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Do Temporal Link Predictors Need Learned Memory? A Smoothed-Count Baseline with a Handful of Parameters
Lisi Qarkaxhija, Ingo Scholtes
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Abstract: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.
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DO TEMPORAL LINK PREDICTORS NEED LEARNED MEMORY? A SMOOTHED-COUNT BASELINE WITH A HANDFUL OF PARAMETERS Lisi Qarkaxhija Ingo Scholtes Chair of Machine Learning for Complex Networks Center for Artificial Intelligence and Data Science (CAIDAS) Julius-Maximilians-Universität Würzburg, DE name.surname@uni-wuerzburg.de ABSTRACT Many temporal link predictors summarize past interactions through learned node representations. We examine whether simple counts of recurring interaction pat- terns 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 frequen- cies 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. 1INTRODUCTION Temporal link prediction models learn from past interactions to predict future links. Many methods represent this history through learned node states, embeddings, or neighborhood encodings (Kumar et al., 2019; Trivedi et al., 2019; Rossi et al., 2020; Wang et al., 2021; Yu et al., 2023; Lu et al., 2024). Simple temporal patterns also carry predictive information. Edges repeat, and destination frequencies change over time (Poursafaei et al., 2022; Daniluk & D ̨abrowski, 2023). Recent work therefore questions whether complex architectures are needed for temporal prediction (Cong et al., 2023). Strong statistical baselines help measure the predictive gains from learned representations. Existing count-based methods use only part of this information. EdgeBank predicts the recurrence of previously observed edges (Poursafaei et al., 2022). PopTrack ranks destinations by decayed frequency (Daniluk & D ̨abrowski, 2023). Other methods combine recency, popularity, and co- occurrence through fixed rules (Cornell et al., 2025a; Kondrup, 2025). These methods have mainly been studied on datasets with repeated edges. Their predictive value when sources rarely revisit a destination remains less understood. TGB-Seq tests this setting (Yi et al., 2025). Temporal interactions provide recurring prediction contexts. The recent destinations of a source can inform its next destination, but individual histories often contain few observations of each transition. Statistical language modelling addresses this problem by pooling observations of recurring contexts and smoothing sparse estimates toward a broader distribution (Katz, 1987; Chen & Goodman, 1999). We use this construction to build a temporal link predictor from smoothed counts and recency fea- tures, with a shared log-linear scoring rule. We consider two backoff distributions for contexts with few observations. Marginal backoff uses destination frequency, favoring items that are common overall. This follows the use of unigram frequencies in language-model interpolation (MacKay & Peto, 1995). Kneser-Ney continuation backoff uses the number of distinct preceding destinations, favoring items observed across many transition contexts (Kneser & Ney, 1995). 1 arXiv:2609.35364v1 [cs.LG] 28 Sep 2026 1 EVENT HISTORY 2 COUNT STATISTICS 3 FEATURES 4 LEARNED COMBINATION 5 CANDIDATE RANKING Past destinations of source u a t 1 b t 2 c t 3 b t 4 c t 5 Another source: u′ → d at t 1 Next query: (u, ?, t = 6) Recent history: v 1 = c, v 2 = b Destinationabcd All sources1221 Source u1220 Pooled transition counts a → b: 1 b → c: 2 c → b: 1 No successors observed for d abcd P ̂ (z)0.200.300.300.20 P ̂ (z | u)0.200.380.380.03 r(u, z)0.080.370.610.00 P ̂ (z | c)0.100.650.150.10 P ̂ (z | b)0.070.100.770.07 Empty rows use the backoff. s(z) = w 0 log P ̂ (z) + w 1 log P ̂ (z | u) + w 2 r(u, z) + w 3 log P ̂ (z | v 1 ) + w 4 log P ̂ (z | v 2 ) + β Example: w = (1, 1, 0.3, 1, 0.4), β = 0 Shared weights, no learned node embeddings bar ∝ exp s(z)s(z) b−3.4 c−4.0 a−6.6 d−8.4 b is held out. Midrank for ties. Figure 1: From six observed interactions to candidate ranking. The reference configuration uses K = 2, α = 1, undecayed counts, and marginal backoff. We set t i = i, query at t = 6, and use recency scale τ r T = 2. Panels 1–3 form the features. Panels 4–5 apply illustrative weights and rank candidates. Appendix E gives the calculations and further features. A destination can receive support from several statistics (Figure 1). It may be popular overall, frequent in the history of the source, or recently visited. It may also commonly follow a recent destination of the source in the histories of other sources. Transitions measure this relation between consecutive interactions. Windowed co-occurrence also includes destinations separated by interven- ing events. Both can support a link that the source has never formed. The model stores decayed counts and recent destination lists. It learns only the weights used to combine the resulting esti- mates. The model has 9–13 learned parameters at context depth K = 5, shared across all nodes, and no learned node embeddings. Fixed update rules allow us to compute training features once and reuse them across epochs. Across 16 TGB and TGB-Seq datasets, the model exceeds EdgeBank and Base3 on all datasets and the heuristic family on 14 under matched event-wise and batch-wise updates. The coverage analysis shows that source-specific transition contexts can be absent while pooled transition evidence remains available. This distinction helps explain prediction beyond repeated source-specific patterns. Contributions. • A statistical model of interaction history. A log-linear model combines smoothed tem- poral counts and recency features, with weights shared across nodes and no learned node embeddings (Section 4). • Evaluation across two benchmark protocols. On 16 TGB and TGB-Seq datasets, we compare against recomputed count baselines and reported graph and sequential models (Section 5). • Analysis of statistical context. Controlled comparisons measure the effects of context depth, co-occurrence, and backoff distributions. Context coverage distinguishes source- specific transition evidence from evidence pooled across sources, including where the for- mer is absent (Sections 5.1–6). 