Fenying Cai | Search arXiv

arXiv2026

Stability-Shaped Deep Graph Learning

In deep graph neural networks, increasing depth enlarges the receptive field but often leads to over-smoothing, where node representations tend to align. We develop a unified, mode-wise stability framework for deep GNN propagation that provides a principled characterization of over-smoothing. By interpreting layer depth as time and layer updates as graph-coupled dynamics, over-smoothing can be understood as an undesirable dynamical synchronization of features, for which the master stability curve provides a theoretical tool to assess the stability of synchrony. Guided by this theory, we further propose Stability-Shaped Deep Graph Learning (SDGL) to mitigate over-smoothing in deep GNNs. SDGL has two complementary instantiations: one induces controlled Turing instability to replace synchronization with spatial pattern formation, and the other maintains stable near-critical propagation. Experiments on diverse node- and graph-level benchmarks demonstrate the improved depth scaling and consistent accuracy gains over strong baselines, including graphs exhibiting long-range dependencies.

cs.LG↗

arXiv2026

WaveGSSM: Graph Wave State Space Models for Propagating Spatio-Temporal Patterns

Spatio-temporal graph models typically encode each snapshot with a GNN and then connect the resulting representations through a temporal module. This space-then-time design is effective, yet it does not explicitly represent how a pattern moves across the graph. We show empirically that, for a propagating process, the same present field can lead to different futures when its recent rate of change differs, motivating an explicit representation of motion in the predictive state. We introduce WaveGSSM, a second-order graph state-space model that maintains two coupled latent states at each node, one for the current pattern and one for its temporal rate of change. A graph-wave transition updates the motion state through graph interactions and uses it to advance the pattern state, coupling spatial propagation and temporal evolution within a single rollout. We evaluate WaveGSSM on four temporal-graph benchmarks and global weather forecasting. It consistently achieves the best mean performance across the temporal-graph benchmarks and reduces the geopotential RMSE by 20.2% on average for 1- to 5-day weather forecasts relative to a backbone-matched snapshot model, while better preserving large-scale atmospheric patterns.

cs.LG↗