Chapter 7
Backprop through a convolution.
A network learns by asking each weight one question: if you changed a little, would the answer get better or worse? This chapter works out that question for a convolution.
Chapter 1 said that training adjusts a network’s weights, little by little, until it gives good answers, and chapter 2 said that a CNN’s kernels are learned rather than designed. This chapter shows how.
It starts with a single weight: how to measure how wrong an answer is, and which way to nudge the weight to make it less wrong. Then it does the same for a convolution, on chapter 2’s 4×4 example, by hand. Weight sharing turns out to matter here too: every weight is used at every position, so its nudge has to account for all of them. The chapter ends by putting the pieces together and watching a kernel learn itself from scratch.
The math is multiplication and addition, the same as the forward direction. No calculus is needed beyond the idea of a slope, and the first module explains that.
Modules
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