2RELATED WORK Graph-based models. JODIE, DyRep, and TGN learn recurrent node states that evolve with inter- actions (Kumar et al., 2019; Trivedi et al., 2019; Rossi et al., 2020). CAWN and DyGFormer encode 2 temporal walks and neighborhood sequences (Wang et al., 2021; Yu et al., 2023). DBGNNs ap- ply message passing to De Bruijn graphs that capture higher-order dependencies in time-respecting walks (Qarkaxhija et al., 2022). TPNet combines recent interactions with time-decayed tempo- ral walk counts (Lu et al., 2024). GraphMixer shows that simpler encoders can also perform well (Cong et al., 2023). These temporal models learn how to encode interaction history. For static graphs, Qarkaxhija et al. (2025) show that removing trainable parameters from message passing layers can preserve or improve link prediction performance. Our model represents interaction his- tory with smoothed counts and learns a shared scoring rule. Count-based methods. EdgeBank predicts whether an edge has occurred before (Poursafaei et al., 2022). PopTrack uses decayed destination frequencies (Daniluk & D ̨abrowski, 2023). Cornell et al. (2025a) combine local and global recency and popularity through a fixed priority order. Base3 interpolates EdgeBank, PopTrack, and a co-occurrence memory (Kondrup, 2025). Our model adds smoothed conditional estimates and learns their contribution to the score. Sequential recommenders. Session-based methods predict the next item from recent interactions. SKNN uses session co-occurrence (Ludewig & Jannach, 2018). SGNN-HN propagates informa- tion through a session graph with learned item embeddings (Pan et al., 2020). CRAFT uses cross- attention between each candidate and the recent interactions of the source (Yi et al., 2026). SGNN- HN and CRAFT provide the strongest reported TGB-Seq scores used in our comparison. Their use of recent sequences motivates our comparison with pooled transition and co-occurrence counts. Evaluation. Temporal link prediction scores depend on the evaluation protocol. Negative sam- pling can change method rankings (Poursafaei et al., 2022; Cornell et al., 2025b), sampled metrics can reverse the ordering obtained from full rankings (Krichene & Rendle, 2020), and batch evalua- tion can withhold recent interactions (Lampert et al., 2026). Analyses of learned models and simple baselines motivate closer control of these factors (Hayes et al., 2025; Bechler-Speicher et al., 2025). We recompute count baselines on the benchmark candidates and measure sensitivity to history- update timing. Context coverage complements the edge-based surprise index of Poursafaei et al. (2022) by measuring whether a transition context has prior observations. Statistical language modelling. Interpolation and backoff combine estimates from contexts with different amounts of evidence (Katz, 1987; Chen & Goodman, 1999). Unigram interpolation sup- plies background probabilities from overall word frequencies (MacKay & Peto, 1995). Kneser-Ney smoothing uses the number of distinct preceding contexts to estimate a continuation distribution (Kneser & Ney, 1995). Chen & Goodman (1999) found this approach effective in language mod- elling. In temporal link prediction, the corresponding counts describe source histories and destina- tion transitions, with exponential decay accounting for their age. 3PROBLEM SETTING AND EVALUATION An interaction stream consists of events (u,v,t), where u is a source, v a destination, and t a timestamp. At a query (u,t), the task is to rank the observed destination above the benchmark negative candidates. Both benchmarks report mean reciprocal rank (MRR) over test queries. We follow their midrank tie rule. The observed destination has rank 1 + n > + 1 2 n = , where n > counts negatives with a higher score and n = counts negatives with the same score. Only the rank of the observed destination enters MRR. This treatment matters for count models, which often assign equal scores to unobserved candidates. TGB-Seq (Yi et al., 2025) provides 100 uniformly sampled negative destinations for each test event. TGB (Huang et al., 2023) uses dataset-specific candidate sets. For example, tgbl-wiki uses all possible negative destinations, whereas tgbl-review uses 100 sampled negatives per posi- tive edge. Historical-random sampling includes destinations visited by the source during training. Historical negatives test whether a model can distinguish the positive from previously visited desti- nations. Because candidate distributions differ, we analyse each benchmark separately. We use the splits, negative candidates, and MRR evaluation supplied by TGB and TGB-Seq. We compare with reported neural benchmark results and recompute the count baselines. Appendix A documents the score sources and evaluation details. 3 Notation. Throughout, u denotes the source of the current query and z a candidate destina- tion from the destination vocabulary V . The K most recent destinations of u at query time are v 1 ,...,v K , ordered from most recent. The vocabulary is fixed for each dataset and includes can- didate destinations first observed after training. t is the query time, and T is the duration of the training split. Probabilities written with a hat, such as ˆ P(z | u), are smoothed estimates (Section 4). 4A STATISTICAL MODEL FOR TEMPORAL LINK PREDICTION The model represents history through count tables and recent destination lists. Count estimates describe how often a destination occurs in a particular context. Recency features describe how recently it was visited. A shared log-linear rule combines these two kinds of evidence. The stored counts, timestamps, and destination lists follow fixed update rules, and learning determines the contribution of each feature to the score. 4.1FROM COMPLETE HISTORIES TO RECURRING CONTEXTS Complete interaction histories rarely repeat, leaving little evidence for estimating their conditional destination distributions. We use shorter contexts that recur across queries. The marginal ˆ P(z) esti- mates destination frequency. The source conditional ˆ P(z | u) estimates the choices of a particular source. We use the last K destinations visited by the source. For each destination v k , the transition conditional ˆ P(z | v k ) estimates what immediately follows it using transitions observed across all sources. Windowed co-occurrence broadens this context to include pairs separated by intervening interactions. It pools counts over the recent destinations to form the estimate ˆ P co (z | v 1 ,...,v K ). In film recommendation, suppose Alice recently watched films A and B. The marginal estimate describes how popular a film is across all viewers. The source conditional describes how often Alice has watched it. The transition conditionals use what all viewers watched immediately after A or B to estimate her next choice. Co-occurrence also counts films watched within a few choices after A or B. These estimates use different parts of the same history. 4.2STREAMING COUNT STATE The count state records destination frequencies, source histories, transitions, and windowed co- occurrences. Each source also retains its recent destination list. Destination counts c(z;t) mea- sure decayed popularity, as in PopTrack (Daniluk & D ̨abrowski, 2023). Their total is C(t) = P z∈V c(z;t). Source-destination counts c(u,z;t) record pair history together with the last inter- action time. Their keys form the edge memory used by EdgeBank (Poursafaei et al., 2022). Tran- sition counts c(v,z;t) record how often a source moves from v to z in consecutive interactions, pooled across all sources. At query time, each of the last K destinations selects a separate row from this transition table. The model combines these estimates without treating the full sequence as one context. Windowed co-occurrence counts c co (v,z;t) record how often z follows v within the last K interac- tions of the same source. These counts are also pooled across sources. An event updates the count for each destination in the recent window, including repeated occurrences. The table can there- fore contain pairs that never occur consecutively, as in session-based recommendation (Ludewig & Jannach, 2018). Tables store only keys that have occurred. Missing keys have count zero. Each event at time t i contributes e −(t−t i )/τ at query time t, and each count sums these contributions over its matching events. Decay is applied lazily when a cell is accessed. Updating popularity, source history, and con- secutive transitions takes O(1) operations per event. Co-occurrence requires up to K count updates. Exponential decay preserves the relation between row entries and their totals, so the normalised es- timators remain proper probabilities. The time constant τ is set from timestamps and is not tuned (Appendix G). 