Speaker
Jose I. Rodriguez, University of Wisconsin-Madison
Abstract
Neuroalgebraic geometry studies function spaces parameterized by machine learning models when they are algebraic or semialgebraic. In this setting, algebro-geometric invariants can be related to notions of expressivity and training behavior. In this talk, we focus on feedforward polynomial neural networks (also known as monomial multilayer perceptrons). For these models, geometric properties such as dimension translate directly into statements about expressivity.
We discuss a conjecture of Kileel, Trager, and Bruna concerning the structure of minimal filling architectures, i.e., networks achieving maximal expressivity with minimal size. Our main result is a counterexample to this conjecture, obtained in joint work with Kevin Dao, demonstrating that the proposed characterization does not hold in general. We conclude with several open problems and directions for future research.