Is it possible that can estimate convolutional kernel that have multi channels and multi filters ?

I saw answer from this to link to estimate kernel for one channel and one filter (Estimating Convolution Kernel from Input and Output Images). When I tried to implement it, I found that it cannot do correlation because the channel of output is not equal with the channel of input.

For example of data,

Input = 20 x 20 x 3 output = 20 x 20 x 32 kernel size = 3 x 3 x 3 x 32

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    $\begingroup$ so? do it for each output layer individually. -- why are you even trying to do that to the conv2d layer of a neural network? those are usually trained with backprop/gradient descent $\endgroup$ Jan 17, 2023 at 16:49

1 Answer 1


It is possible as things are staying linear and spatially invariant.

First, you can basically solve 32 times the same problem of input of size 20x20x3 filtered by 3x3x3 filter with output of size 20x20.

There are several computational approaches to solve this:


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