4 4.3SMOOTHED CONDITIONAL ESTIMATORS For a context x ∈ u,v 1 ,...,v K , let n(x;t) = P z∈V c(x,z;t) denote its total decayed count. Each context contributes one smoothed estimator. We add pseudocounts from a base distribution B, using the Dirichlet smoothing form of MacKay & Peto (1995): ˆ P(z | x) = c(x,z;t) + αB(z) n(x;t) + α ,(1) B(z)∈ n ˆ P(z) = c(z;t) + α C(t) + α|V| , ˆ P c (z) = N 1+ (·z) + α P z ′ N 1+ (·z ′ ) + α|V| o ,(2) with α = 1, |V| the size of the destination vocabulary, and N 1+ (·z) = |v : c(v,z;t) > 0| the number of distinct destinations v after which z has been observed. A context with no observations satisfies ˆ P(z | x) = B(z) exactly, so an empty context uses the base distribution. Equation 2 defines two backoff distributions. The marginal ˆ P(z) measures how frequently z oc- curs. The continuation base ˆ P c (z) measures how many distinct destinations have preceded z. A destination that occurs often after only one predecessor can therefore have high frequency but a continuation count of one. The continuation count is the number of observed cells in column z of the transition table. These counts do not decay, so the base retains predecessor types from the full observed history. The continuation counts come from Kneser-Ney smoothing (Kneser & Ney, 1995; Chen & Good- man, 1999). The resulting base assigns more backoff probability to items observed in many contexts. This matters most when the conditioning row has few observations. Both bases use the same Dirich- let smoothing rule. This isolates the effect of the backoff distribution. The marginal also remains a separate feature under either base. The co-occurrence estimate combines evidence from the whole recent window. We sum the candi- date counts over the corresponding rows, normalize by their total count, and smooth toward B. For L≤ K available history positions, ˆ P co (z | v 1 ,...,v L ) = P L k=1 c co (v k ,z;t) + αB(z) P L k=1 P z ′ c co (v k ,z ′ ;t) + α .(3) Repeated destinations contribute once per history position. With no co-occurrence observations, Equation 3 returns B(z). Appendix E illustrates each estimator on a worked stream. 4.4RECENCY FEATURES Recency describes the time of the latest interaction with a candidate. Source-specific recency uses the last visit by u: r(u,z) = e −(t−t last (u,z))/(τ r T) , where T is the training duration and τ r is a fixed fraction. It is zero if u has never visited z. In the film example, this feature measures how recently Alice watched the candidate film. Global recency measures how recently any source interacted with a candidate.Its value is e −(t−t last (z))/(τ r T) , where t last (z) is the last interaction time of z across all sources. This is the global-recency signal used by Cornell et al. (2025a). It can favor a film watched recently by some- one other than the current viewer. Multi-scale recency measures the same source-destination interaction as r(u,z) at three fixed scales, τ r /10, τ r , and 10τ r . The middle scale is r(u,z), so this representation contributes two further features. Multiple scales allow the model to combine fast and slow recency effects. This choice is motivated by retention curves that decay more slowly than a single exponential (Anderson & Schooler, 1991). The learned weights determine the influence of each scale. 4.5LEARNED COMBINATION Let φ(u,z,t) contain the log-probabilities from the count estimates and the untransformed recency values. We score each candidate with a shared log-linear rule: s(z) = w T φ(u,z,t) + β.(4) 5 Each feature has one learned weight, and β is a learned bias. The weights are unconstrained. A negative weight makes a larger feature value evidence against a candidate. Probability mixtures instead require nonnegative weights. If a source has fewer than K past interactions, transition features for unavailable history positions are zero for every candidate. These inactive features do not affect the ranking. An available destination with no observed successors instead uses the backoff distribution in Equation 1. Figure 1 shows how individual features contribute to a candidate score. The evaluated configurations have 9–13 learned parameters at K = 5, including the bias. Chang- ing the backoff distribution adds no parameters. There are no node or item embeddings, message passing, or learned per-node state. A source enters through its recent destinations and count rows. The same scoring rule applies to nodes first observed at test time. The statistical state grows with the number of observed destinations and pairs, so the parameter count alone does not describe the memory cost. 4.6FITTING Features are extracted in a single chronological pass, before adding each event to history. The result- ing vectors are reused across epochs and shuffled into minibatches to fit only the scoring weights. Training minimises a sampled softmax loss with one positive and one uniformly sampled nega- tive destination per query. The number of negatives per positive follows TGN (Rossi et al., 2020, Appendix A.4). Test candidates are provided by the benchmark. 5RESULTS AND DISCUSSION Setup. We evaluate on 9 TGB and 7 TGB-Seq datasets. Main comparisons use five runs. Feature, depth, and smoothing analyses use three runs. Timing comparisons reuse the five main fits. Tables report means and sample standard deviations. Hyperparameters are fixed as specified in Section 4 and Appendix G. Tables 1 and 2 report TGB and TGB-Seq separately. We fix one feature configuration per dataset and backoff distribution, as listed in Appendix G. These feature sets were chosen on validation data before the reported fits. Mean validation MRR over five runs chooses between the two backoff configurations. We also choose the heuristic rule on validation MRR. All performance rankings use test MRR. For controlled comparisons, the reference configuration contains popularity, source history, the K transition estimates, and source-specific recency at scale τ r . We add co-occurrence, global recency, or two further source-recency scales separately and together, under each backoff. These comparisons use the same three seeds for both configurations. Following the streaming setting of TGB, observed test interactions enter history for later predictions while learned weights remain fixed (Huang et al., 2023, Appendix C). Our history updates use fixed count operations, making