arXiv：cs.LG（机器学习，全量分类）· Jennifer Rozenblit, Chenguang Yang, Yuxin Liu, Yuzhou Chen, Yulia Gel·· 14 小时前AI 评分32
用离散 Morse 理论与配边理论做图表示：MG-Diff 提升图扩散模型性能
Graph Representation via Elements of Discrete Morse and Cobordism Theories
AI 导读
研究者提出 MG-Diff 流程，将配边理论概念与离散 Morse 理论工具引入图扩散模型以提升其性能，并给出理论保证与充分条件，证明在正决策间隔下 Morse 理论工具及其诱导扩散引导在小扰动下保持稳定。该工作展示了离散 Morse 理论在时空图预测与图再生任务中的应用。
正文
Abstract:Topology is, by its nature and design, suited to structure that is nonlinear, multiscale, and nonstationary - however, within machine learning, its use remains largely confined to topological data analysis. We advocate that tools from low-dimensional topology which have remained almost exclusively contained within the domain of pure mathematics (such as Morse theory) offer a strong, complementary, and yet virtually unexplored perspective on the hidden structure of data-generating processes and learning tasks built upon them. Here we introduce concepts from cobordism theory and harness tools from discrete Morse theory to improve the performance of graph diffusion models through our pipeline MG-Diff. Further, we derive theoretical guarantees and sufficient conditions so that under a positive decision-gap, the Morse-theoretic tools and their application for induced diffusion guidance are stable under small perturbations. Finally, we illustrate the utility of discrete Morse theory in application to graph diffusion models for spatio-temporal graph forecasting and graph regeneration, and argue that these applications are only a small window into the part of what low-dimensional topology can offer to the field of machine learning.
| Subjects: | Machine Learning (cs.LG); General Topology (math.GN) |
| Cite as: | arXiv:2610.01937 [cs.LG] |
| (or arXiv:2610.01937v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.01937 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jennifer Rozenblit [view email]
[v1]
Thu, 1 Oct 2026 16:06:55 UTC (727 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org