Convolutional Neural Network with constant kernels I'm starting to learn about CNNs, and I have this question that I haven't been able to answer. Sorry if it is too basic.

I know that in a CNN, the network learns to extract relevant features of images in order to classify them. My question is: if I just update the weights of the fully-connected layer and leave the kernels constant, will the network learn how to classify as well?

(The kernels might be a Gaussian blur or a sharpenning, or whatever comes to mind).
A fully connected layer is able to classify images better than random. If you make the kernels constant and there is still information in the result, the network is essentially only a FCN operating on a preprocessed image. Of course it will learn how to classify the image. But it will certainly be worse than a similar network where the convolutional weights are learned.