507],[33,13425,13427],{"className":13426},[391],[33,13428,13430],{"className":13429,"style":3315},[395],[33,13431],{},[33,13433],{"className":13434,"style":187},[161],[33,13436,13438,13441,13444,13447,13450,13453,13456,13459,13462,13465,13468,13471,13474,13553],{"className":13437},[191],[33,13439,248],{"className":13440,"style":717},[449,716],[33,13442,132],{"className":13443},[76],[33,13445,12441],{"className":13446},[449],[33,13448,3448],{"className":13449},[76,77],[33,13451],{"className":13452,"style":162},[161],[33,13454,128],{"className":13455},[166],[33,13457],{"className":13458,"style":162},[161],[33,13460,1521],{"className":13461,"style":1638},[76,77],[33,13463,12450],{"className":13464},[456],[33,13466],{"className":13467,"style":638},[161],[33,13469,290],{"className":13470},[628],[33,13472],{"className":13473,"style":638},[161],[33,13475,13477,13519],{"className":13476},[76],[33,13478,13480],{"className":13479},[76,1300],[33,13481,13483,13511],{"className":13482},[386,387],[33,13484,13486,13508],{"className":13485},[391],[33,13487,13489,13497],{"className":13488,"style":105},[395],[33,13490,13491,13494],{"style":1313},[33,13492],{"className":13493,"style":1317},[403],[33,13495,1227],{"className":13496,"style":706},[76,77],[33,13498,13499,13502],{"style":1313},[33,13500],{"className":13501,"style":1317},[403],[33,13503,13505],{"className":13504,"style":11487},[1331],[33,13506,1230],{"className":13507},[76],[33,13509,508],{"className":13510},[507],[33,13512,13514],{"className":13513},[391],[33,13515,13517],{"className":13516,"style":1345},[395],[33,13518],{},[33,13520,13522],{"className":13521},[418],[33,13523,13525,13545],{"className":13524},[386,387],[33,13526,13528,13542],{"className":13527},[391],[33,13529,13531],{"className":13530,"style":3717},[395],[33,13532,13533,13536],{"style":11421},[33,13534],{"className":13535,"style":435},[403],[33,13537,13539],{"className":13538},[439,440,441,442],[33,13540,1521],{"className":13541,"style":1638},[76,77,442],[33,13543,508],{"className":13544},[507],[33,13546,13548],{"className":13547},[391],[33,13549,13551],{"className":13550,"style":12605},[395],[33,13552],{},[33,13554,253],{"className":13555,"style":717},[456,716],[33,13557],{"className":13558,"style":162},[161],[33,13560,128],{"className":13561},[166],[33,13563],{"className":13564,"style":162},[161],[33,13566,13568,13572,13575,13615,13618,13621],{"className":13567},[67],[33,13569],{"className":13570,"style":13571},[71],"height:0.8694em;vertical-align:-0.2861em;",[33,13573,290],{"className":13574},[76],[33,13576,13578,13581],{"className":13577},[76],[33,13579,1227],{"className":13580,"style":706},[76,77],[33,13582,13584],{"className":13583},[418],[33,13585,13587,13607],{"className":135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1638},[76,77,442],[33,13885,508],{"className":13886},[507],[33,13888,13890],{"className":13889},[391],[33,13891,13893],{"className":13892,"style":12605},[395],[33,13894],{},[33,13896],{"className":13897,"style":638},[161],[33,13899,290],{"className":13900},[628],[33,13902],{"className":13903,"style":638},[161],[33,13905,13907,13911],{"className":13906},[67],[33,13908],{"className":13909,"style":13910},[71],"height:0.7167em;vertical-align:-0.2861em;",[33,13912,13914,13917],{"className":13913},[76],[33,13915,1227],{"className":13916,"style":706},[76,77],[33,13918,13920],{"className":13919},[418],[33,13921,13923,13943],{"className":13922},[386,387],[33,13924,13926,13940],{"className":13925},[391],[33,13927,13929],{"className":13928,"style":3717},[395],[33,13930,13931,13934],{"style":11421},[33,13932],{"className":13933,"style":435},[403],[33,13935,13937],{"className":13936},[439,440,441,442],[33,13938,1521],{"className":13939,"style":1638},[76,77,442],[33,13941,508],{"className":13942},[507],[33,13944,13946],{"className":13945},[391],[33,13947,13949],{"className":13948,"style":12605},[395],[33,13950],{},[10,13952,13953,13954,14095],{},"最後の等号では、one-hot ベクトルなので ",[33,13955,13957,13985],{"className":13956},[36],[33,13958,13960],{"className":13959},[40],[42,13961,13962],{"xmlns":44},[46,13963,13964,13982],{},[49,13965,13966,13972,13978,13980],{},[1533,13967,13968,13970],{},[126,13969,1537],{},[52,13971,3448],{},[1533,13973,13974,13976],{},[52,13975,1227],{},[52,13977,3448],{},[126,13979,128],{},[130,13981,132],{},[56,13983,13984],{"encoding":58},"\\sum_i y_i = 1",[33,13986,13988,14086],{"className":13987,"ariaHidden":63},[62],[33,13989,13991,13994,14034,14037,14077,14080,14083],{"className":13990},[67],[33,13992],{"className":13993,"style":11351},[71],[33,13995,13997,14000],{"className":13996},[1691],[33,13998,1537],{"className":13999,"style":1697},[1691,1695,1696],[33,14001,14003],{"className":14002},[418],[33,14004,14006,14026],{"className":14005},[386,387],[33,14007,14009,14023],{"className":14008},[391],[33,14010,14012],{"className":14011,"style":6516},[395],[33,14013,14014,14017],{"style":1713},[33,14015],{"className":14016,"style":435},[403],[33,14018,14020],{"className":14019},[439,440,441,442],[33,14021,3448],{"className":14022},[76,77,442],[33,14024,508],{"className":14025},[507],[33,14027,14029],{"className":14028},[391],[33,14030,14032],{"className":14031,"style":1733},[395],[33,14033],{},[33,14035],{"className":14036,"style":187},[161],[33,14038,14040,14043],{"className":14039},[76],[33,14041,1227],{"className":14042,"style":706},[76,77],[33,14044,14046],{"className":14045},[418],[33,14047,14049,14069],{"className":14048},[386,387],[33,14050,14052,14066],{"className":14051},[391],[33,14053,14055],{"className":14054,"style":3717},[395],[33,14056,14057,14060],{"style":11421},[33,14058],{"className":14059,"style":435},[403],[33,14061,14063],{"className":14062},[439,440,441,442],[33,14064,3448],{"className":14065},[76,77,442],[33,14067,508],{"className":14068},[507],[33,14070,14072],{"className":14071},[391],[33,14073,14075],{"className":14074,"style":3315},[395],[33,14076],{},[33,14078],{"className":14079,"style":162},[161],[33,14081,128],{"className":14082},[166],[33,14084],{"className":14085,"style":162},[161],[33,14087,14089,14092],{"className":14088},[67],[33,14090],{"className":14091,"style":9082},[71],[33,14093,132],{"className":14094},[76]," であることを使いました。",[14097,14098,14100],"warning",{"title":14099},"シグモイド + 二乗誤差の落とし穴",[10,14101,14102,14103,14181,14182,14281],{},"シグモイドと二乗誤差の組み合わせでは、",[33,14104,14106,14130],{"className":14105},[36],[33,14107,14109],{"className":14108},[40],[42,14110,14111],{"xmlns":44},[46,14112,14113,14127],{},[49,14114,14115,14121,14123,14125],{},[237,14116,14117,14119],{},[52,14118,341],{},[126,14120,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[126,14122,248],{"stretchy":247},[52,14124,242],{},[126,14126,253],{"stretchy":247},[56,14128,14129],{"encoding":58},"\\sigma'(z)",[33,14131,14133],{"className":14132,"ariaHidden":63},[62],[33,14134,14136,14140,14172,14175,14178],{"className":14135},[67],[33,14137],{"className":14138,"style":14139},[71],"height:1.0019em;vertical-align:-0.25em;",[33,14141,14143,14146],{"className":14142},[76],[33,14144,341],{"className":14145,"style":706},[76,77],[33,14147,14149],{"className":14148},[418],[33,14150,14152],{"className":14151},[386],[33,14153,14155],{"className":14154},[391],[33,14156,14158],{"className":14157,"style":11802},[395],[33,14159,14160,14163],{"style":864},[33,14161],{"className":14162,"style":435},[403],[33,14164,14166],{"className":14165},[439,440,441,442],[33,14167,14169],{"className":14168},[76,442],[33,14170,4370],{"className":14171},[76,442],[33,14173,248],{"className":14174},[449],[33,14176,242],{"className":14177,"style":1612},[76,77],[33,14179,253],{"className":14180},[456]," が掛かります。出力が飽和すると（",[33,14183,14185,14213],{"className":14184},[36],[33,14186,14188],{"className":14187},[40],[42,14189,14190],{"xmlns":44},[46,14191,14192,14210],{},[49,14193,14194,14200,14202,14204,14206,14208],{},[237,14195,14196,14198],{},[52,14197,341],{},[126,14199,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[126,14201,248],{"stretchy":247},[52,14203,242],{},[126,14205,253],{"stretchy":247},[126,14207,10662],{},[130,14209,235],{},[56,14211,14212],{"encoding":58},"\\sigma'(z) \\approx 0",[33,14214,14216,14272],{"className":14215,"ariaHidden":63},[62],[33,14217,14219,14222,14254,14257,14260,14263,14266,14269],{"className":14218},[67],[33,14220],{"className":14221,"style":14139},[71],[33,14223,14225,14228],{"className":14224},[76],[33,14226,341],{"className":14227,"style":706},[76,77],[33,14229,14231],{"className":14230},[418],[33,14232,14234],{"className":14233},[386],[33,14235,14237],{"className":14236},[391],[33,14238,14240],{"className":14239,"style":11802},[395],[33,14241,14242,14245],{"style":864},[33,14243],{"className":14244,"style":435},[403],[33,14246,14248],{"className":14247},[439,440,441,442],[33,14249,14251],{"className":14250},[76,442],[33,14252,4370],{"className":14253},[76,442],[33,14255,248],{"className":14256},[449],[33,14258,242],{"className":14259,"style":1612},[76,77],[33,14261,253],{"className":14262},[456],[33,14264],{"className":14265,"style":162},[161],[33,14267,10662],{"className":14268},[166],[33,14270],{"className":14271,"style":162},[161],[33,14273,14275,14278],{"className":14274},[67],[33,14276],{"className":14277,"style":9082},[71],[33,14279,235],{"className":14280},[76],"）、大きく間違えていても勾配が小さくなり、学習が進みにくくなります。分類問題で交差エントロピーが好まれる理由の一つです。",[26,14283,14285],{"id":14284},"_6-アルゴリズム","6. アルゴリズム",[10,14287,14288],{},"ここまでの4つの式をまとめておきます。",[14290,14291,14293],"key-equation",{"title":14292},"バックプロパゲーションの基本式",[33,14294,14296],{"className":14295},[208],[33,14297,14299,14673],{"className":14298},[36],[33,14300,14302],{"className":14301},[40],[42,14303,14304],{"xmlns":44,"display":217},[46,14305,14306,14670],{},[221,14307,14310,14398,14516,14580],{"rowspacing":223,"columnalign":14308,"columnspacing":14309},"right left right left","0em 1em 0em",[227,14311,14312,14328,14382,14388],{},[230,14313,14314],{},[233,14315,14316],{"scriptlevel":235,"displaystyle":63},[237,14317,14318,14320],{},[52,14319,2581],{"mathvariant":2580},[49,14321,14322,14324,14326],{},[126,14323,248],{"stretchy":247},[52,14325,54],{},[126,14327,253],{"stretchy":247},[230,14329,14330],{},[233,14331,14332],{"scriptlevel":235,"displaystyle":63},[49,14333,14334,14336,14338,14354,14356,14358,14364],{},[49,14335],{},[126,14337,128],{},[1533,14339,14340,14342],{},[52,14341,4795],{"mathvariant":2173},[237,14343,14344,14346],{},[52,14345,281],{"mathvariant":241},[49,14347,14348,14350,14352],{},[126,14349,248],{"stretchy":247},[52,14351,54],{},[126,14353,253],{"stretchy":247},[52,14355,54],{"mathvariant":1369},[126,14357,4734],{},[237,14359,14360,14362],{},[52,14361,341],{},[126,14363,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[49,14365,14366,14368,14380],{},[126,14367,248],{"fence":63},[237,14369,14370,14372],{},[52,14371,242],{"mathvariant":241},[49,14373,14374,14376,14378],{},[126,14375,248],{"stretchy":247},[52,14377,54],{},[126,14379,253],{"stretchy":247},[126,14381,253],{"fence":63},[230,14383,14384],{},[233,14385,14386],{"scriptlevel":235,"displaystyle":63},[49,14387],{},[230,14389,14390],{},[233,14391,14392],{"scriptlevel":235,"displaystyle":63},[49,14393,14394,14396],{},[49,14395],{},[4361,14397,4842],{},[227,14399,14400,14416,14500,14506],{},[230,14401,14402],{},[233,14403,14404],{"scriptlevel":235,"displaystyle":63},[237,14405,14406,14408],{},[52,14407,2581],{"mathvariant":2580},[49,14409,14410,14412,14414],{},[126,14411,248],{"stretchy":247},[52,14413,93],{},[126,14415,253],{"stretchy":247},[230,14417,14418],{},[233,14419,14420],{"scriptlevel":235,"displaystyle":63},[49,14421,14422,14424,14426,14474,14476,14482],{},[49,14423],{},[126,14425,128],{},[49,14427,14428,14430,14456,14472],{},[126,14429,248],{"fence":63},[237,14431,14432,14454],{},[49,14433,14434,14436,14452],{},[126,14435,248],{"fence":63},[237,14437,14438,14440],{},[52,14439,268],{},[49,14441,14442,14444,14446,14448,14450],{},[126,14443,248],{"stretchy":247},[52,14445,93],{},[126,14447,297],{},[130,14449,132],{},[126,14451,253],{"stretchy":247},[126,14453,253],{"fence":63},[52,14455,8081],{"mathvariant":2173},[237,14457,14458,14460],{},[52,14459,2581],{"mathvariant":2580},[49,14461,14462,14464,14466,14468,14470],{},[126,14463,248],{"stretchy":247},[52,14465,93],{},[126,14467,297],{},[130,14469,132],{},[126,14471,253],{"stretchy":247},[126,14473,253],{"fence":63},[126,14475,4734],{},[237,14477,14478,14480],{},[52,14479,341],{},[126,14481,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[49,14483,14484,14486,14498],{},[126,14485,248],{"fence":63},[237,14487,14488,14490],{},[52,14489,242],{"mathvariant":241},[49,14491,14492,14494,14496],{},[126,14493,248],{"stretchy":247},[52,14495,93],{},[126,14497,253],{"stretchy":247},[126,14499,253],{"fence":63},[230,14501,14502],{},[233,14503,14504],{"scriptlevel":235,"displaystyle":63},[49,14505],{},[230,14507,14508],{},[233,14509,14510],{"scriptlevel":235,"displaystyle":63},[49,14511,14512,14514],{},[49,14513],{},[4361,14515,8420],{},[227,14517,14518,14542,14564,14570],{},[230,14519,14520],{},[233,14521,14522],{"scriptlevel":235,"displaystyle":63},[49,14523,14524,14540],{},[1533,14525,14526,14528],{},[52,14527,4795],{"mathvariant":2173},[237,14529,14530,14532],{},[52,14531,302],{"mathvariant":241},[49,14533,14534,14536,14538],{},[126,14535,248],{"stretchy":247},[52,14537,93],{},[126,14539,253],{"stretchy":247},[52,14541,54],{"mathvariant":1369},[230,14543,14544],{},[233,14545,14546],{"scriptlevel":235,"displaystyle":63},[49,14547,14548,14550,14552],{},[49,14549],{},[126,14551,128],{},[237,14553,14554,14556],{},[52,14555,2581],{"mathvariant":2580},[49,14557,14558,14560,14562],{},[126,14559,248],{"stretchy":247},[52,14561,93],{},[126,14563,253],{"stretchy":247},[230,14565,14566],{},[233,14567,14568],{"scriptlevel":235,"displaystyle":63},[49,14569],{},[230,14571,14572],{},[233,14573,14574],{"scriptlevel":235,"displaystyle":63},[49,14575,14576,14578],{},[49,14577],{},[4361,14579,9198],{},[227,14581,14582,14606,14654,14660],{},[230,14583,14584],{},[233,14585,14586],{"scriptlevel":235,"displaystyle":63},[49,14587,14588,14604],{},[1533,14589,14590,14592],{},[52,14591,4795],{"mathvariant":2173},[237,14593,14594,14596],{},[52,14595,268],{},[49,14597,14598,14600,14602],{},[126,14599,248],{"stretchy":247},[52,14601,93],{},[126,14603,253],{"stretchy":247},[52,14605,54],{"mathvariant":1369},[230,14607,14608],{},[233,14609,14610],{"scriptlevel":235,"displaystyle":63},[49,14611,14612,14614,14616,14628],{},[49,14613],{},[126,14615,128],{},[237,14617,14618,14620],{},[52,14619,2581],{"mathvariant":2580},[49,14621,14622,14624,14626],{},[126,14623,248],{"stretchy":247},[52,14625,93],{},[126,14627,253],{"stretchy":247},[237,14629,14630,14652],{},[49,14631,14632,14634,14650],{},[126,14633,248],{"fence":63},[237,14635,14636,14638],{},[52,14637,281],{"mathvariant":241},[49,14639,14640,14642,14644,14646,14648],{},[126,14641,248],{"stretchy":247},[52,14643,93],{},[126,14645,290],{},[130,14647,132],{},[126,14649,253],{"stretchy":247},[126,14651,253],{"fence":63},[52,14653,8081],{"mathvariant":2173},[230,14655,14656],{},[233,14657,14658],{"scriptlevel":235,"displaystyle":63},[49,14659],{},[230,14661,14662],{},[233,14663,14664],{"scriptlevel":235,"displaystyle":63},[49,14665,14666,14668],{},[49,14667],{},[4361,14669,10058],{},[56,14671,14672],{"encoding":58},"\\begin{aligned}\n\\boldsymbol{\\delta}^{(L)} &= \\nabla_{\\mathbf{a}^{(L)}} \\mathcal{L} \\odot \\sigma'\\left(\\mathbf{z}^{(L)}\\right) && \\text{(BP1)} \\\\\n\\boldsymbol{\\delta}^{(l)} &= \\left( \\left(W^{(l+1)}\\right)^\\top \\boldsymbol{\\delta}^{(l+1)} \\right) \\odot \\sigma'\\left(\\mathbf{z}^{(l)}\\right) && \\text{(BP2)} \\\\\n\\nabla_{\\mathbf{b}^{(l)}} \\mathcal{L} &= \\boldsymbol{\\delta}^{(l)} && \\text{(BP3)} \\\\\n\\nabla_{W^{(l)}} \\mathcal{L} &= \\boldsymbol{\\delta}^{(l)} \\left(\\mathbf{a}^{(l-1)}\\right)^\\top && \\text{(BP4)}\n\\end{aligned}",[33,14674,14676],{"className":14675,"ariaHidden":63},[62],[33,14677,14679,14683],{"className":14678},[67],[33,14680],{"className":14681,"style":14682},[71],"height:8.4714em;vertical-align:-3.9857em;",[33,14684,14686],{"className":14685},[76],[33,14687,14689,15001,15708,15713,15768],{"className":14688},[221],[33,14690,14692],{"className":14691},[382],[33,14693,14695,14992],{"className":14694},[386,387],[33,14696,14698,14989],{"className":14697},[391],[33,14699,14702,14756,14809,14899],{"className":14700,"style":14701},[395],"height:4.4857em;",[33,14703,14705,14709],{"style":14704},"top:-6.7857em;",[33,14706],{"className":14707,"style":14708},[403],"height:3.45em;",[33,14710,14712],{"className":14711},[76],[33,14713,14715,14724],{"className":14714},[76],[33,14716,14718],{"className":14717},[76],[33,14719,14721],{"className":14720},[76],[33,14722,2581],{"className":14723,"style":2616},[76,2615],[33,14725,14727],{"className":14726},[418],[33,14728,14730],{"className":14729},[386],[33,14731,14733],{"className":14732},[391],[33,14734,14736],{"className":14735,"style":2602},[395],[33,14737,14738,14741],{"style":2631},[33,14739],{"className":14740,"style":435},[403],[33,14742,14744],{"className":14743},[439,440,441,442],[33,14745,14747,14750,14753],{"className":14746},[76,442],[33,14748,248],{"className":14749},[449,442],[33,14751,54],{"className":14752},[76,77,442],[33,14754,253],{"className":14755},[456,442],[33,14757,14759,14762],{"style":14758},"top:-4.3857em;",[33,14760],{"className":14761,"style":14708},[403],[33,14763,14765],{"className":14764},[76],[33,14766,14768,14777],{"className":14767},[76],[33,14769,14771],{"className":14770},[76],[33,14772,14774],{"className":14773},[76],[33,14775,2581],{"className":14776,"style":2616},[76,2615],[33,14778,14780],{"className":14779},[418],[33,14781,14783],{"className":14782},[386],[33,14784,14786],{"className":14785},[391],[33,14787,14789],{"className":14788,"style":2602},[395],[33,14790,14791,14794],{"style":2631},[33,14792],{"className":14793,"style":435},[403],[33,14795,14797],{"className":14796},[439,440,441,442],[33,14798,14800,14803,14806],{"className":14799},[76,442],[33,14801,248],{"className":14802},[449,442],[33,14804,93],{"className":14805,"style":109},[76,77,442],[33,14807,253],{"className":14808},[456,442],[33,14810,14812,14815],{"style":14811},"top:-2.1633em;",[33,14813],{"className":14814,"style":14708},[403],[33,14816,14818,14896],{"className":14817},[76],[33,14819,14821,14824],{"className":14820},[76],[33,14822,4795],{"className":14823},[76],[33,14825,14827],{"className":14826},[418],[33,14828,14830,14888],{"className":14829},[386,387],[33,14831,14833,14885],{"className":14832},[391],[33,14834,14836],{"className":14835,"style":4933},[395],[33,14837,14838,14841],{"style":4936},[33,14839],{"className":14840,"style":435},[403],[33,14842,14844],{"className":14843},[439,440,441,442],[33,14845,14847],{"className":14846},[76,442],[33,14848,14850,14853],{"className":14849},[76,442],[33,14851,302],{"className":14852},[76,414,442],[33,14854,14856],{"className":14855},[418],[33,14857,14859],{"className":14858},[386],[33,14860,14862],{"className":14861},[391],[33,14863,14865],{"className":14864,"style":4964},[395],[33,14866,14867,14870],{"style":4967},[33,14868],{"className":14869,"style":4971},[403],[33,14871,14873],{"className":14872},[439,4975,4976,442],[33,14874,14876,14879,14882],{"className":14875},[76,442],[33,14877,248],{"className":14878},[449,442],[33,14880,93],{"className":14881,"style":109},[76,77,442],[33,14883,253],{"className":14884},[456,442],[33,14886,508],{"className":14887},[507],[33,14889,14891],{"className":14890},[391],[33,14892,14894],{"className":14893,"style":4998},[395],[33,14895],{},[33,14897,54],{"className":14898},[76,1400],[33,14900,14902,14905],{"style":14901},"top:-0.1143em;",[33,14903],{"className":14904,"style":14708},[403],[33,14906,14908,14986],{"className":14907},[76],[33,14909,14911,14914],{"className":14910},[76],[33,14912,4795],{"className":14913},[76],[33,14915,14917],{"className":14916},[418],[33,14918,14920,14978],{"className":14919},[386,387],[33,14921,14923,14975],{"className":14922},[391],[33,14924,14926],{"className":14925,"style":4933},[395],[33,14927,14928,14931],{"style":4936},[33,14929],{"className":14930,"style":435},[403],[33,14932,14934],{"className":14933},[439,440,441,442],[33,14935,14937],{"className":14936},[76,442],[33,14938,14940,14943],{"className":14939},[76,442],[33,14941,268],{"className":14942,"style":557},[76,77,442],[33,14944,14946],{"className":14945},[418],[33,14947,14949],{"className":14948},[386],[33,14950,14952],{"className":14951},[391],[33,14953,14955],{"className":14954,"style":4964},[395],[33,14956,14957,14960],{"style":4967},[33,14958],{"className":14959,"style":4971},[403],[33,14961,14963],{"className":14962},[439,4975,4976,442],[33,14964,14966,14969,14972],{"className":14965},[76,442],[33,14967,248],{"className":14968},[449,442],[33,14970,93],{"className"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から始め、各層の ",[33,15966,15968,16006],{"className":15967},[36],[33,15969,15971],{"className":15970},[40],[42,15972,15973],{"xmlns":44},[46,15974,15975,16003],{},[49,15976,15977,15989,15991],{},[237,15978,15979,15981],{},[52,15980,242],{"mathvariant":241},[49,15982,15983,15985,15987],{},[126,15984,248],{"stretchy":247},[52,15986,93],{},[126,15988,253],{"stretchy":247},[126,15990,135],{"separator":63},[237,15992,15993,15995],{},[52,15994,281],{"mathvariant":241},[49,15996,15997,15999,16001],{},[126,15998,248],{"stretchy":247},[52,16000,93],{},[126,16002,253],{"stretchy":247},[56,16004,16005],{"encoding":58},"\\mathbf{z}^{(l)}, \\mathbf{a}^{(l)}",[33,16007,16009],{"className":16008,"ariaHidden":63},[62],[33,16010,16012,16015,16053,16056,16059],{"className":16011},[67],[33,16013],{"className":16014,"style":959},[71],[33,16016,16018,16021],{"className":16017},[76],[33,16019,242],{"className":16020},[76,414],[33,16022,16024],{"className":16023},[418],[33,16025,16027],{"className":16026},[386],[33,16028,16030],{"className":16029},[391],[33,16031,16033],{"className":16032,"style":843},[395],[33,16034,16035,16038],{"style":864},[33,16036],{"className":16037,"style":435},[403],[33,16039,16041],{"className":16040},[439,440,441,442],[33,16042,16044,16047,16050],{"className":16043},[76,442],[33,16045,248],{"className":16046},[449,442],[33,16048,93],{"className":16049,"style":109},[76,77,442],[33,16051,253],{"className":16052},[456,442],[33,16054,135],{"className":16055},[183],[33,16057],{"className":16058,"style":187},[161],[33,16060,16062,16065],{"className":16061},[76],[33,16063,281],{"className":16064},[76,414],[33,16066,16068],{"className":16067},[418],[33,16069,16071],{"className":16070},[386],[33,16072,16074],{"className":16073},[391],[33,16075,16077],{"className":16076,"style":843},[395],[33,16078,16079,16082],{"style":864},[33,16080],{"className":16081,"style":435},[403],[33,16083,16085],{"className":16084},[439,440,441,442],[33,16086,16088,16091,16094],{"className":16087},[76,442],[33,16089,248],{"className":16090},[449,442],[33,16092,93],{"className":16093,"style":109},[76,77,442],[33,16095,253],{"className":16096},[456,442]," を計算して ",[14,16099,16100],{},"保存"," しておく。",[15863,16103,16104,16107,16108,16187],{},[14,16105,16106],{},"出力層の誤差","：(BP1) で ",[33,16109,16111,16134],{"className":16110},[36],[33,16112,16114],{"className":16113},[40],[42,16115,16116],{"xmlns":44},[46,16117,16118,16132],{},[49,16119,16120],{},[237,16121,16122,16124],{},[52,16123,2581],{"mathvariant":2580},[49,16125,16126,16128,16130],{},[126,16127,248],{"stretchy":247},[52,16129,54],{},[126,16131,253],{"stretchy":247},[56,16133,10809],{"encoding":58},[33,16135,16137],{"className":16136,"ariaHidden":63},[62],[33,16138,16140,16143],{"className":16139},[67],[33,16141],{"className":16142,"style":2602},[71],[33,16144,16146,16155],{"className":16145},[76],[33,16147,16149],{"className":16148},[76],[33,16150,16152],{"className":16151},[76],[33,16153,2581],{"className":16154,"style":2616},[76,2615],[33,16156,16158],{"className":16157},[418],[33,16159,16161],{"className":16160},[386],[33,16162,16164],{"className":16163},[391],[33,16165,16167],{"className":16166,"style":2602},[395],[33,16168,16169,16172],{"style":2631},[33,16170],{"className":16171,"style":435},[403],[33,16173,16175],{"className":16174},[439,440,441,442],[33,16176,16178,16181,16184],{"className":16177},[76,442],[33,16179,248],{"className":16180},[449,442],[33,16182,54],{"className":16183},[76,77,442],[33,16185,253],{"className":16186},[456,442]," を求める。",[15863,16189,16190,15868,16193,16297,16298,16187],{},[14,16191,16192],{},"逆伝播",[33,16194,16196,16226],{"className":16195},[36],[33,16197,16199],{"className":16198},[40],[42,16200,16201],{"xmlns":44},[46,16202,16203,16223],{},[49,16204,16205,16207,16209,16211,16213,16215,16217,16219,16221],{},[52,16206,93],{},[126,16208,128],{},[52,16210,54],{},[126,16212,290],{},[130,16214,132],{},[126,16216,135],{"separator":63},[126,16218,138],{},[126,16220,135],{"separator":63},[130,16222,132],{},[56,16224,16225],{"encoding":58},"l = L-1, \\dots, 1",[33,16227,16229,16247,16266],{"className":16228,"ariaHidden":63},[62],[33,16230,16232,16235,16238,16241,16244],{"className":16231},[67],[33,16233],{"className":16234,"style":105},[71],[33,16236,93],{"className":16237,"style":109},[76,77],[33,16239],{"className":16240,"style":162},[161],[33,16242,128],{"className":16243},[166],[33,16245],{"className":16246,"style":162},[161],[33,16248,16250,16254,16257,16260,16263],{"className":16249},[67],[33,16251],{"className":16252,"style":16253},[71],"height:0.7667em;vertical-align:-0.0833em;",[33,16255,54],{"className":16256},[76,77],[33,16258],{"className":16259,"style":638},[161],[33,16261,290],{"className":16262},[628],[33,16264],{"className":16265,"style":638},[161],[33,16267,16269,16273,16276,16279,16282,16285,16288,16291,16294],{"className":16268},[67],[33,16270],{"className":16271,"style":16272},[71],"height:0.8389em;vertical-align:-0.1944em;",[33,16274,132],{"className":16275},[76],[33,16277,135],{"className":16278},[183],[33,16280],{"className":16281,"style":187},[161],[33,16283,138],{"className":16284},[191],[33,16286],{"className":16287,"style":187},[161],[33,16289,135],{"className":16290},[183],[33,16292],{"className":16293,"style":187},[161],[33,16295,132],{"className":16296},[76]," の順に (BP2) で ",[33,16299,16301,16324],{"className":16300},[36],[33,16302,16304],{"className":16303},[40],[42,16305,16306],{"xmlns":44},[46,16307,16308,16322],{},[49,16309,16310],{},[237,16311,16312,16314],{},[52,16313,2581],{"mathvariant":2580},[49,16315,16316,16318,16320],{},[126,16317,248],{"stretchy":247},[52,16319,93],{},[126,16321,253],{"stretchy":247},[56,16323,2592],{"encoding":58},[33,16325,16327],{"className":16326,"ariaHidden":63},[62],[33,16328,16330,16333],{"className":16329},[67],[33,16331],{"className":16332,"style":2602},[71],[33,16334,16336,16345],{"className":16335},[76],[33,16337,16339],{"className":16338},[76],[33,16340,16342],{"className":16341},[76],[33,16343,2581],{"className":16344,"style":2616},[76,2615],[33,16346,16348],{"className":16347},[418],[33,16349,16351],{"className":16350},[386],[33,16352,16354],{"className":16353},[391],[33,16355,16357],{"className":16356,"style":2602},[395],[33,16358,16359,16362],{"style":2631},[33,16360],{"className":16361,"style":435},[403],[33,16363,16365],{"className":16364},[439,440,441,442],[33,16366,16368,16371,16374],{"className":16367},[76,442],[33,16369,248],{"className":16370},[449,442],[33,16372,93],{"className":16373,"style":109},[76,77,442],[33,16375,253],{"className":16376},[456,442],[15863,16378,16379,16382],{},[14,16380,16381],{},"勾配","：(BP3) と (BP4) で各層の勾配を求める。",[15863,16384,16385,16388,16389,16419],{},[14,16386,16387],{},"更新","：学習率 ",[33,16390,16392,16407],{"className":16391},[36],[33,16393,16395],{"className":16394},[40],[42,16396,16397],{"xmlns":44},[46,16398,16399,16404],{},[49,16400,16401],{},[52,16402,16403],{},"η",[56,16405,16406],{"encoding":58},"\\eta",[33,16408,16410],{"className":16409,"ariaHidden":63},[62],[33,16411,16413,16416],{"className":16412},[67],[33,16414],{"className":16415,"style":3274},[71],[33,16417,16403],{"className":16418,"style":706},[76,77]," で勾配降下する。",[33,16421,16423],{"className":16422},[208],[33,16424,16426,16543],{"className":16425},[36],[33,16427,16429],{"className":16428},[40],[42,16430,16431],{"xmlns":44,"display":217},[46,16432,16433,16540],{},[49,16434,16435,16447,16450,16462,16464,16466,16468,16484,16486,16488,16490,16502,16504,16516,16518,16520,16522,16538],{},[237,16436,16437,16439],{},[52,16438,268],{},[49,16440,16441,16443,16445],{},[126,16442,248],{"stretchy":247},[52,16444,93],{},[126,16446,253],{"stretchy":247},[126,16448,16449],{},"←",[237,16451,16452,16454],{},[52,16453,268],{},[49,16455,16456,16458,16460],{},[126,16457,248],{"stretchy":247},[52,16459,93],{},[126,16461,253],{"stretchy":247},[126,16463,290],{},[52,16465,16403],{},[4361,16467,4363],{},[1533,16469,16470,16472],{},[52,16471,4795],{"mathvariant":2173},[237,16473,16474,16476],{},[52,16475,268],{},[49,16477,16478,16480,16482],{},[126,16479,248],{"stretchy":247},[52,16481,93],{},[126,16483,253],{"stretchy":247},[52,16485,54],{"mathvariant":1369},[126,16487,135],{"separator":63},[161,16489],{"width":2203},[237,16491,16492,16494],{},[52,16493,302],{"mathvariant":241},[49,16495,16496,16498,16500],{},[126,16497,248],{"stretchy":247},[52,16499,93],{},[126,16501,253],{"stretchy":247},[126,16503,16449],{},[237,16505,16506,16508],{},[52,16507,302],{"mathvariant":241},[49,16509,16510,16512,16514],{},[126,16511,248],{"stretchy":247},[52,16513,93],{},[126,16515,253],{"stretchy":247},[126,16517,290],{},[52,16519,16403],{},[4361,16521,4363],{},[1533,16523,16524,16526],{},[52,16525,4795],{"mathvariant":2173},[237,16527,16528,16530],{},[52,16529,302],{"mathvariant":241},[49,16531,16532,16534,16536],{},[126,16533,248],{"stretchy":247},[52,16535,93],{},[126,16537,253],{"stretchy":247},[52,16539,54],{"mathvariant":1369},[56,16541,16542],{"encoding":58},"W^{(l)} \\leftarrow W^{(l)} - \\eta \\, \\nabla_{W^{(l)}} \\mathcal{L}, \\qquad\n\\mathbf{b}^{(l)} \\leftarrow \\mathbf{b}^{(l)} - \\eta \\, \\nabla_{\\mathbf{b}^{(l)}} \\mathcal{L}",[33,16544,16546,16599,16653,16803,16856],{"className":16545,"ariaHidden":63},[62],[33,16547,16549,16552,16590,16593,16596],{"className":16548},[67],[33,16550],{"className":16551,"style":428},[71],[33,16553,16555,16558],{"className":16554},[76],[33,16556,268],{"className":16557,"style":557},[76,77],[33,16559,16561],{"className":16560},[418],[33,16562,16564],{"className":16563},[386],[33,16565,16567],{"className":16566},[391],[33,16568,16570],{"className":16569,"style":428},[395],[33,16571,16572,16575],{"style":431},[33,16573],{"className":16574,"style":435},[403],[33,16576,16578],{"className":16577},[439,440,441,442],[33,16579,16581,16584,16587],{"className":16580},[76,442],[33,16582,248],{"className":16583},[449,442],[33,16585,93],{"className":16586,"style":109},[76,77,442],[33,16588,253],{"className":16589},[456,442],[33,16591],{"className":16592,"style":162},[161],[33,16594,16449],{"className":16595},[166],[33,16597],{"className":16598,"style":162},[161],[33,16600,16602,16606,16644,16647,16650],{"className":16601},[67],[33,16603],{"className":16604,"style":16605},[71],"height:1.0213em;vertical-align:-0.0833em;",[33,16607,16609,16612],{"className":16608},[76],[33,16610,268],{"className":16611,"style":557},[76,77],[33,16613,16615],{"className":16614},[418],[33,16616,16618],{"className":16617},[386],[33,16619,16621],{"className":16620},[391],[33,16622,16624],{"className":16623,"style":428},[395],[33,16625,16626,16629],{"style":431},[33,16627],{"className":16628,"style":435},[403],[33,16630,16632],{"className":16631},[439,440,441,442],[33,16633,16635,16638,16641],{"className":16634},[76,442],[33,16636,248],{"className":16637},[449,442],[33,16639,93],{"className":16640,"style":109},[76,77,442],[33,16642,253],{"className":16643},[456,442],[33,16645],{"className":16646,"style":638},[161],[33,16648,290],{"className":16649},[628],[33,16651],{"className":16652,"style":638},[161],[33,16654,16656,16660,16663,16666,16744,16747,16750,16753,16756,16794,16797,16800],{"className":16655},[67],[33,16657],{"className":16658,"style":16659},[71],"height:1.1686em;vertical-align:-0.2306em;",[33,16661,16403],{"className":16662,"style":706},[76,77],[33,16664],{"className":16665,"style":187},[161],[33,16667,16669,16672],{"className":16668},[76],[33,16670,4795],{"className":16671},[76],[33,16673,16675],{"className":16674},[418],[33,16676,16678,16736],{"className":16677},[386,387],[33,16679,16681,16733],{"className":16680},[391],[33,16682,16684],{"className":16683,"style":4933},[395],[33,16685,16686,16689],{"style":4936},[33,16687],{"className":16688,"style":435},[403],[33,16690,16692],{"className":16691},[439,440,441,442],[33,16693,16695],{"className":16694},[76,442],[33,16696,16698,16701],{"className":16697},[76,442],[33,16699,268],{"className":16700,"style":557},[76,77,442],[33,16702,16704],{"className":16703},[418],[33,16705,16707],{"className":16706},[386],[33,16708,16710],{"className":16709},[391],[33,16711,16713],{"className":16712,"style":4964},[395],[33,16714,16715,16718],{"style":4967},[33,16716],{"className":16717,"style":4971},[403],[33,16719,16721],{"className":16720},[439,4975,4976,442],[33,16722,16724,16727,16730],{"className":16723},[76,442],[33,16725,248],{"className":16726},[449,442],[33,16728,93],{"className":16729,"style":109},[76,77,442],[33,16731,253],{"className":16732},[456,442],[33,16734,508],{"className":16735},[507],[33,16737,16739],{"className":16738},[391],[33,16740,16742],{"className":16741,"style":4998},[395],[33,16743],{},[33,16745,54],{"className":16746},[76,1400],[33,16748,135],{"className":16749},[183],[33,16751],{"className":16752,"style":2390},[161],[33,16754],{"className":16755,"style":187},[161],[33,16757,16759,16762],{"className":16758},[76],[33,16760,302],{"className":16761},[76,414],[33,16763,16765],{"className":16764},[418],[33,16766,16768],{"className":16767},[386],[33,16769,16771],{"className":16770},[391],[33,16772,16774],{"className":16773,"style":428},[395],[33,16775,16776,16779],{"style":431},[33,16777],{"className":16778,"style":435},[403],[33,16780,16782],{"className":16781},[439,440,441,442],[33,16783,16785,16788,16791],{"className":16784},[76,442],[33,16786,248],{"className":16787},[449,442],[33,16789,93],{"className":16790,"style":109},[76,77,442],[33,16792,253],{"className":16793},[456,442],[33,16795],{"className":16796,"style":162},[161],[33,16798,16449],{"className":16799},[166],[33,16801],{"className":16802,"style":162},[161],[33,16804,16806,16809,16847,16850,16853],{"className":16805},[67],[33,16807],{"className":16808,"style":16605},[71],[33,16810,16812,16815],{"className":16811},[76],[33,16813,302],{"className":16814},[76,414],[33,16816,16818],{"className":16817},[418],[33,16819,16821],{"className":16820},[386],[33,16822,16824],{"className":16823},[391],[33,16825,16827],{"className":16826,"style":428},[395],[33,16828,16829,16832],{"style":431},[33,16830],{"className":16831,"style":435},[403],[33,16833,16835],{"className":16834},[439,440,441,442],[33,16836,16838,16841,16844],{"className":16837},[76,442],[33,16839,248],{"className":16840},[449,442],[33,16842,93],{"className":16843,"style":109},[76,77,442],[33,16845,253],{"className":16846},[456,442],[33,16848],{"className":16849,"style":638},[161],[33,16851,290],{"className":16852},[628],[33,16854],{"className":16855,"style":638},[161],[33,16857,16859,16862,16865,16868,16946],{"className":16858},[67],[33,16860],{"className":16861,"style":4914},[71],[33,16863,16403],{"className":16864,"style":706},[76,77],[33,16866],{"className":16867,"style":187},[161],[33,16869,16871,16874],{"className":16870},[76],[33,16872,4795],{"className":16873},[76],[33,16875,16877],{"className":16876},[418],[33,16878,16880,16938],{"className":16879},[386,387],[33,16881,16883,16935],{"className":16882},[391],[33,16884,16886],{"className":16885,"style":4933},[395],[33,16887,16888,16891],{"style":4936},[33,16889],{"className":16890,"style":435},[403],[33,16892,16894],{"className":16893},[439,440,441,442],[33,16895,16897],{"className":16896},[76,442],[33,16898,16900,16903],{"className":16899},[76,442],[33,16901,302],{"className":16902},[76,414,442],[33,16904,16906],{"className":16905},[418],[33,16907,16909],{"className":16908},[386],[33,16910,16912],{"className":16911},[391],[33,16913,16915],{"className":16914,"style":4964},[395],[33,16916,16917,16920],{"style":4967},[33,16918],{"className":16919,"style":4971},[403],[33,16921,16923],{"className":16922},[439,4975,4976,442],[33,16924,16926,16929,16932],{"className":16925},[76,442],[33,16927,248],{"className":16928},[449,442],[33,16930,93],{"className":16931,"style":109},[76,77,442],[33,16933,253],{"className":16934},[456,442],[33,16936,508],{"className":16937},[507],[33,16939,16941],{"className":16940},[391],[33,16942,16944],{"className":16943,"style":4998},[395],[33,16945],{},[33,16947,54],{"className":16948},[76,1400],[10,16950,16951,16952,16980],{},"ミニバッチ（",[33,16953,16955,16968],{"className":16954},[36],[33,16956,16958],{"className":16957},[40],[42,16959,16960],{"xmlns":44},[46,16961,16962,16966],{},[49,16963,16964],{},[52,16965,12075],{},[56,16967,12075],{"encoding":58},[33,16969,16971],{"className":16970,"ariaHidden":63},[62],[33,16972,16974,16977],{"className":16973},[67],[33,16975],{"className":16976,"style":1185},[71],[33,16978,12075],{"className":16979},[76,77]," 個のサンプル）で損失を平均する場合は、各サンプルの勾配を平均します。",[26,16982,16984],{"id":16983},"_7-手計算で確かめる","7. 