Convolution Neural Networks on microcontrollers I am wondering if an already trained convolutional neural network can be represented as a formula just like a perceptron can ($x_1w_1 + x_2w_2 + \ldots =$ PREDICTION). I know that the formula could be a lot more complicated like this, but in general would it be possible to train a CNN in Python or Matlab, get the weights and create an arithmetic, exponential, whatever formula made with those acquired weights?

I want to do this because I am trying classify in a PIC32 which I think does not have the capacity to perform a CNN within itself. 

Or do you know if there is a "c library" that can do CNNs?
What you are looking for is often called an inference engine. Tensorflow Lite for microcontrollers was just announced. I have not seen anyone use it on PIC32, but it should be possible to port it to that platform.

For ARM Cortex-M microcontrollers there are a couple more options, for instance uTensor and CMSIS-NN. The latter is low level implementation using integer math only, which could be a good inspiration if your microcontroller does not have hardware support for floating point.