Geometry of Deep Neural Networks

Abstract

In this chapter, which is mathematically intensive, we will try to answer perhaps the most important questions of machine learning: what does the deep neural network learn? How does a deep neural network, especially a CNN, accomplish these goals? The full answer to these basic questions is still a long way off. Here are some of the insights we’ve obtained while traveling towards that destination. In particular, we explain why the classic approaches to machine learning such as single-layer perceptron or kernel machines are not enough to achieve the goal and why a modern CNN turns out to be a promising tool.