Expressivity and Complexity of ReLU Networks

Neural networks have achieved remarkable success across many domains, but their theoretical foundations remain poorly understood. In this talk, I will present results from my thesis on the mathematical structure of ReLU neural networks. Focusing on expressivity and verification, we exploit the fact that ReLU networks compute continuous piecewise linear functions. This perspective enables the use of tools from polyhedral geometry, combinatorics, and computational complexity to study these networks.