Adjusting convolutional layer filter kernel weights?

Question

Neural networks

Good afternoon!
I'm trying to write a convolutional neural network and I have a question:
How to adjust the filter kernel weights? As far as I understand, the kernel weights are adjusted as follows:
W = W - learning_rate*error(delta)*derivative_of_activation_function_at_point*input_value

That is, how to change the weights, given that there are many outputs and deltas?
Picture from the Internet, if suddenly mine is not clear.

Answer 1

You also run the core over the layer and add the resulting weight errors from your cells. Those. the error for the central cell will be the sum of all the kernel locations that fall on that cell. In general, it’s difficult to explain on the fingers, see the finished code, or even a little better.
https://github.com/karpathy/convnetjs/blob/master/...