Talk
Tropical Geometry of Deep Neural Networks
- Liwen Zhang (University of Chicago)
Abstract
In this talk, we show that the family of feedforward neural networks with ReLU activation is equivalent to the family of tropical rational maps. Given this observation, we relate decision boundaries of ReLU-activated networks to tropical hypersurfaces. And we study the expressiveness of these neural networks via the vertices of polytopes associated with tropical rational functions. As an application of this tropical formulation, we reproduce the upper bound on the number of linear regions achievable by deep ReLU neural networks.
