arXiv cs.AI· Anita Yang, Ken-ichi Kawarabayashi, Yohan Jung·· 11 小时前AI 评分20
LaSFM：为谱图生成引入拉普拉斯零空间约束的流匹配方法
Constraint-Preserving Flow Matching for Spectral Graph Generation
AI 导读
研究者提出 Laplacian-Constrained Stiefel Flow Matching（LaSFM），在生成过程中同时保持特征向量正交归一、正特征值以及此前方法忽略的拉普拉斯零空间约束，并在对应的约束 Stiefel 流形上构建流匹配。该方法还扩展到性质引导生成，可在维持约束的同时将样本导向目标图性质。实验显示其在谱层面与图层面指标上均有提升，且与目标性质的对齐更好。
正文 · 原文
Abstract:Spectral graph generation models graphs through the eigenvalues and eigenvectors of their Laplacians, providing a compact and continuous alternative to direct graph construction. However, these eigensystems must retain the structural properties of graph Laplacians. Existing approaches preserve eigenvector orthonormality but do not enforce the Laplacian nullspace constraint, potentially producing eigensystems inconsistent with Laplacian structure. To address this, we introduce Laplacian-Constrained Stiefel Flow Matching (LaSFM), which preserves the nullspace condition alongside eigenvector orthonormality and positive eigenvalues during generation. We characterize the underlying constrained Stiefel manifold and formulate flow matching on it. We further extend LaSFM to property-guided generation, steering samples toward desired graph properties while maintaining these constraints. Experiments demonstrate improved performance on both spectral and graph-level metrics, along with better alignment with target properties.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI) |
| Cite as: | arXiv:2611.05436 [cs.LG] |
| (or arXiv:2611.05436v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.05436 arXiv-issued DOI via DataCite |
Submission history
From: Anita Yang [view email]
[v1]
Tue, 3 Nov 2026 09:51:49 UTC (1,142 KB)
来源：arXiv cs.AI · arxiv.org