手計算で確かめる",[10,16986,16987],{},"入力1つ、隠れユニット1つ、出力1つの最小のネットワークで計算してみます。",[16989,16990,16991,17351,17662],"ul",{},[15863,16992,16993,16994,17201,17202,17350],{},"隠れ層：",[33,16995,16997,17034],{"className":16996},[36],[33,16998,17000],{"className":16999},[40],[42,17001,17002],{"xmlns":44},[46,17003,17004,17031],{},[49,17005,17006,17012,17014,17021,17023,17025],{},[1533,17007,17008,17010],{},[52,17009,242],{},[130,17011,132],{},[126,17013,128],{},[1533,17015,17016,17019],{},[52,17017,17018],{},"w",[130,17020,132],{},[52,17022,830],{},[126,17024,297],{},[1533,17026,17027,17029],{},[52,17028,302],{},[130,17030,132],{},[56,17032,17033],{"encoding":58},"z_1 = w_1 x + b_1",[33,17035,17037,17093,17154],{"className":17036,"ariaHidden":63},[62],[33,17038,17040,17044,17084,17087,17090],{"className":17039},[67],[33,17041],{"className":17042,"style":17043},[71],"height:0.5806em;vertical-align:-0.15em;",[33,17045,17047,17050],{"className":17046},[76],[33,17048,242],{"className":17049,"style":1612},[76,77],[33,17051,17053],{"className":17052},[418],[33,17054,17056,17076],{"className":17055},[386,387],[33,17057,17059,17073],{"className":17058},[391],[33,17060,17062],{"className":17061,"style":3293},[395],[33,17063,17064,17067],{"style":12586},[33,17065],{"className":17066,"style":435},[403],[33,17068,17070],{"className":17069},[439,440,441,442],[33,17071,132],{"className":17072},[76,442],[33,17074,508],{"className":17075},[507],[33,17077,17079],{"className":17078},[391],[33,17080,17082],{"className":17081,"style":3315},[395],[33,17083],{},[33,17085],{"className":17086,"style":162},[161],[33,17088,128],{"className":17089},[166],[33,17091],{"className":17092,"style":162},[161],[33,17094,17096,17100,17142,17145,17148,17151],{"className":17095},[67],[33,17097],{"className":17098,"style":17099},[71],"height:0.7333em;vertical-align:-0.15em;",[33,17101,17103,17107],{"className":17102},[76],[33,17104,17018],{"className":17105,"style":17106},[76,77],"margin-right:0.0269em;",[33,17108,17110],{"className":17109},[418],[33,17111,17113,17134],{"className":17112},[386,387],[33,17114,17116,17131],{"className":17115},[391],[33,17117,17119],{"className":17118,"style":3293},[395],[33,17120,17122,17125],{"style":17121},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[33,17123],{"className":17124,"style":435},[403],[33,17126,17128],{"className":17127},[439,440,441,442],[33,17129,132],{"className":17130},[76,442],[33,17132,508],{"className":17133},[507],[33,17135,17137],{"className":17136},[391],[33,17138,17140],{"className":17139,"style":3315},[395],[33,17141],{},[33,17143,830],{"className":17144},[76,77],[33,17146],{"className":17147,"style":638},[161],[33,17149,297],{"className":17150},[628],[33,17152],{"className":17153,"style":638},[161],[33,17155,17157,17161],{"className":17156},[67],[33,17158],{"className":17159,"style":17160},[71],"height:0.8444em;vertical-align:-0.15em;",[33,17162,17164,17167],{"className":17163},[76],[33,17165,302],{"className":17166},[76,77],[33,17168,17170],{"className":17169},[418],[33,17171,17173,17193],{"className":17172},[386,387],[33,17174,17176,17190],{"className":17175},[391],[33,17177,17179],{"className":17178,"style":3293},[395],[33,17180,17181,17184],{"style":3296},[33,17182],{"className":17183,"style":435},[403],[33,17185,17187],{"className":17186},[439,440,441,442],[33,17188,132],{"className":17189},[76,442],[33,17191,508],{"className":17192},[507],[33,17194,17196],{"className":17195},[391],[33,17197,17199],{"className":17198,"style":3315},[395],[33,17200],{},"、",[33,17203,17205,17237],{"className":17204},[36],[33,17206,17208],{"className":17207},[40],[42,17209,17210],{"xmlns":44},[46,17211,17212,17234],{},[49,17213,17214,17220,17222,17224,17226,17232],{},[1533,17215,17216,17218],{},[52,17217,281],{},[130,17219,132],{},[126,17221,128],{},[52,17223,341],{},[126,17225,248],{"stretchy":247},[1533,17227,17228,17230],{},[52,17229,242],{},[130,17231,132],{},[126,17233,253],{"stretchy":247},[56,17235,17236],{"encoding":58},"a_1 = \\sigma(z_1)",[33,17238,17240,17295],{"className":17239,"ariaHidden":63},[62],[33,17241,17243,17246,17286,17289,17292],{"className":17242},[67],[33,17244],{"className":17245,"style":17043},[71],[33,17247,17249,17252],{"className":17248},[76],[33,17250,281],{"className":17251},[76,77],[33,17253,17255],{"className":17254},[418],[33,17256,17258,17278],{"className":17257},[386,387],[33,17259,17261,17275],{"className":17260},[391],[33,17262,17264],{"className":17263,"style":3293},[395],[33,17265,17266,17269],{"style":3296},[33,17267],{"className":17268,"style":435},[403],[33,17270,17272],{"className":17271},[439,440,441,442],[33,17273,132],{"className":17274},[76,442],[33,17276,508],{"className":17277},[507],[33,17279,17281],{"className":17280},[391],[33,17282,17284],{"className":17283,"style":3315},[395],[33,17285],{},[33,17287],{"className":17288,"style":162},[161],[33,17290,128],{"className":17291},[166],[33,17293],{"className":17294,"style":162},[161],[33,17296,17298,17301,17304,17307,17347],{"className":17297},[67],[33,17299],{"className":17300,"style":1396},[71],[33,17302,341],{"className":17303,"style":706},[76,77],[33,17305,248],{"className":17306},[449],[33,17308,17310,17313],{"className":17309},[76],[33,17311,242],{"className":17312,"style":1612},[76,77],[33,17314,17316],{"className":17315},[418],[33,17317,17319,17339],{"className":17318},[386,387],[33,17320,17322,17336],{"className":17321},[391],[33,17323,17325],{"className":17324,"style":3293},[395],[33,17326,17327,17330],{"style":12586},[33,17328],{"className":17329,"style":435},[403],[33,17331,17333],{"className":17332},[439,440,441,442],[33,17334,132],{"className":17335},[76,442],[33,17337,508],{"className":17338},[507],[33,17340,17342],{"className":17341},[391],[33,17343,17345],{"className":17344,"style":3315},[395],[33,17346],{},[33,17348,253],{"className":17349},[456],"（シグモイド）",[15863,17352,17353,17354,17661],{},"出力層：",[33,17355,17357,17405],{"className":17356},[36],[33,17358,17360],{"className":17359},[40],[42,17361,17362],{"xmlns":44},[46,17363,17364,17402],{},[49,17365,17366,17372,17374,17380,17382,17388,17394,17396],{},[1223,17367,17368,17370],{"accent":63},[52,17369,1227],{},[126,17371,1230],{},[126,17373,128],{},[1533,17375,17376,17378],{},[52,17377,242],{},[130,17379,10891],{},[126,17381,128],{},[1533,17383,17384,17386],{},[52,17385,17018],{},[130,17387,10891],{},[1533,17389,17390,17392],{},[52,17391,281],{},[130,17393,132],{},[126,17395,297],{},[1533,17397,17398,17400],{},[52,17399,302],{},[130,17401,10891],{},[56,17403,17404],{"encoding":58},"\\hat{y} = z_2 = w_2 a_1 + b_2",[33,17406,17408,17465,17520,17615],{"className":17407,"ariaHidden":63},[62],[33,17409,17411,17414,17456,17459,17462],{"className":17410},[67],[33,17412],{"className":17413,"style":12098},[71],[33,17415,17417],{"className":17416},[76,1300],[33,17418,17420,17448],{"className":17419},[386,387],[33,17421,17423,17445],{"className":17422},[391],[33,17424,17426,17434],{"className":17425,"style":105},[395],[33,17427,17428,17431],{"style":1313},[33,17429],{"className":17430,"style":1317},[403],[33,17432,1227],{"className":17433,"style":706},[76,77],[33,17435,17436,17439],{"style":1313},[33,17437],{"className":17438,"style":1317},[403],[33,17440,17442],{"className":17441,"style":11487},[1331],[33,17443,1230],{"className":17444},[76],[33,17446,508],{"className":17447},[507],[33,17449,17451],{"className":17450},[391],[33,17452,17454],{"className":17453,"style":1345},[395],[33,17455],{},[33,17457],{"className":17458,"style":162},[161],[33,17460,128],{"className":17461},[166],[33,17463],{"className":17464,"style":162},[161],[33,17466,17468,17471,17511,17514,17517],{"className":17467},[67],[33,17469],{"className":17470,"style":17043},[71],[33,17472,17474,17477],{"className":17473},[76],[33,17475,242],{"className":17476,"style":1612},[76,77],[33,17478,17480],{"className":17479},[418],[33,17481,17483,17503],{"className":17482},[386,387],[33,17484,17486,17500],{"className":17485},[391],[33,17487,17489],{"className":17488,"style":3293},[395],[33,17490,17491,17494],{"style":12586},[33,17492],{"className":17493,"style":435},[403],[33,17495,17497],{"className":17496},[439,440,441,442],[33,17498,10891],{"className":17499},[76,442],[33,17501,508],{"className":17502},[507],[33,17504,17506],{"className":17505},[391],[33,17507,17509],{"className":17508,"style":3315},[395],[33,17510],{},[33,17512],{"className":17513,"style":162},[161],[33,17515,128],{"className":17516},[166],[33,17518],{"className":17519,"style":162},[161],[33,17521,17523,17526,17566,17606,17609,17612],{"className":17522},[67],[33,17524],{"className":17525,"style":17099},[71],[33,17527,17529,17532],{"className":17528},[76],[33,17530,17018],{"className":17531,"style":17106},[76,77],[33,17533,17535],{"className":17534},[418],[33,17536,17538,17558],{"className":17537},[386,387],[33,17539,17541,17555],{"className":17540},[391],[33,17542,17544],{"className":17543,"style":3293},[395],[33,17545,17546,17549],{"style":17121},[33,17547],{"className":17548,"style":435},[403],[33,17550,17552],{"className":17551},[439,440,441,442],[33,17553,10891],{"className":17554},[76,442],[33,17556,508],{"className":17557},[507],[33,17559,17561],{"className":17560},[391],[33,17562,17564],{"className":17563,"style":3315},[395],[33,17565],{},[33,17567,17569,17572],{"className":17568},[76],[33,17570,281],{"className":17571},[76,77],[33,17573,17575],{"className":17574},[418],[33,17576,17578,17598],{"className":17577},[386,387],[33,17579,17581,17595],{"className":17580},[391],[33,17582,17584],{"className":17583,"style":3293},[395],[33,17585,17586,17589],{"style":3296},[33,17587],{"className":17588,"style":435},[403],[33,17590,17592],{"className":17591},[439,440,441,442],[33,17593,132],{"className":17594},[76,442],[33,17596,508],{"className":17597},[507],[33,17599,17601],{"className":17600},[391],[33,17602,17604],{"className":17603,"style":3315},[395],[33,17605],{},[33,17607],{"className":17608,"style":638},[161],[33,17610,297],{"className":17611},[628],[33,17613],{"className":17614,"style":638},[161],[33,17616,17618,17621],{"className":17617},[67],[33,17619],{"className":17620,"style":17160},[71],[33,17622,17624,17627],{"className":17623},[76],[33,17625,302],{"className":17626},[76,77],[33,17628,17630],{"className":17629},[418],[33,17631,17633,17653],{"className":17632},[386,387],[33,17634,17636,17650],{"className":17635},[391],[33,17637,17639],{"className":17638,"style":3293},[395],[33,17640,17641,17644],{"style":3296},[33,17642],{"className":17643,"style":435},[403],[33,17645,17647],{"className":17646},[439,440,441,442],[33,17648,10891],{"className":17649},[76,442],[33,17651,508],{"className":17652},[507],[33,17654,17656],{"className":17655},[391],[33,17657,17659],{"className":17658,"style":3315},[395],[33,17660],{},"（恒等関数）",[15863,17663,17664,17665],{},"損失：",[33,17666,17668,17708],{"className":17667},[36],[33,17669,17671],{"className":17670},[40],[42,17672,17673],{"xmlns":44},[46,17674,17675,17705],{},[49,17676,17677,17679,17681,17687,17689,17695,17697,17699],{},[52,17678,54],{"mathvariant":1369},[126,17680,128],{},[2167,17682,17683,17685],{},[130,17684,132],{},[130,17686,10891],{},[126,17688,248],{"stretchy":247},[1223,17690,17691,17693],{"accent":63},[52,17692,1227],{},[126,17694,1230],{},[126,17696,290],{},[52,17698,1227],{},[237,17700,17701,17703],{},[126,17702,253],{"stretchy":247},[130,17704,10891],{},[56,17706,17707],{"encoding":58},"\\mathcal{L} = \\frac{1}{2}(\\hat{y} - y)^2",[33,17709,17711,17729,17857],{"className":17710,"ariaHidden":63},[62],[33,17712,17714,17717,17720,17723,17726],{"className":17713},[67],[33,17715],{"className":17716,"style":72},[71],[33,17718,54],{"className":17719},[76,1400],[33,17721],{"className":17722,"style":162},[161],[33,17724,128],{"className":17725},[166],[33,17727],{"className":17728,"style":162},[161],[33,17730,17732,17735,17803,17806,17848,17851,17854],{"className":17731},[67],[33,17733],{"className":17734,"style":10923},[71],[33,17736,17738,17741,17800],{"className":17737},[76],[33,17739],{"className":17740},[449,2249],[33,17742,17744],{"className":17743},[2167],[33,17745,17747,17792],{"className":17746},[386,387],[33,17748,17750,17789],{"className":17749},[391],[33,17751,17753,17767,17775],{"className":17752,"style":10942},[395],[33,17754,17755,17758],{"style":10945},[33,17756],{"className":17757,"style":1317},[403],[33,17759,17761],{"className":17760},[439,440,441,442],[33,17762,17764],{"className":17763},[76,442],[33,17765,10891],{"className":17766},[76,442],[33,17768,17769,17772],{"style":3539},[33,17770],{"className":17771,"style":1317},[403],[33,17773],{"className":17774,"style":2353},[2352],[33,17776,17777,17780],{"style":10968},[33,17778],{"className":17779,"style":1317},[403],[33,17781,17783],{"className":17782},[439,440,441,442],[33,17784,17786],{"className":17785},[76,442],[33,17787,132],{"className":17788},[76,442],[33,17790,508],{"className":17791},[507],[33,17793,17795],{"className":17794},[391],[33,17796,17798],{"className":17797,"style":10990},[395],[33,17799],{},[33,17801],{"className":17802},[456,2249],[33,17804,248],{"className":17805},[449],[33,17807,17809],{"className":17808},[76,1300],[33,17810,17812,17840],{"className":17811},[386,387],[33,17813,17815,17837],{"className":17814},[391],[33,17816,17818,17826],{"className":17817,"style":105},[395],[33,17819,17820,17823],{"style":1313},[33,17821],{"className":17822,"style":1317},[403],[33,17824,1227],{"className":17825,"style":706},[76,77],[33,17827,17828,17831],{"style":1313},[33,17829],{"className":17830,"style":1317},[403],[33,17832,17834],{"className":17833,"style":11487},[1331],[33,17835,1230],{"className":17836},[76],[33,17838,508],{"className":17839},[507],[33,17841,17843],{"className":17842},[391],[33,17844,17846],{"className":17845,"style":1345},[395],[33,17847],{},[33,17849],{"className":17850,"style":638},[161],[33,17852,290],{"className":17853},[628],[33,17855],{"className":17856,"style":638},[161],[33,17858,17860,17863,17866],{"className":17859},[67],[33,17861],{"className":17862,"style":11056},[71],[33,17864,1227],{"className":17865,"style":706},[76,77],[33,17867,17869,17872],{"className":17868},[456],[33,17870,253],{"className":17871},[456],[33,17873,17875],{"className":17874},[418],[33,17876,17878],{"className":17877},[386],[33,17879,17881],{"className":17880},[391],[33,17882,17884],{"className":17883,"style":11078},[395],[33,17885,17886,17889],{"style":864},[33,17887],{"className":17888,"style":435},[403],[33,17890,17892],{"className":17891},[439,440,441,442],[33,17893,10891],{"className":17894},[76,442],[10,17896,17897,17898,17201,17949,17201,18000,17201,18093,17201,18185,17201,18277,18369],{},"値は ",[33,17899,17901,17919],{"className":17900},[36],[33,17902,17904],{"className":17903},[40],[42,17905,17906],{"xmlns":44},[46,17907,17908,17916],{},[49,17909,17910,17912,17914],{},[52,17911,830],{},[126,17913,128],{},[130,17915,132],{},[56,17917,17918],{"encoding":58},"x = 1",[33,17920,17922,17940],{"className":17921,"ariaHidden":63},[62],[33,17923,17925,17928,17931,17934,17937],{"className":17924},[67],[33,17926],{"className":17927,"style":1185},[71],[33,17929,830],{"className":17930},[76,77],[33,17932],{"className":17933,"style":162},[161],[33,17935,128],{"className":17936},[166],[33,17938],{"className":17939,"style":162},[161],[33,17941,17943,17946],{"className":17942},[67],[33,17944],{"className":17945,"style":9082},[71],[33,17947,132],{"className":17948},[76],[33,17950,17952,17970],{"className":17951},[36],[33,17953,17955],{"className":17954},[40],[42,17956,17957],{"xmlns":44},[46,17958,17959,17967],{},[49,17960,17961,17963,17965],{},[52,17962,1227],{},[126,17964,128],{},[130,17966,132],{},[56,17968,17969],{"encoding":58},"y = 1",[33,17971,17973,17991],{"className":17972,"ariaHidden":63},[62],[33,17974,17976,17979,17982,17985,17988],{"className":17975},[67],[33,17977],{"className":17978,"style":3274},[71],[33,17980,1227],{"className":17981,"style":706},[76,77],[33,17983],{"className":17984,"style":162},[161],[33,17986,128],{"className":17987},[166],[33,17989],{"className":17990,"style":162},[161],[33,17992,17994,17997],{"className":17993},[67],[33,17995],{"className":17996,"style":9082},[71],[33,17998,132],{"className":17999},[76],[33,18001,18003,18026],{"className":18002},[36],[33,18004,18006],{"className":18005},[40],[42,18007,18008],{"xmlns":44},[46,18009,18010,18023],{},[49,18011,18012,18018,18020],{},[1533,18013,18014,18016],{},[52,18015,17018],{},[130,18017,132],{},[126,18019,128],{},[130,18021,18022],{},"0.5",[56,18024,18025],{"encoding":58},"w_1 = 0.5",[33,18027,18029,18084],{"className":18028,"ariaHidden":63},[62],[33,18030,18032,18035,18075,18078,18081],{"className":18031},[67],[33,18033],{"className":18034,"style":17043},[71],[33,18036,18038,18041],{"className":18037},[76],[33,18039,17018],{"className":18040,"style":17106},[76,77],[33,18042,18044],{"className":18043},[418],[33,18045,18047,18067],{"className":18046},[386,387],[33,18048,18050,18064],{"className":18049},[391],[33,18051,18053],{"className":18052,"style":3293},[395],[33,18054,18055,18058],{"style":17121},[33,18056],{"className":18057,"style":435},[403],[33,18059,18061],{"className":18060},[439,440,441,442],[33,18062,132],{"className":18063},[76,442],[33,18065,508],{"className":18066},[507],[33,18068,18070],{"className":18069},[391],[33,18071,18073],{"className":18072,"style":3315},[395],[33,18074],{},[33,18076],{"className":18077,"style":162},[161],[33,18079,128],{"className":18080},[166],[33,18082],{"className":18083,"style":162},[161],[33,18085,18087,18090],{"className":18086},[67],[33,18088],{"className":18089,"style":9082},[71],[33,18091,18022],{"className":18092},[76],[33,18094,18096,18118],{"className":18095},[36],[33,18097,18099],{"className":18098},[40],[42,18100,18101],{"xmlns":44},[46,18102,18103,18115],{},[49,18104,18105,18111,18113],{},[1533,18106,18107,18109],{},[52,18108,302],{},[130,18110,132],{},[126,18112,128],{},[130,18114,235],{},[56,18116,18117],{"encoding":58},"b_1 = 