Your Temporal Link Predictor Is Blind to Who Is Active: A Missing Factor That Transfers Across Models

Many temporal link predictors summarize past interactions through learned node representations. We examine whether simple counts of recurring interaction patterns can provide competitive predictions without learning these representations. We propose a temporal link predictor based on statistical language modelling. It pools transition and co-occurrence counts across sources to predict links that a source has never formed. We smooth sparse estimates using destination frequencies or Kneser-Ney continuation counts. A shared log-linear rule combines these estimates with popularity, source history, and recency, without node embeddings. In our main evaluation, the model achieves the highest MRR among the compared methods on 7 out of 16 datasets from TGB and TGB-Seq. It also outperforms EdgeBank and Base3 on all 16 datasets and the heuristic family on 14. These gains extend to datasets designed to limit repeated edges. With only 9--13 learned parameters, our model provides a simple and competitive baseline for evaluating future neural temporal link predictors.

Networks of timestamped interactions arise across social, financial, and biological domains, where forecasting future events requires modeling both evolving topology and temporal ordering. Temporal link prediction methods typically frame the task as binary classification with negative sampling, discarding the sequential and correlated nature of real-world interactions. We introduce STEP (STochastic Event Predictor), a framework that reformulates temporal link prediction as a sequential forecasting problem in continuous time. STEP models event dynamics through discrete temporal motif transitions governed by Poisson processes, maintaining a set of open motif instances that evolve as new interactions arrive. At each step, the framework decides whether to initiate a new temporal motif or extend an existing one, selecting the most probable event via Bayesian scoring of temporal likelihoods and structural priors. STEP also produces compact, temporal motif-based feature vectors that can be concatenated with existing temporal graph neural network outputs, enriching their representations without architectural modifications. Experiments on five real-world datasets demonstrate up to 21% average precision gains over state-of-the-art baselines in classification and 0.99 precision in next $k$ sequential forecasting, with consistently lower runtime than competing motif-aware methods.

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.