Title: A Sensitivity Analysis of State-Space Models on Graphs
Primary area: learning on graphs and other geometries & topologies
Keywords: graph neural networks, state space models

Abstract: The recent success of State-Space Models (SSMs) in sequence modeling has inspired their extension to graphs, giving rise to Graph State-Space Models (GSSMs). While effective, existing approaches often rely on sequentializations or spectral decompositions that lack permutation equivariance, message-passing compatibility, and computational efficiency. Moreover, they typically target either static or temporal graphs in isolation and, crucially, provide only loose or qualitative results on information propagation, offering no exact guarantees on challenges such as vanishing gradients and over-squashing.
In this work, we revisit the design of GSSMs through the lens of sensitivity analysis. We introduce a principled integration of modern SSM computation into the Message-Passing Neural Network framework, yielding a unified architecture that is computationally efficient, permutation equivariant, and supports fast parallelism. Our formulation admits closed-form Jacobian computations, enabling an exact sensitivity analysis of node-to-node dependencies and rigorous lower bounds on information flow, contrasting sharply with prior heuristic approaches. These theoretical insights clarify when and how stable long-range propagation can be achieved. Finally, we validate our model across a wide range of benchmarks, including node classification, graph property prediction, long-range reasoning, and spatiotemporal forecasting, where it achieves strong empirical performance while preserving the simplicity of message passing.

TL;DR: We revisit GSSMs via sensitivity analysis. We integrate modern SSMs into message passing, yielding a parallel model with Jacobians for exact flow bounds, enabling stable long-range propagation and strong results on static and temporal graphs.