event-wise evaluation practical. We update statistics after each scored event, retaining file order for tied timestamps. Our model, EdgeBank, Base3, and the heuristic family use the same candidates and event-wise updates. Appendix I examines batch-wise and strict- timestamp updates. The model achieves the highest MRR among all compared methods on 7 of 16 datasets. Each of these leads holds in all five runs. CRAFT and CRAFT-R together lead on 6 datasets, the next highest count. On TGB, the lead over TPNet on tgbl-wiki is 0.14 points. The largest gains over reported TGB references occur on tgbl-uci, tgbl-enron, and tgbl-lastfm. Recomputed heuristics are also strong on these datasets, and exceed our model on tgbl-uci. On TGB-Seq, the model leads on ML-20M, Flickr, and YouTube. These datasets have no previously observed source-specific transition contexts at test time (Section 6). The model remains below the reported references on 4 TGB and 4 TGB-Seq datasets. The largest deficits within each benchmark occur on tgbl-comment and GoogleLocal. Against recom- puted count methods, it exceeds EdgeBank and Base3 on 16 of 16 datasets and the heuristic rule on 14 of 16. These gains persist when all counting methods use batch-200 updates. Under this schedule, our model still achieves the highest MRR in the comparison on 4 of 16 datasets (Appendix I). 6 Table 1: Test MRR (%) on TGB. Our entries are means and sample standard deviations over five runs. EdgeBank is the stronger of its two variants. Best neural gives the strongest reported neural benchmark score (Appendix A). Bold marks the highest MRR per row. OursBest neural DatasetEdgeBankHeuristicBase3marginalcontinuationMRRMethod wiki64.4082.0673.26 82.84±0.0482.72±0.1082.70TPNet uci32.4052.7535.2251.57±0.3251.25±0.2624.50TNCN enron15.6084.6648.6586.82±0.01 86.83±0.0337.90TNCN subreddit59.2274.1974.25 74.90±0.0674.79±0.0469.60TNCN lastfm2.6316.5811.3732.84±0.18 32.87±0.1215.60TNCN review2.6933.9312.8736.66±0.7445.76±0.39 52.10GraphMixer coin58.3181.1077.7182.09±0.0681.65±0.02 88.47CRAFT-R comment15.0372.3845.4147.94±1.2754.76±0.87 91.72CRAFT flight38.7188.9279.3489.93±0.0689.99±0.04 91.39CRAFT-R Table 2: Test MRR (%) on TGB-Seq. Columns follow Table 1. Count baselines use the TGB-Seq candidate sets. OursBest neural DatasetEdgeBankHeuristicBase3marginalcontinuationMRRMethod GoogleLocal1.9618.393.9731.27±0.0231.42±0.03 62.88SGNN-HN Yelp9.7730.8111.9953.21±0.0652.16±0.09 72.69CRAFT Taobao20.2842.9920.1759.58±0.0358.90±0.06 70.68CRAFT ML-20M1.9417.716.64 39.24±0.1539.00±0.1035.91CRAFT Flickr1.9638.3834.81 62.68±0.0762.66±0.0862.34CRAFT YouTube1.9656.6438.09 65.27±0.0665.12±0.0459.64SGNN-HN WikiLink1.9647.7026.6167.95±0.0567.97±0.04 75.48CRAFT 5.1THE EFFECT OF THE BACKOFF DISTRIBUTION We compare marginal and continuation backoff with the reference configuration fixed at K = 5. Both models are fitted with the same three seeds and training settings. The three largest backoff effects occur on datasets with low source-specific transition coverage (Sec- tion 6). Continuation backoff improves MRR by 9.13 points on tgbl-review and 3.83 points on tgbl-comment (Figure 2). Marginal backoff is stronger on Yelp by 5.01 points. On the remain- ing datasets, the absolute difference is at most 1.39 points. Continuation backoff favors destinations reached from many distinct predecessors. Its gains show the value of this distinction from raw frequency. Sparse history alone therefore does not determine the better background distribution. 5.2THE CONTRIBUTION OF CO-OCCURRENCE AND RECENCY Adding co-occurrence to the reference configuration gives a larger median gain than adding global recency or further recency scales, under either backoff distribution. With marginal backoff, the median gain is 0.82 MRR points (Appendix F). Relative to the reference configuration with the same backoff distribution, the main model gains 1.44 points at the median. Its largest gain is 13.01 points on Yelp. The co-occurrence gains suggest that useful associations between destinations extend beyond im- mediate succession. Pooling these observations across the recent window supplies evidence that consecutive transition counts omit. 7 review comment Yelp −5 0 5 10 MRR difference (points) +9.13 +3.83 -5.01 (a) Largest changes GoogleLocal ML-20M Flickr YouTube flight lastfm enron wiki subreddit WikiLink uci coin Taobao −1.5 −1.0 −0.5 0.0 MRR difference (points) (b) Remaining datasets (expanded scale) Figure 2: Effect of changing marginal to continuation backoff with the reference configuration fixed at K = 5. Bars show mean test MRR differences across three paired runs. Dots show individual runs, and whiskers show one sample standard deviation. Positive values favor continuation. Panel (a) shows the three largest absolute mean changes. Panel (b) uses an expanded linear scale for the remaining datasets. 5.3THE LEARNED SCORING RULE We examine mean coefficients with the reference configuration and marginal backoff on every dataset. Features differ in scale, so we interpret signs and relative weights within the transition features. Appendix C reports coefficients for both backoffs and all feature additions. The source-history coefficient is positive on all 9 TGB datasets, and recency is positive on 8. On TGB-Seq, both coefficients are negative on 5 of 7 datasets. Source history can thus play two roles: its counts can discourage a return to a visited destination, while its recent destinations still provide contexts for predicting a new link through pooled transitions. The most recent destination has the largest transition coefficient on 16 of 16 datasets. 5.4THE VALUE OF LONGER CONTEXTS We fit the reference configuration with marginal backoff separately at each depth from K = 1 to K = 20. Increasing K from one to 20 improves mean test MRR on all 7 TGB-Seq datasets, with gains in every seed (Figure 3). Most of the improvement occurs within the first 5 destinations. On these datasets, extending the context from 5 to 20 adds at most 0.41 MRR points. On TGB, the same increase from one to 20 improves mean MRR on 5 of 9 datasets. The smaller gains beyond K = 5 and the mixed TGB results favor a short recent history as a practical default. Appendix D gives the sweep protocol. 6WHEN IS CONTEXT AVAILABLE? Coverage measures whether a context has prior observations when a query is scored. For a source u with previous destination v 1 , we distinguish two kinds of evidence. A pooled transition is available if any source has previously moved from v 1 to another destination. A source-specific transition is available if u has previously done so. Histories follow the event ordering in Section 5. Let n u (v 1 ;t) be the decayed count of transitions from v 1 contributed by source u, so n(v 1 ;t) = P u ′ n u ′ (v 1 ;t). Here v 1 = v 1 (u,t) depends on the source and query time. Over the test queries Q, pooled coverage is the fraction|(u,t) ∈ Q : n(v 1 ;t) > 0|/|Q|. Pair coverage is the fraction |(u,t) ∈ Q : n u (v 1 ;t) > 0|/|Q|. The model uses pooled transitions, with exact backoff for empty rows (Equation 1). Pooled transition evidence is available on at least 96.1% of test queries on every dataset. By con- trast, 5 TGB-Seq datasets have zero pair coverage. On ML-20M, pooled coverage is complete, so transitions observed for other sources remain available. 