Im learning about Convolutional Neural Networks and right now i'm confused about how to implement it.
I know about regular neural networks and concepts like Gradient Descent and Back Propagation, And i can understand how CNN's how works intuitively.
My question is about Back Propagation in CNN's. How it happens? The last fully connected layers is the regular Neural Networks and there is no problem about that. But how i can update filters in convolution layers? How I can Back Propagate error from fully connected layers to these filters? My problem is updating Filters!
Filters are only simple matrixes? Or they have structures like regular NN's and connections between layers simulates that capability? I read about Sparse Connectivity and Shared Weights but I cant relate them to CNN's. Im really confused about implementing CNN's and i cant find any tutorials that talks about these concept. I can't read Papers because I'm new to these things and my Math is not good.
i dont want to use TensorFlow or tools like this, Im learning the main concept and using pure Python.
First off, I can recommend this introduction to CNNs. Maybe you can grasp the idea of it better with this.
To answer some of your questions in short:
Let's say you want to use a CNN for image classification. The picture consists of NxM pixels and has 3 channels (RBG). To apply a convolutional layer on it, you use a filter. Filters are matrices of (usually, but not necessarily) quadratic shape (e. g. PxP) and a number of channels that equals the number of channels of the representation it is applied on. Therefore, the first Conv layer filter has also 3 channels. Channels are the number of layers of the filter, so to speak.
When applying a filter to a picture, you do something called discrete convolution. You take your filter (which is usually smaller than your image) and slide it over the picture step by step, and calculate the convolution. This basically is a matrix multiplication. Then you apply a activation function on it and maybe even a pooling layer. Important to note is that the filter for all performed convolutions on this layer stays the same, so you only have P*P parameters per layer. You tweak the filter in a way, so that it fits the training data as well as possible. That's why its parameters are called shared weights. When applying GD, you simply have to apply it on said filter weights.
Also, you can find a nice demo for the convolutions here.
Implementing these things are certainly possible, but for starting out you could try out tensorflow for experimenting. At least that's the way I learn new concepts :)