[{"data":1,"prerenderedAt":2840},["ShallowReactive",2],{"article-9":3},{"id":4,"title":5,"body":6,"create":2828,"description":2819,"extension":2829,"labels":2830,"locked":2832,"meta":2833,"navigation":2834,"path":2835,"seo":2836,"stem":2837,"update":2838,"__hash__":2839},"articles/article/9.md","可分离卷积",{"type":7,"value":8,"toc":2818},"minimark",[9,13,249,251,254,258,460,1272,1564,1567,1570,1772,2222,2815],[10,11,12],"h2",{"id":12},"卷积神经网络中的卷积",[14,15,16,17,91,92,144,145,195,196,248],"p",{},"卷积神经网络中的卷积一般是用于提取图像中的特征，卷积运算中包括两个矩阵，卷积核和图像。其中，卷积核一般是行列式，它的行和列都是等长的。图像是由一个个像素点组成的，如果我们将图像看做一个矩阵，并且以左上角作为原点建立笛卡尔坐标系，向右和向下分别为\nx 轴和 y 轴的正方向，卷积核也是这样。那么对于一个 ",[18,19,22,51],"span",{"className":20},[21],"katex",[18,23,26],{"className":24},[25],"katex-mathml",[27,28,30],"math",{"xmlns":29},"http://www.w3.org/1998/Math/MathML",[31,32,33,46],"semantics",{},[34,35,36,40,44],"mrow",{},[37,38,39],"mn",{},"8",[41,42,43],"mo",{},"×",[37,45,39],{},[47,48,50],"annotation",{"encoding":49},"application/x-tex","8 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\\times3",[18,115,117,135],{"className":116,"ariaHidden":55},[54],[18,118,120,123,126,129,132],{"className":119},[59],[18,121],{"className":122,"style":64},[63],[18,124,106],{"className":125},[68],[18,127],{"className":128,"style":73},[72],[18,130,43],{"className":131},[77],[18,133],{"className":134,"style":73},[72],[18,136,138,141],{"className":137},[59],[18,139],{"className":140,"style":87},[63],[18,142,106],{"className":143},[68],"\n的卷积核对其进行卷积运算，先将图片和卷积核的原点对齐，对 ",[18,146,148,165],{"className":147},[21],[18,149,151],{"className":150},[25],[27,152,153],{"xmlns":29},[31,154,155,163],{},[34,156,157,159,161],{},[37,158,106],{},[41,160,43],{},[37,162,106],{},[47,164,113],{"encoding":49},[18,166,168,186],{"className":167,"ariaHidden":55},[54],[18,169,171,174,177,180,183],{"className":170},[59],[18,172],{"className":173,"style":64},[63],[18,175,106],{"className":176},[68],[18,178],{"className":179,"style":73},[72],[18,181,43],{"className":182},[77],[18,184],{"className":185,"style":73},[72],[18,187,189,192],{"className":188},[59],[18,190],{"className":191,"style":87},[63],[18,193,106],{"className":194},[68]," 范围内图片中的像素一一与卷积核中的元素进行乘法运算，然后将\n9 个元素相加得到最终的结果，最终结果的位置放在卷积核的中心位置。如果步长为\n1，也就是我的卷积核每次只移动一个像素，那么卷积核就会计算一次移动一次，从左到右，从上到下，直到卷积核的右下角与图像右下角重合为止。最终运算出来的结果是一个 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的两个小卷积核：",[18,461,464],{"className":462},[463],"katex-display",[18,465,467,643],{"className":466},[21],[18,468,470],{"className":469},[25],[27,471,473],{"xmlns":29,"display":472},"block",[31,474,475,640],{},[34,476,477,570,573,606,608],{},[34,478,479,482,567],{},[41,480,481],{"fence":55},"[",[483,484,488,518,543],"mtable",{"rowspacing":485,"columnalign":486,"columnspacing":487},"0.16em","center center 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1759 V0 H0 V84 H263 V1759 v0 v1759 H0 v84 H347z\nM347 1759 V0 H263 V1759 v0 v1759 h84z",[18,947,706],{"className":948},[705],[18,950,952],{"className":951},[674],[18,953,955],{"className":954,"style":713},[678],[18,956],{},[18,958],{"className":959,"style":960},[72],"margin-right:0.2778em;",[18,962,572],{"className":963},[964],"mrel",[18,966],{"className":967,"style":960},[72],[18,969,971,974,1113,1116,1119],{"className":970},[59],[18,972],{"className":973,"style":652},[63],[18,975,977,1014,1076],{"className":976},[656],[18,978,980],{"className":979},[660],[18,981,983],{"className":982},[664,665],[18,984,986,1006],{"className":985},[669,670],[18,987,989,1003],{"className":988},[674],[18,990,992],{"className":991,"style":679},[678],[18,993,994,997],{"style":682},[18,995],{"className":996,"style":687},[686],[18,998,999],{"style":690},[692,1000,1001],{"xmlns":694,"width":695,"height":696,"viewBox":697},[699,1002],{"d":701},[18,1004,706],{"className":1005},[705],[18,1007,1009],{"className":1008},[674],[18