0",[33,18119,18121,18176],{"className":18120,"ariaHidden":63},[62],[33,18122,18124,18127,18167,18170,18173],{"className":18123},[67],[33,18125],{"className":18126,"style":17160},[71],[33,18128,18130,18133],{"className":18129},[76],[33,18131,302],{"className":18132},[76,77],[33,18134,18136],{"className":18135},[418],[33,18137,18139,18159],{"className":18138},[386,387],[33,18140,18142,18156],{"className":18141},[391],[33,18143,18145],{"className":18144,"style":3293},[395],[33,18146,18147,18150],{"style":3296},[33,18148],{"className":18149,"style":435},[403],[33,18151,18153],{"className":18152},[439,440,441,442],[33,18154,132],{"className":18155},[76,442],[33,18157,508],{"className":18158},[507],[33,18160,18162],{"className":18161},[391],[33,18163,18165],{"className":18164,"style":3315},[395],[33,18166],{},[33,18168],{"className":18169,"style":162},[161],[33,18171,128],{"className":18172},[166],[33,18174],{"className":18175,"style":162},[161],[33,18177,18179,18182],{"className":18178},[67],[33,18180],{"className":18181,"style":9082},[71],[33,18183,235],{"className":18184},[76],[33,18186,18188,18210],{"className":18187},[36],[33,18189,18191],{"className":18190},[40],[42,18192,18193],{"xmlns":44},[46,18194,18195,18207],{},[49,18196,18197,18203,18205],{},[1533,18198,18199,18201],{},[52,18200,17018],{},[130,18202,10891],{},[126,18204,128],{},[130,18206,10891],{},[56,18208,18209],{"encoding":58},"w_2 = 2",[33,18211,18213,18268],{"className":18212,"ariaHidden":63},[62],[33,18214,18216,18219,18259,18262,18265],{"className":18215},[67],[33,18217],{"className":18218,"style":17043},[71],[33,18220,18222,18225],{"className":18221},[76],[33,18223,17018],{"className":18224,"style":17106},[76,77],[33,18226,18228],{"className":18227},[418],[33,18229,18231,18251],{"className":18230},[386,387],[33,18232,18234,18248],{"className":18233},[391],[33,18235,18237],{"className":18236,"style":3293},[395],[33,18238,18239,18242],{"style":17121},[33,18240],{"className":18241,"style":435},[403],[33,18243,18245],{"className":18244},[439,440,441,442],[33,18246,10891],{"className":18247},[76,442],[33,18249,508],{"className":18250},[507],[33,18252,18254],{"className":18253},[391],[33,18255,18257],{"className":18256,"style":3315},[395],[33,18258],{},[33,18260],{"className":18261,"style":162},[161],[33,18263,128],{"className":18264},[166],[33,18266],{"className":18267,"style":162},[161],[33,18269,18271,18274],{"className":18270},[67],[33,18272],{"className":18273,"style":9082},[71],[33,18275,10891],{"className":18276},[76],[33,18278,18280,18302],{"className":18279},[36],[33,18281,18283],{"className":18282},[40],[42,18284,18285],{"xmlns":44},[46,18286,18287,18299],{},[49,18288,18289,18295,18297],{},[1533,18290,18291,18293],{},[52,18292,302],{},[130,18294,10891],{},[126,18296,128],{},[130,18298,235],{},[56,18300,18301],{"encoding":58},"b_2 = 0",[33,18303,18305,18360],{"className":18304,"ariaHidden":63},[62],[33,18306,18308,18311,18351,18354,18357],{"className":18307},[67],[33,18309],{"className":18310,"style":17160},[71],[33,18312,18314,18317],{"className":18313},[76],[33,18315,302],{"className":18316},[76,77],[33,18318,18320],{"className":18319},[418],[33,18321,18323,18343],{"className":18322},[386,387],[33,18324,18326,18340],{"className":18325},[391],[33,18327,18329],{"className":18328,"style":3293},[395],[33,18330,18331,18334],{"style":3296},[33,18332],{"className":18333,"style":435},[403],[33,18335,18337],{"className":18336},[439,440,441,442],[33,18338,10891],{"className":18339},[76,442],[33,18341,508],{"className":18342},[507],[33,18344,18346],{"className":18345},[391],[33,18347,18349],{"className":18348,"style":3315},[395],[33,18350],{},[33,18352],{"className":18353,"style":162},[161],[33,18355,128],{"className":18356},[166],[33,18358],{"className":18359,"style":162},[161],[33,18361,18363,18366],{"className":18362},[67],[33,18364],{"className":18365,"style":9082},[71],[33,18367,235],{"className":18368},[76]," とします。",[10,18371,18372],{},[14,18373,15867],{},[33,18375,18377],{"className":18376},[208],[33,18378,18380,18546],{"className":18379},[36],[33,18381,18383],{"className":18382},[40],[42,18384,18385],{"xmlns":44,"display":217},[46,18386,18387,18543],{},[221,18388,18389,18426,18461,18498],{"rowspacing":223,"columnalign":224,"columnspacing":225},[227,18390,18391,18401],{},[230,18392,18393],{},[233,18394,18395],{"scriptlevel":235,"displaystyle":63},[1533,18396,18397,18399],{},[52,18398,242],{},[130,18400,132],{},[230,18402,18403],{},[233,18404,18405],{"scriptlevel":235,"displaystyle":63},[49,18406,18407,18409,18411,18413,18416,18418,18420,18422,18424],{},[49,18408],{},[126,18410,128],{},[130,18412,18022],{},[126,18414,18415],{},"×",[130,18417,132],{},[126,18419,297],{},[130,18421,235],{},[126,18423,128],{},[130,18425,18022],{},[227,18427,18428,18438],{},[230,18429,18430],{},[233,18431,18432],{"scriptlevel":235,"displaystyle":63},[1533,18433,18434,18436],{},[52,18435,281],{},[130,18437,132],{},[230,18439,18440],{},[233,18441,18442],{"scriptlevel":235,"displaystyle":63},[49,18443,18444,18446,18448,18450,18452,18454,18456,18458],{},[49,18445],{},[126,18447,128],{},[52,18449,341],{},[126,18451,248],{"stretchy":247},[130,18453,18022],{},[126,18455,253],{"stretchy":247},[126,18457,10662],{},[130,18459,18460],{},"0.62246",[227,18462,18463,18473],{},[230,18464,18465],{},[233,18466,18467],{"scriptlevel":235,"displaystyle":63},[1223,18468,18469,18471],{"accent":63},[52,18470,1227],{},[126,18472,1230],{},[230,18474,18475],{},[233,18476,18477],{"scriptlevel":235,"displaystyle":63},[49,18478,18479,18481,18483,18485,18487,18489,18491,18493,18495],{},[49,18480],{},[126,18482,128],{},[130,18484,10891],{},[126,18486,18415],{},[130,18488,18460],{},[126,18490,297],{},[130,18492,235],{},[126,18494,10662],{},[130,18496,18497],{},"1.24492",[227,18499,18500,18506],{},[230,18501,18502],{},[233,18503,18504],{"scriptlevel":235,"displaystyle":63},[52,18505,54],{"mathvariant":1369},[230,18507,18508],{},[233,18509,18510],{"scriptlevel":235,"displaystyle":63},[49,18511,18512,18514,18516,18524,18526,18528,18530,18532,18538,18540],{},[49,18513],{},[126,18515,128],{},[233,18517,18518],{"scriptlevel":235,"displaystyle":247},[2167,18519,18520,18522],{},[130,18521,132],{},[130,18523,10891],{},[126,18525,248],{"stretchy":247},[130,18527,18497],{},[126,18529,290],{},[130,18531,132],{},[237,18533,18534,18536],{},[126,18535,253],{"stretchy":247},[130,18537,10891],{},[126,18539,10662],{},[130,18541,18542],{},"0.029993",[56,18544,18545],{"encoding":58},"\\begin{aligned}\nz_1 &= 0.5 \\times 1 + 0 = 0.5 \\\\\na_1 &= \\sigma(0.5) \\approx 0.62246 \\\\\n\\hat{y} &= 2 \\times 0.62246 + 0 \\approx 1.24492 \\\\\n\\mathcal{L} &= \\tfrac{1}{2}(1.24492 - 1)^2 \\approx 0.029993\n\\end{aligned}",[33,18547,18549],{"className":18548,"ariaHidden":63},[62],[33,18550,18552,18556],{"className":18551},[67],[33,18553],{"className":18554,"style":18555},[71],"height:5.7241em;vertical-align:-2.6121em;",[33,18557,18559],{"className":18558},[76],[33,18560,18562,18748],{"className":18561},[221],[33,18563,18565],{"className":18564},[382],[33,18566,18568,18739],{"className":18567},[386,387],[33,18569,18571,18736],{"className":18570},[391],[33,18572,18575,18624,18673,18724],{"className":18573,"style":18574},[395],"height:3.1121em;",[33,18576,18578,18581],{"style":18577},"top:-5.2721em;",[33,18579],{"className":18580,"style":1317},[403],[33,18582,18584],{"className":18583},[76],[33,18585,18587,18590],{"className":18586},[76],[33,18588,242],{"className":18589,"style":1612},[76,77],[33,18591,18593],{"className":18592},[418],[33,18594,18596,18616],{"className":18595},[386,387],[33,18597,18599,18613],{"className":18598},[391],[33,18600,18602],{"className":18601,"style":3293},[395],[33,18603,18604,18607],{"style":12586},[33,18605],{"className":18606,"style":435},[403],[33,18608,18610],{"className":18609},[439,440,441,442],[33,18611,132],{"className":18612},[76,442],[33,18614,508],{"className":18615},[507],[33,18617,18619],{"className":18618},[391],[33,18620,18622],{"className":18621,"style":3315},[395],[33,18623],{},[33,18625,18627,18630],{"style":18626},"top:-3.7721em;",[33,18628],{"className":18629,"style":1317},[403],[33,18631,18633],{"className":18632},[76],[33,18634,18636,18639],{"className":18635},[76],[33,18637,281],{"className":18638},[76,77],[33,18640,18642],{"className":18641},[418],[33,18643,18645,18665],{"className":18644},[386,387],[33,18646,18648,18662],{"className":18647},[391],[33,18649,18651],{"className":18650,"style":3293},[395],[33,18652,18653,18656],{"style":3296},[33,18654],{"className":18655,"style":435},[403],[33,18657,18659],{"className":18658},[439,440,441,442],[33,18660,132],{"className":18661},[76,442],[33,18663,508],{"className":18664},[507],[33,18666,18668],{"className":18667},[391],[33,18669,18671],{"className":18670,"style":3315},[395],[33,18672],{},[33,18674,18676,18679],{"style":18675},"top:-2.2721em;",[33,18677],{"className":18678,"style":1317},[403],[33,18680,18682],{"className":18681},[76],[33,18683,18685],{"className":18684},[76,1300],[33,18686,18688,18716],{"className":18687},[386,387],[33,18689,18691,18713],{"className":18690},[391],[33,18692,18694,18702],{"className":18693,"style":105},[395],[33,18695,18696,18699],{"style":1313},[33,18697],{"className":18698,"style":1317},[403],[33,18700,1227],{"className":18701,"style":706},[76,77],[33,18703,18704,18707],{"style":1313},[33,18705],{"className":18706,"style":1317},[403],[33,18708,18710],{"className":18709,"style":11487},[1331],[33,18711,1230],{"className":18712},[76],[33,18714,508],{"className":18715},[507],[33,18717,18719],{"className":18718},[391],[33,18720,18722],{"className":18721,"style":1345},[395],[33,18723],{},[33,18725,18727,18730],{"style":18726},"top:-0.7479em;",[33,18728],{"className":18729,"style":1317},[403],[33,18731,18733],{"className":18732},[76],[33,18734,54],{"className":18735},[76,1400],[33,18737,508],{"className":18738},[507],[33,18740,18742],{"className":18741},[391],[33,18743,18746],{"className":18744,"style":18745},[395],"height:2.6121em;",[33,18747],{},[33,18749,18751],{"className":18750},[521],[33,18752,18754,19073],{"className":18753},[386,387],[33,18755,18757,19070],{"className":18756},[391],[33,18758,18760,18819,18863,18922],{"className":18759,"style":18574},[395],[33,18761,18762,18765],{"style":18577},[33,18763],{"className":18764,"style":1317},[403],[33,18766,18768,18771,18774,18777,18780,18783,18786,18789,18792,18795,18798,18801,18804,18807,18810,18813,18816],{"className":18767},[76],[33,18769],{"className":18770},[76],[33,18772],{"className":18773,"style":162},[161],[33,18775,128],{"className":18776},[166],[33,18778],{"className":18779,"style":162},[161],[33,18781,18022],{"className":18782},[76],[33,18784],{"className":18785,"style":638},[161],[33,18787,18415],{"className":18788},[628],[33,18790],{"className":18791,"style":638},[161],[33,18793,132],{"className":18794},[76],[33,18796],{"className":18797,"style":638},[161],[33,18799,297],{"className":18800},[628],[33,18802],{"className":18803,"style":638},[161],[33,18805,235],{"className":18806},[76],[33,18808],{"className":18809,"style":162},[161],[33,18811,128],{"className":18812},[166],[33,18814],{"className":18815,"style":162},[161],[33,18817,18022],{"className":18818},[76],[33,18820,18821,18824],{"style":18626},[33,18822],{"className":18823,"style":1317},[403],[33,18825,18827,18830,18833,18836,18839,18842,18845,18848,18851,18854,18857,18860],{"className":18826},[76],[33,18828],{"className":18829},[76],[33,18831],{"className":18832,"style":162},[161],[33,18834,128],{"className":18835},[166],[33,18837],{"className":18838,"style":162},[161],[33,18840,341],{"className":18841,"style":706},[76,77],[33,18843,248],{"className":18844},[449],[33,18846,18022],{"className":18847},[76],[33,18849,253],{"className":18850},[456],[33,18852],{"className":18853,"style":162},[161],[33,18855,10662],{"className":18856},[166],[33,18858],{"className":18859,"style":162},[161],[33,18861,18460],{"className":18862},[76],[33,18864,18865,18868],{"style":18675},[33,18866],{"className":18867,"style":1317},[403],[33,18869,18871,18874,18877,18880,18883,18886,18889,18892,18895,18898,18901,18904,18907,18910,18913,18916,18919],{"className":18870},[76],[33,18872],{"className":18873},[76],[33,18875],{"className":18876,"style":162},[161],[33,18878,128],{"className":18879},[166],[33,18881],{"className":18882,"style":162},[161],[33,18884,10891],{"className":18885},[76],[33,18887],{"className":18888,"style":638},[161],[33,18890,18415],{"className":18891},[628],[33,18893],{"className":18894,"style":638},[161],[33,18896,18460],{"className":18897},[76],[33,18899],{"className":18900,"style":638},[161],[33,18902,297],{"className":18903},[628],[33,18905],{"className":18906,"style":638},[161],[33,18908,235],{"className":18909},[76],[33,18911],{"className":18912,"style":162},[161],[33,18914,10662],{"className":18915},[166],[33,18917],{"className":18918,"style":162},[161],[33,18920,18497],{"className":18921},[76],[33,18923,18924,18927],{"style":18726},[33,18925],{"className":18926,"style":1317},[403],[33,18928,18930,18933,18936,18939,18942,19010,19013,19016,19019,19022,19025,19028,19058,19061,19064,19067],{"className":18929},[76],[33,18931],{"className":18932},[76],[33,18934],{"className":18935,"style":162},[161],[33,18937,128],{"className":18938},[166],[33,18940],{"className":18941,"style":162},[161],[33,18943,18945,18948,19007],{"className":18944},[76],[33,18946],{"className":18947},[449,2249],[33,18949,18951],{"className":18950},[2167],[33,18952,18954,18999],{"className":18953},[386,387],[33,18955,18957,18996],{"className":18956},[391],[33,18958,18960,18974,18982],{"className":18959,"style":10942},[395],[33,18961,18962,18965],{"style":10945},[33,18963],{"className":18964,"style":1317},[403],[33,18966,18968],{"className":18967},[439,440,441,442],[33,18969,18971],{"className":18970},[76,442],[33,18972,10891],{"className":18973},[76,442],[33,18975,18976,18979],{"style":3539},[33,18977],{"className":18978,"style":1317},[403],[33,18980],{"className":18981,"style":2353},[2352],[33,18983,18984,18987],{"style":10968},[33,18985],{"className":18986,"style":1317},[403],[33,18988,18990],{"className":18989},[439,440,441,442],[33,18991,18993],{"className":18992},[76,442],[33,18994,132],{"className":18995},[76,442],[33,18997,508],{"className":18998},[507],[33,19000,19002],{"className":19001},[391],[33,19003,19005],{"className":19004,"style":10990},[395],[33,19006],{},[33,19008],{"className":19009},[456,2249],[33,19011,248],{"className":19012},[449],[33,19014,18497],{"className":19015},[76],[33,19017],{"className":19018,"style":638},[161],[33,19020,290],{"className":19021},[628],[33,19023],{"className":19024,"style":638},[161],[33,19026,132],{"className":19027},[76],[33,19029,19031,19034],{"className":19030},[456],[33,19032,253],{"className":19033},[456],[33,19035,19037],{"className":19036},[418],[33,19038,19040],{"className":19039},[386],[33,19041,19043],{"className":19042},[391],[33,19044,19047],{"className":19045,"style":19046},[395],"height:0.8641em;",[33,19048,19049,19052],{"style":431},[33,19050],{"className":19051,"style":435},[403],[33,19053,19055],{"className":19054},[439,440,441,442],[33,19056,10891],{"className":19057},[76,442],[33,19059],{"className":19060,"style":162},[161],[33,19062,10662],{"className":19063},[166],[33,19065],{"className":19066,"style":162},[161],[33,19068,18542],{"className":19069},[76],[33,19071,508],{"className":19072},[507],[33,19074,19076],{"className":19075},[391],[33,19077,19079],{"className":19078,"style":18745},[395],[33,19080],{},[10,19082,19083],{},[14,19084,16192],{},[10,19086,19087,19088,19270,19271,4104,19439,19585],{},"出力層は恒等関数と二乗誤差の組み合わせなので、",[33,19089,19091,19126],{"className":19090},[36],[33,19092,19094],{"className":19093},[40],[42,19095,19096],{"xmlns":44},[46,19097,19098,19123],{},[49,19099,19100,19106,19108,19114,19116,19118,19120],{},[1533,19101,19102,19104],{},[52,19103,2581],{},[130,19105,10891],{},[126,19107,128],{},[1223,19109,19110,19112],{"accent":63},[52,19111,1227],{},[126,19113,1230],{},[126,19115,290],{},[52,19117,1227],{},[126,19119,10662],{},[130,19121,19122],{},"0.24492",[56,19124,19125],{"encoding":58},"\\delta_2 = \\hat{y} - y \\approx 0.24492",[33,19127,19129,19185,19242,19261],{"className":19128,"ariaHidden":63},[62],[33,19130,19132,19135,19176,19179,19182],{"className":19131},[67],[33,19133],{"className":19134,"style":17160},[71],[33,19136,19138,19141],{"className":19137},[76],[33,19139,2581],{"className":19140,"style":2727},[76,77],[33,19142,19144],{"className":19143},[418],[33,19145,19147,19168],{"className":19146},[386,387],[33,19148,19150,19165],{"className":19149},[391],[33,19151,19153],{"className":19152,"style":3293},[395],[33,19154,19156,19159],{"style":19155},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[33,19157],{"className":19158,"style":435},[403],[33,19160,19162],{"className":19161},[439,440,441,442],[33,19163,10891],{"className":19164},[76,442],[33,19166,508],{"className":19167},[507],[33,19169,19171],{"className":19170},[391],[33,19172,19174],{"className":19173,"style":3315},[395],[33,19175],{},[33,19177],{"className":19178,"style":162},[161],[33,19180,128],{"className":19181},[166],[33,19183],{"className":19184,"style":162},[161],[33,19186,19188,19191,19233,19236,19239],{"className":19187},[67],[33,19189],{"className":19190,"style":12098},[71],[33,19192,19194],{"className":19193},[76,1300],[33,19195,19197,19225],{"className":19196},[386,387],[33,19198,19200,19222],{"className":19199},[391],[33,19201,19203,19211],{"className":19202,"style":105},[395],[33,19204,19205,19208],{"style":1313},[33,19206],{"className":19207,"style":1317},[403],[33,19209,1227],{"className":19210,"style":706},[76,77],[33,19212,19213,19216],{"style":1313},[33,19214],{"className":19215,"style":1317},[403],[33,19217,19219],{"className":19218,"style":11487},[1331],[33,19220,1230],{"className":19221},[76],[33,19223,508],{"className":19224},[507],[33,19226,19228],{"className":19227},[391],[33,19229,19231],{"className":19230,"style":1345},[395],[33,19232],{},[33,19234],{"className":19235,"style":638},[161],[33,19237,290],{"className":19238},[628],[33,19240],{"className":19241,"style":638},[161],[33,19243,19245,19249,19252,19255,19258],{"className":19244},[67],[33,19246],{"className":19247,"style":19248},[71],"height:0.6776em;vertical-align:-0.1944em;",[33,19250,1227],{"className":19251,"style":706},[76,77],[33,19253],{"className":19254,"style":162},[161],[33,19256,10662],{"className":19257},[166],[33,19259],{"className":19260,"style":162},[161],[33,19262,19264,19267],{"className":19263},[67],[33,19265],{"className":19266,"style":9082},[71],[33,19268,19122],{"className":19269},[76]," です。