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, we obtain the so-called GENEOs. We then study the spaces of measurements, whose domains are subjected 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.
A topological model for partial equivariance in deep learning and data analysis / Ferrari L.; Frosini P.; Quercioli N.; Tombari F.. - In: FRONTIERS IN ARTIFICIAL INTELLIGENCE. - ISSN 2624-8212. - ELETTRONICO. - 6:(2023), pp. 1-11. [10.3389/frai.2023.1272619]
A topological model for partial equivariance in deep learning and data analysis
Frosini P.;Quercioli N.
;
2023
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, we obtain the so-called GENEOs. We then study the spaces of measurements, whose domains are subjected 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.File | Dimensione | Formato | |
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