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The actual numbers are just for the sake of clarifying my question, of course. What I mean is, since each channel in a multi-channel convolution has its own filter, what difference does it make if, given three 2d-arrays of data, one first combines that into a multi-channel input that undergoes a multi-channel convolution, vs. use three separate one channel convolutions?

The "channels" just seem to exist for organizing related inputs conceptually rather than mathematically changing anything. Am I missing something?

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  • $\begingroup$ There is a difference. The output of a "multi-channel convolution" (e.g. 5x5x3) can potentially combine information across channels. For example, it can compute the sum or difference of two channels. This is not possible using a per-channel convolution. $\endgroup$
    – bogovicj
    Commented Oct 15 at 1:00

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