10 papers
Singular Learning and Occam's Razor in Deep Monomial Networks
Kathlén Kohn, Giovanni Luca Marchetti, Farhan Shabir +2
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…
Conservation Laws from Data Symmetry in Neural Networks
Jakob Galley, Vahid Shahverdi, Axel Flinth
We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks. Under the assumption that the loss funct…
Identifiable Equivariant Networks are Layerwise Equivariant
Vahid Shahverdi, Giovanni Luca Marchetti, Georg Bökman +1
We investigate the relation between end-to-end equivariance and layerwise equivariance in deep neural networks. We prove the following: For a network whose end-to-end function is e…
Learning on a Razor's Edge: Identifiability and Singularity of Polynomial Neural Networks
Vahid Shahverdi, Giovanni Luca Marchetti, Kathlén Kohn
We study function spaces parametrized by neural networks, referred to as neuromanifolds. Specifically, we focus on deep Multi-Layer Perceptrons (MLPs) and Convolutional Neural Netw…
Algebra Unveils Deep Learning -- An Invitation to Neuroalgebraic Geometry
Giovanni Luca Marchetti, Vahid Shahverdi, Stefano Mereta +2
In this position paper, we promote the study of function spaces parameterized by machine learning models through the lens of algebraic geometry. To this end, we focus on algebraic…
On the Geometry and Optimization of Polynomial Convolutional Networks
Vahid Shahverdi, Giovanni Luca Marchetti, Kathlén Kohn
We study convolutional neural networks with monomial activation functions. Specifically, we prove that their parameterization map is regular and is an isomorphism almost everywhere…