用对称空间理论构建可解释的神经网络，提升模型几何一致性。
Navigation through Non-Compact Symmetric Spaces: a mathematical perspective on Cartan Neural Networks
- 基于非紧对称空间构造神经网络层，实现几何协变性。
- 证明层间映射保持对称结构，确保网络可解释性。
- 适合研究几何深度学习与群论驱动模型的学者。
近期研究表明，非紧对称空间 U/H 是发展几何一致神经网络理论的有前景的齐性流形类别。前序论文提出名为 Cartan Neural Networks 的初步实现，验证了这些几何概念在机器学习中的可行性与性能。本文深入探讨了 Cartan 神经网络背后的数学结构，详细描述了各层的几何特性，以及层间映射如何与这些结构相互作用，使网络具备协变性与几何可解释性。这两篇论文共同构成利用群论结构实现完全几何可解释神经网络理论的第一步。
原文摘要 · Abstract (English)
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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