シグモイドの微分は ",[33,19272,19274,19326],{"className":19273},[36],[33,19275,19277],{"className":19276},[40],[42,19278,19279],{"xmlns":44},[46,19280,19281,19323],{},[49,19282,19283,19289,19291,19293,19295,19297,19299,19301,19303,19305],{},[237,19284,19285,19287],{},[52,19286,341],{},[126,19288,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[126,19290,248],{"stretchy":247},[52,19292,242],{},[126,19294,253],{"stretchy":247},[126,19296,128],{},[52,19298,341],{},[126,19300,248],{"stretchy":247},[52,19302,242],{},[126,19304,253],{"stretchy":247},[49,19306,19307,19309,19311,19313,19315,19317,19319,19321],{},[126,19308,248],{"fence":63},[130,19310,132],{},[126,19312,290],{},[52,19314,341],{},[126,19316,248],{"stretchy":247},[52,19318,242],{},[126,19320,253],{"stretchy":247},[126,19322,253],{"fence":63},[56,19324,19325],{"encoding":58},"\\sigma'(z) = \\sigma(z)\\left(1 - \\sigma(z)\\right)",[33,19327,19329,19385],{"className":19328,"ariaHidden":63},[62],[33,19330,19332,19335,19367,19370,19373,19376,19379,19382],{"className":19331},[67],[33,19333],{"className":19334,"style":14139},[71],[33,19336,19338,19341],{"className":19337},[76],[33,19339,341],{"className":19340,"style":706},[76,77],[33,19342,19344],{"className":19343},[418],[33,19345,19347],{"className":19346},[386],[33,19348,19350],{"className":19349},[391],[33,19351,19353],{"className":19352,"style":11802},[395],[33,19354,19355,19358],{"style":864},[33,19356],{"className":19357,"style":435},[403],[33,19359,19361],{"className":19360},[439,440,441,442],[33,19362,19364],{"className":19363},[76,442],[33,19365,4370],{"className":19366},[76,442],[33,19368,248],{"className":19369},[449],[33,19371,242],{"className":19372,"style":1612},[76,77],[33,19374,253],{"className":19375},[456],[33,19377],{"className":19378,"style":162},[161],[33,19380,128],{"className":19381},[166],[33,19383],{"className":19384,"style":162},[161],[33,19386,19388,19391,19394,19397,19400,19403,19406],{"className":19387},[67],[33,19389],{"className":19390,"style":1396},[71],[33,19392,341],{"className":19393,"style":706},[76,77],[33,19395,248],{"className":19396},[449],[33,19398,242],{"className":19399,"style":1612},[76,77],[33,19401,253],{"className":19402},[456],[33,19404],{"className":19405,"style":187},[161],[33,19407,19409,19412,19415,19418,19421,19424,19427,19430,19433,19436],{"className":19408},[191],[33,19410,248],{"className":19411,"style":717},[449,716],[33,19413,132],{"className":19414},[76],[33,19416],{"className":19417,"style":638},[161],[33,19419,290],{"className":19420},[628],[33,19422],{"className":19423,"style":638},[161],[33,19425,341],{"className":19426,"style":706},[76,77],[33,19428,248],{"className":19429},[449],[33,19431,242],{"className":19432,"style":1612},[76,77],[33,19434,253],{"className":19435},[456],[33,19437,253],{"className":19438,"style":717},[456,716],[33,19440,19442,19480],{"className":19441},[36],[33,19443,19445],{"className":19444},[40],[42,19446,19447],{"xmlns":44},[46,19448,19449,19477],{},[49,19450,19451,19457,19459,19461,19463,19465,19467,19469,19472,19474],{},[237,19452,19453,19455],{},[52,19454,341],{},[126,19456,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[126,19458,248],{"stretchy":247},[130,19460,18022],{},[126,19462,253],{"stretchy":247},[126,19464,10662],{},[130,19466,18460],{},[126,19468,18415],{},[130,19470,19471],{},"0.37754",[126,19473,10662],{},[130,19475,19476],{},"0.23500",[56,19478,19479],{"encoding":58},"\\sigma'(0.5) \\approx 0.62246 \\times 0.37754 \\approx 0.23500",[33,19481,19483,19539,19558,19576],{"className":19482,"ariaHidden":63},[62],[33,19484,19486,19489,19521,19524,19527,19530,19533,19536],{"className":19485},[67],[33,19487],{"className":19488,"style":14139},[71],[33,19490,19492,19495],{"className":19491},[76],[33,19493,341],{"className":19494,"style":706},[76,77],[33,19496,19498],{"className":19497},[418],[33,19499,19501],{"className":19500},[386],[33,19502,19504],{"className":19503},[391],[33,19505,19507],{"className":19506,"style":11802},[395],[33,19508,19509,19512],{"style":864},[33,19510],{"className":19511,"style":435},[403],[33,19513,19515],{"className":19514},[439,440,441,442],[33,19516,19518],{"className":19517},[76,442],[33,19519,4370],{"className":19520},[76,442],[33,19522,248],{"className":19523},[449],[33,19525,18022],{"className":19526},[76],[33,19528,253],{"className":19529},[456],[33,19531],{"className":19532,"style":162},[161],[33,19534,10662],{"className":19535},[166],[33,19537],{"className":19538,"style":162},[161],[33,19540,19542,19546,19549,19552,19555],{"className":19541},[67],[33,19543],{"className":19544,"style":19545},[71],"height:0.7278em;vertical-align:-0.0833em;",[33,19547,18460],{"className":19548},[76],[33,19550],{"className":19551,"style":638},[161],[33,19553,18415],{"className":19554},[628],[33,19556],{"className":19557,"style":638},[161],[33,19559,19561,19564,19567,19570,19573],{"className":19560},[67],[33,19562],{"className":19563,"style":9082},[71],[33,19565,19471],{"className":19566},[76],[33,19568],{"className":19569,"style":162},[161],[33,19571,10662],{"className":19572},[166],[33,19574],{"className":19575,"style":162},[161],[33,19577,19579,19582],{"className":19578},[67],[33,19580],{"className":19581,"style":9082},[71],[33,19583,19476],{"className":19584},[76]," となります。",[33,19587,19589],{"className":19588},[208],[33,19590,19592,19952],{"className":19591},[36],[33,19593,19595],{"className":19594},[40],[42,19596,19597],{"xmlns":44,"display":217},[46,19598,19599,19949],{},[221,19600,19601,19678,19738,19825,19889],{"rowspacing":223,"columnalign":14308,"columnspacing":14309},[227,19602,19603,19625,19662,19668],{},[230,19604,19605],{},[233,19606,19607],{"scriptlevel":235,"displaystyle":63},[2167,19608,19609,19615],{},[49,19610,19611,19613],{},[52,19612,2174],{"mathvariant":2173},[52,19614,54],{"mathvariant":1369},[49,19616,19617,19619],{},[52,19618,2174],{"mathvariant":2173},[1533,19620,19621,19623],{},[52,19622,17018],{},[130,19624,10891],{},[230,19626,19627],{},[233,19628,19629],{"scriptlevel":235,"displaystyle":63},[49,19630,19631,19633,19635,19641,19643,19649,19651,19653,19655,19657,19659],{},[49,19632],{},[126,19634,128],{},[1533,19636,19637,19639],{},[52,19638,2581],{},[130,19640,10891],{},[4361,19642,4363],{},[1533,19644,19645,19647],{},[52,19646,281],{},[130,19648,132],{},[126,19650,10662],{},[130,19652,19122],{},[126,19654,18415],{},[130,19656,18460],{},[126,19658,10662],{},[130,19660,19661],{},"0.15245",[230,19663,19664],{},[233,19665,19666],{"scriptlevel":235,"displaystyle":63},[49,19667],{},[230,19669,19670],{},[233,19671,19672],{"scriptlevel":235,"displaystyle":63},[49,19673,19674,19676],{},[49,19675],{},[4361,19677,10058],{},[227,19679,19680,19702,19722,19728],{},[230,19681,19682],{},[233,19683,19684],{"scriptlevel":235,"displaystyle":63},[2167,19685,19686,19692],{},[49,19687,19688,19690],{},[52,19689,2174],{"mathvariant":2173},[52,19691,54],{"mathvariant":1369},[49,19693,19694,19696],{},[52,19695,2174],{"mathvariant":2173},[1533,19697,19698,19700],{},[52,19699,302],{},[130,19701,10891],{},[230,19703,19704],{},[233,19705,19706],{"scriptlevel":235,"displaystyle":63},[49,19707,19708,19710,19712,19718,19720],{},[49,19709],{},[126,19711,128],{},[1533,19713,19714,19716],{},[52,19715,2581],{},[130,19717,10891],{},[126,19719,10662],{},[130,19721,19122],{},[230,19723,19724],{},[233,19725,19726],{"scriptlevel":235,"displaystyle":63},[49,19727],{},[230,19729,19730],{},[233,19731,19732],{"scriptlevel":235,"displaystyle":63},[49,19733,19734,19736],{},[49,19735],{},[4361,19737,9198],{},[227,19739,19740,19750,19809,19815],{},[230,19741,19742],{},[233,19743,19744],{"scriptlevel":235,"displaystyle":63},[1533,19745,19746,19748],{},[52,19747,2581],{},[130,19749,132],{},[230,19751,19752],{},[233,19753,19754],{"scriptlevel":235,"displaystyle":63},[49,19755,19756,19758,19760,19766,19768,19774,19776,19782,19784,19790,19792,19794,19796,19798,19800,19802,19804,19806],{},[49,19757],{},[126,19759,128],{},[1533,19761,19762,19764],{},[52,19763,17018],{},[130,19765,10891],{},[4361,19767,4363],{},[1533,19769,19770,19772],{},[52,19771,2581],{},[130,19773,10891],{},[4361,19775,4363],{},[237,19777,19778,19780],{},[52,19779,341],{},[126,19781,4370],{"mathvariant":2173,"lspace":225,"rspace":225},[126,19783,248],{"stretchy":247},[1533,19785,19786,19788],{},[52,19787,242],{},[130,19789,132],{},[126,19791,253],{"stretchy":247},[126,19793,10662],{},[130,19795,10891],{},[126,19797,18415],{},[130,19799,19122],{},[126,19801,18415],{},[130,19803,19476],{},[126,19805,10662],{},[130,19807,19808],{},"0.11511",[230,19810,19811],{},[233,19812,19813],{"scriptlevel":235,"displaystyle":63},[49,19814],{},[230,19816,19817],{},[233,19818,19819],{"scriptlevel":235,"displaystyle":63},[49,19820,19821,19823],{},[49,19822],{},[4361,19824,8420],{},[227,19826,19827,19849,19873,19879],{},[230,19828,19829],{},[233,19830,19831],{"scriptlevel":235,"displaystyle":63},[2167,19832,19833,19839],{},[49,19834,19835,19837],{},[52,19836,2174],{"mathvariant":2173},[52,19838,54],{"mathvariant":1369},[49,19840,19841,19843],{},[52,19842,2174],{"mathvariant":2173},[1533,19844,19845,19847],{},[52,19846,17018],{},[130,19848,132],{},[230,19850,19851],{},[233,19852,19853],{"scriptlevel":235,"displaystyle":63},[49,19854,19855,19857,19859,19865,19867,19869,19871],{},[49,19856],{},[126,19858,128],{},[1533,19860,19861,19863],{},[52,19862,2581],{},[130,19864,132],{},[4361,19866,4363],{},[52,19868,830],{},[126,19870,10662],{},[130,19872,19808],{},[230,19874,19875],{},[233,19876,19877],{"scriptlevel":235,"displaystyle":63},[49,19878],{},[230,19880,19881],{},[233,19882,19883],{"scriptlevel":235,"displaystyle":63},[49,19884,19885,19887],{},[49,19886],{},[4361,19888,10058],{},[227,19890,19891,19913,19933,19939],{},[230,19892,19893],{},[233,19894,19895],{"scriptlevel":235,"displaystyle":63},[2167,19896,19897,19903],{},[49,19898,19899,19901],{},[52,19900,2174],{"mathvariant":2173},[52,19902,54],{"mathvariant":1369},[49,19904,19905,19907],{},[52,19906,2174],{"mathvariant":2173},[1533,19908,19909,19911],{},[52,19910,302],{},[130,19912,132],{},[230,19914,19915],{},[233,19916,19917],{"scriptlevel":235,"displaystyle":63},[49,19918,19919,19921,19923,19929,19931],{},[49,19920],{},[126,19922,128],{},[1533,19924,19925,19927],{},[52,19926,2581],{},[130,19928,132],{},[126,19930,10662],{},[130,19932,19808],{},[230,19934,19935],{},[233,19936,19937],{"scriptlevel":235,"displaystyle":63},[49,19938],{},[230,19940,19941],{},[233,19942,19943],{"scriptlevel":235,"displaystyle":63},[49,19944,19945,19947],{},[49,19946],{},[4361,19948,9198],{},[56,19950,19951],{"encoding":58},"\\begin{aligned}\n\\frac{\\partial \\mathcal{L}}{\\partial w_2} &= \\delta_2 \\, a_1 \\approx 0.24492 \\times 0.62246 \\approx 0.15245 && \\text{(BP4)} \\\\\n\\frac{\\partial \\mathcal{L}}{\\partial b_2} &= \\delta_2 \\approx 0.24492 && \\text{(BP3)} \\\\\n\\delta_1 &= w_2 \\, \\delta_2 \\, \\sigma'(z_1) \\approx 2 \\times 0.24492 \\times 0.23500 \\approx 0.11511 && \\text{(BP2)} \\\\\n\\frac{\\partial \\mathcal{L}}{\\partial w_1} &= \\delta_1 \\, x \\approx 0.11511 && \\text{(BP4)} \\\\\n\\frac{\\partial \\mathcal{L}}{\\partial b_1} &= \\delta_1 \\approx 0.11511 && \\text{(BP3)}\n\\end{aligned}",[33,19953,19955],{"className":19954,"ariaHidden":63},[62],[33,19956,19958,19962],{"className":19957},[67],[33,19959],{"className":19960,"style":19961},[71],"height:11.2298em;vertical-align:-5.3649em;",[33,19963,19965],{"className":19964},[76],[33,19966,19968,20499,21115,21118,21181],{"className":19967},[221],[33,19969,19971],{"className":19970},[382],[33,19972,19974,20490],{"className":19973},[386,387],[33,19975,19977,20487],{"className":19976},[391],[33,19978,19981,20096,20210,20259,20373],{"className":19979,"style":19980},[395],"height:5.8649em;",[33,19982,19984,19988],{"style":19983},"top:-7.8649em;",[33,19985],{"className":19986,"style":19987},[403],"height:3.3714em;",[33,19989,19991],{"className":19990},[76],[33,19992,19994,19997,20093],{"className":19993},[76],[33,19995],{"className":19996},[449,2249],[33,19998,20000],{"className":19999},[2167],[33,20001,20003,20085],{"className":20002},[386,387],[33,20004,20006,20082],{"className":20005},[391],[33,20007,20009,20060,20068],{"className":20008,"style":2262},[395],[33,20010,20011,20014],{"style":3524},[33,20012],{"className":20013,"style":1317},[403],[33,20015,20017,20020],{"className":20016},[76],[33,20018,2174],{"className":20019,"style":2276},[76],[33,20021,20023,20026],{"className":20022},[76],[33,20024,17018],{"className":20025,"style":17106},[76,77],[33,20027,20029],{"className":20028},[418],[33,20030,20032,20052],{"className":20031},[386,387],[33,20033,20035,20049],{"className":20034},[391],[33,20036,20038],{"className":20037,"style":3293},[395],[33,20039,20040,20043],{"style":17121},[33,20041],{"className":20042,"style":435},[403],[33,20044,20046],{"className":20045},[439,440,441,442],[33,20047,10891],{"className":20048},[76,442],[33,20050,508],{"className":20051},[507],[33,20053,20055],{"className":20054},[391],[33,20056,20058],{"className":20057,"style":3315},[395],[33,20059],{},[33,20061,20062,20065],{"style":3539},[33,20063],{"className":20064,"style":1317},[403],[33,20066],{"className":20067,"style":2353},[2352],[33,20069,20070,20073],{"style":3548},[33,20071],{"className":20072,"style":1317},[403],[33,20074,20076,20079],{"className":20075},[76],[33,20077,2174],{"className":20078,"style":2276},[76],[33,20080,54],{"className":20081},[76,1400],[33,20083,508],{"className":20084},[507],[33,20086,20088],{"className":20087},[391],[33,20089,20091],{"className":20090,"style":3771},[395],[33,20092],{},[33,20094],{"className":20095},[456,2249],[33,20097,20099,20102],{"style":20098},"top:-5.3574em;",[33,20100],{"className":20101,"style":19987},[403],[33,20103,20105],{"className":20104},[76],[33,20106,20108,20111,20207],{"className":20107},[76],[33,20109],{"className":20110},[449,2249],[33,20112,20114],{"className":20113},[2167],[33,20115,20117,20199],{"className":20116},[386,387],[33,20118,20120,20196],{"className":20119},[391],[33,20121,20123,20174,20182],{"className":20122,"style":2262},[395],[33,20124,20125,20128],{"style":3524},[33,20126],{"className":20127,"style":1317},[403],[33,20129,20131,20134],{"className":20130},[76],[33,20132,2174],{"className":20133,"style":2276},[76],[33,20135,20137,20140],{"className":20136},[76],[33,20138,302],{"className":20139},[76,77],[33,20141,20143],{"className":20142},[418],[33,20144,20146,20166],{"className":20145},[386,387],[33,20147,20149,20163],{"className":20148},[391],[33,20150,20152],{"className":20151,"style":3293},[395],[33,20153,20154,20157],{"style":3296},[33,20155],{"className":20156,"style":435},[403],[33,20158,20160],{"className":20159},[439,440,441,442],[33,20161,10891],{"className":20162},[76,442],[33,20164,508],{"className":20165},[507],[33,20167,20169],{"className":20168},[391],[33,20170,20172],{"className":20171,"style":3315},[395],[33,20173],{},[33,20175,20176,20179],{"style":3539},[33,20177],{"className":20178,"style":1317},[403],[33,20180],{"className":20181,"style":2353},[2352],[33,20183,20184,20187],{"style":3548},[33,20185],{"className":20186,"style":1317},[403],[33,20188,20190,20193],{"className":20189},[76],[33,20191,2174],{"className":20192,"style":2276},[76],[33,20194,54],{"className":20195},[76,1400],[33,20197,508],{"className":20198},[507],[33,20200,20202],{"className":20201},[391],[33,20203,20205],{"className":20204,"style":3771},[395],[33,20206],{},[33,20208],{"className":20209},[456,2249],[33,20211,20213,20216],{"style":20212},"top:-3.3814em;",[33,20214],{"className":20215,"style":19987},[403],[33,20217,20219],{"className":20218},[76],[33,20220,20222,20225],{"className":20221},[76],[33,20223,2581],{"className":20224,"style":2727},[76,77],[33,20226,20228],{"className":20227},[418],[33,20229,20231,20251],{"className":20230},[386,387],[33,20232,20234,20248],{"className":20233},[391],[33,20235,20237],{"className":20236,"style":3293},[395],[33,20238,20239,20242],{"style":19155},[33,20240],{"className":20241,"style":435},[403],[33,20243,20245],{"className":20244},[439,440,441,442],[33,20246,132],{"className":20247},[76,442],[33,20249,508],{"className":2025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",[33,21297,21299,21317],{"className":21298},[36],[33,21300,21302],{"className":21301},[40],[42,21303,21304],{"xmlns":44},[46,21305,21306,21314],{},[49,21307,21308,21310,21312],{},[52,21309,16403],{},[126,21311,128],{},[130,21313,18022],{},[56,21315,21316],{"encoding":58},"\\eta = 0.5",[33,21318,21320,21338],{"className":21319,"ariaHidden":63},[62],[33,21321,21323,21326,21329,21332,21335],{"className":21322},[67],[33,21324],{"className":21325,"style":3274},[71],[33,21327,16403],{"className":21328,"style":706},[76,77],[33,21330],{"className":21331,"style":162},[161],[33,21333,128],{"className":21334},[166],[33,21336],{"className":21337,"style":162},[161],[33,21339,21341,21344],{"className":21340},[67],[33,21342],{"className":21343,"style":9082},[71],[33,21345,18022],{"className":21346},[76]," で1回更新すると、パラメータは ",[33,21349,21351,21374],{"className":21350},[36],[33,21352,21354],{"className":21353},[40],[42,21355,21356],{"xmlns":44},[46,21357,21358,21371],{},[49,21359,21360,21366,21368],{},[1533,21361,21362,21364],{},[52,21363,17018],{},[130,21365,132],{},[126,21367,10662],{},[130,21369,21370],{},"0.44244",[56,21372,21373],{"encoding":58},"w_1 \\approx 0.44244",[33,21375,21377,21433],{"className":21376,"ariaHidden":63},[62],[33,21378,21380,21384,21424,21427,21430],{"className":21379},[67],[33,21381],{"className":21382,"style":21383},[71],"height:0.6331em;vertical-align:-0.15em;",[33,21385,21387,21390],{"className":21386},[76],[33,21388,17018],{"className":21389,"style":17106},[76,77],[33,21391,21393],{"className":21392},[418],[33,21394,21396,21416],{"className":21395},[386,387],[33,21397,21399,21413],{"className":21398},[391],[33,21400,21402],{"className":21401,"style":3293},[395],[33,21403,21404,21407],{"style":17121},[33,21405],{"className":21406,"style":435},[403],[33,21408,21410],{"className":21409},[439,440,441,442],[33,21411,132],{"className":21412},[76,442],[33,21414,508],{"className":21415},[507],[33,21417,21419],{"className":21418},[391],[33,21420,21422],{"className":21421,"style":3315},[395],[33,21423],{},[33,21425],{"className":21426,"style":162},[161],[33,21428,10662],{"className":21429},[166],[33,21431],{"className":21432,"style":162},[161],[33,21434,21436,21439],{"className":21435},[67],[33,21437],{"className":21438,"style":9082},[71],[33,21440,21370],{"className":21441},[76],[33,21443,21445,21470],{"className":21444},[36],[33,21446,21448],{"className":21447},[40],[42,21449,21450],{"xmlns":44},[46,21451,21452,21467],{},[49,21453,21454,21460,21462,21464],{},[1533,21455,21456,21458],{},[52,21457,302],{},[130,21459,132],{},[126,21461,10662],{},[126,21463,290],{},[130,21465,21466],{},"0.05756",[56,21468,21469],{"encoding":58},"b_1 \\approx -0.05756",[33,21471,21473,21528],{"className":21472,"ariaHidden":63},[62],[33,21474,21476,21479,21519,21522,21525],{"className":21475},[67],[33,21477],{"className":21478,"style":17160},[71],[33,21480,21482,21485],{"className":21481},[76],[33,21483,302],{"className":21484},[76,77],[33,21486,21488],{"className":21487},[418],[33,21489,21491,21511],{"className":21490},[386,387],[33,21492,21494,21508],{"className":21493},[391],[33,21495,21497],{"className":21496,"style":3293},[395],[33,21498,21499,21502],{"style":3296},[33,21500],{"className":21501,"style":435},[403],[33,21503,21505],{"className":21504},[439,440,441,442],[33,21506,132],{"className":21507},[76,442],[33,21509,508],{"className":21510},[507],[33,21512,21514],{"className":21513},[391],[33,21515,21517],{"className":21516,"style":3315},[395],[33,21518],{},[33,21520],{"className":21521,"style":162},[161],[33,21523,10662],{"className":21524},[166],[33,21526],{"className":21527,"style":162},[161],[33,21529,21531,21534,21537],{"className":21530},[67],[33,21532],{"className":21533,"style":19545},[71],[33,21535,290],{"className":21536},[76],[33,21538,21466],{"className":21539},[76],[33,21541,21543,21566],{"className":21542},[36],[33,21544,21546],{"className":21545},[40],[42,21547,21548],{"xmlns":44},[46,21549,21550,21563],{},[49,21551,21552,21558,21560],{},[1533,21553,21554,21556],{},[52,21555,17018],{},[130,21557,10891],{},[126,21559,10662],{},[130,21561,21562],{},"1.92377",[56,21564,21565],{"encoding":58},"w_2 \\approx 1.92377",[33,21567,21569,21624],{"className":21568,"ariaHidden":63},[62],[33,21570,21572,21575,21615,21618,21621],{"className":21571},[67],[33,21573],{"className":21574,"style":21383},[71],[33,21576,21578,21581],{"className":21577},[76],[33,21579,17018],{"className":21580,"style":17106},[76,77],[33,21582,21584],{"className":21583},[418],[33,21585,21587,21607],{"className":21586},[386,387],[33,21588,21590,21604],{"className":21589},[391],[33,21591,21593],{"className":21592,"style":3293},[395],[33,21594,21595,21598],{"style":17121},[33,21596],{"className":21597,"style":435},[403],[33,21599,21601],{"className":21600},[439,440,441,442],[33,21602,10891],{"className":21603},[76,442],[33,21605,508],{"className":21606},[507],[33,21608,21610],{"className":21609},[391],[33,21611,21613],{"className":21612,"style":3315},[395],[33,21614],{},[33,21616],{"className":21617,"style":162},[161],[33,21619,10662],{"className":21620},[166],[33,21622],{"className":21623,"style":162},[161],[33,21625,21627,21630],{"className":21626},[67],[33,21628],{"className":21629,"style":9082},[71],[33,21631,21562],{"className":21632},[76],[33,21634,21636,21661],{"className":21635},[36],[33,21637,21639],{"className":21638},[40],[42,21640,21641],{"xmlns":44},[46,21642,21643,21658],{},[49,21644,21645,21651,21653,21655],{},[1533,21646,21647,21649],{},[52,21648,302],{},[130,21650,10891],{},[126,21652,10662],{},[126,21654,290],{},[130,21656,21657],{},"0.12246",[56,21659,21660],{"encoding":58},"b_2 \\approx -0.12246",[33,21662,21664,21719],{"className":21663,"ariaHidden":63},[62],[33,21665,21667,21670,21710,21713,21716],{"className":21666},[67],[33,21668],{"className":21669,"style":17160},[71],[33,21671,21673,21676],{"className":21672},[76],[33,21674,302],{"className":21675},[76,77],[33,21677,21679],{"className":21678},[418],[33,21680,21682,21702],{"className":21681},[386,387],[33,21683,21685,21699],{"className":21684},[391],[33,21686,21688],{"className":21687,"style":3293},[395],[33,21689,21690,21693],{"style":3296},[33,21691],{"className":21692,"style":435},[403],[33,21694,21696],{"className":21695},[439,440,441,442],[33,21697,10891],{"className":21698},[76,442],[33,21700,508],{"className":21701},[507],[33,21703,21705],{"className":21704},[391],[33,21706,21708],{"className":21707,"style":3315},[395],[33,21709],{},[33,21711],{"className":21712,"style":162},[161],[33,21714,10662],{"className":21715},[166],[33,21717],{"className":21718,"style":162},[161],[33,21720,21722,21725,21728],{"className":21721},[67],[33,21723],{"className":21724,"style":19545},[71],[33,21726,290],{"className":21727},[76],[33,21729,21657],{"className":21730},[76]," になります。損失は ",[33,21733,21735,21748],{"className":21734},[36],[33,21736,21738],{"className":21737},[40],[42,21739,21740],{"xmlns":44},[46,21741,21742,21746],{},[49,21743,21744],{},[130,21745,18542],{},[56,21747,18542],{"encoding":58},[33,21749,21751],{"className":21750,"ariaHidden":63},[62],[33,21752,21754,21757],{"className":21753},[67],[33,21755],{"className":21756,"style":9082},[71],[33,21758,18542],{"className":21759},[76]," から約 ",[33,21762,21764,21778],{"className":21763},[36],[33,21765,21767],{"className":21766},[40],[42,21768,21769],{"xmlns":44},[46,21770,21771,21776],{},[49,21772,21773],{},[130,21774,21775],{},"0.000248",[56,21777,21775],{"encoding":58},[33,21779,21781],{"className":21780,"ariaHidden":63},[62],[33,21782,21784,21787],{"className":21783},[67],[33,21785],{"className":21786,"style":9082},[71],[33,21788,21775],{"className":21789},[76]," へ下がりました。",[26,21792,21794],{"id":21793},"_8-正しさの確認勾配チェック","8. 正しさの確認：勾配チェック",[10,21796,21797,21798,21801],{},"実装した勾配が正しいかは、",[14,21799,21800],{},"数値微分（中心差分）"," と比べて確かめられます。",[33,21803,21805],{"className":21804},[208],[33,21806,21808,21874],{"className":21807},[36],[33,21809,21811],{"className":21810},[40],[42,21812,21813],{"xmlns":44,"display":217},[46,21814,21815,21871],{},[49,21816,21817,21832,21834],{},[2167,21818,21819,21825],{},[49,21820,21821,21823],{},[52,21822,2174],{"mathvariant":2173},[52,21824,54],{"mathvariant":1369},[49,21826,21827,21829],{},[52,21828,2174],{"mathvariant":2173},[52,21830,21831],{},"θ",[126,21833,10662],{},[2167,21835,21836,21865],{},[49,21837,21838,21840,21842,21844,21846,21849,21851,21853,21855,21857,21859,21861,21863],{},[52,21839,54],{"mathvariant":1369},[126,21841,248],{"stretchy":247},[52,21843,21831],{},[126,21845,297],{},[52,21847,21848],{},"ε",[126,21850,253],{"stretchy":247},[126,21852,290],{},[52,21854,54],{"mathvariant":1369},[126,21856,248],{"stretchy":247},[52,21858,21831],{},[126,21860,290],{},[52,21862,21848],{},[126,21864,253],{"stretchy":247},[49,21866,21867,21869],{},[130,21868,10891],{},[52,21870,21848],{},[56,21872,21873],{"encoding":58},"\\frac{\\partial \\mathcal{L}}{\\partial \\theta} \\approx \\frac{\\mathcal{L}(\\theta + \\varepsilon) - \\mathcal{L}(\\theta - \\varepsilon)}{2\\varepsilon}",[33,21875,21877,21961],{"className":21876,"ariaHidden":63},[62],[33,21878,21880,21883,21952,21955,21958],{"className":21879},[67],[33,21881],{"className":21882,"style":3503},[71],[33,21884,21886,21889,21949],{"className":21885},[76],[33,21887],{"className":21888},[449,2249],[33,21890,21892],{"className":21891},[2167],[33,21893,21895,21941],{"className":21894},[386,387],[33,21896,21898,21938],{"className":21897},[391],[33,21899,21901,21916,21924],{"className":21900,"style":2262},[395],[33,21902,21903,21906],{"style":3524},[33,21904],{"className":21905,"style":1317},[403],[33,21907,21909,21912],{"className":21908},[76],[33,21910,2174],{"className":21911,"style":2276},[76],[33,21913,21831],{"className":21914,"style":21915},[76,77],"margin-right:0.0278em;",[33,21917,21918,21921],{"style":3539},[33,21919],{"className":21920,"style":1317},[403],[33,21922],{"className":21923,"style":2353},[2352],[33,21925,21926,21929],{"style":3548},[33,21927],{"className":21928,"style":1317},[403],[33,21930,21932,21935],{"className":21931},[76],[33,21933,2174],{"className":21934,"style":2276},[76],[33,21936,54],{"className":21937},[76,1400],[33,21939,508],{"className":21940},[507],[33,21942,21944],{"className":21943},[391],[33,21945,21947],{"className":21946,"style":3570},[395],[33,21948],{},[33,21950],{"className":21951},[456,2249],[33,21953],{"className":21954,"style":162},[161],[33,21956,10662],{"className":21957},[166],[33,21959],{"className":21960,"style":162},[161],[33,21962,21964,21968],{"className":21963},[67],[33,21965],{"className":21966,"style":21967},[71],"height:2.113em;vertical-align:-0.686em;",[33,21969,21971,21974,22085],{"className":21970},[76],[33,21972],{"className":21973},[449,2249],[33,21975,21977],{"className":21976},[2167],[33,21978,21980,22077],{"className":21979},[386,387],[33,21981,21983,22074],{"className":21982},[391],[33,21984,21987,22001,22009],{"className":21985,"style":21986},[395],"height:1.427em;",[33,21988,21989,21992],{"style":3524},[33,21990],{"className":21991,"style":1317},[403],[33,21993,21995,21998],{"className":21994},[76],[33,21996,10891],{"className":21997},[76],[33,21999,21848],{"className":22000},[76,77],[33,22002,22003,22006],{"style":3539},[33,22004],{"className":22005,"style":1317},[403],[33,22007],{"className":22008,"style":2353},[2352],[33,22010,22011,22014],{"style":3548},[33,22012],{"className":22013,"style":1317},[403],[33,22015,22017,22020,22023,22026,22029,22032,22035,22038,22041,22044,22047,22050,22053,22056,22059,22062,22065,22068,22071],{"className":22016},[76],[33,22018,54],{"className":22019},[76,1400],[33,22021,248],{"className":22022},[449],[33,22024,21831],{"className":22025,"style":21915},[76,77],[33,22027],{"className":22028,"style":638},[161],[33,22030,297],{"className":22031},[628],[33,22033],{"className":22034,"style":638},[161],[33,22036,21848],{"className":22037},[76,77],[33,22039,253],{"className":22040},[456],[33,22042],{"className":22043,"style":638},[161],[33,22045,290],{"className":22046},[628],[33,22048],{"className":22049,"style":638},[161],[33,22051,54],{"className":22052},[76,1400],[33,22054,248],{"className":22055},[449],[33,22057,21831],{"className":22058,"style":21915},[76,77],[33,22060],{"className":22061,"style":638},[161],[33,22063,290],{"className":22064},[628],[33,22066],{"className":22067,"style":638},[161],[33,22069,21848],{"className":22070},[76,77],[33,22072,253],{"className":22073},[456],[33,22075,508],{"className":22076},[507],[33,22078,22080],{"className":22079},[391],[33,22081,22083],{"className":22082,"style":3570},[395],[33,22084],{},[33,22086],{"className":22087},[456,2249],[10,22089,22090,22091,22187,22188,17201,22301,22414],{},"上の例で ",[33,22092,22094,22122],{"className":22093},[36],[33,22095,22097],{"className":22096},[40],[42,22098,22099],{"xmlns":44},[46,22100,22101,22119],{},[49,22102,22103,22105,22107],{},[52,22104,21848],{},[126,22106,128],{},[237,22108,22109,22112],{},[130,22110,22111],{},"10",[49,22113,22114,22116],{},[126,22115,290],{},[130,22117,22118],{},"6",[56,22120,22121],{"encoding":58},"\\varepsilon = 10^{-6}",[33,22123,22125,22143],{"className":22124,"ariaHidden":63},[62],[33,22126,22128,22131,22134,22137,22140],{"className":22127},[67],[33,22129],{"className":22130,"style":1185},[71],[33,22132,21848],{"className":22133},[76,77],[33,22135],{"className":22136,"style":162},[161],[33,22138,128],{"className":22139},[166],[33,22141],{"className":22142,"style":162},[161],[33,22144,22146,22149,22152],{"className":22145},[67],[33,22147],{"className":22148,"style":11078},[71],[33,22150,132],{"className":22151},[76],[33,22153,22155,22158],{"className":22154},[76],[33,22156,235],{"className":22157},[76],[33,22159,22161],{"className":22160},[418],[33,22162,22164],{"className":22163},[386],[33,22165,22167],{"className":22166},[391],[33,22168,22170],{"className":22169,"style":11078},[395],[33,22171,22172,22175],{"style":864},[33,22173],{"className":22174,"style":435},[403],[33,22176,22178],{"className":22177},[439,440,441,442],[33,22179,22181,22184],{"className":22180},[76,442],[33,22182,290],{"className":22183},[76,442],[33,22185,22118],{"className":22186},[76,442]," として計算すると、",[33,22189,22191,22222],{"className":22190},[36],[33,22192,22194],{"className":22193},[40],[42,22195,22196],{"xmlns":44},[46,22197,22198,22219],{},[49,22199,22200,22202,22204,22206,22208,22214,22216],{},[52,22201,2174],{"mathvariant":2173},[52,22203,54],{"mathvariant":1369},[52,22205,8905],{"mathvariant":2173},[52,22207,2174],{"mathvariant":2173},[1533,22209,22210,22212],{},[52,22211,17018],{},[130,22213,132],{},[126,22215,10662],{},[130,22217,22218],{},"0.115114",[56,22220,22221],{"encoding":58},"\\partial \\mathcal{L} \u002F \\partial w_1 \\approx 0.115114",[33,22223,22225,22292],{"className":22224,"ariaHidden":63},[62],[33,22226,22228,22231,22234,22237,22240,22243,22283,22286,22289],{"className":22227},[67],[33,22229],{"className":22230,"style":1396},[71],[33,22232,2174],{"className":22233,"style":2276},[76],[33,22235,54],{"className":22236},[76,1400],[33,22238,8905],{"className":22239},[76],[33,22241,2174],{"className":22242,"style":2276},[76],[33,22244,22246,22249],{"className":22245},[76],[33,22247,17018],{"className":22248,"style":17106},[76,77],[33,22250,22252],{"className":22251},[418],[33,22253,22255,22275],{"className":22254},[386,387],[33,22256,22258,22272],{"className":22257},[391],[33,22259,22261],{"className":22260,"style":3293},[395],[33,22262,22263,22266],{"style":17121},[33,22264],{"className":22265,"style":435},[403],[33,22267,22269],{"className":22268},[439,440,441,442],[33,22270,132],{"className":22271},[76,442],[33,22273,508],{"className":22274},[507],[33,22276,22278],{"className":22277},[391],[33,22279,22281],{"className":22280,"style":3315},[395],[33,22282],{},[33,22284],{"className":22285,"style":162},[161],[33,22287,10662],{"className":22288},[166],[33,22290],{"className":22291,"style":162},[161],[33,22293,22295,22298],{"className":22294},[67],[33,22296],{"className":22297,"style":9082},[71],[33,22299,22218],{"className":22300},[76],[33,22302,22304,22335],{"className":22303},[36],[33,22305,22307],{"className":22306},[40],[42,22308,22309],{"xmlns":44},[46,22310,22311,22332],{},[49,22312,22313,22315,22317,22319,22321,22327,22329],{},[52,22314,2174],{"mathvariant":2173},[52,22316,54],{"mathvariant":1369},[52,22318,8905],{"mathvariant":2173},[52,22320,2174],{"mathvariant":2173},[1533,22322,22323,22325],{},[52,22324,17018],{},[130,22326,10891],{},[126,22328,10662],{},[130,22330,22331],{},"0.152452",[56,22333,22334],{"encoding":58},"\\partial \\mathcal{L} \u002F \\partial w_2 \\approx 0.152452",[33,22336,22338,22405],{"className":22337,"ariaHidden":63},[62],[33,22339,22341,22344,22347,22350,22353,22356,22396,22399,22402],{"className":22340},[67],[33,22342],{"className":22343,"style":1396},[71],[33,22345,2174],{"className":22346,"style":2276},[76],[33,22348,54],{"className":22349},[76,1400],[33,22351,8905],{"className":22352},[76],[33,22354,2174],{"className":22355,"style":2276},[76],[33,22357,22359,22362],{"className":22358},[76],[33,22360,17018],{"className":22361,"style":17106},[76,77],[33,22363,22365],{"className":22364},[418],[33,22366,22368,22388],{"className":22367},[386,387],[33,22369,22371,22385],{"className":22370},[391],[33,22372,22374],{"className":22373,"style":3293},[395],[33,22375,22376,22379],{"style":17121},[33,22377],{"className":22378,"style":435},[403],[33,22380,22382],{"className":22381},[439,440,441,442],[33,22383,10891],{"className":22384},[76,442],[33,22386,508],{"className":22387},[507],[33,22389,22391],{"className":22390},[391],[33,22392,22394],{"className":22393,"style":3315},[395],[33,22395],{},[33,22397],{"className":22398,"style":162},[161],[33,22400,10662],{"className":22401},[166],[33,22403],{"className":22404,"style":162},[161],[33,22406,22408,22411],{"className":22407},[67],[33,22409],{"className":22410,"style":9082},[71],[33,22412,22331],{"className":22413},[76]," となり、逆伝播の結果と一致します。",[22416,22417,22419],"tip",{"title":22418},"勾配チェックのコツ",[10,22420,22421,22422,22425,22426,22779,22780,22853],{},"差の絶対値ではなく ",[14,22423,22424],{},"相対誤差"," ",[33,22427,22429,22492],{"className":22428},[36],[33,22430,22432],{"className":22431},[40],[42,22433,22434],{"xmlns":44},[46,22435,22436,22489],{},[49,22437,22438],{},[233,22439,22440],{"scriptlevel":235,"displaystyle":63},[2167,22441,22442,22465],{},[49,22443,22444,22447,22454,22456,22463],{},[52,22445,22446],{"mathvariant":2173},"∣",[1533,22448,22449,22451],{},[52,22450,11452],{},[4361,22452,22453],{},"num",[126,22455,290],{},[1533,22457,22458,22460],{},[52,22459,11452],{},[4361,22461,22462],{},"bp",[52,22464,22446],{"mathvariant":2173},[49,22466,22467,22469,22475,22477,22479,22481,22487],{},[52,22468,22446],{"mathvariant":2173},[1533,22470,22471,22473],{},[52,22472,11452],{},[4361,22474,22453],{},[52,22476,22446],{"mathvariant":2173},[126,22478,297],{},[52,22480,22446],{"mathvariant":2173},[1533,22482,22483,22485],{},[52,22484,11452],{},[4361,22486,22462],{},[52,22488,22446],{"mathvariant":2173},[56,22490,22491],{"encoding":58},"\\dfrac{|g_{\\text{num}} - g_{\\text{bp}}|}{|g_{\\text{num}}| + |g_{\\text{bp}}|}",[33,22493,22495],{"className":22494,"ariaHidden":63},[62],[33,22496,22498,22502],{"className":22497},[67],[33,22499],{"className":22500,"style":22501},[71],"height:2.3991em;vertical-align:-0.9721em;",[33,22503,22505,22508,22776],{"className":22504},[76],[33,22506],{"className":22507},[449,2249],[33,22509,22511],{"className":22510},[2167],[33,22512,22514,22768],{"className":22513},[386,387],[33,22515,22517,22765],{"className":22516},[391],[33,22518,22520,22642,22650],{"className":22519,"style":21986},[395],[33,22521,22522,22525],{"style":3524},[33,22523],{"className":22524,"style":1317},[403],[33,22526,22528,22531,22577,22580,22583,22586,22589,22592,22639],{"className":22527},[76],[33,22529,22446],{"className":22530},[76],[33,22532,22534,22537],{"className":22533},[76],[33,22535,11452],{"className":22536,"style":706},[76,77],[33,22538,22540],{"className":22539},[418],[33,22541,22543,22569],{"className":22542},[386,387],[33,22544,22546,22566],{"className":22545},[391],[33,22547,22549],{"className":22548,"style":3354},[395],[33,22550,22551,22554],{"style":11421},[33,22552],{"className":22553,"style":435},[403],[33,22555,22557],{"className":22556},[439,440,441,442],[33,22558,22560],{"className":22559},[76,442],[33,22561,22563],{"className":22562},[76,5118,442],[33,22564,22453],{"className":22565},[76,442],[33,22567,508],{"className":22568},[507],[33,22570,22572],{"className":22571},[391],[33,22573,22575],{"className":22574,"style":3315},[395],[33,22576],{},[33,22578,22446],{"className":22579},[76],[33,22581],{"className":22582,"style":638},[161],[33,22584,297],{"className":22585},[628],[33,22587],{"className":22588,"style":638},[161],[33,22590,22446],{"className":22591},[76],[33,22593,22595,22598],{"className":22594},[76],[33,22596,11452],{"className":22597,"style":706},[76,77],[33,22599,22601],{"className":22600},[418],[33,22602,22604,22631],{"className":22603},[386,387],[33,22605,22607,22628],{"className":22606},[391],[33,22608,22611],{"className":22609,"style":22610},[395],"height:0.3361em;",[33,22612,22613,22616],{"style":11421},[33,22614],{"className":22615,"style":435},[403],[33,22617,22619],{"className":22618},[439,440,441,442],[33,22620,22622],{"className":22621},[76,442],[33,22623,22625],{"className":22624},[76,5118,442],[33,22626,22462],{"className":22627},[76,442],[33,22629,508],{"className":22630},[507],[33,22632,22634],{"className":22633},[391],[33,22635,22637],{"className":22636,"style":12605},[395],[33,22638],{},[33,22640,22446],{"className":22641},[76],[33,22643,22644,22647],{"style":3539},[33,22645],{"className":22646,"style":1317},[403],[33,22648],{"className":22649,"style":2353},[2352],[33,22651,22652,22655],{"style":3548},[33,22653],{"className":22654,"style":1317},[403],[33,22656,22658,22661,22707,22710,22713,22716,22762],{"className":22657},[76],[33,22659,22446],{"className":22660},[76],[33,22662,22664,22667],{"className":22663},[76],[33,22665,11452],{"className":22666,"style":706},[76,77],[33,22668,22670],{"className":22669},[418],[33,22671,22673,22699],{"className":22672},[386,387],[33,22674,22676,22696],{"className":22675},[391],[33,22677,22679],{"className":22678,"style":3354},[395],[33,22680,22681,22684],{"style":11421},[33,22682],{"className":22683,"style":435},[403],[33,22685,22687],{"className":22686},[439,440,441,442],[33,22688,22690],{"className":22689},[76,442],[33,22691,22693],{"className":22692},[76,5118,442],[33,22694,22453],{"className":22695},[76,442],[33,22697,508],{"className":22698},[507],[33,22700,22702],{"className":22701},[391],[33,22703,22705],{"className":22704,"style":3315},[395],[33,22706],{},[33,22708],{"className":22709,"style":638},[161],[33,22711,290],{"className":22712},[628],[33,22714],{"className":22715,"style":638},[161],[33,22717,22719,22722],{"className":22718},[76],[33,22720,11452],{"className":22721,"style":706},[76,77],[33,22723,22725],{"className":22724},[418],[33,22726,22728,22754],{"className":22727},[386,387],[33,22729,22731,22751],{"className":22730},[391],[33,22732,22734],{"className":22733,"style":22610},[395],[33,22735,22736,22739],{"style":11421},[33,22737],{"className":22738,"style":435},[403],[33,22740,22742],{"className":22741},[439,440,441,442],[33,22743,22745],{"className":22744},[76,442],[33,22746,22748],{"className":22747},[76,5118,442],[33,22749,22462],{"className":22750},[76,442],[33,22752,508],{"className":22753},[507],[33,22755,22757],{"className":22756},[391],[33,22758,22760],{"className":22759,"style":12605},[395],[33,22761],{},[33,22763,22446],{"className":22764},[76],[33,22766,508],{"className":22767},[507],[33,22769,22771],{"className":22770},[391],[33,22772,22774],{"className":22773,"style":13101},[395],[33,22775],{},[33,22777],{"className":22778},[456,2249]," で比べます。倍精度（float64）で計算し、",[33,22781,22783,22806],{"className":22782},[36],[33,22784,22786],{"className":22785},[40],[42,22787,22788],{"xmlns":44},[46,22789,22790,22803],{},[49,22791,22792],{},[237,22793,22794,22796],{},[130,22795,22111],{},[49,22797,22798,22800],{},[126,22799,290],{},[130,22801,22802],{},"7",[56,22804,22805],{"encoding":58},"10^{-7}",[33,22807,22809],{"className":22808,"ariaHidden":63},[62],[33,22810,22812,22815,22818],{"className":22811},[67],[33,22813],{"className":22814,"style":11078},[71],[33,22816,132],{"className":22817},[76],[33,22819,22821,22824],{"className":22820},[76],[33,22822,235],{"className":22823},[76],[33,22825,22827],{"className":22826},[418],[33,22828,22830],{"className":22829},[386],[33,22831,22833],{"className":22832},[391],[33,22834,22836],{"className":22835,"style":11078},[395],[33,22837,22838,22841],{"style":864},[33,22839],{"className":22840,"style":435},[403],[33,22842,22844],{"className":22843},[439,440,441,442],[33,22845,22847,22850],{"className":22846},[76,442],[33,22848,290],{"className":22849},[76,442],[33,22851,22802],{"className":22852},[76,442]," 程度以下なら実装はほぼ正しいと考えてよいでしょう。ReLU のように微分できない点を持つ関数では、その付近で誤差が大きく出ることがあります。",[10,22855,22856,22857,22886,22887,22921,22922,22925,22926,22954],{},"ただし、数値微分はパラメータ1つにつき損失を2回計算する必要があります。パラメータ数を ",[33,22858,22860,22874],{"className":22859},[36],[33,22861,22863],{"className":22862},[40],[42,22864,22865],{"xmlns":44},[46,22866,22867,22872],{},[49,22868,22869],{},[52,22870,22871],{},"P",[56,22873,22871],{"encoding":58},[33,22875,22877],{"className":22876,"ariaHidden":63},[62],[33,22878,22880,22883],{"className":22879},[67],[33,22881],{"className":22882,"style":72},[71],[33,22884,22871],{"className":22885,"style":557},[76,77]," とすると、順伝播を ",[33,22888,22890,22906],{"className":22889},[36],[33,22891,22893],{"className":22892},[40],[42,22894,22895],{"xmlns":44},[46,22896,22897,22903],{},[49,22898,22899,22901],{},[130,22900,10891],{},[52,22902,22871],{},[56,22904,22905],{"encoding":58},"2P",[33,22907,22909],{"className":22908,"ariaHidden":63},[62],[33,22910,22912,22915,22918],{"className":22911},[67],[33,22913],{"className":22914,"style":72},[71],[33,22916,10891],{"className":22917},[76],[33,22919,22871],{"className":22920,"style":557},[76,77]," 回行うことになります。一方バックプロパゲーションは、",[14,22923,22924],{},"順伝播1回と逆伝播1回（順伝播の定数倍の計算量）"," で全パラメータの勾配が求まります。",[33,22927,22929,22942],{"className":22928},[36],[33,22930,22932],{"className":22931},[40],[42,22933,22934],{"xmlns":44},[46,22935,22936,22940],{},[49,22937,22938],{},[52,22939,22871],{},[56,22941,22871],{"encoding":58},[33,22943,22945],{"className":22944,"ariaHidden":63},[62],[33,22946,22948,22951],{"className":22947},[67],[33,22949],{"className":22950,"style":72},[71],[33,22952,22871],{"className":22953,"style":557},[76,77]," が数百万〜数十億になる現代のネットワークでは、この差が決定的です。",[26,22956,22958],{"id":22957},"_9-numpy-で実装する","9. NumPy で実装する",[10,22960,22961],{},"XOR（2入力の排他的論理和）を、隠れ層4ユニット（シグモイド）と出力層（ソフトマックス + 交差エントロピー）で学習します。サンプルは列ベクトルとして横に並べています。",[22963,22964,22970],"pre",{"className":22965,"code":22966,"filename":22967,"language":22968,"meta":22969,"style":22969},"language-python shiki shiki-themes github-light github-dark","import numpy as np\n\nrng = np.random.default_rng(0)\n\n\ndef sigmoid(z):\n    return 1.0 \u002F (1.0 + np.exp(-z))\n\n\ndef softmax(z):\n    z = z - z.max(axis=0, keepdims=True)  # オーバーフロー対策\n    e = np.exp(z)\n    return e \u002F e.sum(axis=0, keepdims=True)\n\n\n# データは列ベクトルを横に並べる：X は (入力次元, m)、Y は one-hot で (クラス数, m)\nX = np.array([[0, 0, 1, 1],\n              [0, 1, 0, 1]], dtype=float)\nY = np.array([[1, 0, 0, 1],    # クラス0：XOR が 0\n              [0, 1, 1, 0]],   # クラス1：XOR が 1\n             dtype=float)\n\nn_in, n_hidden, n_out = 2, 4, 2\nparams = {\n    \"W1\": rng.normal(0, 1, (n_hidden, n_in)),\n    \"b1\": np.zeros((n_hidden, 1)),\n    \"W2\": rng.normal(0, 1, (n_out, n_hidden)),\n    \"b2\": np.zeros((n_out, 1)),\n}\n\n\ndef forward(p, X):\n    Z1 = p[\"W1\"] @ X + p[\"b1\"]\n    A1 = sigmoid(Z1)\n    Z2 = p[\"W2\"] @ A1 + p[\"b2\"]\n    A2 = softmax(Z2)\n    return A1, A2\n\n\ndef loss(A2, Y):\n    m = Y.shape[1]\n    return -np.sum(Y * np.log(A2 + 1e-12)) \u002F m\n\n\ndef backward(p, X, Y, A1, A2):\n    m = X.shape[1]\n    d2 = (A2 - Y) \u002F m                      # (BP1) softmax + 交差エントロピー\n    d1 = (p[\"W2\"].T @ d2) * A1 * (1 - A1)  # (BP2) σ'(z) = σ(z)(1 - σ(z))\n    return {\n        \"W2\": d2 @ A1.T,                   # (BP4)\n        \"b2\": d2.sum(axis=1, keepdims=True),  # (BP3) バッチ方向に和をとる\n        \"W1\": d1 @ X.T,\n        \"b1\": d1.sum(axis=1, keepdims=True),\n    }\n\n\neta = 1.0\nfor step in range(5001):\n    A1, A2 = forward(params, X)\n    grads = backward(params, X, Y, A1, A2)\n    for name in params:\n        params[name] -= eta * grads[name]\n    if step % 1000 == 0:\n        print(f\"step {step:4d}  loss = {loss(A2, Y):.4f}\")\n\n_, A2 = forward(params, X)\nprint(\"予測クラス:\", A2.argmax(axis=0))  # 正解は [0 1 1 0]\n","backprop_xor.py","python","",[22971,22972,22973,22991,22998,23015,23020,23025,23038,23068,23073,23078,23088,23130,23141,23170,23175,23180,23186,23214,23247,23277,23302,23314,23319,23340,23351,23370,23384,23401,23414,23420,23425,23430,23441,23474,23485,23514,23525,23533,23538,23543,23554,23569,23599,23604,23609,23620,23634,23658,23697,23704,23721,23750,23764,23790,23796,23801,23806,23817,23840,23851,23862,23876,23893,23916,23960,23965,23975],"code",{"__ignoreMap":22969},[33,22974,22977,22981,22985,22988],{"class":22975,"line":22976},"line",1,[33,22978,22980],{"class":22979},"szBVR","import",[33,22982,22984],{"class":22983},"sVt8B"," numpy ",[33,22986,22987],{"class":22979},"as",[33,22989,22990],{"class":22983}," np\n",[33,22992,22994],{"class":22975,"line":22993},2,[33,22995,22997],{"emptyLinePlaceholder":22996},true,"\n",[33,22999,23001,23004,23006,23009,23012],{"class":22975,"line":23000},3,[33,23002,23003],{"class":22983},"rng ",[33,23005,128],{"class":22979},[33,23007,23008],{"class":22983}," np.random.default_rng(",[33,23010,235],{"class":23011},"sj4cs",[33,23013,23014],{"class":22983},")\n",[33,23016,23018],{"class":22975,"line":23017},4,[33,23019,22997],{"emptyLinePlaceholder":22996},[33,23021,23023],{"class":22975,"line":23022},5,[33,23024,22997],{"emptyLinePlaceholder":22996},[33,23026,23028,23031,23035],{"class":22975,"line":23027},6,[33,23029,23030],{"class":22979},"def",[33,23032,23034],{"class":23033},"sScJk"," sigmoid",[33,23036,23037],{"class":22983},"(z):\n",[33,23039,23041,23044,23047,23050,23053,23056,23059,23062,23065],{"class":22975,"line":23040},7,[33,23042,23043],{"class":22979},"    return",[33,23045,23046],{"class":23011}," 1.0",[33,23048,23049],{"class":22979}," \u002F",[33,23051,23052],{"class":22983}," (",[33,23054,23055],{"class":23011},"1.0",[33,23057,23058],{"class":22979}," +",[33,23060,23061],{"class":22983}," np.exp(",[33,23063,23064],{"class":22979},"-",[33,23066,23067],{"class":22983},"z))\n",[33,23069,23071],{"class":22975,"line":23070},8,[33,23072,22997],{"emptyLinePlaceholder":22996},[33,23074,23076],{"class":22975,"line":23075},9,[33,23077,22997],{"emptyLinePlaceholder":22996},[33,23079,23081,23083,23086],{"class":22975,"line":23080},10,[33,23082,23030],{"class":22979},[33,23084,23085],{"class":23033}," softmax",[33,23087,23037],{"class":22983},[33,23089,23091,23094,23096,23099,23101,23104,23108,23110,23112,23115,23118,23120,23123,23126],{"class":22975,"line":23090},11,[33,23092,23093],{"class":22983},"    z ",[33,23095,128],{"class":22979},[33,23097,23098],{"class":22983}," z ",[33,23100,23064],{"class":22979},[33,23102,23103],{"class":22983}," z.max(",[33,23105,23107],{"class":23106},"s4XuR","axis",[33,23109,128],{"class":22979},[33,23111,235],{"class":23011},[33,23113,23114],{"class":22983},", ",[33,23116,23117],{"class":23106},"keepdims",[33,23119,128],{"class":22979},[33,23121,23122],{"class":23011},"True",[33,23124,23125],{"class":22983},")  ",[33,23127,23129],{"class":23128},"sJ8bj","# オーバーフロー対策\n",[33,23131,23133,23136,23138],{"class":22975,"line":23132},12,[33,23134,23135],{"class":22983},"    e ",[33,23137,128],{"class":22979},[33,23139,23140],{"class":22983}," np.exp(z)\n",[33,23142,23144,23146,23149,23151,23154,23156,23158,23160,23162,23164,23166,23168],{"class":22975,"line":23143},13,[33,23145,23043],{"class":22979},[33,23147,23148],{"class":22983}," e ",[33,23150,8905],{"class":22979},[33,23152,23153],{"class":22983}," e.sum(",[33,23155,23107],{"class":23106},[33,23157,128],{"class":22979},[33,23159,235],{"class":23011},[33,23161,23114],{"class":22983},[33,23163,23117],{"class":23106},[33,23165,128],{"class":22979},[33,23167,23122],{"class":23011},[33,23169,23014],{"class":22983},[33,23171,23173],{"class":22975,"line":23172},14,[33,23174,22997],{"emptyLinePlaceholder":22996},[33,23176,23178],{"class":22975,"line":23177},15,[33,23179,22997],{"emptyLinePlaceholder":22996},[33,23181,23183],{"class":22975,"line":23182},16,[33,23184,23185],{"class":23128},"# データは列ベクトルを横に並べる：X は (入力次元, m)、Y は one-hot で (クラス数, m)\n",[33,23187,23189,23192,23194,23197,23199,23201,23203,23205,23207,23209,23211],{"class":22975,"line":23188},17,[33,23190,23191],{"class":22983},"X ",[33,23193,128],{"class":22979},[33,23195,23196],{"class":22983}," np.array([[",[33,23198,235],{"class":23011},[33,23200,23114],{"class":22983},[33,23202,235],{"class":23011},[33,23204,23114],{"class":22983},[33,23206,132],{"class":23011},[33,23208,23114],{"class":22983},[33,23210,132],{"class":23011},[33,23212,23213],{"class":22983},"],\n",[33,23215,23217,23220,23222,23224,23226,23228,23230,23232,23234,23237,23240,23242,23245],{"class":22975,"line":23216},18,[33,23218,23219],{"class":22983},"              [",[33,23221,235],{"class":23011},[33,23223,23114],{"class":22983},[33,23225,132],{"class":23011},[33,23227,23114],{"class":22983},[33,23229,235],{"class":23011},[33,23231,23114],{"class":22983},[33,23233,132],{"class":23011},[33,23235,23236],{"class":22983},"]], ",[33,23238,23239],{"class":23106},"dtype",[33,23241,128],{"class":22979},[33,23243,23244],{"class":23011},"float",[33,23246,23014],{"class":22983},[33,23248,23250,23253,23255,23257,23259,23261,23263,23265,23267,23269,23271,23274],{"class":22975,"line":23249},19,[33,23251,23252],{"class":22983},"Y ",[33,23254,128],{"class":22979},[33,23256,23196],{"class":22983},[33,23258,132],{"class":23011},[33,23260,23114],{"class":22983},[33,23262,235],{"class":23011},[33,23264,23114],{"class":22983},[33,23266,235],{"class":23011},[33,23268,23114],{"class":22983},[33,23270,132],{"class":23011},[33,23272,23273],{"class":22983},"],    ",[33,23275,23276],{"class":23128},"# クラス0：XOR が 0\n",[33,23278,23280,23282,23284,23286,23288,23290,23292,23294,23296,23299],{"class":22975,"line":23279},20,[33,23281,23219],{"class":22983},[33,23283,235],{"class":23011},[33,23285,23114],{"class":22983},[33,23287,132],{"class":23011},[33,23289,23114],{"class":22983},[33,23291,132],{"class":23011},[33,23293,23114],{"class":22983},[33,23295,235],{"class":23011},[33,23297,23298],{"class":22983},"]],   ",[33,23300,23301],{"class":23128},"# クラス1：XOR が 1\n",[33,23303,23305,23308,23310,23312],{"class":22975,"line":23304},21,[33,23306,23307],{"class":23106},"             dtype",[33,23309,128],{"class":22979},[33,23311,23244],{"class":23011},[33,23313,23014],{"class":22983},[33,23315,23317],{"class":22975,"line":23316},22,[33,23318,22997],{"emptyLinePlaceholder":22996},[33,23320,23322,23325,23327,23330,23332,23335,23337],{"class":22975,"line":23321},23,[33,23323,23324],{"class":22983},"n_in, n_hidden, n_out ",[33,23326,128],{"class":22979},[33,23328,23329],{"class":23011}," 2",[33,23331,23114],{"class":22983},[33,23333,23334],{"class":23011},"4",[33,23336,23114],{"class":22983},[33,23338,23339],{"class":23011},"2\n",[33,23341,23343,23346,23348],{"class":22975,"line":23342},24,[33,23344,23345],{"class":22983},"params ",[33,23347,128],{"class":22979},[33,23349,23350],{"class":22983}," {\n",[33,23352,23354,23358,23361,23363,23365,23367],{"class":22975,"line":23353},25,[33,23355,23357],{"class":23356},"sZZnC","    \"W1\"",[33,23359,23360],{"class":22983},": rng.normal(",[33,23362,235],{"class":23011},[33,23364,23114],{"class":22983},[33,23366,132],{"class":23011},[33,23368,23369],{"class":22983},", (n_hidden, n_in)),\n",[33,23371,23373,23376,23379,23381],{"class":22975,"line":23372},26,[33,23374,23375],{"class":23356},"    \"b1\"",[33,23377,23378],{"class":22983},": np.zeros((n_hidden, ",[33,23380,132],{"class":23011},[33,23382,23383],{"class":22983},")),\n",[33,23385,23387,23390,23392,23394,23396,23398],{"class":22975,"line":23386},27,[33,23388,23389],{"class":23356},"    \"W2\"",[33,23391,23360],{"class":22983},[33,23393,235],{"class":23011},[33,23395,23114],{"class":22983},[33,23397,132],{"class":23011},[33,23399,23400],{"class":22983},", (n_out, n_hidden)),\n",[33,23402,23404,23407,23410,23412],{"class":22975,"line":23403},28,[33,23405,23406],{"class":23356},"    \"b2\"",[33,23408,23409],{"class":22983},": np.zeros((n_out, ",[33,23411,132],{"class":23011},[33,23413,23383],{"class":22983},[33,23415,23417],{"class":22975,"line":23416},29,[33,23418,23419],{"class":22983},"}\n",[33,23421,23423],{"class":22975,"line":23422},30,[33,23424,22997],{"emptyLinePlaceholder":22996},[33,23426,23428],{"class":22975,"line":23427},31,[33,23429,22997],{"emptyLinePlaceholder":22996},[33,23431,23433,23435,23438],{"class":22975,"line":23432},32,[33,23434,23030],{"class":22979},[33,23436,23437],{"class":23033}," forward",[33,23439,23440],{"class":22983},"(p, X):\n",[33,23442,23444,23447,23449,23452,23455,23458,23461,23464,23466,23468,23471],{"class":22975,"line":23443},33,[33,23445,23446],{"class":22983},"    Z1 ",[33,23448,128],{"class":22979},[33,23450,23451],{"class":22983}," p[",[33,23453,23454],{"class":23356},"\"W1\"",[33,23456,23457],{"class":22983},"] ",[33,23459,23460],{"class":22979},"@",[33,23462,23463],{"class":22983}," X ",[33,23465,297],{"class":22979},[33,23467,23451],{"class":22983},[33,23469,23470],{"class":23356},"\"b1\"",[33,23472,23473],{"class":22983},"]\n",[33,23475,23477,23480,23482],{"class":22975,"line":23476},34,[33,23478,23479],{"class":22983},"    A1 ",[33,23481,128],{"class":22979},[33,23483,23484],{"class":22983}," sigmoid(Z1)\n",[33,23486,23488,23491,23493,23495,23498,23500,23502,23505,23507,23509,23512],{"class":22975,"line":23487},35,[33,23489,23490],{"class":22983},"    Z2 ",[33,23492,128],{"class":22979},[33,23494,23451],{"class":22983},[33,23496,23497],{"class":23356},"\"W2\"",[33,23499,23457],{"class":22983},[33,23501,23460],{"class":22979},[33,23503,23504],{"class":22983}," A1 ",[33,23506,297],{"class":22979},[33,23508,23451],{"class":22983},[33,23510,23511],{"class":23356},"\"b2\"",[33,23513,23473],{"class":22983},[33,23515,23517,23520,23522],{"class":22975,"line":23516},36,[33,23518,23519],{"class":22983},"    A2 ",[33,23521,128],{"class":22979},[33,23523,23524],{"class":22983}," softmax(Z2)\n",[33,23526,23528,23530],{"class":22975,"line":23527},37,[33,23529,23043],{"class":22979},[33,23531,23532],{"class":22983}," A1, A2\n",[33,23534,23536],{"class":22975,"line":23535},38,[33,23537,22997],{"emptyLinePlaceholder":22996},[33,23539,23541],{"class":22975,"line":23540},39,[33,23542,22997],{"emptyLinePlaceholder":22996},[33,23544,23546,23548,23551],{"class":22975,"line":23545},40,[33,23547,23030],{"class":22979},[33,23549,23550],{"class":23033}," loss",[33,23552,23553],{"class":22983},"(A2, Y):\n",[33,23555,23557,23560,23562,23565,23567],{"class":22975,"line":23556},41,[33,23558,23559],{"class":22983},"    