Constructive Bounds for the Topological Expressivity of Neural Networks
Provides theoretical foundations for understanding neural network capacity through topological measures, essential for ML researchers.
AI Summary
Researchers prove constructive bounds on neural network expressivity using algebraic topology, establishing architectural requirements for expressing complex topological spaces.
Excerpt
The expressivity of a neural network $Φ$ describes the class of functions that a network can express. The term topological expressivity refers to a family of measures particularly suited to understand binary classification and is often formulated in terms of the Betti numbers of a decision boundary $β(Φ^{-1}(0))$. Despite its popularity, this measure is not as useful for regression and other problems that do not involve a decision boundary. Instead, we propose to study topological expressivity i