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複数スタイルの融合と 部分的適用を可能とする Multi-style Feed-forward Networkの提案

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Ryosuke Tanno
Ryosuke Tanno

This document describes the mathematical operations of a convolutional layer in a neural network. It shows that a convolutional layer can be represented as a matrix multiplication between the input feature maps and the convolutional kernels. To perform this matrix multiplication, the input is first transformed using im2col to form a 2D matrix, where each column consists of a patch from the input. This matrix is then multiplied with the kernel matrix to produce the output feature maps.

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複数スタイルの融合と 部分的適用を可能とする Multi-style Feed-forward Networkの提案
複数スタイルの融合と 部分的適用を可能とする Multi-style Feed-forward Networkの提案
複数スタイルの融合と 部分的適用を可能とする Multi-style Feed-forward Networkの提案
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複数スタイルの融合と 部分的適用を可能とする Multi-style Feed-forward Networkの提案
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複数スタイルの融合と 部分的適用を可能とする Multi-style Feed-forward Networkの提案
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1 4 + = ( 1/2 23 C l 6 2 – BG- E ) l 1 4> A ( + = 1 4 1/2 23 + =conv. kernels input feature maps 2 3 patch 1 patch 2 patch 3 patch 4 patch 5 1 4 matrix multiplication (=conv. layer computation) L im2col kernel 2 kernel 3 kernel 1 kernel 4 patch1 patch2 patch3 patch4 patch5 patch1 patch2 patch3 patch4 patch5 kernel 1 L + 3 Lkernel 2 patch1 patch2 patch3 patch4 patch5 + 3 + 3 Lkernel 3 patch1 patch2 patch3 patch4 patch5 + 3 L patch1 patch2 patch3 patch4 patch5 kernel 4

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複数スタイルの融合と 部分的適用を可能とする Multi-style Feed-forward Networkの提案

  • 2. l 5 1 – 2 I 0 ( A ( 0 5 – A 1 ) 2 2 1 ( 1 – 1 5 2 0 81
  • 3. - l 2 2 5 a 0 2 6 +, 1 – ie ] – VT o [ – GN Rn P CSd – l A f l – G – P V argmin '()(*+ = -'.)/(0/( + 2'3(4+0 '()(*+ '.)/(0/( '3(4+0 2 input conv3_1 conv1_1 conv2_1 conv4_1 conv5_1 conv4_2 ( - ) ( 5+ = 6789+ 6789+ : U G P ?< ?= ?>
  • 4. ( l 332 1 2 G F – ) !" – -E JC G F + 6 6 . 0
  • 5. ) ( l 4p dL 3 , 4pC mb 3 )3 . Rao UR_l 1. W #R $% F &' Rg 2. &', '*, '+R,-.. /01 2 2 Lk S LnRg g nC 3 ( 3 ( R ULe iDcR N 3 Rao
  • 6. ) ( l G 8 G6!" C #$ + 5 1 - %&'()*() %+),-* 8 5 5 G ./ 5 5 G arg345 ./ = 7%&'()*() + 9%+),-* + D
  • 7. 1 0 l - 6 6 F – C E NJ 1 + 21 1 – T C E NJ ? J ? 1 l G – ? ? S !" 110 26 0 6
  • 9. 1 () 0 l 3 – 0 1 J – 0 1 : 1 1 () ,
  • 10. l () )3 – > – 1 J 0 - , , , ,
  • 11. l ) ( ) (, D C1 , , ),(), 0 0
  • 12. l -1 > S CD GMP S !" N #$ 0 5 6 5 2,, ( %&'()*() %+),-* CD G S -1 + 5 S ./ -1 + 5 S arg345 ./ = 7%&'()*() + 9%+),-* + O CD G G 1 5 ) 1 5 )
  • 16. J7 7 – e :m 2.1 21 7 i h n ) + ) 5 ) + + )0 3.21
  • 17. l a C – 13- e – -3 -6 3 > l G Pb – > 3 R c – M U 6 1
  • 18. l : – - - - : : ? 7 E ? C 1
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  • 22. - l – > l – + 1 ? 1 ) J ? l – > ? 1 ? 1 2 ( ? 1 – > >
  • 23. 0 D N IS OL B D 3 9 0 1 2 -
  • 25. l – 5 4 -3 2 4 -> -3 2 4 -> CL – 54 -> D E C – -2 2 3 49 C
  • 26. l EB O a e A C D C B O L 525 / ( ) O S d MN L C /1 -/ / 2- + > ü + / - / +2 !"#$% C D
  • 27. 1 4 + = ( 1/2 23 C l 6 2 – BG- E ) l 1 4> A ( + = 1 4 1/2 23 + =conv. kernels input feature maps 2 3 patch 1 patch 2 patch 3 patch 4 patch 5 1 4 matrix multiplication (=conv. layer computation) L im2col kernel 2 kernel 3 kernel 1 kernel 4 patch1 patch2 patch3 patch4 patch5 patch1 patch2 patch3 patch4 patch5 kernel 1 L + 3 Lkernel 2 patch1 patch2 patch3 patch4 patch5 + 3 + 3 Lkernel 3 patch1 patch2 patch3 patch4 patch5 + 3 L patch1 patch2 patch3 patch4 patch5 kernel 4