8 15101520 context depth K −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 test MRR change from K = 1 (points) lastfm enron flight wiki review coin comment subreddit uci (a) TGB 15101520 context depth K 0 1 2 3 YouTube WikiLink Yelp GoogleLocal Taobao ML-20M Flickr (b) TGB-Seq Figure 3: Context depth with marginal backoff and the reference configuration. Lines show mean test MRR changes from K = 1 across three runs. The dotted line marks K = 5. Panels use different vertical scales. 020406080100 pair coverage (%) −40 −20 0 20 40 margin over neural reference (MRR) wiki uci enron subreddit lastfm review coin comment flight GoogleLocal Yelp Taobao ML-20M Flickr YouTube WikiLink TGB TGB-Seq Figure 4: Source-specific transition cover- age against the MRR margin over the neural reference, one point per dataset. Figure 4 relates context availability to perfor- mance. Among the datasets with zero pair cover- age, the model exceeds the reported references on ML-20M, Flickr, and YouTube, but remains be- low them on GoogleLocal and WikiLink. At the other end of the coverage range, tgbl-coin and tgbl-flight remain below their references despite pair coverage of at least 87.1%. Context avail- ability alone does not determine performance. Pair coverage concerns a particular transition context, not the entire source history. A learned node memory can still encode earlier interactions when pair cover- age is zero. Coverage also differs from the surprise index, which measures whether a test edge occurred during training (Poursafaei et al., 2022). Suppose a source previously visited A followed by B and has now returned to A. Its next destination C can be new to the source even though the transition context is fa- miliar. Pair coverage also includes observations after training. 7CONCLUSION Our work shows that statistical language modelling can predict temporal links beyond repeated edges. The proposed model draws on transition and co-occurrence patterns pooled across sources. These patterns support new links even when the current source has not encountered the same tran- sition before. 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 results show that fixed statistical summaries can provide a competitive alternative to learned node states. Limitations and future work. The timing analysis keeps the configuration and weights fixed (Appendix I). Future work could test whether choosing marginal or continuation backoff separately for each query improves prediction. With only 9–13 learned parameters, our model provides a simple and competitive baseline against which future neural temporal link predictors should be evaluated. 9 REPRODUCIBILITY STATEMENT Tables, figures, and numerical results in the text are generated from the per-run result files and recorded reference scores. Our count baselines use the same candidate sets as the model. Code is available at https://doi.org/10.5281/zenodo.22914326. We use the public TGB and TGB-Seq distributions with their supplied splits and negative candidates. REFERENCES John R. Anderson and Lael J. Schooler. Reflections of the environment in memory. 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We evaluate the 9 TGB link-prediction datasets and 7 TGB-Seq datasets, each under the shipped candidate sets of its benchmark and evaluator. Sources of the neural reference scores.The leaderboards are https://tgb. complexdatalab.com/docs/leader_linkprop/ and https://tgb-seq.github. io/leaderboard/, last accessed September 18, 2026. The reference columns contain neural methods. Counting baselines appear in their separate columns under matched evaluation schedules. For tgbl-wiki and tgbl-review, we use the leaderboard scores for TPNet and GraphMixer, respectively.For tgbl-coin, tgbl-comment, and tgbl-flight it is CRAFT, from Tables 2 and 3 of Yi et al. (2026), evaluated on TGB’s shipped negatives with baseline rows that match the leaderboard, and stronger than any leaderboard entry. For tgbl-uci, tgbl-enron, tgbl-lastfm, and tgbl-subreddit it is TNCN (Zhang et al., 2025) as reported by Huang et al. (2025). Reproduction of EdgeBank. We evaluate unlimited memory and the TGB time window, whose duration is fifteen percent of the training time span. The main tables use event-wise updates. With batch-200 updates, both variants match the reported scores at their displayed precision on all five current TGB leaderboard datasets. On tgbl-wiki, unlimited and windowed memory give 49.47 and 57.10, compared with the reported 49.50 and 57.10. Reproduction of the heuristic family. We implement the four heuristics of Cornell et al. (2025a) using the same candidates, tie rule, and event ordering as our model. This extends their evaluation to 10 additional datasets. Our implementation reproduces their combined score within one point on five of the six TGB datasets they report. On tgbl-review, their evaluation uses a dataset- specific inverse-recency variant. The combination stated in their method section obtains 17.69 in our implementation, compared with their reported 52.20. The result files include scores for every individual heuristic. Appendix I compares the same heuristic rule under event-wise and batch-wise updates. Reproduction of Base3. We implement Base3 from the released code and evaluate both update schedules. The main tables use event-wise updates. With batch-200 updates, our results are within 12 half a point of the reported scores on tgbl-comment, tgbl-flight, and tgbl-coin. They are lower on tgbl-review and tgbl-wiki. The released code refers to negative-candidate files that are absent from the repository and specifies paths for a single dataset. We therefore cannot reconstruct the exact candidates used for those reported results. Our comparisons use the candidates supplied by TGB. TNCN reference scores.For tgbl-uci, tgbl-enron, tgbl-lastfm,and tgbl-subreddit, we use the TNCN results reported by Huang et al. (2025). Their eval- uation measures MRR using negatives generated according to the TGB procedure. Our evaluation uses the candidate files distributed with TGB. The comparisons therefore share a sampling procedure, but may differ in the particular candidates and the timing of history updates. TGB-Seq references. The neural reference scores come from Table 2 of Yi et al. (2026), which reports CRAFT and SGNN-HN on every TGB-Seq dataset. BTHE COMPARED METHODS EdgeBank, the heuristic family, and Base3 are recomputed in our experiments. The other methods are compared through their reported results. Appendix A gives the source of each score. Our model stores history in count tables with fixed update rules and learns the weights of smoothed estimates and recency features. The methods below differ in their history representations, update rules, and scoring functions. JODIE (Kumar et al., 2019) assigns each user and item a static and a dynamic embedding. Two recurrent networks update the dynamic embeddings at each interaction using the counterpart, inter- action