# Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

arXiv: https://arxiv.org/abs/2606.10071 · HTML: https://mlsanity.com/paper/2606.10071/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 27 of 27)

- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Temporal Graph Networks for Deep Learning on Dynamic Graphs](https://mlsanity.com/paper/2006.10637/) (2020)
- [Inductive Representation Learning on Temporal Graphs](https://mlsanity.com/paper/2002.07962/) (2020)
- [Predicting Dynamic Embedding Trajectory in Temporal Interaction Networks](https://mlsanity.com/paper/1908.01207/) (2019)
- [Inductive Representation Learning in Temporal Networks via Causal Anonymous Walks](https://mlsanity.com/paper/2101.05974/) (2021)
- [Towards Better Dynamic Graph Learning: New Architecture and Unified Library](https://mlsanity.com/paper/2303.13047/) (2023)
- [Do We Really Need Complicated Model Architectures For Temporal Networks?](https://mlsanity.com/paper/2302.11636/) (2023)
- [Temporal Graph Benchmark for Machine Learning on Temporal Graphs](https://mlsanity.com/paper/2307.01026/) (2023)
- [Towards Better Evaluation for Dynamic Link Prediction](https://mlsanity.com/paper/2207.10128/) (2022)
- [Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphs](https://mlsanity.com/paper/2003.05425/) (2020)
- [Sheaf Neural Networks](https://mlsanity.com/paper/2012.06333/) (2020)
- [SE(3) Equivariant Graph Neural Networks with Complete Local Frames](https://mlsanity.com/paper/2110.14811/) (2021)
- [TCL: Transformer-based Dynamic Graph Modelling via Contrastive Learning](https://mlsanity.com/paper/2105.07944/) (2021)
- [Sheaf Neural Networks with Connection Laplacians](https://mlsanity.com/paper/2206.08702/) (2022)
- [Provably expressive temporal graph networks](https://mlsanity.com/paper/2209.15059/) (2022)
- [Neighborhood-aware Scalable Temporal Network Representation Learning](https://mlsanity.com/paper/2209.01084/) (2022)
- [TGB 2.0: A Benchmark for Learning on Temporal Knowledge Graphs and Heterogeneous Graphs](https://mlsanity.com/paper/2406.09639/) (2024)
- [Long Range Propagation on Continuous-Time Dynamic Graphs](https://mlsanity.com/paper/2406.02740/) (2024)
- [Roto-translated Local Coordinate Frames For Interacting Dynamical Systems](https://mlsanity.com/paper/2110.14961/) (2021)
- [Improving Temporal Link Prediction via Temporal Walk Matrix Projection](https://mlsanity.com/paper/2410.04013/) (2024)
- [DyG-Mamba: Continuous State Space Modeling on Dynamic Graphs](https://mlsanity.com/paper/2408.06966/) (2024)
- [Bundle Neural Networks for message diffusion on graphs](https://mlsanity.com/paper/2405.15540/) (2024)
- [Cooperative Sheaf Neural Networks](https://mlsanity.com/paper/2507.00647/) (2025)
- [Polynomial Neural Sheaf Diffusion: A Spectral Filtering Approach on Cellular Sheaves](https://mlsanity.com/paper/2512.00242/) (2025)
- [ConTIG: Continuous Representation Learning on Temporal Interaction Graphs](https://mlsanity.com/paper/2110.06088/) (2021)
- [Modeling Dynamics over Meshes with Gauge Equivariant Nonlinear Message Passing](https://mlsanity.com/paper/2310.19589/) (2023)
- [Sheaf Graph Neural Networks via PAC-Bayes Spectral Optimization](https://mlsanity.com/paper/2508.00357/) (2025)

## Abstract (arXiv)

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.