Topological Deep Learning: Classification Neural Networks
It provides a foundational mathematical framework for deep learning, potentially benefiting researchers by offering new insights into classification problems, though it appears incremental as an initial study in a series.
The paper introduces a topological formalism to deep learning, focusing on the classification problem, and demonstrates conditions under which classification is possible or impossible in neural networks, highlighting aspects not easily seen with traditional methods.
Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning problem. This is the first of a sequence of articles with the purpose of introducing and studying this formalism. In this article, we define and study the classification problem in machine learning in a topological setting. Using this topological framework, we show when the classification problem is possible or not possible in the context of neural networks. Finally, we demonstrate how our topological setting immediately illuminates aspects of this problem that are not as readily apparent using traditional tools.