Convolution Neural Networks on microcontrollers
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.