Temporal Sheaf Neural Networks: Coordinate-Consistent Memory for Link Prediction Across Temporal Graphs

Temporal link prediction requires persistent memory that incorporates new interactions while retaining useful history. We introduce Temporal Sheaf Neural Networks (TSNN), one memory architecture for homogeneous, knowledge-graph, heterogeneous, and sequential temporal graphs under a single typed event schema. TSNN pairs node memories with evolving orthogonal frames: each event updates the endpoint frames, exact carry-over preserves the represented vectors across that coordinate change, and recurrent updates and sheaf diffusion over the retained history graph then update the content. All queries at a timestamp are scored from one strict-history snapshot before any update is committed. Our analysis identifies how frames can influence predictions of the base scorer: only through coordinate-dependent content updates or anisotropic diffusion. With exact carry, equivariant content updates, and a scalar diffusion gain, its ambient trajectories and scores coincide with those of a matched frame-free model; with a fixed gain and a small step, its diffusion maps are non-expansive in a weighted norm as the graph evolves. Across 21 TGB, TGB 2.0, and TGB-Seq datasets, TSNN exceeds every listed comparator on 18, including all eight TGB-Seq datasets, and improves thgl-forum MRR by 0.1075; the same architecture also has the best mean rank in transductive AP on 13 DGB datasets (1.23 among 13 methods, against 1.96 for TPNet). In matched ablations on five datasets, evolving frames have higher mean MRR than frame-free, fixed-frame, shared-frame, side-state, and FiLM controls, with significant gains of 0.0091–0.0245 over the frame-free model (Welch $t$-test, $p<0.005$).