The equivariance relaxation morphism, which preserves functionality while reparameterizing a group equivariant layer to operate with equivariance constraints on a subgroup, and the [ G ]-mixed equivariant layer, which mixes operations constrained to equivariance to different groups to enable within-layer equivariance optimization.
A detailed and in-depth characterization of symmetry increase is provided together with a principled framework for its reduction and practical guidelines for feature design to prevent harmful symmetry increases are proposed.
Ning Lin, Jiacheng Cen, Anyi Li et al.· 1 citation
This paper formalizes data-dependent parameter symmetries and characterize loss invariance and the group-action axioms through infinitesimal conditions, which provide objectives for jointly learning group generators and nonlinear action maps.
Bo Zhao, Nima Dehmamy, Robin Walters et al.· 0 citations
ESNN is introduced, an Equivariant Sheaf Neural Network that enriches this interaction by learning directed, matrix-valued transport between neighboring vector features while preserving exact Euclidean equivariance.
Alessio Borgi, M. Severino, Fabrizio Silvestri et al.· 0 citations
Artificial neural networks are often regarded as powerful yet opaque black boxes. Here, we demonstrate that learning in deep neural networks generates local symmetries known in graph theory as fibrations and coverings. We prove that covering symmetries are stable attractors of stochastic gradient descent. Consistent wi...
O. Velarde, Lucas C. Parra, Alireza Hashemi et al.· 1 citation
Many learning tasks require stability to small transformations while retaining sensitivity to larger ones. We introduce \emph{transversal pooling neural networks}, which generalize spatial max pooling to affine group actions. We establish equivariance to a chosen subgroup and derive explicit stability bounds for indivi...
Emily J. King, D. Mixon, Michael Perlmutter et al.· 0 citations
This tutorial provides a comprehensive introduction to rotational equivariance, starting from the physical and geometric intuition behind coordinate independence and building up the necessary machinery from geometric deep learning, group theory, and representation theory.
Peter Lippmann, Fred A. Hamprecht· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.