,1010,1012],{"className":1011,"style":713},[678],[18,1013],{},[18,1015,1017],{"className":1016},[68],[18,1018,1020],{"className":1019},[483],[18,1021,1023],{"className":1022},[725],[18,1024,1026,1068],{"className":1025},[669,670],[18,1027,1029,1065],{"className":1028},[674],[18,1030,1032,1043,1054],{"className":1031,"style":679},[678],[18,1033,1034,1037],{"style":737},[18,1035],{"className":1036,"style":741},[686],[18,1038,1040],{"className":1039},[68],[18,1041,381],{"className":1042},[68],[18,1044,1045,1048],{"style":753},[18,1046],{"className":1047,"style":741},[686],[18,1049,1051],{"className":1050},[68],[18,1052,530],{"className":1053},[68],[18,1055,1056,1059],{"style":768},[18,1057],{"className":1058,"style":741},[686],[18,1060,1062],{"className":1061},[68],[18,1063,381],{"className":1064},[68],[18,1066,706],{"className":1067},[705],[18,1069,1071],{"className":1070},[674],[18,1072,1074],{"className":1073,"style":713},[678],[18,1075],{},[18,1077,1079],{"className":1078},[921],[18,1080,1082],{"className":1081},[664,665],[18,1083,1085,1105],{"className":1084},[669,670],[18,1086,1088,1102],{"className":1087},[674],[18,1089,1091],{"className":1090,"style":679},[678],[18,1092,1093,1096],{"style":682},[18,1094],{"className":1095,"style":687},[686],[18,1097,1098],{"style":690},[692,1099,1100],{"xmlns":694,"width":695,"height":696,"viewBox":697},[699,1101],{"d":945},[18,1103,706],{"className":1104},[705],[18,1106,1108],{"className":1107},[674],[18,1109,1111],{"className":1110,"style":713},[678],[18,1112],{},[18,1114],{"className":1115,"style":73},[72],[18,1117,43],{"className":1118},[77],[18,1120],{"className":1121,"style":73},[72],[18,1123,1125,1129],{"className":1124},[59],[18,1126],{"className":1127,"style":1128},[63],"height:1.2em;vertical-align:-0.35em;",[18,1130,1132,1141,1266],{"className":1131},[656],[18,1133,1137],{"className":1134,"style":1136},[660,1135],"delimcenter","top:0em;",[18,1138,481],{"className":1139},[664,1140],"size1",[18,1142,1144],{"className":1143},[68],[18,1145,1147,1186,1189,1192,1226,1229,1232],{"className":1146},[483],[18,1148,1150],{"className":1149},[725],[18,1151,1153,1177],{"className":1152},[669,670],[18,1154,1156,1174],{"className":1155},[674],[18,1157,1160],{"className":1158,"style":1159},[678],"height:0.85em;",[18,1161,1162,1165],{"style":753},[18,1163],{"className":1164,"style":741},[686],[18,1166,1168,1171],{"className":1167},[68],[18,1169,503],{"className":1170},[68],[18,1172,381],{"className":1173},[68],[18,1175,706],{"className":1176},[705],[18,1178,1180],{"className":1179},[674],[18,1181,1184],{"className":1182,"style":1183},[678],"height:0.35em;",[18,1185],{},[18,1187],{"className":1188,"style":796},[795],[18,1190],{"className":1191,"style":796},[795],[18,1193,1195],{"className":1194},[725],[18,1196,1198,1218],{"className":1197},[669,670],[18,1199,1201,1215],{"className":1200},[674],[18,1202,1204],{"className":1203,"style":1159},[678],[18,1205,1206,1209],{"style":753},[18,1207],{"className":1208,"style":741},[686],[18,1210,1212],{"className":1211},[68],[18,1213,497],{"className":1214},[68],[18,1216,706],{"className":1217},[705],[18,1219,1221],{"className":1220},[674],[18,1222,1224],{"className":1223,"style":1183},[678],[18,1225],{},[18,1227],{"className":1228,"style":796},[795],[18,1230],{"className":1231,"style":796},[795],[18,1233,1235],{"className":1234},[725],[18,1236,1238,1258],{"className":1237},[669,670],[18,1239,1241,1255],{"className":1240},[674],[18,1242,1244],{"className":1243,"style":1159},[678],[18,1245,1246,1249],{"style":753},[18,1247],{"className":1248,"style":741},[686],[18,1250,1252],{"className":1251},[68],[18,1253,381],{"className":1254},[68],[18,1256,706],{"className":1257},[705],[18,1259,1261],{"className":1260},[674],[18,1262,1264],{"className":1263,"style":1183},[678],[18,1265],{},[18,1267,1269],{"className":1268,"style":1136},[921,1135],[18,1270,569],{"className":1271},[664,1140],[14,1273,1274,1275,1325,1326,1444,1445,1563],{},"在拆分之前，我们的卷积核中有 9 个元素，每次卷积运算都要进行 9 次乘法运算。