Topological Complexity of Decision Boundaries

Abstract

Complex data requires complex models, or so the saying goes. However, the reason why classifying two concentric circles is challenging is not because they are circles, but because they are concentric. Our contribution aims at shifting the focus from data-driven to task-oriented models. To this aim, we study the topology of the decision boundary of a classification problem as a measure of its intrinsic complexity. We employ a topological approach to understand how the architecture of a model can limit its topological expressiveness and how complex data might not equate with difficult classification problems.

António Leitão

Student

Topological analysis of learning systems.