Stable graph filters improve generating signals on networks
Stable Filters for Generative Modeling of Graph Signals
Machine Learning
Summary
Generating data on network-like structures needs models that stay reliable when the network changes a bit. The authors studied how small changes in the network affect these models and created stable filters that handle such changes better. These filters keep the helpful smoothing effects of known approaches but make the output less sensitive to changes in the network. Tests on simulated and brain activity data show these filters match or beat previous methods in quality while being more stable.
What this means in practice
- •For neuroimaging teams: Improve generative models for brain signal data that remain robust despite small changes in brain network structures.
- •For network analytics engineers: Build graph signal generators that maintain output quality even when the underlying network structure varies or is noisy.
Authors
Martin Schmidt, Gonzalo Mateos
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.