{"id":2175,"date":"2020-01-29T14:51:06","date_gmt":"2020-01-29T05:51:06","guid":{"rendered":"http:\/\/43.203.250.216\/?p=2175"},"modified":"2026-02-04T11:39:35","modified_gmt":"2026-02-04T02:39:35","slug":"back-propgation%ec%97%90%ec%84%9c%ec%9d%98-%ec%a0%84%ec%b9%98%ed%96%89%eb%a0%actranspose-matrix-1%ed%8e%b8","status":"publish","type":"post","link":"https:\/\/litcoder.com\/?p=2175","title":{"rendered":"Back propgation\uc5d0\uc11c\uc758 \uc804\uce58\ud589\ub82c(transpose matrix) – 1\ud3b8"},"content":{"rendered":"\n
\n

\uc2e4\uc81c\ub85c \uc804\uac1c\ud574\ubcf4\uba74 \ub2e4\uc74c \uc2dd\uc774 \ub3c4\ucd9c\ub429\ub2c8\ub2e4([\uc2dd 5.13]\uc73c\ub85c \uc774\ub044\ub294 \uacfc\uc815\uc740 \uc0dd\ub7b5\ud569\ub2c8\ub2e4).<\/p>\n– p172, 5.6.1 Affine \uacc4\uce35, \ubc11\ubc14\ub2e5\ubd80\ud130 \uc2dc\uc791\ud558\ub294 \ub525\ub7ec\ub2dd<\/cite><\/blockquote>\n\n\n\n

\uc544\ub2c8! \uadf8\uac78 \uc0dd\ub7b5\ud558\uba74 \uc5b4\ub5a1\ud574\uc694!!<\/h2>\n\n\n\n

“\ubc11\ubc14\ub2e5\ubd80\ud130 \uc2dc\uc791\ud558\ub294 \ub525\ub7ec\ub2dd”\uc744 \uc77d\uc73c\uba74\uc11c \ub525\ub7ec\ub2dd\uc758 \uac1c\ub150\uc744 \uc7a1\ub294\ub370 \ub9ce\uc740 \ub3c4\uc6c0\uc744 \ubc1b\uace0 \uc788\uc9c0\ub9cc \uad73\uc774 \ub2e8\uc810\uc744 \ub4e4\uc790\uba74 \uc8fc\uc694\ud55c \uacf5\uc2dd \ub4e4\uc5d0 \ub300\ud574 \uc124\uba85\ud558\uc9c0 \uc54a\uace0 \uadf8\ub0e5 \ub118\uc5b4 \uac00\ubc84\ub9ac\ub294 \uacbd\uc6b0\uac00 \uac00\ub054 \uc788\ub2e4. \uc704\uc5d0\uc11c \ub9d0\ud558\ub294 [\uc2dd 5.13]\uc740 back propagataion\uc5d0\uc11c \uc785\ub825\uc5d0 \ub300\ud55c loss function\uc758 \uc601\ud5a5\uacfc weight\uc5d0 \ub300\ud55c loss function\uc758 \uc601\ud5a5\uc744 \uacc4\uc0b0\ud558\ub294 \ub2e4\uc74c \uc2dd\uc744 \uc758\ubbf8\ud55c\ub2e4.<\/p>\n\n\n\n

\"\frac{\partial<\/p>\n\n\n\n

\uc774 \uc2dd\uc774 \ub3c4\ub300\uccb4 \uc5b4\ub5bb\uac8c \uc720\ub3c4\ub41c \uac83\uc778\uc9c0 \uc774\ub9ac \uc800\ub9ac \ucc3e\ub2e4\uac00 \ub9c8\uce68 \uc774 \ubd80\ubd84\uc744 \uc790\uc138\ud788 \uc124\uba85\ud574 \uc8fc\uace0 \uc788\ub294 \ubbf8\uad6d \uc5b4\ub290 \ub300\ud559(!)\uc758 \ud6cc\ub96d\ud55c \ubb38\uc11c<\/a>(Backpropagation for a Linear Layer, Justin Johnson, April 19, 2017)\ub97c \ubc1c\uacac\ud588\ub2e4. \uc774 \ud3ec\uc2a4\ud305\uc740 \ud574\ub2f9 \ubb38\uc11c\uc5d0 \ub300\ud55c \ub098\ub984\uc758 \uc774\ud574\ub97c \uc815\ub9ac\ud55c \uac83\uc774\ub2e4.<\/p>\n\n\n\n

