# Adjusting weights in an convolutional neural network

I'm trying to implement a convolutional neural network at the moment. A simple feedforward network is not the problem but I'm having some trouble with the weight adjustment in the conv layer.

Lets assume I have four layers. Input, convolution, hidden and output.

In the picture above we just see the input and the convolution layer. The deltas of the convolution layer are calculated as in a normal feedforward network. But how do I update the weights/filtermatrix between input and convolutionlayer?

For learning kernel/filter matrix in convolution layer, we find partial derivative of loss w.r.t. filter matrix and use gradient descent method to update filters. $$W = W - \alpha\frac{\partial L}{\partial W}$$