如果拆成两个算子，我们的卷积核总共有 6\n个元素，那么两次卷积运算只需要 6 次乘法。未拆分之前，我们对一个 ",[18,1276,1278,1295],{"className":1277},[21],[18,1279,1281],{"className":1280},[25],[27,1282,1283],{"xmlns":29},[31,1284,1285,1293],{},[34,1286,1287,1289,1291],{},[37,1288,39],{},[41,1290,43],{},[37,1292,39],{},[47,1294,50],{"encoding":49},[18,1296,1298,1316],{"className":1297,"ariaHidden":55},[54],[18,1299,1301,1304,1307,1310,1313],{"className":1300},[59],[18,1302],{"className":1303,"style":64},[63],[18,1305,39],{"className":1306},[68],[18,1308],{"className":1309,"style":73},[72],[18,1311,43],{"className":1312},[77],[18,1314],{"className":1315,"style":73},[72],[18,1317,1319,1322],{"className":1318},[59],[18,1320],{"className":1321,"style":87},[63],[18,1323,39],{"className":1324},[68],"\n图像卷积，总共要进行 ",[18,1327,1329,1360],{"className":1328},[21],[18,1330,1332],{"className":1331},[25],[27,1333,1334],{"xmlns":29},[31,1335,1336,1357],{},[34,1337,1338,1340,1342,1344,1346,1348,1350,1352,1354],{},[37,1339,106],{},[41,1341,43],{},[37,1343,106],{},[41,1345,43],{},[37,1347,210],{},[41,1349,43],{},[37,1351,210],{},[41,1353,572],{},[37,1355,1356],{},"324",[47,1358,1359],{"encoding":49},"3 \\times3 \\times6 \\times6 = 324",[18,1361,1363,1381,1399,1417,1435],{"className":1362,"ariaHidden":55},[54],[18,1364,1366,1369,1372,1375,1378],{"className":1365},[59],[18,1367],{"className":1368,"style":64},[63],[18,1370,106],{"className":1371},[68],[18,1373],{"className":1374,"style":73},[72],[18,1376,43],{"className":1377},[77],[18,1379],{"className":1380,"style":73},[72],[18,1382,1384,1387,1390,1393,1396],{"className":1383},[59],[18,1385],{"className":1386,"style":64},[63],[18,1388,106],{"className":1389},[68],[18,1391],{"className":1392,"style":73},[72],[18,1394,43],{"className":1395},[77],[18,1397],{"className":1398,"style":73},[72],[18,1400,1402,1405,1408,1411,1414],{"className":1401},[59],[18,1403],{"className":1404,"style":64},[63],[18,1406,210],{"className":1407},[68],[18,1409],{"className":1410,"style":73},[72],[18,1412,43],{"className":1413},[77],[18,1415],{"className":1416,"style":73},[72],[18,1418,1420,1423,1426,1429,1432],{"className":1419},[59],[18,1421],{"className":1422,"style":87},[63],[18,1424,210],{"className":1425},[68],[18,1427],{"className":1428,"style":960},[72],[18,1430,572],{"className":1431},[964],[18,1433],{"className":1434,"style":960},[72],[18,1436,1438,1441],{"className":1437},[59],[18,1439],{"className":1440,"style":87},[63],[18,1442,1356],{"className":1443},[68]," 次乘法运算；拆分之后，总共要进行 ",[18,1446,1448,1479],{"className":1447},[21],[18,1449,1451],{"className":1450},[25],[27,1452,1453],{"xmlns":29},[31,1454,1455,1476],{},[34,1456,1457,1459,1461,1463,1465,1467,1469,1471,1473],{},[37,1458,530],{},[41,1460,43],{},[37,1462,106],{},[41,1464,43],{},[37,1466,210],{},[41,1468,43],{},[37,1470,210],{},[41,1472,572],{},[37,1474,1475],{},"216",[47,1477,1478],{"encoding":49},"2 \\times3 \\times6 \\times6 = 216",[18,1480,1482,1500,1518,1536,1554],{"className":1481,"ariaHidden":55},[54],[18,1483,1485,1488,1491,1494,1497],{"className":1484},[59],[18,1486],{"className":1487,"style":64},[63],[18,1489,530],{"className":1490},[68],[18,1492],{"className":1493,"style":73},[72],[18,1495,43],{"className":1496},[77],[18,1498],{"className":1499,"style":73},[72],[18,1501,1503,1506,1509,1512,1515],{"className":1502},[59],[18,1504],{"className":1505,"style":64},[63],[18,1507,106],{"className":1508},[68],[18,1510],{"className":1511,"style":73},[72],[18,1513,43],{"className":1514},[77],[18,1516],{"className":1517,"style":73},[72],[18,1519,1521,1524,1527,1530,1533],{"className":1520},[59],[18,1522],{"className":1523,"style":64},[63],[18,1525,210],{"className":1526},[68],[18,1528],{"className":1529,"style":73},[72],[18,1531,43],{"className":1532},[77],[18,1534],{"className":1535,"style":73},[72],[18,1537,1539,1542,1545,1548,1551],{"className":1538},[59],[18,1540],{"className":1541,"style":87},[63],[18,1543,210],{"className":1544},[68],[18,1546],{"className":1547,"style":960},[72],[18,1549,572],{"className":1550},[964],[18,1552],{"className":1553,"style":960},[72],[18,1555,1557,1560],{"className":1556},[59],[18,1558],{"className":1559,"style":87},[63],[18,1561,1475],{"className":1562},[68],"\n次乘法运算。",[255,1565,1566],{"id":1566},"深度可分离卷积",[14,1568,1569],{},"一般我们的图像有 