Suggestion of article or book for convolution

Question

I need a good book or article to learn about convolution.I have a course in Neural Networks and we have to make calculations by hand.

Answer 1

Here are a few references concerning convolutions, specifically regarding their applications to deep networks and machine learning:

• A guide to convolution arithmetic for deep learning by Dumoulin and Visin

• An Introduction to Convolutional Neural Networks by O'Shea and Nash

• Chapter 9, Convolutional Networks in the Deep Learning book by Goodfellow et al

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I also like the way presented here. Convolution (in 2D) can be written: $$ (I\ast K)(s,t) = F_I(s,t|K) = \sum_{\alpha,\beta} I(s-\alpha,t-\beta) K(\alpha,\beta) $$ where $I$ is the image (signal) and $K$ is the kernel (filter). We can think of this operation as generating the filtered output $F_I$ by copying local parts of $I$ over and over, each time translating and scaling it based on the values in $K$. Or, we can think of it getting each entry by flipping $K$, and then iteratively shifting it over $I$, taking the dot product at each point (across both dimensions).

Note that most deep learning frameworks actually do not do convolution. They perform cross-correlation. There is a difference. (It is why $K$ has to be flipped in the paragraph above, before computing the sliding "dot products", while many ML implementations will not do this. This can be confusing if you need to go into the details.)