arXiv:2609.25987v1 Announce Type: new
Abstract: Equivariant convolutional neural networks are usually built from a group acting globally on the space of signals. This hypothesis is inappropriate for...
By Alberto Ibort, Maria Jimenez-Vazquez, Juan M. Perez-Pardo
arXiv:2510. 15814v2 Announce Type: replace-cross Abstract: Universality results for equivariant neural networks remain rare.
By Marco Pacini, Mircea Petrache, Bruno Lepri, Shubhendu Trivedi, Robin Walters
The paper introduces a new mathematical framework for polynomial group convolutional neural networks (PGCNNs) using graded group algebras. It presents two natural parametrizations of the architecture—based on Hadamard and Kronecker products—that are related by a linear map. The authors compute the dimension of the resulting neuromanifold, show it depends only on the number of layers and group size, and describe the general fiber of the Kronecker parametrization, conjecturing a similar description for the Hadamard case, supported by explicit computations for small groups and shallow networks.
By Yacoub Hendi, Daniel Persson, Magdalena Larfors
arXiv:2609.36237v1 Announce Type: new
Abstract: Many learning tasks require stability to small transformations while retaining sensitivity to larger ones. We introduce \emph{transversal pooling neura...
By Emily J. King, Dustin G. Mixon, Michael Perlmutter, Lander Ver Hoef
arXiv:2408.08823v2 Announce Type: replace
Abstract: We develop a theoretical foundation for designing group-equivariant neural networks that align the choice of symmetries with the underlying probabi...
By Vishal S. Ngairangbam, Michael Spannowsky
arXiv:2607. 03798v1 Announce Type: cross Abstract: Symmetry is everywhere in nature and society.
By Yoshihiro Maruyama