Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

2026-06-08

AI Summary

This work addresses the challenge of link prediction in temporal graphs, where node interaction semantics evolve over time and exhibit role heterogeneity. The authors propose a modeling approach based on dynamic local orthogonal frames, equipping each node with a time-evolving orthogonal coordinate system and employing an orthogonal transport mechanism to align historical states, thereby enabling causal, history-driven predictions. The dynamic frames are parameterized via low-rank Householder products, and the model incorporates a geometric residual decoder alongside a sheaf Dirichlet energy–driven, degree-agnostic diffusion process to preserve state fidelity under strict causality constraints. Evaluated on TGB v2, temporal heterogeneous leaderboards, and DGB benchmarks, the method achieves state-of-the-art or competitive performance across most metrics, with particularly notable gains in scenarios featuring strong role heterogeneity.

Abstract

We introduce Temporal Sheaf Neural Networks (TSNN), a temporal link prediction framework that equips each node with a time-varying orthogonal frame and compares node states only after explicit transport between local coordinate systems. In contrast to existing continuous-time graph models that operate in a shared global embedding space, TSNN models node-specific and evolving interaction semantics through dynamic local frames. The model parameterizes per-node frames via efficient low-rank Householder products, preserves stored hidden states exactly under frame updates, and uses a geometric-residual decoder that anchors predictions on transported distances while learning residual corrections. All computations are strictly causal and use only the pre-event history. We show that the symmetric degree-normalized sheaf Laplacian is orthogonally similar to the symmetric normalized graph Laplacian, with the random-walk normalized form similar in the corresponding degree metric; the full-active, feature-scaled diffusion used by TSNN is exactly a metric-gradient step on the combinatorial sheaf Dirichlet energy, with a degree-free monotone-descent and non-expansiveness guarantee. Frame drift perturbs updates only linearly. Across TGB v2 link-prediction and temporal-heterogeneous leaderboards, together with the DGB benchmark suite, TSNN matches or surpasses the strongest prior methods on most benchmarks, with the largest improvements on graphs exhibiting strong node-role heterogeneity. Ablations confirm the distinct benefit of dynamic frames, orthogonal transport, and geometric-residual decoding.

Problem

• temporal link prediction
• node-role heterogeneity
• dynamic interaction semantics
• continuous-time graph models
• orthogonal transport

Innovation

• Temporal Sheaf Neural Networks
• Dynamic Orthogonal Frames
• Orthogonal Transport
• Geometric-Residual Decoder
• Sheaf Laplacian