Stable Filters for Generative Modeling of Graph Signals

2026-09-16

AI Summary

本文解决了图信号生成中的结构稳定性问题，通过结合图滤波器和学习的图神经网络的方法，并设计了稳定图滤波器来提高模型对图扰动的鲁棒性。

Abstract

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.

Problem

• graph signals
• permutation-equivariant models
• structural perturbations
• stability

Innovation

• Stable Filters
• Graph Signals
• Wasserstein Stability Bounds
• Structural Robustness
• Graph Neural Network