I've already seen many articles about this topic and Backpropagation In Convolutional Neural Networks by Jefkine (5 September 2016) seems to be the best. Although, as author said,

For the purposes of simplicity we shall use the case where the input image is grayscale i.e single channel C = 1.

Also, he uses stride = 1 and assumes only 1 filter, for the same purpose.

These are the final equations for backpropagation (taken from the article):


The autor's notation explained:


I figured out how to do the forward pass with stride, depth and more filters, but couldn't do the same with the backpropagation. Do you know where to put the 3rd dimension, stride and filters number in those equations?

Also, how to backpropagate the bias (assuming there's 1 bias per filter)?

Thanks in advance.

  • $\begingroup$ (3) The thing @quintumnia may have thought might be hindering effective feedback is that by "shooting images" of the math you obfuscated the original writing. $\endgroup$ – FauChristian Jul 22 '18 at 9:54
  • $\begingroup$ Just ask the question and let people open another tab for the article. ... I suggest doing those three things now before naysayers start down voting and locking your otherwise excellent question (one which I want to answer once I know the whole thread won't get shut down). $\endgroup$ – FauChristian Jul 22 '18 at 9:56
  • $\begingroup$ Thank you very much for clarifying that! Shall I get rid of the images of the math? I wanted to bring the most important equations, so people won't need to read the entire article (it might be necessary to read that, though). $\endgroup$ – anx199 Jul 22 '18 at 11:25
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    $\begingroup$ Welcome to AI.SE! I think what people are getting at is that each question should be posted to exactly one Stack Exchange site, since cross-posting duplicates efforts across the communities. Since you've also posted this question on Data Science (where it is a better fit), I'll close this copy. Sorry for the confusion! $\endgroup$ – Ben N Jul 22 '18 at 15:46
  • $\begingroup$ @BenN Sorry about the copy, I've read a post on meta about this site and though it could be a better fit than data sciene. Anyway, I think no one is going to answer my question. $\endgroup$ – anx199 Jul 22 '18 at 16:36