Let's say a convolutional layer takes an input $X$ with dimensions of 5x100x100 and applies 10 filters $F$ 5x5x5, thus produces an output $O$ 10 feature maps 96x96.
During the backpropagation the layer receives $\frac{dE}{dO}$ of shape 10x96x96.
My question is how to compute $\frac{dE}{dF}$ ?
According to that article $\frac{dE}{dF}$ can be calculated as convolution between $X$ and $\frac{dE}{dO}$. Unfortunately, the article does not cover a case with multiple filters and multiple input channels.
Since $X$ has shape 5x100x100 and $\frac{dE}{dO}$ has shape 10X96x96 the depth of $X$ equals to 5 and the depth of $\frac{dE}{dO}$ equals to 10. So the depth dimension does not match. How to compute convolution in that case ?