RGB 3 个通道，也就是说我们的矩阵从 2D 转成了 3D，3D 卷积的操作与 2D\n类似。通道数也是输入特征的深度。而深度可分离卷积有两个步骤，就是深度卷积与点卷积。",[14,1571,1572,1573,1646,1647,1720,1721,1771],{},"首先，如果一共有 ",[18,1574,1576,1598],{"className":1575},[21],[18,1577,1579],{"className":1578},[25],[27,1580,1581],{"xmlns":29},[31,1582,1583,1595],{},[34,1584,1585,1587,1589,1591,1593],{},[37,1586,39],{},[41,1588,43],{},[37,1590,39],{},[41,1592,43],{},[37,1594,106],{},[47,1596,1597],{"encoding":49},"8 \\times8 \\times3",[18,1599,1601,1619,1637],{"className":1600,"ariaHidden":55},[54],[18,1602,1604,1607,1610,1613,1616],{"className":1603},[59],[18,1605],{"className":1606,"style":64},[63],[18,1608,39],{"className":1609},[68],[18,1611],{"className":1612,"style":73},[72],[18,1614,43],{"className":1615},[77],[18,1617],{"className":1618,"style":73},[72],[18,1620,1622,1625,1628,1631,1634],{"className":1621},[59],[18,1623],{"className":1624,"style":64},[63],[18,1626,39],{"className":1627},[68],[18,1629],{"className":1630,"style":73},[72],[18,1632,43],{"className":1633},[77],[18,1635],{"className":1636,"style":73},[72],[18,1638,1640,1643],{"className":1639},[59],[18,1641],{"className":1642,"style":87},[63],[18,1644,106],{"className":1645},[68]," 的输入特征，我们用一个 ",[18,1648,1650,1672],{"className":1649},[21],[18,1651,1653],{"className":1652},[25],[27,1654,1655],{"xmlns":29},[31,1656,1657,1669],{},[34,1658,1659,1661,1663,1665,1667],{},[37,1660,106],{},[41,1662,43],{},[37,1664,106],{},[41,1666,43],{},[37,1668,106],{},[47,1670,1671],{"encoding":49},"3 \\times3 \\times3",[18,1673,1675,1693,1711],{"className":1674,"ariaHidden":55},[54],[18,1676,1678,1681,1684,1687,1690],{"className":1677},[59],[18,1679],{"className":1680,"style":64},[63],[18,1682,106],{"className":1683},[68],[18,1685],{"className":1686,"style":73},[72],[18,1688,43],{"className":1689},[77],[18,1691],{"className":1692,"style":73},[72],[18,1694,1696,1699,1702,1705,1708],{"className":1695},[59],[18,1697],{"className":1698,"style":64},[63],[18,1700,106],{"className":1701},[68],[18,1703],{"className":1704,"style":73},[72],[18,1706,43],{"className":1707},[77],[18,1709],{"className":1710,"style":73},[72],[18,1712,1714,1717],{"className":1713},[59],[18,1715],{"className":1716,"style":87},[63],[18,1718,106],{"className":1719},[68],"\n的卷积核对其进行卷积，最终得到的结果是一个 ",[18,1722,1724,1741],{"className":1723},[21],[18,1725,1727],{"className":1726},[25],[27,1728,1729],{"xmlns":29},[31,1730,1731,1739],{},[34,1732,1733,1735,1737],{},[37,1734,210],{},[41,1736,43],{},[37,1738,210],{},[47,1740,217],{"encoding":49},[18,1742,1744,1762],{"className":1743,"ariaHidden":55},[54],[18,1745,1747,1750,1753,1756,1759],{"className":1746},[59],[18,1748],{"className":1749,"style":64},[63],[18,1751,210],{"className":1752},[68],[18,1754],{"className":1755,"style":73},[72],[18,1757,43],{"className":1758},[77],[18,1760],{"className":1761,"style":73},[72],[18,1763,1765,1768],{"className":1764},[59],[18,1766],{"className":1767,"style":87},[63],[18,1769,210],{"className":1770},[68]," 的特征图。