A topological model for partial equivariance in deep learning and data analysis
Nicola Quercioli
Patrizio Frosini- 1University of Bologna, Italy
- 2Royal Institute of Technology, Sweden
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.
Keywords: partial-equivariant neural network, P-GENEO, Pseudo-metric space, Compactness, convexity
Received: 04 Aug 2023;
Accepted: 27 Nov 2023.
Copyright: © 2023 Quercioli, Ferrari, Frosini and Tombari. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Mx. Nicola Quercioli, University of Bologna, Bologna, Italy