Deep neural networks architectures from the perspective of manifold learning

Understand

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion.

• The purpose of this paper is a comprehensive comparison and description of neural network architectures in terms of ge-ometry and topology.
• We focus on the internal representation of neural networks and on the dynamics of changes in the topology and geometry of a data manifold on different layers.
• In this paper, we use the concepts of topological data analysis (TDA) and persistent homological fractal dimension.