\ubc11\ubc25 \uae54\uae30<\/h2>\n\n\n\n

Matrix\uc778 \uc785\ub825 X, Weight W\uac00 \uc788\ub2e4\uace0 \ud560 \ub54c, \uc774 \ub458\uc758 dot product\uc778 Y\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ubaa8\uc2b5\uc774\ub2e4.<\/p>\n\n\n\n\"X\n\n\n\n\"Y\n\n\n\n

Back propagation\uc744 \ud1b5\ud574 \ucd5c\uc885\uc73c\ub85c \uad6c\ud558\uace0\uc790 \ud558\ub294 \uac83\uc740 \uc785\ub825\uc758 \ubcc0\ud654\uc5d0 \ub530\ub978 loss function\uc758 \ubcc0\ud654\ub7c9 \"\frac{\partial\uacfc Weight \ubcc0\ud654\uc5d0 \ub530\ub978 loss function\uc758 \ubcc0\ud654\ub7c9 \"\frac{\partial\uc774\ub2e4. \uc774\uac83\uacfc \uad00\ub828\ud574 \uc5f0\uc1c4 \ubc95\uce59(chain rule)\uc5d0 \ub530\ub77c \uc774\uc804 layer\uc5d0\uc11c \uc804\ub2ec \ubc1b\uc740 \"Y\uc758 \ubcc0\ud654\uc5d0 \ub530\ub978 loss function\uc758 \ubcc0\ud654\ub7c9\uc778 \"\frac{\partial\ub97c \uace0\ub824\ud558\uba74 \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

Y\uc758 \ubcc0\ud654\uc5d0 \ub530\ub978 Loss function\uc758 \ubcc0\ud654 \"\frac{\partial<\/h2>\n\n\n\n

\uc5ec\uae30\uc5d0\uc11c \"\partial\uc740 scalar \uac12 \uc774\uace0 \"Y\"\ub294 matrix\uc774\ubbc0\ub85c \"\frac{\partial\uc758 \ubaa8\uc2b5\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\n\n\n\n\"\begin{bmatrix}\frac{\partial\n\n\n\n

\ubcf5\uc7a1\ud558\ub2c8\uae4c \uc870\uae08 \uac04\ub2e8\ud788 \ub2e4\uc74c\uacfc \uac19\uc774 \uc778\ub371\uc2a4\ub85c \ub098\ud0c0\ub0b4\uc790.<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

\uc774\uc81c, \"\frac{\partial\uc640 \"\frac{\partial\uac00 \ub0a8\uc558\ub2e4.<\/p>\n\n\n\n

\ud589\ub82c X\uc758 \uc6d0\uc18c\ub4e4\uc5d0 \ub300\ud55c \ud589\ub82c Y\uc758 \ud3b8\ubbf8\ubd84 \"\frac{\partial<\/h2>\n\n\n\n

\uba3c\uc800 \"\frac{\partial\ub97c \ubcf4\uba74, X\uc640 Y \ubaa8\ub450 matrix\uc774\ub2c8 \"\frac\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc0dd\uacbc\ub2e4.<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

\uac01 \uc6d0\uc18c\ub4e4\uc740 scalar \uac12\uc778\ub370 \uadf8 \uc911 \uccab\ubc88\uc9f8 \uc6d0\uc18c\uc778 \"\frac{\partial\ub97c \uad6c\ud558\uae30 \uc704\ud574 Y\uc758 \uc6d0\uc18c\ub4e4\uc744 \"x_{1,1}\"\ub85c \ud3b8\ubbf8\ubd84 \ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \ub41c\ub2e4.<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

