State-of-the-art temporal-link-prediction (TLP) models are, in essence, multi-channel information aggregators: they combine an interaction-history channel, a time-encoding channel, and a structure channel. The first two have been refined relentlessly; the structure channel remains a crude afterthought -- DyGFormer encodes it as a 1--2-bit neighbour-cooccurrence count. We begin with a measurement: on sparse temporal graphs the classical 1-hop common-neighbour signal is near-random (discriminative AUC $\approx 0.50$), because two nodes almost never share a direct neighbour; the genuinely discriminative signal lies one hop deeper -- the 2-hop cohesive bridge, whose discAUC reaches 0.73--0.98, on both bipartite and non-bipartite graphs. Motivated by this, we propose HAWKEYE, a cohesion-aware structural channel that incrementally maintains the classical k-family of cohesiveness indicators (degree $\to$ k-core $\to$ k-truss) and forms 2-hop cohesive-bridge features. HAWKEYE is a drop-in replacement for a temporal-graph model's native structure channel, with no change to the backbone. Swapping HAWKEYE into DyGFormer improves test AP/MRR over the cooccurrence channel by +0.6 to +10.8 points across six multi-seed-validated datasets (uci, enron, USLegis, CanParl, reddit, mooc). On the bipartite recommendation benchmark tgbl-subreddit, a 3-seed single-pass struct-only ablation shows HAWKEYE nearly doubling the baseline test MRR (0.103$\pm$0.003 $\to$ 0.204$\pm$0.005, +10.1 points across all three seeds); the streaming pipeline scales to the 67M-edge tgbl-flight in five minutes per pass. We further characterise when it helps: the gain tracks a graph's training-free 2-hop discAUC and vanishes on degenerate or saturated graphs -- a predictable boundary. All code, data, and figure-generation scripts are released.
Temporal link prediction (TLP) is typically evaluated by predictive performance on unseen edges, but this criterion can conflate predictive accuracy with recovery of the underlying causal mechanism. In stochastic models, Fisher information governs the Cramér--Rao (CR) bound on parameter estimation error: higher Fisher information permits more accurate parameter recovery. We show that, under comonotonicity conditions between Fisher information and entropy, binary logistic models exhibit an estimation--prediction tradeoff: regimes with higher Fisher information, and hence smaller CR bounds, also have higher irreducible predictive entropy. To study this tradeoff in TLP, we introduce a probabilistic causal generator for temporal graphs with transient edges and known ground-truth causal structure, and validate the phenomenon empirically.
Md Sadek Hossain Asif, Tanzila Khan, Md. Mosaddek Khancs.LG cs.AI
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.