Related papers: Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks

Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks

URL: http://arxiv.org/abs/2507.16871v1
Date: Tue, 22 Jul 2025 07:34:53 GMT
Title: Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks
Authors: Pietro Giuseppe Fré, Federico Milanesio, Guido Sanguinetti, Matteo Santoro,
Abstract summary: An initial implementation of these concepts has been presented in a twin paper under the moniker of Cartan Neural Networks.<n>The current paper expands on the mathematical structures underpinning Cartan Neural Networks, detailing the geometric properties of the layers.<n>Together, these papers constitute a first step towards a fully geometrically interpretable theory of neural networks exploiting group-theoretic structures.
Score: 0.3749861135832073
License: http://creativecommons.org/licenses/by/4.0/
Abstract: Recent work has identified non-compact symmetric spaces U/H as a promising class of homogeneous manifolds to develop a geometrically consistent theory of neural networks. An initial implementation of these concepts has been presented in a twin paper under the moniker of Cartan Neural Networks, showing both the feasibility and the performance of these geometric concepts in a machine learning context. The current paper expands on the mathematical structures underpinning Cartan Neural Networks, detailing the geometric properties of the layers and how the maps between layers interact with such structures to make Cartan Neural Networks covariant and geometrically interpretable. Together, these twin papers constitute a first step towards a fully geometrically interpretable theory of neural networks exploiting group-theoretic structures

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