How CNN Filters Are Trained: Convolution Backpropagation Step by Step

How does a convolutional neural network learn the numbers inside its filters? This video works through backpropagation in a convolution layer by hand, with a tiny example you can check yourself. Start with the slopes that arrive from the layers above, then find the slope of one kernel weight by adding pixel times slope over every position it touched. See the shortcut of sliding the slope grid over the input to get all weight slopes at once, why the bias slope is the sum of the output slopes, and how shared weights collect slope from the whole image. Then update the filter with gradient descent and pass slopes back to the input pixels for the previous layer.