Dynamic Graph World Modelling: Learning Future Dynamics from Temporal Context

1 INTRODUCTION

• Dynamic graph world modelling learns transitions from historical graph observations into compact latent states to predict future system dynamics.The broader aim is to predict future graph states for planning and decision-making, beyond forecasting a single edge or node label.Source: §1 · p. 1
• Task-oriented methods bind representations to particular tasks, while self-supervised contrastive or reconstruction objectives have limitations for learning predictable graph dynamics.Contrastive methods depend on temporally meaningful positive-negative pairs, while reconstruction can emphasize observed graph details over dynamics.Source: §1 · p. 2
• DYG-WM jointly predicts future node and relation representations, using historical contexts and path signatures rather than reconstructing a single future graph realization.Its context encoder summarizes node-neighborhood trajectories and pair-specific histories, while its path-signature encoder captures ordered changes.Source: §1 · pp. 2–3
• Across 12 link-prediction datasets, DYG-WM achieves the best average rank in every evaluated setting, and the best Macro-F1 and Micro-F1 across label ratios.Ablation and latent-alignment analyses also support the effectiveness of its components.Source: §1 · p. 3

2 RELATED WORKS

• Most self-supervised dynamic graph neural networks remain node-centric, with pair-level information mainly used for link prediction.DYG-WM instead models and predicts future representations at both node and relation levels.Source: §2 · p. 3
• Existing object-centric graph world models mainly address action-conditioned physical systems, where relations support object-state updates rather than being predicted themselves.DYG-WM instead constructs historical node and relation contexts and jointly predicts future representations as an action-free relational transition model, not a full planning system.Source: §2 · p. 3

3.1 PRELIMINARY

• For a target bin, the historical snapshot context uses preceding snapshots, while query-time relation representations additionally use the strict event history before the query.Equal-timestamp events are excluded from one another’s histories, and the target snapshot is hidden from the online branch.Source: §3.1 · p. 4

3.2 HISTORICAL NODE-RELATION CONTEXT ENCODER

• The context encoder combines a node’s recent state with ordered node and neighborhood trajectories, while a pair-specific encoder pools representations of selected historical context nodes.Pair-context candidates include the endpoints and historical neighbors, ranked using recency and common-neighbor bridging information.Source: §3.2 · pp. 4–5

3.3 NODE-RELATION PATH-SIGNATURE ENCODER

• Second-order path signatures encode cumulative changes and their ordered interactions, complementing historical state summaries at both node and relation levels.Node paths use structural descriptors, while relation paths use pair states that include connectivity, endpoint degrees, common neighbors, neighborhood overlap, activity, and context coverage.Source: Figure 2 · p. 4, §3.3 · pp. 5–6

3.4 DUAL-LEVEL JOINT-EMBEDDING PREDICTIVE OBJECTIVE

• The dual-level predictive objective predicts target-snapshot node and relation latents from historical information, using an EMA target branch during training.The target branch encodes the target snapshot; inference uses historical snapshot context and the strict event prefix, and equal-timestamp events are excluded from event-history statistics.Source: Figure 2 · p. 4, §3.4 · pp. 6–7

4 EXPERIMENTS

• Link prediction uses 12 DyGLib benchmark datasets and eleven baselines; evaluation also specifies chronological splits, sampling settings, and held-out-node classification metrics.The experiments use 70%/15%/15% chronological splits, and report AP and AUC-ROC for link prediction and Macro-F1 and Micro-F1 for node classification.Source: §4 · pp. 7–8

4.1 MAIN RESULTS

• DYG-WM performs well on both tasks; evaluation includes inductive AUC-ROC, node-classification Macro-/Micro-F1, and a Can. Parl. alignment comparison with versus without the predictive objective.Source: Table 2 · p. 8, Table 3 · p. 8, Figure 3 · p. 8

4.2 ABLATION STUDY

• 74.99 to 59.09 AUC-ROC on Enron, 78.19 to 60.31 on Can. Parl., and 77.36 to 70.17 on LastFM follow path-signature removal; every component removal lowers AUC-ROC across all three datasets.Historical context and the predictive objective also provide consistent gains.Source: Table 4 · p. 9, §4.2 · p. 9