但是我们想输出的特征深度更大，也就是更多的特征，那么我们需要进行多次类似的操作。",[14,1773,1774,1775,1825,1826,1876,1877,1950,1951,2023,2024,2097,2098,2170,2171,2221],{},"而应深度可分离卷积的操作就是，分别用 3 个 ",[18,1776,1778,1795],{"className":1777},[21],[18,1779,1781],{"className":1780},[25],[27,1782,1783],{"xmlns":29},[31,1784,1785,1793],{},[34,1786,1787,1789,1791],{},[37,1788,106],{},[41,1790,43],{},[37,1792,106],{},[47,1794,113],{"encoding":49},[18,1796,1798,1816],{"className":1797,"ariaHidden":55},[54],[18,1799,1801,1804,1807,1810,1813],{"className":1800},[59],[18,1802],{"className":1803,"style":64},[63],[18,1805,106],{"className":1806},[68],[18,1808],{"className":1809,"style":73},[72],[18,1811,43],{"className":1812},[77],[18,1814],{"className":1815,"style":73},[72],[18,1817,1819,1822],{"className":1818},[59],[18,1820],{"className":1821,"style":87},[63],[18,1823,106],{"className":1824},[68]," 的卷积核对 3 个 8 \\times8 的特征图进行卷积操作。在卷积操作之后，将得到的\n3 张 ",[18,1827,1829,1846],{"className":1828},[21],[18,1830,1832],{"className":1831},[25],[27,1833,1834],{"xmlns":29},[31,1835,1836,1844],{},[34,1837,1838,1840,1842],{},[37,1839,210],{},[41,1841,43],{},[37,1843,210],{},[47,1845,217],{"encoding":49},[18,1847,1849,1867],{"className":1848,"ariaHidden":55},[54],[18,1850,1852,1855,1858,1861,1864],{"className":1851},[59],[18,1853],{"className":1854,"style":64},[63],[18,1856,210],{"className":1857},[68],[18,1859],{"className":1860,"style":73},[72],[18,1862,43],{"className":1863},[77],[18,1865],{"className":1866,"style":73},[72],[18,1868,1870,1873],{"className":1869},[59],[18,1871],{"className":1872,"style":87},[63],[18,1874,210],{"className":1875},[68]," 的卷积图进行拼接，得到 ",[18,1878,1880,1902],{"className":1879},[21],[18,1881,1883],{"className":1882},[25],[27,1884,1885],{"xmlns":29},[31,1886,1887,1899],{},[34,1888,1889,1891,1893,1895,1897],{},[37,1890,210],{},[41,1892,43],{},[37,1894,210],{},[41,1896,43],{},[37,1898,106],{},[47,1900,1901],{"encoding":49},"6 \\times6 \\times3",[18,1903,1905,1923,1941],{"className":1904,"ariaHidden":55},[54],[18,1906,1908,1911,1914,1917,1920],{"className":1907},[59],[18,1909],{"className":1910,"style":64},[63],[18,1912,210],{"className":1913},[68],[18,1915],{"className":1916,"style":73},[72],[18,1918,43],{"className":1919},[77],[18,1921],{"className":1922,"style":73},[72],[18,1924,1926,1929,1932,1935,1938],{"className":1925},[59],[18,1927],{"className":1928,"style":64},[63],[18,1930,210],{"className":1931},[68],[18,1933],{"className":1934,"style":73},[72],[18,1936,43],{"className":1937},[77],[18,1939],{"className":1940,"style":73},[72],[18,1942,1944,1947],{"className":1943},[59],[18,1945],{"className":1946,"style":87},[63],[18,1948,106],{"className":1949},[68]," 的特征并没有得到像 ",[18,1952,1954,1975],{"className":1953},[21],[18,1955,1957],{"className":1956},[25],[27,1958,1959],{"xmlns":29},[31,1960,1961,1973],{},[34,1962,1963,1965,1967,1969,1971],{},[37,1964,106],{},[41,1966,43],{},[37,1968,106],{},[41,1970,43],{},[37,1972,106],{},[47,1974,1671],{"encoding":49},[18,1976,1978,1996,2014],{"className":1977,"ariaHidden":55},[54],[18,1979,1981,1984,1987,1990,1993],{"className":1980},[59],[18,1982],{"className":1983,"style":64},[63],[18,1985,106],{"className":1986},[68],[18,1988],{"className":1989,"style":73},[72],[18,1991,43],{"className":1992},[77],[18,1994],{"className":1995,"style":73},[72],[18,1997,1999,2002,2005,2008,2011],{"className":1998},[59],[18,2000],{"className":2001,"style":64},[63],[18,2003,106],{"className":2004},[68],[18,2006],{"className":2007,"style":73},[72],[18,2009,43],{"className":2010},[77],[18,2012],{"className":2013,"style":73},[72],[18,2015,2017,2020],{"className":2016},[59],[18,2018],{"className":2019,"style":87},[63],[18,2021,106],{"className":2022},[68],"\n的卷积核那样的输出结果。