Understanding ReLU Networks Through Graph Problems and Polyhedra

Explore the theoretical foundations of ReLU neural networks through this conference talk that bridges machine learning with mathematical optimization. Delve into fundamental questions about feedforward ReLU networks, including the precise characterization of piecewise linear functions representable by networks of given depth and the identification of functions that can be represented by polynomial-size neural networks. Learn how tools from polyhedral geometry, graph theory, and combinatorial optimization provide new insights into these complex theoretical problems. Discover recent progress in understanding the representational capabilities and limitations of simple neural network architectures, moving beyond the complexity of modern large-scale models to examine the mathematical structures underlying basic ReLU networks. Gain insights into how graph problems and polyhedra relate to neural network expressivity and computational complexity in machine learning theory.