Qinhan Hou

Qinhan Hou, Jing Tang

Graph Transformers can mix information globally, but this flexibility also creates failure modes: some tasks require long-range communication while others are better served by local interaction. We study this through a synthetic node-classification benchmark on contextual stochastic block model graphs, where labels are generated by a controllable mixture of local and far-shell signals. We define distance-misaligned training as a mismatch between where label-relevant information lies and where the model allocates communication over graph distance. On this benchmark, we find three points. First, the preferred graph-distance bias changes systematically with task locality. Second, an oracle adaptive controller, given offline access to the task-side distance target, nearly matches the best fixed bias across regimes and strongly improves over a neutral baseline on mixed and local tasks. Third, a task-agnostic zero-gap controller is weaker, indicating that adaptation alone is not enough and that the control target matters. These results suggest that distance-resolved diagnosis is useful for understanding Graph Transformer failures and for designing graph-aware control.

Qinhan Hou, Jing Tang

Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with strictly positive irreducible mixing operators face an inherent \emph{monostability trap}: in the long-time regime, information leakage is unavoidable and the dynamics converge to a single global consensus attractor. We propose the \textbf{Hysteresis Graph ODE (HGODE)}, which couples feature evolution with a latent topological potential driven by a learned pairwise force. A double-well edge potential and bipolarized gate allow edge states to polarize into connected or insulated phases while preserving differentiability. We provide asymptotic analysis of the collapse mechanism and the proposed hysteretic topology dynamics, and validate HGODE on theory-driven synthetic diagnostics and real-world graph benchmarks.

Qinhan Hou, Yilun Zheng, Xichun Zhang et al.

While heterophily has been widely studied in node-level tasks, its impact on graph-level tasks remains unclear. We present the first analysis of heterophily in graph-level learning, combining theoretical insights with empirical validation. We first introduce a taxonomy of graph-level labeling schemes, and focus on motif-based tasks within local structure labeling, which is a popular labeling scheme. Using energy-based gradient flow analysis, we reveal a key insight: unlike frequency-dominated regimes in node-level tasks, motif detection requires mixed-frequency dynamics to remain flexible across multiple spectral components. Our theory shows that motif objectives are inherently misaligned with global frequency dominance, demanding distinct architectural considerations. Experiments on synthetic datasets with controlled heterophily and real-world molecular property prediction support our findings, showing that frequency-adaptive model outperform frequency-dominated models. This work establishes a new theoretical understanding of heterophily in graph-level learning and offers guidance for designing effective GNN architectures.