features, and elapsed time. A learned projection evolves an embedding between interactions, and a linear layer predicts the next item embedding. DyRep (Trivedi et al., 2019) models long-lived associations and transient communications with tem- poral point processes. A recurrent architecture updates node embeddings at each event. A learned intensity over the endpoint embeddings determines the likelihood of an interaction. Embeddings continue to update during evaluation. TGN (Rossi et al., 2020) maintains a memory vector for each node. Events generate messages that are aggregated and passed to a learned memory updater. A temporal embedding module combines this memory with neighborhood information. Memory continues to update during evaluation. SGNN-HN (Pan et al., 2020) constructs a graph from the items in a session and connects them through a central node. A gated GNN propagates information through this graph. A highway gate combines the initial and updated item embeddings. An attention-based session representation then scores candidate items. TGB-Seq retains only nodes seen during training for all compared methods (Yi et al., 2025). CAWN (Wang et al., 2021) samples walks backward in time from both endpoints of a query. It replaces node identities with occurrence counts relative to the sampled walks. An RNN encodes the anonymised walks and their time gaps, and an MLP scores the pair from these encodings. EdgeBank (Poursafaei et al., 2022) stores observed source-destination pairs. It predicts an edge as positive if that pair is in memory. The unlimited variant retains every observed pair. The time- window variant retains pairs from a recent interval. We use the window rule in the TGB reference implementation for this variant. GraphMixer (Cong et al., 2023) uses an MLP-Mixer to encode recent links with fixed cosine time features. A separate node encoder averages neighbor features over a time window. An MLP com- bines the two representations to score a pair. The method learns a representation of recent interac- tions without recurrent networks or self-attention. DyGFormer (Yu et al., 2023) encodes the first-hop interaction sequences of both query nodes. Features include neighbor attributes, time, and the frequency with which neighbors occur in both sequences. The sequences are divided into patches and processed by a transformer. An MLP scores the pair from the resulting representations. 13 PopTrack (Daniluk & D ̨abrowski, 2023) maintains decayed destination counts. It scores a batch from the current counts, then updates and decays them. The decay factor is selected on validation. TPNet (Lu et al., 2024) maintains random projections of time-decayed temporal walk counts. Learned MLPs combine the recovered walk features with recent-interaction encodings to score each pair. TNCN (Zhang et al., 2025) combines node memory with neural common-neighbor features. Events update the memories, and a graph transformer computes embeddings from temporal neighborhoods. The pair score combines endpoint embeddings with information from temporal common neighbors. The heuristic family of Cornell et al. (2025a) uses local and global recency and popularity. The first statistic in a fixed priority order ranks candidates. Subsequent statistics break remaining ties. Base3 (Kondrup, 2025) combines EdgeBank membership, PopTrack popularity, and a windowed co- occurrence memory. The co-occurrence component uses decayed neighbor popularity and saturating counts. Binary confidence indicators determine the interpolation weights through a fixed lookup. CRAFT (Yi et al., 2026) learns node embeddings and uses cross-attention from each candidate to the recent neighbors of the source. It includes positional information and the time since the candidate was last active. An MLP produces the final score. CRAFT-R is its variant for datasets dominated by repeated edges and provides the reference scores on tgbl-coin and tgbl-flight. CTHE FITTED WEIGHTS Figure 5 reports the mean coefficients of the reference configuration under both backoff distributions. Figure 6 reports the weights of co-occurrence, global recency, and further recency scales when each is added separately. All means use three runs. A larger weight does not always mean a stronger effect on the score. Recency and log-probability features have different numerical ranges. We therefore compare weight sizes only for features of the same kind, such as transition estimates at different history positions. 0123 wiki uci enron subreddit lastfm review coin comment flight GoogleLocal Yelp Taobao ML-20M Flickr YouTube WikiLink popularity −2−10 source history −10010 -98 -24 -28 13 -29 40 20 -240 -57 -16 -80 source recency 12345 depth k 0.00 0.05 0.10 0.15 0.20 0.25 transition weights, group means TGB, marginal TGB-Seq, marginal TGB, continuation TGB-Seq, continuation marginal backoffcontinuation backoff Figure 5: Mean fitted weights of the reference configuration over three runs. Plain bars use marginal backoff and hatched bars use continuation backoff. TGB datasets appear above the divider. Blue denotes positive weights and red negative weights. Recency weights beyond±10 are printed beside the clipped bars. Right: mean transition coefficients at each history position, grouped by benchmark and backoff distribution. 14 0.00.20.40.60.8 wiki uci enron subreddit lastfm review coin comment flight GoogleLocal Yelp Taobao ML-20M Flickr YouTube WikiLink co-occurrence 024 global recency −10010 -226 -61 -16 -68 10 -19 57 45 -231 -106 -30 -111 multi-scale recency, slow −10010 37 21 multi-scale recency, fast marginal backoffcontinuation backoff Figure 6: Mean weights of co-occurrence and recency features when added to the reference config- uration, over three runs. Backoff distributions follow Figure 5. The two multi-scale panels show the additional slow (10τ r ) and fast (τ r /10) recency features. Weights beyond ±10 are printed beside the clipped bars. DSENSITIVITY TO THE CONTEXT DEPTH The sweep uses the reference configuration with marginal backoff and three runs on every dataset. It varies K from one to 20 while holding the smoothing, decay, and recency settings fixed. The context depth is fixed at K = 5 in the main experiments. A model at depth k uses popularity, source history, source recency, and the first k transition features. We extract features once at depth 20, fit a separate scoring rule for each prefix, and evaluate all depths in one pass. At K = 5, we reuse the corresponding reference fit. Each fit uses every training query, at most 100 epochs, and validation patience 10. The sweep measures sensitivity within this configuration and does not change the configurations reported in the main tables. The largest depth equals the smallest sampled-neighbor budget in the TGB-Seq baseline grids, which range from 20 to 60 neighbors (Yi et al., 2025). The TGB-Seq gains from K = 1 to K = 20 range from 0.57 to 3.19 MRR points. The largest gain occurs on Flickr, where source-specific transition coverage is zero (Section 6). The model can still draw on earlier destinations because its transition estimates pool observations across