Temporal Sheaf Neural Networks with Dynamic Orthogonal Transport

Continuous-time graph models keep one memory per node and compare memories coordinate by coordinate, which presumes that a coordinate means the same thing at every time. As a node's role changes, it does not. We introduce Temporal Sheaf Neural Networks (TSNN), a causal link-prediction framework that gives each node a time-varying orthogonal frame, transports memories into a common frame before comparing them, and carries a stored state exactly into new coordinates when its frame moves. Frames are products of $k$ Householder reflections, so transport costs $O(kd)$ and never forms a $d \times d$ matrix. One event schema serves homogeneous and heterogeneous graphs: relation and node-type information, where available, conditions the transport without changing the architecture. We show that the induced sheaf Laplacian is orthogonally similar to the normalized graph Laplacian, that the diffusion step descends a Dirichlet energy monotonically under a stated step-size bound, and that its sensitivity to frame drift is linear. Across two TGB v2 link-prediction graphs, TGB 2.0's heterogeneous thgl-software, and 13 DGB graphs, TSNN attains average rank 1.23 for both AP and AUC and places first or second on all three TGB tasks.