Extending current mathematical theory behind CNNs and its variants

Deep Learning has been very flourishing in recent years. Unfortunately, as was stated by many researchers in their publications, the theory behind it did not manage to keep up with this development, leaving us with several very sophisticated and unfathomed-like models. Trying to understand how the individual components affect the performance of those models using ablation study rather than strict mathematical verification and employing empirical evidence in place of robust proofs does not lead to a complete understanding of a model and halts its further advancement. That is why this research aims to focus on extending the mathematical foundations used by theoreticians in understanding of Convolutional Neural Networks and their variants.