\uc751? \uac11\uc790\uae30 \uc774\uac74 \ubb50\ub0d0!<\/strong><\/h3>\n\n\n\n

\uc608\ub97c \ub4e4\uc5b4 \"y_{1,1}\"\uc5d0 \uc788\ub294 \"x_{1,1}w_{1,1}\ub97c \"x_{1,1}\"\ub85c \ud3b8\ubbf8\ubd84\ud558\uba74 \"w_{1,1}\"\uac00 \ub418\uace0, \"x_{1,1}w_{1,2}\uc5d0 \ub300\ud574\uc11c\ub3c4 \uac19\uc740 \ubc29\uc2dd\uc73c\ub85c \ud558\uba74 \"w_{1,2}\"\uac00 \ub418\ub294 \uc2dd\uc73c\ub85c Y\uc758 \ubaa8\ub4e0 6\uac1c\uc758 \uc6d0\uc18c\uc5d0 \uc801\uc6a9\ud55c \uac83\uc774\ub2e4. \uc774\ub7f0 \uc9d3\uc744 matrix X\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\uc778 \"x_{1,\uc5d0 \ub300\ud574\uc11c\ub3c4 \ubaa8\ub450 \uad6c\ud558\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \ub41c\ub2e4.<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

\ud589\ub82c X\uc5d0 \ub300\ud55c scalar L\uc758 \ud3b8\ubbf8\ubd84 \"\frac<\/h2>\n\n\n\n

\"\frac{\partial\uc740 matrix X\ub97c \uad6c\uc131\ud558\ub294 element\uc778 scalar\uac12\uc774\ub2e4. \uc704\uc5d0\uc11c \ub9d0\ud55c\uac83 \ucc98\ub7fc \uc5f0\uc1c4\ubc95\uce59(Chain rule)\uc5d0 \uc758\ud574 Y\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\ub4e4\uc5d0 \ub300\ud558\uc5ec \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4.<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

Matrix X\uc758 \uccab\ubc88\uc9f8 \uc6d0\uc18c\ub294 \"{\partial\ub97c matrix Y\uc758 \uac01 \uc6d0\uc18c\ub4e4\ub85c \ub098\ub208 \uac12\ub4e4\uc5d0 Y\uc758 \uac01\uc6d0\uc18c\ub4e4\uc744 X\uc758 \uccab\ubc88\uc9f8 \uc6d0\uc18c\ub85c \ud3b8\ubbf8\ubd84\ud55c \uac12\ub4e4\uc744 \uacf1\ud55c \uac83\uc744 \ubaa8\ub450 \ub354\ud55c \uac83\uc774\ub2e4. \ub9d0\uc774 \ub4dc\ub7fd\uac8c \ubcf5\uc7a1\ud574 \ubcf4\uc774\uc9c0\ub9cc, \uc608\ub97c\ub4e4\uc5b4, \uccab\ubc88\uc9f8 \uc6d0\uc18c\uc778 \"\frac{\partial\uc758 \uac12\uc774 \ub2e4\uc74c\uacfc \uac19\uc774 \uacc4\uc0b0\ub41c\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/span><\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

\uc774\uac83\ub3c4 \ubb50 \ub531\ud788 \uae68\ub057\ud574 \ubcf4\uc774\uc9c4 \uc54a\uc9c0\ub9cc… \uc5ec\ud2bc, matrix Y\uc758 \uac01\uc6d0\uc18c\ub4e4\uc5d0 \ub300\ud574 \"x_{1,1}\"\ub85c \ud3b8\ubbf8\ubd84\ud55c \uacb0\uacfc\ub97c \uc704 \uc2dd\uc5d0 \uc801\uc6a9\ud574 \ubcf4\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \ub41c\ub2e4.<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

\uac19\uc740 \ubc29\ubc95\uc744 \"\frac{\partial\uc758 \ubaa8\ub4e0 \uc6d0\uc18c\ub4e4\uc5d0 \uc801\uc6a9\ud558\uba74<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

\uc774\uac83\uc744 matrix\uc758 \ud615\ud0dc\ub85c \ub098\ud0c0\ub0b4\uba74<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