这个时候我们就要通过点卷积将每层特征结合起来，也就是用 ",[18,2025,2027,2049],{"className":2026},[21],[18,2028,2030],{"className":2029},[25],[27,2031,2032],{"xmlns":29},[31,2033,2034,2046],{},[34,2035,2036,2038,2040,2042,2044],{},[37,2037,381],{},[41,2039,43],{},[37,2041,381],{},[41,2043,43],{},[37,2045,106],{},[47,2047,2048],{"encoding":49},"1 \\times1 \\times3",[18,2050,2052,2070,2088],{"className":2051,"ariaHidden":55},[54],[18,2053,2055,2058,2061,2064,2067],{"className":2054},[59],[18,2056],{"className":2057,"style":64},[63],[18,2059,381],{"className":2060},[68],[18,2062],{"className":2063,"style":73},[72],[18,2065,43],{"className":2066},[77],[18,2068],{"className":2069,"style":73},[72],[18,2071,2073,2076,2079,2082,2085],{"className":2072},[59],[18,2074],{"className":2075,"style":64},[63],[18,2077,381],{"className":2078},[68],[18,2080],{"className":2081,"style":73},[72],[18,2083,43],{"className":2084},[77],[18,2086],{"className":2087,"style":73},[72],[18,2089,2091,2094],{"className":2090},[59],[18,2092],{"className":2093,"style":87},[63],[18,2095,106],{"className":2096},[68],"\n的卷积核对这个 ",[18,2099,2101,2122],{"className":2100},[21],[18,2102,2104],{"className":2103},[25],[27,2105,2106],{"xmlns":29},[31,2107,2108,2120],{},[34,2109,2110,2112,2114,2116,2118],{},[37,2111,210],{},[41,2113,43],{},[37,2115,210],{},[41,2117,43],{},[37,2119,106],{},[47,2121,1901],{"encoding":49},[18,2123,2125,2143,2161],{"className":2124,"ariaHidden":55},[54],[18,2126,2128,2131,2134,2137,2140],{"className":2127},[59],[18,2129],{"className":2130,"style":64},[63],[18,2132,210],{"className":2133},[68],[18,2135],{"className":2136,"style":73},[72],[18,2138,43],{"className":2139},[77],[18,2141],{"className":2142,"style":73},[72],[18,2144,2146,2149,2152,2155,2158],{"className":2145},[59],[18,2147],{"className":2148,"style":64},[63],[18,2150,210],{"className":2151},[68],[18,2153],{"className":2154,"style":73},[72],[18,2156,43],{"className":2157},[77],[18,2159],{"className":2160,"style":73},[72],[18,2162,2164,2167],{"className":2163},[59],[18,2165],{"className":2166,"style":87},[63],[18,2168,106],{"className":2169},[68]," 的特征进行卷积操作，最终得到一个 ",[18,2172,2174,2191],{"className":2173},[21],[18,2175,2177],{"className":2176},[25],[27,2178,2179],{"xmlns":29},[31,2180,2181,2189],{},[34,2182,2183,2185,2187],{},[37,2184,210],{},[41,2186,43],{},[37,2188,210],{},[47,2190,217],{"encoding":49},[18,2192,2194,2212],{"className":2193,"ariaHidden":55},[54],[18,2195,2197,2200,2203,2206,2209],{"className":2196},[59],[18,2198],{"className":2199,"style":64},[63],[18,2201,210],{"className":2202},[68],[18,2204],{"className":2205,"style":73},[72],[18,2207,43],{"className":2208},[77],[18,2210],{"className":2211,"style":73},[72],[18,2213,2215,2218],{"className":2214},[59],[18,2216],{"className":2217,"style":87},[63],[18,2219,210],{"className":2220},[68],"\n的输出特征。如果我们想得到更大的深度，只需要在最后的点卷积多进行几次运算后拼接即可。",[14,2223,2224,2225,2297,2298,2370,2371,2443,2444,2606,2607,2814],{},"前面说过，可分离卷积是为了减少乘法操作，那么深度可分离卷积是否减少了乘法操作？这里以输入 ",[18,2226,2228,2249],{"className":2227},[21],[18,2229,2231],{"className":2230},[25],[27,2232,2233],{"xmlns":29},[31,2234,2235,2247],{},[34,2236,2237,2239,2241,2243,2245],{},[37,2238,39],{},[41,2240,43],{},[37,2242,39],{},[41,2244,43],{},[37,2246,106],{},[47,2248,1597],{"encoding":49},[18,2250,2252,2270,2288],{"className":2251,"ariaHidden":55},[54],[18,2253,2255,2258,2261,2264,2267],{"className":2254},[59],[18,2256],{"className":2257,"style":64},[63],[18,2259,39],{"className":2260},[68],[18,2262],{"className":2263,"style":73},[72],[18,2265,43],{"className":2266},[77],[18,2268],{"className":2269,"style":73},[72],[18,2271,2273,2276,2279,2282,2285],{"className":2272},[59],[18,2274],{"className":2275,"style":64},[63],[18,2277,39],{"className":2278},[68],[18,2280],{"className":2281,"style":73},[72],[18,2283,43],{"className":2284},[77],[18,2286],{"className":2287,"style":73},[72],[18,2289,2291,2294],{"className":2290},[59],[18,2292],{"className":2293,"style":87},[63],[18,2295,106],{"className":2296},[68],"\n，卷积核为 ",[18,2299,2301,2322],{"className":2300},[21],[18,2302,2304],{"className":2303},[25],[27,2305,2306],{"xmlns":29},[31,2307,2308,2320],{},[34,2309,2310,2312,2314,2316,2318],{},[37,2311,106],{},[41,2313,43],{},[37,2315,106],{},[41,2317,43],{},[37,2319,106],{},[47,2321,1671],{"encoding":49},[18,2323,2325,2343,2361],{"className":2324,"ariaHidden":55},[54],[18,2326,2328,2331,2334,2337,2340],{"className":2327},[59],[18,2329],{"className":2330,"style":64},[63],[18,2332,106],{"className":2333},[68],[18,2335],{"className":2336,"style":73},[72],[18,2338,43],{"className":2339},[77],[18,2341],{"className":2342,"style":73},[72],[18,2344,2346,2349,2352,2355,2358],{"className":2345},[59],[18,2347],{"className":2348,"style":64},[63],[18,2350,106],{"className":2351},[68],[18,2353],{"className":2354,"style":73},[72],[18,2356,43],{"className":2357},[77],[18,2359],{"className":2360,"style":73},[72],[18,2362,2364,2367],{"className":2363},[59],[18,2365],{"className":2366,"style":87},[63],[18,2368,106],{"className":2369},[68],"，输出的特征图是 ",[18,2372,2374,2395],{"className":2373},[21],[18,2375,2377],{"className":2376},[25],[27,2378,2379],{"xmlns":29},[31,2380,2381,2393],{},[34,2382,2383,2385,2387,2389,2391],{},[37,2384,210],{},[41,2386,43],{},[37,2388,210],{},[41,2390,43],{},[37,2392,106],{},[47,2394,1901],{"encoding":49},[18,2396,2398,2416,2434],{"className":2397,"ariaHidden":55},[54],[18,2399,2401,2404,2407,2410,2413],{"className":2400},[59],[18,2402],{"className":2403,"style":64},[63],[18,2405,210],{"className":2406},[68],[18,2408],{"className":2409,"style":73},[72],[18,2411,43],{"className":2412},[77],[18,2414],{"className":2415,"style":73},[72],[18,2417,2419,2422,2425,2428,2431],{"className":2418},[59],[18,2420],{"className":2421,"style":64},[63],[18,2423,210],{"className":2424},[68],[18,2426],{"className":2427,"style":73},[72],[18,2429,43],{"className":2430},[77],[18,2432],{"className":2433,"style":73},[72],[18,2435,2437,2440],{"className":2436},[59],[18,2438],{"className":2439,"style":87},[63],[18,2441,106],{"className":2442},[68],"\n的话，我们一共需要 ",[18,2445,2447,2486],{"className":2446},[21],[18,2448,2450],{"className":2449},[25],[27,2451,2452],{"xmlns":29},[31,2453,2454,2483],{},[34,2455,2456,2458,2460,2462,2464,2466,2468,2470,2472,2474,2476,2478,2480],{},[37,2457,106],{},[41,2459,43],{},[37,2461,106],{},[41,2463,43],{},[37,2465,106],{},[41,2467,43],{},[37,2469,210],{},[41,2471,43],{},[37,2473,210],{},[41,2475,43],{},[37,2477,106],{},[41,2479,572],{},[37,2481,2482],{},"2916",[47,2484,2485],{"encoding":49},"3 \\times3 \\times3 \\times6 \\times6 \\times3 = 2916",[18,2487,2489,2507,2525,2543,2561,2579,2597],{"className":2488,"ariaHidden":55},[54],[18,2490,2492,2495,2498,2501,2504],{"className":2491},[59],[18,2493],{"className":2494,"style":64},[63],[18,2496,106],{"className":2497},[68],[18,2499],{"className":2500,"style":73},[72],[18,2502,43],{"className":2503},[77],[18,2505],{"className":2506,"style":73},[72],[18,2508,2510,2513,2516,2519,2522],{"className":2509},[59],[18,2511],{"className":2512,"style":64},[63],[18,2514,106],{"className":2515},[68],[18,2517],{"className":2518,"style":73},[72],[18,2520,43],{"className":2521},[77],[18,2523],{"className":2524,"style":73},[72],[18,2526,2528,2531,2534,2537,2540],{"className":2527},[59],[18,2529],{"className":2530,"style":64},[63],[18,2532,106],{"className":2533},[68],[18,2535],{"className":2536,"style":73},[72],[18,2538,43],{"className":2539},[77],[18,2541],{"className":2542,"style":73},[72],[18,2544,2546,2549,2552,2555,2558],{"className":2545},[59],[18,2547],{"className":2548,"style":64},[63],[18,2550,210],{"className":2551},[68],[18,2553],{"className":2554,"style":73},[72],[18,2556,43],{"className":2557},[77],[18,2559],{"className":2560,"style":73},[72],[18,2562,2564,2567,2570,2573,2576],{"className":2563},[59],[18,2565],{"className":2566,"style":64},[63],[18,2568,210],{"className":2569},[68],[18,2571],{"className":2572,"style":73},[72],[18,2574,43],{"className":2575},[77],[18,2577],{"className":2578,"style":73},[72],[18,2580,2582,2585,2588,2591,2594],{"className":2581},[59],[18,2583],{"className":2584,"style":87},[63],[18,2586,106],{"className":2587},[68],[18,2589],{"className":2590,"style":960},[72],[18,2592,572],{"className":2593},[964],[18,2595],{"className":2596,"style":960},[72],[18,2598,2600,2603],{"className":2599},[59],[18,2601],{"className":2602,"style":87},[63],[18,2604,2482],{"className":2605},[68],"\n次乘法运算，而换成深度可分离卷积就要进行 ",[18,2608,2610,2658],{"className":2609},[21],[18,2611,2613],{"className":2612},[25],[27,2614,2615],{"xmlns":29},[31,2616,2617,2655],{},[34,2618,2619,2621,2623,2625,2627,2629,2631,2633,2635,2637,2640,2642,2644,2646,2648,2650,2652],{},[37,2620,106],{},[41,2622,43],{},[37,2624,106],{},[41,2626,43],{},[37,2628,210],{},[41,2630,43],{},[37,2632,210],{},[41,2634,43],{},[37,2636,106],{},[41,2638,2639],{},"+",[37,2641,106],{},[41,2643,43],{},[37,2645,210],{},[41,2647,43],{},[37,2649,210],{},[41,2651,572],{},[37,2653,2654],{},"1080",[47,2656,2657],{"encoding":49},"3 \\times3 \\times6 \\times6 \\times3 + 3 \\times6 \\times6 = 1080",[18,2659,2661,2679,2697,2715,2733,2751,2769,2787,2805],{"className":2660,"ariaHidden":55},[54],[18,2662,2664,2667,2670,2673,2676],{"className":2663},[59],[18,2665],{"className":2666,"style":64},[63],[18,2668,106],{"className":2669},[68],[18,2671],{"className":2672,"style":73},[72],[18,2674,43],{"className":2675},[77],[18,2677],{"className":2678,"style":73},[72],[18,2680,2682,2685,2688,2691,2694],{"className":2681},[59],[18,2683],{"className":2684,"style":64},[63],[18,2686,106],{"className":2687},[68],[18,2689],{"className":2690,"style":73},[72],[18,2692,43],{"className":2693},[77],[18,2695],{"className":2696,"style":73},[72],[18,2698,2700,2703,2706,2709,2712],{"className":2699},[59],[18,2701],{"className":2702,"style":64},[63],[18,2704,210],{"className":2705},[68],[18,2707],{"className":2708,"style":73},[72],[18,2710,43],{"className":2711},[77],[18,2713],{"className":2714,"style":73},[72],[18,2716,2718,2721,2724,2727,2730],{"className":2717},[59],[18,2719],{"className":2720,"style":64},[63],[18,2722,210],{"className":2723},[68],[18,2725],{"className":2726,"style":73},[72],[18,2728,43],{"className":2729},[77],[18,2731],{"className":2732,"style":73},[72],[18,2734,2736,2739,2742,2745,2748],{"className":2735},[59],[18,2737],{"className":2738,"style":64},[63],[18,2740,106],{"className":2741},[68],[18,2743],{"className":2744,"style":73},[72],[18,2746,2639],{"className":2747},[77],[18,2749],{"className":2750,"style":73},[72],[18,2752,2754,2757,2760,2763,2766],{"className":2753},[59],[18,2755],{"className":2756,"style":64},[63],[18,2758,106],{"className":2759},[68],[18,2761],{"className":2762,"style":73},[72],[18,2764,43],{"className":2765},[77],[18,2767],{"className":2768,"style":73},[72],[18,2770,2772,2775,2778,2781,2784],{"className":2771},[59],[18,2773],{"className":2774,"style":64},[63],[18,2776,210],{"className":2777},[68],[18,2779],{"className":2780,"style":73},[72],[18,2782,43],{"className":2783},[77],[18,2785],{"className":2786,"style":73},[72],[18,2788,2790,2793,2796,2799,2802],{"className":2789},[59],[18,2791],{"className":2792,"style":87},[63],[18,2794,210],{"className":2795},[68],[18,2797],{"className":2798,"style":960},[72],[18,2800,572],{"className":2801},[964],[18,2803],{"className":2804,"style":960},[72],[18,2806,2808,2811],{"className":2807},[59],[18,2809],{"className":2810,"style":87},[63],[18,2812,2654],{"className":2813},[68],"\n次乘法运算。深度卷积运算在深度越大的情况下性能提升更高。",[14,2816,2817],{},"EfficientNet 就是通过将部分卷积运算换成深度可分离的深度卷积运算从而在参数增加的时候比其他模型获得较强的性能提升。",{"title":2819,"searchDepth":2820,"depth":2820,"links":2821},"",2,[2822,2823],{"id":12,"depth":2820,"text":12},{"id":5,"depth":2820,"text":5,"children":2824},[2825,2827],{"id":257,"depth":2826,"text":257},3,{"id":1566,"depth":2826,"text":1566},"2023-12-11T11:35:48.000Z","md",[2831],"其他",false,{},true,"/article/9",{"title":5,"description":2819},"article/9",null,"tf59VahlG6igxP9fGTzrrBrw4dZjSrqxSQ8Vvcsx7Ws",1755235549198]