From 0e0198bca2bde6f884757224a4977203bcf3bc64 Mon Sep 17 00:00:00 2001 From: julienChemillier Date: Tue, 14 Feb 2023 15:21:09 +0100 Subject: [PATCH] Add convolution to explaination --- doc/cnn/backpropagation_explaination.md | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/doc/cnn/backpropagation_explaination.md b/doc/cnn/backpropagation_explaination.md index d3b8cf2..b3d69c9 100644 --- a/doc/cnn/backpropagation_explaination.md +++ b/doc/cnn/backpropagation_explaination.md @@ -55,3 +55,18 @@ $\forall i,j: \space b_{i j} = \dfrac{a_{2i \space 2j} + a_{2i+1 \space 2j} + a_ > Derivatives: $\forall i,j: \space \dfrac{\partial E}{\partial a_{i \space j}} = \dfrac{1}{4} \dfrac{\partial E}{\partial b_{k \space l}} $ where $k = \Big\lfloor \dfrac{i}{2} \Big\rfloor$ and $l = \Big\lfloor \dfrac{j}{2} \Big\rfloor$ +--- +--- + +## Backpropagation of a convolutionnal layer + + + + +$\forall i,j: c_{i \space j} = b_{i \space j} + \sum\limits_{0 \leqslant k, l \leqslant 1} \space k_{k \space l} c_{i+k, \space j+l}$ +$ $ + +> Derivatives: +$\dfrac{\partial E}{\partial b_{i,j}} = \dfrac{\partial E}{\partial c_{i, j}}$ +$\dfrac{\partial E}{\partial k_{i,j}} = \sum\limits_{p=0}^{2} \sum\limits_{l=0}^{2} \Big( \dfrac{\partial E}{\partial c_{k \space l}} a_{i+p, j+l}\Big)$ +$\dfrac{\partial E}{\partial a_{i,j}} = \sum\limits_{k=max(0, k\_size-1)}^{min(k\_size, dim\_input-j)} \sum\limits_{l=max(0, k\ _size-1)}^{min(k\_size, dim\_input-k)} \dfrac{}{}$