Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

Researchers introduce Temporal Sheaf Neural Networks (TSNN), a novel framework for temporal link prediction that uses time-varying orthogonal coordinate frames to compare node states rather than operating in a shared global embedding space. The model demonstrates competitive performance on multiple benchmarks while offering theoretical guarantees on convergence and stability, with particular strength on heterogeneous graphs.

TSNN represents a meaningful advancement in temporal graph neural networks by fundamentally reconceptualizing how node interactions are modeled over time. Rather than forcing all nodes into a unified embedding space, the framework assigns each node a dynamic local coordinate system that evolves based on interaction patterns. This approach better captures node-specific semantics and heterogeneous roles within networks, addressing a known limitation of existing continuous-time graph models that assume homogeneous interaction dynamics.

The theoretical contributions substantiate the empirical performance. The authors prove that symmetric degree-normalized sheaf Laplacians maintain specific mathematical properties analogous to standard graph Laplacians, and they demonstrate that TSNN's diffusion process constitutes a metric-gradient step on the sheaf Dirichlet energy with formal guarantees on monotone descent and non-expansiveness. These properties ensure stable training and principled optimization.

The practical implementation efficiently parameterizes per-node frames using low-rank Householder products, reducing computational overhead while maintaining expressiveness. The geometric-residual decoder architecture anchors predictions on transported distances while learning residual corrections, combining geometric interpretability with learned flexibility. Crucially, all computations remain strictly causal, respecting temporal ordering for realistic evaluation.

Benchmark results across TGB v2, temporal-heterogeneous, and DGB datasets show TSNN matches or exceeds prior methods on most tasks, with particularly strong improvements on heterogeneous graphs. The ablations validate that improvements stem from three distinct mechanisms: dynamic frames, orthogonal transport, and geometric-residual decoding rather than individual components.

• →TSNN introduces dynamic orthogonal frames for each node instead of global embeddings, better capturing heterogeneous interaction semantics
• →Theoretical guarantees prove the model performs metric-gradient descent on sheaf Dirichlet energy with monotone descent properties
• →Efficient low-rank Householder parameterization enables scalability while preserving hidden states under frame updates
• →Empirical results demonstrate competitive or superior performance on multiple benchmarks, particularly for heterogeneous graphs
• →Strictly causal computation respects temporal ordering, addressing a critical requirement for realistic temporal prediction tasks