Mathematics of Deep Learning
This is an incremental tutorial that synthesizes existing research to clarify foundational mathematical principles for researchers and practitioners in machine learning.
The paper addresses the lack of mathematical understanding behind the success of deep learning in recognition systems, reviewing recent work that aims to justify properties like global optimality, geometric stability, and invariance in deep networks.
Recently there has been a dramatic increase in the performance of recognition systems due to the introduction of deep architectures for representation learning and classification. However, the mathematical reasons for this success remain elusive. This tutorial will review recent work that aims to provide a mathematical justification for several properties of deep networks, such as global optimality, geometric stability, and invariance of the learned representations.