Codes and Expansions (CodEx) Seminar

Jose Israel Rodriguez (University of Wisconsin)
Activation Degree Thresholds and Expressiveness of Polynomial Neural Networks

Polynomial neural networks are implemented in a range of applications and present an advantageous framework for theoretical machine learning. In this talk, we introduce the notion of the activation degree threshold of a network architecture. This expresses when the dimension of a neurovariety achieves its theoretical maximum. We show that activation degree thresholds of polynomial neural networks exist and provide an upper bound, resolving a conjecture on the dimension of neurovarieties associated to networks with high activation degree. Along the way, we will see several illustrative examples.