Singular Learning and Occam's Razor in Deep Monomial Networks

arXiv:2606.28464v1 Announce Type: new Abstract: In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture. These critical points occur where the Jacobian of the model's parametrization is rank-deficient, and are the most pronounced singularities studied in Singular Learning Theory. We investigate such points in deep fully-connected networks with monomial activations via tools from polynomial algebra such as Mason's Theore...