非平稳监督下的拓扑动力学：用持续同调分析神经网络权重演化
Topological Dynamics Under Non-Stationary Supervision: Persistent Homology of Neural Network Weight Evolution
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一项 arXiv 研究用 H0 和 H1 Vietoris Rips 持续同调，分析同一多层感知机在 Fashion-MNIST 上于正确标签、固定随机排列标签和每轮重新排列标签三种监督下 100 个 epoch、22 个检查点的权重演化。
正文 · 原文
Abstract:We investigate how the persistent topology of neuron- weight point clouds evolves under stable and non-stationary supervision. An identical multilayer perceptron is trained on Fashion-MNIST with correct labels, a fixed random permutation of the training-label vector, or a fresh permutation every epoch. Five paired seeds share initialisation and minibatch order, yielding 15 models trained for 100 epochs. Raw and row-normalised incoming weight clouds are analysed with H0 and H1 Vietoris Rips persistence at 22 checkpoints. Correct-label models reach 89.39% mean true-label test accuracy; fixed-random models fit 67.94% of their assigned training targets without generalising to the original task. Correct-label models have descriptively greater time-averaged normalised fc3 H1 persistence than either random-label condition, but the configured exact comparisons do not reach conventional significance after Holm correction. Early condition classification achieves 60.0% mean balanced accuracy using topology, 66.7% using conventional diagnostics, and 60.0% using both. Thus, no incremental predictive improvement is demonstrated in this setting. The archive contains all 3,300 configured topology cases. Interpretation is limited by five seeds, a single architecture and dataset, 282 capped H1 distance comparisons, and deferred bottleneck analysis.
| Subjects: | Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2611.13701 [cs.AI] |
| (or arXiv:2611.13701v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2611.13701 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Mitra Varun Gogulapati Mr [view email]
[v1]
Tue, 10 Nov 2026 07:46:13 UTC (7,407 KB)
来源：arXiv cs.AI · arxiv.org