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Let's say we have an Input 10x10x3 (WxHxD) and 5 filters 3x3x3. Convolution between Input and filters will be 8x8x5.

During backpropagation we will get error with the same size 8x8x5. While calculating dE/dF how do I perform convolution when depth between filters and error do not match. The same thing goes to dE/dX.

I understand that I need to perform 'FULL' convolution while calculating dE/dF but that's just impossible without the same depth.

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In the forward pass, you can see that each of the five filters is responsible only for one of the depth channels of the output. I think that also applies when calculating dE/dF: doing 'normal' convolution between input and each channel of the output error will give you dE/dF for one filter. By iterating over all output channels, you get dE/dF for all filters.

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