m ",[33,23561,128],{"class":22979},[33,23563,23564],{"class":22983}," Y.shape[",[33,23566,132],{"class":23011},[33,23568,23473],{"class":22983},[33,23570,23572,23574,23577,23580,23583,23586,23588,23591,23594,23596],{"class":22975,"line":23571},42,[33,23573,23043],{"class":22979},[33,23575,23576],{"class":22979}," -",[33,23578,23579],{"class":22983},"np.sum(Y ",[33,23581,23582],{"class":22979},"*",[33,23584,23585],{"class":22983}," np.log(A2 ",[33,23587,297],{"class":22979},[33,23589,23590],{"class":23011}," 1e-12",[33,23592,23593],{"class":22983},")) ",[33,23595,8905],{"class":22979},[33,23597,23598],{"class":22983}," m\n",[33,23600,23602],{"class":22975,"line":23601},43,[33,23603,22997],{"emptyLinePlaceholder":22996},[33,23605,23607],{"class":22975,"line":23606},44,[33,23608,22997],{"emptyLinePlaceholder":22996},[33,23610,23612,23614,23617],{"class":22975,"line":23611},45,[33,23613,23030],{"class":22979},[33,23615,23616],{"class":23033}," backward",[33,23618,23619],{"class":22983},"(p, X, Y, A1, A2):\n",[33,23621,23623,23625,23627,23630,23632],{"class":22975,"line":23622},46,[33,23624,23559],{"class":22983},[33,23626,128],{"class":22979},[33,23628,23629],{"class":22983}," X.shape[",[33,23631,132],{"class":23011},[33,23633,23473],{"class":22983},[33,23635,23637,23640,23642,23645,23647,23650,23652,23655],{"class":22975,"line":23636},47,[33,23638,23639],{"class":22983},"    d2 ",[33,23641,128],{"class":22979},[33,23643,23644],{"class":22983}," (A2 ",[33,23646,23064],{"class":22979},[33,23648,23649],{"class":22983}," Y) ",[33,23651,8905],{"class":22979},[33,23653,23654],{"class":22983}," m                      ",[33,23656,23657],{"class":23128},"# (BP1) softmax + 交差エントロピー\n",[33,23659,23661,23664,23666,23669,23671,23674,23676,23679,23681,23683,23685,23687,23689,23691,23694],{"class":22975,"line":23660},48,[33,23662,23663],{"class":22983},"    d1 ",[33,23665,128],{"class":22979},[33,23667,23668],{"class":22983}," (p[",[33,23670,23497],{"class":23356},[33,23672,23673],{"class":22983},"].T ",[33,23675,23460],{"class":22979},[33,23677,23678],{"class":22983}," d2) ",[33,23680,23582],{"class":22979},[33,23682,23504],{"class":22983},[33,23684,23582],{"class":22979},[33,23686,23052],{"class":22983},[33,23688,132],{"class":23011},[33,23690,23576],{"class":22979},[33,23692,23693],{"class":22983}," A1)  ",[33,23695,23696],{"class":23128},"# (BP2) σ'(z) = σ(z)(1 - σ(z))\n",[33,23698,23700,23702],{"class":22975,"line":23699},49,[33,23701,23043],{"class":22979},[33,23703,23350],{"class":22983},[33,23705,23707,23710,23713,23715,23718],{"class":22975,"line":23706},50,[33,23708,23709],{"class":23356},"        \"W2\"",[33,23711,23712],{"class":22983},": d2 ",[33,23714,23460],{"class":22979},[33,23716,23717],{"class":22983}," A1.T,                   ",[33,23719,23720],{"class":23128},"# (BP4)\n",[33,23722,23724,23727,23730,23732,23734,23736,23738,23740,23742,23744,23747],{"class":22975,"line":23723},51,[33,23725,23726],{"class":23356},"        \"b2\"",[33,23728,23729],{"class":22983},": d2.sum(",[33,23731,23107],{"class":23106},[33,23733,128],{"class":22979},[33,23735,132],{"class":23011},[33,23737,23114],{"class":22983},[33,23739,23117],{"class":23106},[33,23741,128],{"class":22979},[33,23743,23122],{"class":23011},[33,23745,23746],{"class":22983},"),  ",[33,23748,23749],{"class":23128},"# (BP3) バッチ方向に和をとる\n",[33,23751,23753,23756,23759,23761],{"class":22975,"line":23752},52,[33,23754,23755],{"class":23356},"        \"W1\"",[33,23757,23758],{"class":22983},": d1 ",[33,23760,23460],{"class":22979},[33,23762,23763],{"class":22983}," X.T,\n",[33,23765,23767,23770,23773,23775,23777,23779,23781,23783,23785,23787],{"class":22975,"line":23766},53,[33,23768,23769],{"class":23356},"        \"b1\"",[33,23771,23772],{"class":22983},": d1.sum(",[33,23774,23107],{"class":23106},[33,23776,128],{"class":22979},[33,23778,132],{"class":23011},[33,23780,23114],{"class":22983},[33,23782,23117],{"class":23106},[33,23784,128],{"class":22979},[33,23786,23122],{"class":23011},[33,23788,23789],{"class":22983},"),\n",[33,23791,23793],{"class":22975,"line":23792},54,[33,23794,23795],{"class":22983},"    }\n",[33,23797,23799],{"class":22975,"line":23798},55,[33,23800,22997],{"emptyLinePlaceholder":22996},[33,23802,23804],{"class":22975,"line":23803},56,[33,23805,22997],{"emptyLinePlaceholder":22996},[33,23807,23809,23812,23814],{"class":22975,"line":23808},57,[33,23810,23811],{"class":22983},"eta ",[33,23813,128],{"class":22979},[33,23815,23816],{"class":23011}," 1.0\n",[33,23818,23820,23823,23826,23829,23832,23834,23837],{"class":22975,"line":23819},58,[33,23821,23822],{"class":22979},"for",[33,23824,23825],{"class":22983}," step ",[33,23827,23828],{"class":22979},"in",[33,23830,23831],{"class":23011}," range",[33,23833,248],{"class":22983},[33,23835,23836],{"class":23011},"5001",[33,23838,23839],{"class":22983},"):\n",[33,23841,23843,23846,23848],{"class":22975,"line":23842},59,[33,23844,23845],{"class":22983},"    A1, A2 ",[33,23847,128],{"class":22979},[33,23849,23850],{"class":22983}," forward(params, X)\n",[33,23852,23854,23857,23859],{"class":22975,"line":23853},60,[33,23855,23856],{"class":22983},"    grads ",[33,23858,128],{"class":22979},[33,23860,23861],{"class":22983}," backward(params, X, Y, A1, A2)\n",[33,23863,23865,23868,23871,23873],{"class":22975,"line":23864},61,[33,23866,23867],{"class":22979},"    for",[33,23869,23870],{"class":22983}," name ",[33,23872,23828],{"class":22979},[33,23874,23875],{"class":22983}," params:\n",[33,23877,23879,23882,23885,23888,23890],{"class":22975,"line":23878},62,[33,23880,23881],{"class":22983},"        params[name] ",[33,23883,23884],{"class":22979},"-=",[33,23886,23887],{"class":22983}," eta ",[33,23889,23582],{"class":22979},[33,23891,23892],{"class":22983}," grads[name]\n",[33,23894,23896,23899,23901,23904,23907,23910,23913],{"class":22975,"line":23895},63,[33,23897,23898],{"class":22979},"    if",[33,23900,23825],{"class":22983},[33,23902,23903],{"class":22979},"%",[33,23905,23906],{"class":23011}," 1000",[33,23908,23909],{"class":22979}," ==",[33,23911,23912],{"class":23011}," 0",[33,23914,23915],{"class":22983},":\n",[33,23917,23919,23922,23924,23927,23930,23933,23936,23939,23942,23945,23947,23950,23953,23955,23958],{"class":22975,"line":23918},64,[33,23920,23921],{"class":23011},"        print",[33,23923,248],{"class":22983},[33,23925,23926],{"class":22979},"f",[33,23928,23929],{"class":23356},"\"step ",[33,23931,23932],{"class":23011},"{",[33,23934,23935],{"class":22983},"step",[33,23937,23938],{"class":22979},":4d",[33,23940,23941],{"class":23011},"}",[33,23943,23944],{"class":23356},"  loss = ",[33,23946,23932],{"class":23011},[33,23948,23949],{"class":22983},"loss(A2, Y)",[33,23951,23952],{"class":22979},":.4f",[33,23954,23941],{"class":23011},[33,23956,23957],{"class":23356},"\"",[33,23959,23014],{"class":22983},[33,23961,23963],{"class":22975,"line":23962},65,[33,23964,22997],{"emptyLinePlaceholder":22996},[33,23966,23968,23971,23973],{"class":22975,"line":23967},66,[33,23969,23970],{"class":22983},"_, A2 ",[33,23972,128],{"class":22979},[33,23974,23850],{"class":22983},[33,23976,23978,23981,23983,23986,23989,23991,23993,23995,23998],{"class":22975,"line":23977},67,[33,23979,23980],{"class":23011},"print",[33,23982,248],{"class":22983},[33,23984,23985],{"class":23356},"\"予測クラス:\"",[33,23987,23988],{"class":22983},", A2.argmax(",[33,23990,23107],{"class":23106},[33,23992,128],{"class":22979},[33,23994,235],{"class":23011},[33,23996,23997],{"class":22983},"))  ",[33,23999,24000],{"class":23128},"# 正解は [0 1 1 0]\n",[10,24002,24003],{},"実行結果は次のとおりです（NumPy 2.5、乱数シード 0）。",[22963,24005,24010],{"className":24006,"code":24008,"filename":24009,"language":5118,"meta":22969},[24007],"language-text","step    0  loss = 0.8358\nstep 1000  loss = 0.0085\nstep 2000  loss = 0.0034\nstep 3000  loss = 0.0021\nstep 4000  loss = 0.0015\nstep 5000  loss = 0.0012\n予測クラス: [0 1 1 0]\n","実行結果",[22971,24011,24008],{"__ignoreMap":22969},[10,24013,24014,24015,24110],{},"同じコードで中心差分による勾配チェックを行うと、最大相対誤差は約 ",[33,24016,24018,24045],{"className":24017},[36],[33,24019,24021],{"className":24020},[40],[42,24022,24023],{"xmlns":44},[46,24024,24025,24042],{},[49,24026,24027,24030,24032],{},[130,24028,24029],{},"1.7",[126,24031,18415],{},[237,24033,24034,24036],{},[130,24035,22111],{},[49,24037,24038,24040],{},[126,24039,290],{},[130,24041,22111],{},[56,24043,24044],{"encoding":58},"1.7 \\times 10^{-10}",[33,24046,24048,24066],{"className":24047,"ariaHidden":63},[62],[33,24049,24051,24054,24057,24060,24063],{"className":24050},[67],[33,24052],{"className":24053,"style":19545},[71],[33,24055,24029],{"className":24056},[76],[33,24058],{"className":24059,"style":638},[161],[33,24061,18415],{"className":24062},[628],[33,24064],{"className":24065,"style":638},[161],[33,24067,24069,24072,24075],{"className":24068},[67],[33,24070],{"className":24071,"style":11078},[71],[33,24073,132],{"className":24074},[76],[33,24076,24078,24081],{"className":24077},[76],[33,24079,235],{"className":24080},[76],[33,24082,24084],{"className":24083},[418],[33,24085,24087],{"className":24086},[386],[33,24088,24090],{"className":24089},[391],[33,24091,24093],{"className":24092,"style":11078},[395],[33,24094,24095,24098],{"style":864},[33,24096],{"className":24097,"style":435},[403],[33,24099,24101],{"className":24100},[439,440,441,442],[33,24102,24104,24107],{"className":24103},[76,442],[33,24105,290],{"className":24106},[76,442],[33,24108,22111],{"className":24109},[76,442]," でした。逆伝播の実装が正しいことが確認できます。",[10,24112,24113,24114,24142,24143,3188,24146,24174],{},"損失を ",[33,24115,24117,24130],{"className":24116},[36],[33,24118,24120],{"className":24119},[40],[42,24121,24122],{"xmlns":44},[46,24123,24124,24128],{},[49,24125,24126],{},[52,24127,12075],{},[56,24129,12075],{"encoding":58},[33,24131,24133],{"className":24132,"ariaHidden":63},[62],[33,24134,24136,24139],{"className":24135},[67],[33,24137],{"className":24138,"style":1185},[71],[33,24140,12075],{"className":24141},[76,77]," 個の平均にしているので、",[22971,24144,24145],{},"d2",[33,24147,24149,24162],{"className":24148},[36],[33,24150,24152],{"className":24151},[40],[42,24153,24154],{"xmlns":44},[46,24155,24156,24160],{},[49,24157,24158],{},[52,24159,12075],{},[56,24161,12075],{"encoding":58},[33,24163,24165],{"className":24164,"ariaHidden":63},[62],[33,24166,24168,24171],{"className":24167},[67],[33,24169],{"className":24170,"style":1185},[71],[33,24172,12075],{"className":24173},[76,77]," で割っています。こうすると (BP3) と (BP4) の和が、自動的にサンプルごとの勾配の平均になります。",[26,24176,24178],{"id":24177},"_10-少しだけ歴史","10. 少しだけ歴史",[16989,24180,24181,24187,24193],{},[15863,24182,24183,24186],{},[14,24184,24185],{},"1970年","：リンナインマーが、今日のリバースモード自動微分にあたる方法を修士論文で示しました。",[15863,24188,24189,24192],{},[14,24190,24191],{},"1974年","：ワーボスが、博士論文でこの方法をニューラルネットワークの学習に応用することを論じました。",[15863,24194,24195,24198],{},[14,24196,24197],{},"1986年","：ラメルハート、ヒントン、ウィリアムズが Nature 誌の論文で、多層ネットワークが逆伝播によって有用な内部表現を学習できることを示しました。これにより手法が広く知られるようになります。",[10,24200,24201,24202,24205],{},"現在の PyTorch や JAX などのフレームワークは、ここで導いた計算を ",[14,24203,24204],{},"計算グラフ上のリバースモード自動微分"," として一般化し、自動で行っています。",[26,24207,24208],{"id":24208},"まとめ",[16989,24210,24211,24218,24389,24451],{},[15863,24212,24213,24214,24217],{},"バックプロパゲーションは、連鎖律を ",[14,24215,24216],{},"出力側から効率よく"," 適用する方法です。",[15863,24219,24220,24221,24388],{},"誤差 ",[33,24222,24224,24270],{"className":24223},[36],[33,24225,24227],{"className":24226},[40],[42,24228,24229],{"xmlns":44},[46,24230,24231,24267],{},[49,24232,24233,24245,24247,24249,24251,24253,24255],{},[237,24234,24235,24237],{},[52,24236,2581],{"mathvariant":2580},[49,24238,24239,24241,24243],{},[126,24240,248],{"stretchy":247},[52,24242,93],{},[126,24244,253],{"stretchy":247},[126,24246,128],{},[52,24248,2174],{"mathvariant":2173},[52,24250,54],{"mathvariant":1369},[52,24252,8905],{"mathvariant":2173},[52,24254,2174],{"mathvariant":2173},[237,24256,24257,24259],{},[52,24258,242],{"mathvariant":241},[49,24260,24261,24263,24265],{},[126,24262,248],{"stretchy":247},[52,24264,93],{},[126,24266,253],{"stretchy":247},[56,24268,24269],{"encoding":58},"\\boldsymbol{\\delta}^{(l)} = \\partial \\mathcal{L} \u002F \\partial \\mathbf{z}^{(l)}",[33,24271,24273,24332],{"className":24272,"ariaHidden":63},[62],[33,24274,24276,24279,24323,24326,24329],{"className":24275},[67],[33,24277],{"className":24278,"style":2602},[71],[33,24280,24282,24291],{"className":24281},[76],[33,24283,24285],{"className":24284},[76],[33,24286,24288],{"className":24287},[76],[33,24289,2581],{"className":24290,"style":2616},[76,2615],[33,24292,24294],{"className":24293},[418],[33,24295,24297],{"className":24296},[386],[33,24298,24300],{"className":24299},[391],[33,24301,24303],{"className":24302,"style":2602},[395],[33,24304,24305,24308],{"style":2631},[33,24306],{"className":24307,"style":435},[403],[33,24309,24311],{"className":24310},[439,440,441,442],[33,24312,24314,24317,24320],{"className":24313},[76,442],[33,24315,248],{"className":24316},[449,442],[33,24318,93],{"className":24319,"style":109},[76,77,442],[33,24321,253],{"className":24322},[456,442],[33,24324],{"className":24325,"style":162},[161],[33,24327,128],{"className":24328},[166],[33,24330],{"className":24331,"style":162},[161],[33,24333,24335,24338,24341,24344,24347,24350],{"className":24334},[67],[33,24336],{"className":24337,"style":11783},[71],[33,24339,2174],{"className":24340,"style":2276},[76],[33,24342,54],{"className":24343},[76,1400],[33,24345,8905],{"className":24346},[76],[33,24348,2174],{"className":24349,"style":2276},[76],[33,24351,24353,24356],{"className":24352},[76],[33,24354,242],{"className":24355},[76,414],[33,24357,24359],{"className":24358},[418],[33,24360,24362],{"className":24361},[386],[33,24363,24365],{"className":24364},[391],[33,24366,24368],{"className":24367,"style":843},[395],[33,24369,24370,24373],{"style":864},[33,24371],{"className":24372,"style":435},[403],[33,24374,24376],{"className":24375},[439,440,441,442],[33,24377,24379,24382,24385],{"className":24378},[76,442],[33,24380,248],{"className":24381},[449,442],[33,24383,93],{"className":24384,"style":109},[76,77,442],[33,24386,253],{"className":24387},[456,442]," を導入すると、すべてが4つの式 (BP1)〜(BP4) にまとまります。",[15863,24390,24391,24392,24450],{},"逆伝播では ",[33,24393,24395,24412],{"className":24394},[36],[33,24396,24398],{"className":24397},[40],[42,24399,24400],{"xmlns":44},[46,24401,24402,24410],{},[49,24403,24404],{},[237,24405,24406,24408],{},[52,24407,268],{},[52,24409,8081],{"mathvariant":2173},[56,24411,8827],{"encoding":58},[33,24413,24415],{"className":24414,"ariaHidden":63},[62],[33,24416,24418,24421],{"className":24417},[67],[33,24419],{"className":24420,"style":8837},[71],[33,24422,24424,24427],{"className":24423},[76],[33,24425,268],{"className":24426,"style":557},[76,77],[33,24428,24430],{"className":24429},[418],[33,24431,24433],{"className":24432},[386],[33,24434,24436],{"className":24435},[391],[33,24437,24439],{"className":24438,"style":8837},[395],[33,24440,24441,24444],{"style":864},[33,24442],{"className":24443,"style":435},[403],[33,24445,24447],{"className":24446},[439,440,441,442],[33,24448,8081],{"className":24449},[76,442]," を掛けて誤差を後ろへ送り、各重みの勾配は「出口の誤差 × 入口の活性」になります。",[15863,24452,24453],{},"計算量は順伝播の定数倍で、数値微分よりはるかに効率的です。実装したら勾配チェックで確かめましょう。",[24455,24456,24457],"style",{},"html pre.shiki code .szBVR, html code.shiki .szBVR{--shiki-default:#D73A49;--shiki-dark:#F97583}html pre.shiki code .sVt8B, html code.shiki .sVt8B{--shiki-default:#24292E;--shiki-dark:#E1E4E8}html pre.shiki code .sj4cs, html code.shiki .sj4cs{--shiki-default:#005CC5;--shiki-dark:#79B8FF}html pre.shiki code .sScJk, html code.shiki .sScJk{--shiki-default:#6F42C1;--shiki-dark:#B392F0}html pre.shiki code .s4XuR, html code.shiki .s4XuR{--shiki-default:#E36209;--shiki-dark:#FFAB70}html pre.shiki code .sJ8bj, html code.shiki .sJ8bj{--shiki-default:#6A737D;--shiki-dark:#6A737D}html pre.shiki code .sZZnC, html code.shiki .sZZnC{--shiki-default:#032F62;--shiki-dark:#9ECBFF}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: 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var(--shiki-dark-text-decoration);}",{"title":22969,"searchDepth":22993,"depth":22993,"links":24459},[24460,24461,24462,24463,24469,24470,24471,24472,24473,24474,24475],{"id":28,"depth":22993,"text":29},{"id":2522,"depth":22993,"text":2523},{"id":3195,"depth":22993,"text":3196},{"id":3891,"depth":22993,"text":3892,"children":24464},[24465,24466,24467,24468],{"id":3896,"depth":23000,"text":3897},{"id":5134,"depth":23000,"text":5135},{"id":8871,"depth":23000,"text":8872},{"id":9597,"depth":23000,"text":9598},{"id":10764,"depth":22993,"text":10765},{"id":14284,"depth":22993,"text":14285},{"id":16983,"depth":22993,"text":16984},{"id":21793,"depth":22993,"text":21794},{"id":22957,"depth":22993,"text":22958},{"id":24177,"depth":22993,"text":24178},{"id":24208,"depth":22993,"text":24208},"2026-11-14","ニューラルネットワークの学習を支えるバックプロパゲーションを、連鎖律から4つの基本式を導くところまで丁寧に解説します。数値例と NumPy の実装つき。",false,"md",null,{},"\u002Fblog\u002F001-backpropagation",{"title":5,"description":24477},"blog\u002F001-backpropagation",[24486,42],"machine-learning","npliyqqbfuymSjVBHlndUpzosXTDwJ4LbXTfEq5x9LE",[24489,24496,24504,24510],{"path":24490,"title":24491,"no":23017,"date":24476,"updated":24480,"image":24480,"description":24492,"tags":24493,"pinned":24478,"draft":24478},"\u002Fblog\u002F004-completeness-theorem-proofs","完全性定理の2つの証明 ― ゲーデル流とヘンキン流","一階述語論理の完全性定理を、ゲーデルによる元の証明（1929–1930年）と、今日の教科書の標準であるヘンキンの証明（1949年）の2つの道筋で解説します。どちらも「記号からモデルを作る」点は同じですが、足場の置き方が大きく異なります。",[24494,42,24495],"logic","history",{"path":24497,"title":24498,"no":23000,"date":24476,"updated":24480,"image":24480,"description":24499,"tags":24500,"pinned":24478,"draft":24478},"\u002Fblog\u002F003-design-patterns","デザインパターン再入門 ― GoF の23パターンを TypeScript で読み直す","GoF の23パターンの全体像を整理し、現代の TypeScript やフロントエンド開発でも役立つ6つのパターンを、動くコードとともに解説します。使いすぎの落とし穴と、言語やフレームワークに溶け込んだパターンの見つけ方も。",[24501,24502,24503],"design-pattern","programming","typescript",{"path":24505,"title":24506,"no":22993,"date":24476,"updated":24480,"image":24480,"description":24507,"tags":24508,"pinned":24478,"draft":24478},"\u002Fblog\u002F002-mathematical-logic-timeline","年表で見る20世紀の数理論理学 ― ゲーデルとタルスキ","不完全性定理と真理の定義不可能性定理を軸に、20世紀の数理論理学の流れを年表で整理します。",[24494,24495,24509],"timeline",{"path":24482,"title":5,"no":22976,"date":24476,"updated":24480,"image":24480,"description":24477,"tags":24511,"pinned":24478,"draft":24478},[24486,42],1794635675663]