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Title: Activation degree thresholds and expressiveness of polynomial neural networks

Abstract: 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. This is joint work with Bella Finkel, Chenxi Wu, and Thomas Yahl.