The Geometry of Polynomial Group Convolutional Neural Networks

In this talk, we will talk about polynomial group convolutional neural networks (PGCNNs), where layers are group convolutions and the activation function is a monomial, and their associated neuromanifolds. In particular, we compute the dimension of the neuromanifolds and characterize their general fibers. The motivation of this work is due to neuroalgebraic geometry which connects the geometric properties of the neuromanifolds to the expressivity and identifiability of polynomial neural networks. The talk is based on a joint work with Daniel Persson (Chalmers) and Magdalena Larfors (Uppsala University).