sources. On TGB, mean MRR increases on tgbl-uci, tgbl-subreddit, tgbl-review, tgbl-coin, and tgbl-comment, while it decreases on the remaining datasets. The largest de- cline is 1.94 points on tgbl-lastfm. EA WORKED EXAMPLE OF THE ESTIMATORS The six-event stream in Figure 1 gives a concrete example of each estimator. We use α = 1, K = 2, and undecayed counts. The vocabulary isa,b,c,d, so C(t) = 6 and|V| = 4. Candidate b occurs twice, giving ˆ P(b) = (2 + 1)/(6 + 4) = 0.30. Both events belong to u, which has five events in total. The source conditional is therefore ˆ P(b| u) = (2 + 0.30)/(5 + 1) = 0.38. The most recent destination is v 1 = c. There is one observed transition from c, and it leads to b. Thus ˆ P(b | c) = (1 + 0.30)/(1 + 1) = 0.65. For an unobserved successor such as a, smoothing gives ˆ P(a| c) = (0 + 0.20)/(1 + 1) = 0.10. The transition row of d is empty, so ˆ P(z | d) = ˆ P(z) for every candidate. The continuation base changes this fallback distribution. Candidate b has followed 2 distinct pre- decessors, whereas c has followed 1. Neither a nor d has an observed predecessor. The total con- tinuation count is 3, and ˆ P c (b) = (2 + 1)/(3 + 4) = 0.43. Although b and c occur equally often, 15 the continuation base favors b because it follows more distinct predecessors. Under continuation backoff, the empty row of d returns ˆ P c . Table 3 gives all candidate estimates. The two recent destinations favor different candidates. The learned score combines these preferences. Smoothing also assigns positive probability to d, which u has never visited. Table 3: Smoothed estimates on the worked stream of Figure 1, computed by the model implementa- tion (α = 1, counts undecayed). Conditional rows use marginal backoff. Bold marks the candidates each estimator favours. Estimatorabcd ˆ P(z)0.20 0.30 0.300.20 ˆ P c (z)0.14 0.430.290.14 ˆ P(z| u)0.20 0.38 0.380.03 ˆ P(z| v 1 =c)0.10 0.650.150.10 ˆ P(z| v 2 =b)0.070.10 0.770.07 Figure 7 illustrates windowed co-occurrence (Equation 3) and the recency features. The co- occurrence table records (a,c) from nonconsecutive interactions at t 1 and t 3 . Global recency distin- guishes candidate d, which another source visited but u did not. Multi-scale recency applies three fixed decay scales to the time since the source last visited each candidate. The features describe complementary aspects of the stream: associations within a window, activity across sources, and time since the source last visited a candidate. 16 WINDOWED CO-OCCURRENCE GLOBAL RECENCYMULTI-SCALE RECENCY Transition countsCo-occurrence counts from / toabcd a·1· b·2· c·1· d· from / toabcd a·11· b·12· c·11· d· Adjacent destinations onlyHighlighted pairs are within K = 2 candidate ccandidate d equal 0 > 0 source uany sourcesource uany source Schematic heights. Equality and zero are exact. Same event, three decay scales 1 0 012345 τ r /10 τ r 10τ r Time since last visit, in units of τ r T Figure 7: Windowed co-occurrence and recency features on the worked stream of Figure 1. Top: the transition and co-occurrence tables the six events produce. Each event with prior source history updates one transition cell and up to K co-occurrence cells, one for each previous destination in the window. Dots mark unobserved pairs. The highlighted cells, (a,c) from t 1 and t 3 , (b,b) from t 2 and t 4 , and (c,c) from t 3 and t 5 , contain pairs that occur within the window but never consecutively. Bottom left: the two recency features for candidates c and d. The equality for c is exact because its most recent interaction is with u. The source recency of d is zero because u has never visited it. Other bar heights are schematic. Bottom right: the three fixed retention curves of multi-scale recency, independent of the stream. Their learned weights determine how the time since the source last visited a candidate affects its score. FCONTROLLED FEATURE COMPARISONS We add co-occurrence, global recency, and further source-recency scales to the reference configu- ration, first separately and then together. We repeat these comparisons under both backoff distribu- tions, using three runs per configuration. Figure 8 compares each addition with the reference on the same backoff distribution. Co-occurrence gives the largest median gain among the individual addi- tions. With marginal backoff, it improves MRR on 14 of 16 datasets. Combining all features has a larger median gain, but improves fewer datasets. Thus, adding more features does not consistently improve performance. 17 −5051015 test MRR change (points) wiki uci enron subreddit lastfm review coin comment flight GoogleLocal Yelp Taobao ML-20M Flickr YouTube WikiLink co-occurrence −5051015 test MRR change (points) global recency −5051015 test MRR change (points) multi-scale recency −5051015 test MRR change (points) all three marginal backoffcontinuation backoff Figure 8: Change in mean test MRR from adding co-occurrence, global recency, further source- recency scales, or all three to the reference configuration. Each addition is compared under the same backoff distribution. Each comparison uses three runs. Plain bars use marginal backoff and hatched bars use continuation backoff. TGB datasets appear above the divider. GHYPERPARAMETERS AND THEIR PROVENANCE The EdgeBank paper sets the recent-history window to the validation duration (Poursafaei et al., 2022, Section 4). We use the same duration for the count-decay constant τ . Recency uses the training duration T . Each duration is the last timestamp minus the first timestamp in that split. Both constants are fixed during fitting and evaluation. The main comparisons use α = 1. Appendix H examines sensitivity to this choice. The context depth K = 5 and recency constant τ r = 0.01 are also fixed. Appendix D examines context depth, and Appendix F evaluates additional recency scales. Table 4: Feature sets used in the main comparisons. Entries name additions to the reference config- uration. These choices remain fixed across five runs. DatasetMarginal backoffContinuation backoff wikiall threeall three uciall threeall three enronall threeall three subredditreferenceglobal recency lastfmall threeall three reviewco-occurrenceco-occurrence coinall threeall three commentmulti-scale recencyglobal recency flightall threeall three GoogleLocalco-occurrenceco-occurrence Yelpall threeall three Taobaoco-occurrenceco-occurrence ML-20Mco-occurrenceco-occurrence Flickrall threeall three YouTubeall threeall three WikiLinkall threeall three The reference configuration has K + 4 learned parameters, including the bias. Co-occurrence and global recency each add one parameter. Multi-scale recency adds two, and the configuration with all features has K + 8. 