A singular Riemannian geometry approach to deep neural networks. I: Theoretical foundations

DOI10.1016/j.neunet.2022.11.022zbMath1529.68274arXiv2201.09656OpenAlexW4309471870MaRDI QIDQ6077759

Alessandro Benfenati, Alessio Marta

Publication date: 18 October 2023

Published in: Neural Networks (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.09656

zbMATH Keywords

fiber bundlesdeep learningsingular Riemannian metricssmooth neural networks

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Applications of global differential geometry to the sciences (53C80)

Cites Work

• Introduction to the theory of Lie groups. Translated from the French by Urmie Ray
• Lie algebras and Lie groups. 1964 lectures, given at Harvard University.
• Degenerate Riemannian metrics
• Generalized connections in vector bundles
• Multilayer feedforward networks are universal approximators
• Pseudoconnections and manifolds with degenerate metrics
• Community detection in node-attributed social networks: a survey
• The universal approximation property. Characterization, construction, representation, and existence
• An introduction to manifolds. 2nd revised ed.
• Neural Networks and Deep Learning
• Mathematics for Machine Learning
• Approximation by superpositions of a sigmoidal function
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