Deep Neural Networks in a Mathematical Framework

This SpringerBrief describes how to build a rigorous end-to-end mathematical frameworkfor deep neural networks. The authors provide tools to represent and describeneural networks, casting previous results in the field in a more naturallight. In particular, the authors derive gradient descent algorithms in a unified wayfor several neural network structures, including multilayer perceptrons,convolutional neural networks, deep autoencoders and recurrent neuralnetworks. Furthermore, the authors developed framework is both more conciseand mathematically intuitive than previous representations of neuralnetworks. This SpringerBrief is one step towards unlocking the black box of DeepLearning. The authors believe that this framework will help catalyze further discoveriesregarding the mathematical properties of neural networks.This SpringerBrief isaccessible not only to researchers, professionals and students working andstudying in the field of deep learning, but alsoto those outside of the neutralnetwork community.