Matrix Y\uc640 W\ub97c \uad6c\ubd84\ud574 \ubcf4\uba74<\/p>\n\n\n\n\"\frac{\partial\n\n\n\n

Weight matrix W\uc758 \uc804\uce58\ud589\ub82c(transpose matrix)\ub97c \uacf1\ud558\ub294 \uac83\uc774 \ub418\ubbc0\ub85c,<\/p>\n\n\n\n

\"\frac{\partial\uc774 \uc131\ub9bd\ud55c\ub2e4.<\/p>\n\n\n\n

<\/p>\n\n\n\n

Weight\uc5d0 \ub300\ud55c loss function\uc758 \ubcc0\ud654\uc778 \"\frac{\partial\ub3c4 \uae30\ubcf8\uc801\uc73c\ub85c \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uc720\ub3c4 \ub418\ub294\ub370 \ub108\ubb34 \uae38\uc5b4\uc838\uc11c 2\ud3b8\uc5d0\uc11c<\/a> \uac04\ub2e8\ud788 \ub2e4\ub8e8\ub3c4\ub85d \ud55c\ub2e4.<\/p>\n","protected":false},"excerpt":{"rendered":"

\uc2e4\uc81c\ub85c \uc804\uac1c\ud574\ubcf4\uba74 \ub2e4\uc74c \uc2dd\uc774 \ub3c4\ucd9c\ub429\ub2c8\ub2e4([\uc2dd 5.13]\uc73c\ub85c \uc774\ub044\ub294 \uacfc\uc815\uc740 \uc0dd\ub7b5\ud569\ub2c8\ub2e4). – p172, 5.6.1 Affine \uacc4\uce35, \ubc11\ubc14\ub2e5\ubd80\ud130 \uc2dc\uc791\ud558\ub294 \ub525\ub7ec\ub2dd \uc544\ub2c8! \uadf8\uac78 \uc0dd\ub7b5\ud558\uba74 \uc5b4\ub5a1\ud574\uc694!! “\ubc11\ubc14\ub2e5\ubd80\ud130 \uc2dc\uc791\ud558\ub294 \ub525\ub7ec\ub2dd”\uc744 \uc77d\uc73c\uba74\uc11c \ub525\ub7ec\ub2dd\uc758 \uac1c\ub150\uc744 \uc7a1\ub294\ub370 \ub9ce\uc740 \ub3c4\uc6c0\uc744 \ubc1b\uace0 \uc788\uc9c0\ub9cc \uad73\uc774 \ub2e8\uc810\uc744 \ub4e4\uc790\uba74 \uc8fc\uc694\ud55c \uacf5\uc2dd \ub4e4\uc5d0 \ub300\ud574 \uc124\uba85\ud558\uc9c0 \uc54a\uace0 \uadf8\ub0e5 \ub118\uc5b4 \uac00\ubc84\ub9ac\ub294 \uacbd\uc6b0\uac00 \uac00\ub054 \uc788\ub2e4. \uc704\uc5d0\uc11c \ub9d0\ud558\ub294 [\uc2dd 5.13]\uc740 back propagataion\uc5d0\uc11c \uc785\ub825\uc5d0 \ub300\ud55c […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5],"tags":[216,212,213,214,217,215],"class_list":["post-2175","post","type-post","status-publish","format-standard","hentry","category-programming","tag-affine-layer","tag-back-prop","tag-back-propagation","tag-deep-learning","tag-linear-layer","tag-transpose-matrix"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/litcoder.com\/index.php?rest_route=\/wp\/v2\/posts\/2175","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/litcoder.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/litcoder.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/litcoder.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/litcoder.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2175"}],"version-history":[{"count":242,"href":"https:\/\/litcoder.com\/index.php?rest_route=\/wp\/v2\/posts\/2175\/revisions"}],"predecessor-version":[{"id":4131,"href":"https:\/\/litcoder.com\/index.php?rest_route=\/wp\/v2\/posts\/2175\/revisions\/4131"}],"wp:attachment":[{"href":"https:\/\/litcoder.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/litcoder.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/litcoder.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}