图信号生成建模的稳定滤波器
Stable Filters for Generative Modeling of Graph Signals
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中文总结 AI 辅助
本文分析图感知连续时间生成模型的结构稳定性，推导Wasserstein稳定性界，并提出保持热扩散平滑行为的稳定图滤波器设计框架，实验证明其增强鲁棒性且生成质量不逊于基线。
中文摘要 AI 辅助
在图上生成信号需要置换等变模型，这些模型需对相对结构扰动具有稳定性。尽管近期图感知的薛定谔桥模型将拓扑信息直接纳入其参考动力学，但图扰动如何通过这些动力学传播并影响最终生成的分布尚不清楚。本文分析了图感知连续时间生成模型的结构稳定性，其漂移项将图滤波器与学习的图神经网络相结合。我们推导了显式的Wasserstein稳定性界，用以量化相对图扰动对生成分布的影响。受这些界的启发，我们提出了一个设计稳定图滤波器的原则性框架，该框架在保持图热扩散平滑行为的同时增强结构稳定性。在合成信号和fMRI信号上的实验表明，我们的稳定滤波器增强了结构鲁棒性，同时匹配或超过了热方程基线的生成质量。
英文摘要
Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While recent graph-aware Schrödinger bridge models incorporate topology information directly into their reference dynamics, it is unclear how perturbations of the graph propagate through these dynamics and affect the resulting generated distributions. In this paper, we analyze the structural stability of graph-aware continuous-time generative models whose drift combines a graph filter with a learned graph neural network. We derive explicit Wasserstein stability bounds that quantify the effect of relative graph perturbations on the generated distributions. Motivated by these bounds, we introduce a principled framework for designing stable graph filters that preserve the smoothing behavior of graph heat diffusion, while boosting structural stability. Experiments on synthetic and fMRI signals show our stable filters enhance structural robustness while matching or exceeding the generative quality of the heat equation baseline.
发表机构
- University of Rochester（罗切斯特大学）
机构由 AI 辅助整理，请以论文原文为准。
