Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

• URL: http://arxiv.org/abs/2606.10071v1
• Date: Mon, 08 Jun 2026 18:47:31 GMT
• Title: Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport
• Abstract summary: We introduce Temporal Sheaf Neural Networks (TSNN), a temporal link prediction framework.<n>TSNN models node-specific and evolving interaction semantics through dynamic local frames.<n>All computations are strictly causal and use only the pre-event history.
• Score: 0.5709546417287261
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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