LaSFM：面向谱图生成的约束保持流匹配方法
Constraint-Preserving Flow Matching for Spectral Graph Generation
AI 导读
一篇 arXiv 论文提出 Laplacian-Constrained Stiefel Flow Matching（LaSFN），在谱图生成中同时保持特征向量正交性、正特征值和拉普拉斯零空间约束，弥补了现有方法不约束零空间条件的不足。该方法在约束 Stiefel 流形上构建流匹配，并扩展到属性引导生成。实验显示其在谱指标、图级指标及目标属性对齐上均有提升。
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