18 The two decay constants apply to different quantities. The count tables use τ , measured in the timestamp units of the data. The recency feature uses τ r T , a fixed fraction of the training duration. The scoring rule is fitted with Adam at learning rate 10 −2 for at most 100 epochs, using batches of 256 queries and one uniform negative per query. Gradients are clipped to a norm of one. We use no weight decay. We measure validation MRR after each epoch and stop after ten consecutive epochs without improvement. Test evaluation uses the weights from the epoch with the highest validation MRR. Validation candidates remain fixed across epochs. Every training event supplies a training query. Its features are computed before the event updates the count tables. Every main-model fit stops by the patience criterion before reaching the epoch limit. HSENSITIVITY TO SMOOTHING We vary α over10 −1 , 1, 10 with marginal backoff, the reference configuration, and K = 5. The same value is used in the marginal and conditional estimators. Each setting uses three runs on all 16 datasets. The α = 1 results reuse the marginal reference fits from the feature comparisons. This comparison examines sensitivity within a fixed configuration. It does not select α for the main results. Across the three smoothing constants, the median range of mean test MRR is 0.75 points. The largest range is 3.03 points on tgbl-review (Figure 9). −2.0−1.5−1.0−0.50.00.51.01.52.0 wiki uci enron subreddit lastfm review coin comment flight GoogleLocal Yelp Taobao ML-20M Flickr YouTube WikiLink (a) α= 0.1 −2.0−1.5−1.0−0.50.00.51.01.52.0 (b) α= 10 test MRR change from α= 1 (points) Figure 9: Change in test MRR from α = 1 under smaller and larger smoothing constants. Bars show mean changes over three seeds. Error bars show one sample standard deviation of the changes, with runs paired by seed. Blue denotes increases and red denotes decreases. TGB datasets appear above the divider. All settings use marginal backoff, the reference configuration, and K = 5. 19 ISENSITIVITY TO EVALUATION TIMING We vary evaluation history while fixing the model configuration and weights. All conditions use the same five fitted models and test candidates for each dataset. EdgeBank, Base3, and the heuristic family are also evaluated under event-wise and batch-wise updates. The heuristic rule remains fixed across schedules. Event-wise evaluation updates history after each scored event, retaining file order for tied times- tamps. Batch-wise evaluation scores 200 consecutive test events before adding any of them to his- tory. Strict-timestamp evaluation scores all events at time t using only events with earlier times- tamps, including training and validation events. After scoring a group, we update the tables in file order. The transition rule is unchanged, but earlier rows at the query timestamp are excluded from its history. The released EdgeBank and TGB implementations update memory after batches of 200 by default, as in our batch-wise condition. 1 TGN also uses earlier test interactions for later predictions, with batching balancing computation and update frequency (Rossi et al., 2020). Computational batches do not always impose this history boundary. DyGLib models such as TGAT and DyGFormer retrieve neighbors strictly before each query timestamp, including earlier test interactions (Yu et al., 2023). 2 Repeating the event-wise evaluation with the saved weights gives nearly identical test scores. Table 5: Test MRR (%) on TGB under event-wise and batch-200 updates. EdgeBank, Heuristic, Base3, and Ours share the listed schedule and candidates. Our scores are means and sample standard deviations over five runs. Neural reference scores retain their original protocols and are repeated for comparison. Bold marks the highest MRR in each row. Best neural DatasetUpdatesEdgeBankHeuristicBase3OursMRRMethod wikiEvent64.4082.0673.26 82.84±0.0482.70TPNet Batch 20057.1072.9068.0774.08±0.09 82.70TPNet uciEvent32.4052.7535.2251.57±0.3224.50TNCN Batch 20022.1637.4928.22 38.55±0.1624.50TNCN enronEvent15.6084.6648.65 86.83±0.0337.90TNCN Batch 20014.1454.9345.1752.46±0.1737.90TNCN subredditEvent59.2274.1974.25 74.90±0.0669.60TNCN Batch 20058.8574.1874.14 74.30±0.0469.60TNCN lastfmEvent2.6316.5811.37 32.84±0.1815.60TNCN Batch 2002.5715.7411.32 16.60±0.1215.60TNCN reviewEvent2.6933.9312.8745.76±0.39 52.10GraphMixer Batch 2002.5331.418.1745.57±0.39 52.10GraphMixer coinEvent58.3181.1077.7182.09±0.06 88.47CRAFT-R Batch 20057.9680.6476.8781.36±0.04 88.47CRAFT-R commentEvent15.0372.3845.4154.76±0.87 91.72CRAFT Batch 20014.9472.0744.9354.58±0.86 91.72CRAFT flightEvent38.7188.9279.3489.99±0.04 91.39CRAFT-R Batch 20038.7188.9079.2489.95±0.04 91.39CRAFT-R Matched counting baselines. Tables 5 and 6 report absolute scores under each update schedule. Under both schedules, our model exceeds EdgeBank and Base3 on all 16 datasets and the heuristic family on 14. The heuristic is stronger on tgbl-uci and tgbl-comment under event-wise updates, and on tgbl-enron and tgbl-comment under batch-wise updates. EdgeBank uses the TGB window rule under both schedules (Appendix A). 1 EdgeBank code and TGB example. 2 TGN evaluation, DyGLib evaluation, and neighbor sampling. 20 Table 6: Test MRR (%) on TGB-Seq under event-wise and batch-200 updates. Columns and con- ventions follow Table 5. Neural reference scores retain their original protocols. Best neural DatasetUpdatesEdgeBankHeuristicBase3OursMRRMethod GoogleLocalEvent1.9618.393.9731.42±0.03 62.88SGNN-HN Batch 2001.9618.393.7329.00±0.01 62.88SGNN-HN YelpEvent9.7730.8111.9953.21±0.06 72.69CRAFT Batch 2009.7630.8111.8852.26±0.05 72.69CRAFT TaobaoEvent20.2842.9920.1759.58±0.03 70.68CRAFT Batch 20020.2742.9920.1659.57±0.03 70.68CRAFT ML-20MEvent1.9417.716.64 39.00±0.1035.91CRAFT Batch 2001.9417.716.7031.63±0.09 35.91CRAFT FlickrEvent1.9638.3834.81 62.68±0.0762.34CRAFT Batch 2001.9638.3534.5456.61±0.05 62.34CRAFT YouTubeEvent1.9656.6438.09 65.27±0.0559.64SGNN-HN Batch 2001.9656.4837.61 63.89±0.0359.64SGNN-HN WikiLinkEvent1.9647.7026.6167.97±0.04 75.48CRAFT Batch 2001.9647.6724.9358.01±0.02 75.48CRAFT With all counting methods evaluated in batches of 200, our model still achieves the highest MRR on 4 of 16 datasets: tgbl-uci, tgbl-subreddit, tgbl-lastfm, and YouTube, compared with 7 under event-wise updates. Strict-timestamp sensitivity. Table 7 isolates the effect of excluding earlier events at the query timestamp. The largest reductions occur on tgbl-enron, WikiLink, Flickr, and YouTube. Configurations, weights, and candidates remain fixed, so the changes reflect the history available when each query is scored. Baselines were not evaluated under this schedule. Table 7: Strict-timestamp sensitivity of our model. Scores are test MRR (%), with means and sample standard deviations over five runs. Changes from event-wise evaluation use unrounded scores paired by seed. Configurations, weights, and candidates are fixed. DatasetEvent-wiseStrict timestampChange (points) TGB wiki82.84±0.0482.84±0.040.00±0.00 uci51.57±0.3251.43±0.32-0.14±0.00 enron86.83±0.0353.50±0.18-33.33±0.16 subreddit74.90±0.0674.89±0.060.00±0.00 lastfm32.84±0.1832.78±0.18-0.06±0.00 review45.76±0.3944.93±0.41-0.83±0.06 coin82.09±0.0681.67±0.04-0.42±0.03 comment54.76±0.8754.76±0.870.00±0.00 flight89.99±0.0488.94±0.12-1.05±0.10 TGB-Seq GoogleLocal31.42±0.0331.42±0.030.00±0.00 Yelp53.21±0.0653.21±0.060.00±0.00 Taobao59.58±0.0359.58±0.030.00±0.00 ML-20M39.00±0.1039.00±0.090.00±0.00 Flickr62.68±0.0754.97±0.07-7.71±0.05 YouTube65.27±0.0561.58±0.03-3.69±0.05 WikiLink67.97±0.0456.25±0.04-11.72±0.06 21