Q:

What is learned in convolutional network

In a convolutional net (CNN), someone answered to me than filters are initialized randomly.
I'm ok for this, but, when there is the gradient descent, who is learning? The features maps, or the filters ?
My intuition is the filters are learning, because they need to recognize complex things.
But I would like to be sure about this.

A:

In the context of convolutional neural networks, kernel = filter = feature detector.
Here is a great illustration from Stanford's deep learning tutorial (also nicely explained by Denny Britz). 

The filter is the yellow sliding window, and its value is:

The feature map is the pink matrix. Its value depends on both the filter and the image: as a result, it doesn't make sense to learn the feature map. Only the filter is learnt when the network is trained. The network may have other weights to be trained as well.

