Algebraic Complexity and Neurovariety of Linear Convolutional Networks

no code implementations • 29 Jan 2024 • Vahid Shahverdi

Notably, this count significantly surpasses the number of critical points encountered in the training of a fully connected linear network with the same number of parameters.

Geometry of Linear Neural Networks: Equivariance and Invariance under Permutation Groups

no code implementations • 24 Sep 2023 • Kathlén Kohn, Anna-Laura Sattelberger, Vahid Shahverdi

We prove that all invariant linear functions can be parameterized by a single linear autoencoder with a weight-sharing property imposed by the cycle decomposition of the considered permutation.

Function Space and Critical Points of Linear Convolutional Networks

no code implementations • 12 Apr 2023 • Kathlén Kohn, Guido Montúfar, Vahid Shahverdi, Matthew Trager

We study the geometry of linear networks with one-dimensional convolutional layers.