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.



src:http://www.wildml.com/2015/11/understanding-convolutional-neural-networks-for-nlp/ 

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.
$$ W = W - \alpha\frac{\partial L}{\partial W} $$

Convolutional Neural Networks also use back-propagation algorithm to find partial derivatives of loss w.r.t. filter matrix.