arXiv cs.AI· Jingzhou Liu·· 13 小时前AI 评分18
面向神经网络损失景观临界轨道的通用拓扑对称性指数
A General Topological Symmetry Index for Critical Orbits In Neural Network Loss Landscapes
AI 导读
研究者提出一种基于等变度理论的拓扑对称性指数，用于解码神经网络损失景观中由架构与学习目标产生的对称性及其临界轨道。该框架适用于任意网络架构，并包含可处理退化临界轨道的方法，能检测临界点的各向同性并量化相应的净拓扑贡献。论文以 softplus MLP、Transformer 和等变神经网络为例演示了具体计算。
正文 · 原文
Abstract:A systematic understanding of the global structure of neural-network loss landscapes remains challenging due to their high dimensionality. Symmetries arising from network architectures and learning objectives provide a way to investigate aspects of this structure. Although a growing number of studies have drawn attention to these symmetries, a systematic characterization of them, as well as of the critical orbits they give rise to, remains incomplete. To address this gap, in this work we establish a topological symmetry index, based on the methodologies from the family of equivariant degree theories, to decode these symmetries. The frameworks apply to arbitrary network architectures and include methods applicable to degenerate critical orbits. The index detects the isotropy of the critical points and quantifies the corresponding net topological contributions. Several examples, including softplus MLPs, Transformers, and equivariant neural networks, are presented to illustrate the computations.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2610.28864 [cs.LG] |
| (or arXiv:2610.28864v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.28864 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jingzhou Liu [view email]
[v1]
Tue, 20 Oct 2026 19:35:52 UTC (126 KB)
来源：arXiv cs.AI · arxiv.org