A topological model for partial equivariance in deep learning and data analysis
Machine Learning
2023-08-28 v1 Machine Learning
Algebraic Topology
Abstract
In this article, we propose a topological model to encode partial equivariance in neural networks. To this end, we introduce a class of operators, called P-GENEOs, that change data expressed by measurements, respecting the action of certain sets of transformations, in a non-expansive way. If the set of transformations acting is a group, then we obtain the so-called GENEOs. We then study the spaces of measurements, whose domains are subject to the action of certain self-maps, and the space of P-GENEOs between these spaces. We define pseudo-metrics on them and show some properties of the resulting spaces. In particular, we show how such spaces have convenient approximation and convexity properties.
Cite
@article{arxiv.2308.13357,
title = {A topological model for partial equivariance in deep learning and data analysis},
author = {Lucia Ferrari and Patrizio Frosini and Nicola Quercioli and Francesca Tombari},
journal= {arXiv preprint arXiv:2308.13357},
year = {2023}
}