4.3 EFFICIENCY

• On Reddit and LastFM, no compared method is simultaneously faster and more accurate than DYG-WM, which lies on the accuracy-efficiency frontier.DYG-WM attains the highest AUC-ROC while training faster than other high-accuracy models such as DyGFormer and CAWN on Reddit; on LastFM, DyGFormer is slightly more accurate but requires substantially more training time.Source: Figure 4 · p. 9, §4.3 · p. 9

4.4 ROBUSTNESS

• The robustness analysis examines noise on Can. Parl. and Wikipedia.Source: Figure 5 · p. 9

• DYG-WM jointly models node and relation evolution, predicting future representations from historical contexts and ordered structural changes through a dual-level joint-embedding objective.Source: §5 · p. 10
• Experiments on 12 dynamic link-prediction datasets and two dynamic node-classification datasets show performance across both tasks, with ablation and latent-alignment results indicating contributions from the main components.Source: §5 · p. 10
• Future work will consider more complex evolving relational systems and a broader range of downstream tasks.Source: §5 · p. 10

AI USE STATEMENT

• Generative AI tools were used for language polishing, grammar checking, and improving manuscript clarity and readability.Source: AI USE STATEMENT · p. 10
• The authors say AI tools were not used to develop the methodology, conduct experiments, generate results, or analyze or interpret results; revisions were reviewed and verified by the authors.The authors take full responsibility for the final content.Source: AI USE STATEMENT · p. 10

APPENDIX

• The appendix provides additional methodological details, experimental settings, extended results, and further analyses of DYG-WM.Source: APPENDIX · p. 13

• The link-prediction evaluation uses 12 public dynamic graph datasets collected by Poursafaei et al. (2022) and redistributed with DyGLib (Yu et al., 2023).Source: §A.1 · p. 13
• Node classification uses two large-scale datasets released by Lu et al. (2019).Source: §A.1 · p. 13
• Table 5 presents statistics of the datasets, while Table 6 presents statistics for the dynamic node-classification datasets; Table 5 defines N/A as missing node or edge features and #Nodes as node count.Source: Table 5 · p. 13, Table 6 · p. 13

Environment and Reproducibility

• Experiments use Python, PyTorch, and NVIDIA A100 GPUs, with code requiring Python 3.10 or later and PyTorch 2.1 or later.DyG-WM uses second-order path signatures and task-specific loss weights and target-encoder EMA coefficients.Source: §A.2 · p. 13

Shared Architecture Configuration

• Both DyG-WM and snapshot baselines use hidden dimension 128 and two message-passing layers, while task-specific windows contain three link-prediction or two node-classification historical snapshots.Both tasks use a 32-dimensional temporal encoding and 256-dimensional predictor.Source: §A.2 · p. 13

Dynamic Link Prediction

• Link prediction follows the chronological 70/15/15 split, evaluates one uniformly corrupted destination per observed interaction, and selects checkpoints using validation AP and AUC.The test set is evaluated once with the selected checkpoint.Source: §A.2 · pp. 13–14

Dynamic Node Classification

• Node representations are learned for at most 100 epochs, frozen, and evaluated with an MLP probe trained on 40%, 60%, or 80% of labelled nodes.For DyG-WM, separate probes use predicted and online-encoder representations, with logits averaged; the target encoder is not used by the classifier.Source: §A.2 · p. 14

Detailed Settings for Effectiveness Evaluation

• The evaluation distinguishes training-only, train-and-test, and test-only edges, and clarifies that inductive negative sampling is not the new-node inductive setting.The three protocols are random, historical, and inductive negative sampling.Source: §A.3 · p. 14

Historical Negative Sampling

• Historical negatives are previously observed edges absent from the current batch, testing whether the model identifies when an edge reappears rather than whether it remains active.If the historical pool is too small, random negatives fill the remainder.Source: §A.3 · pp. 14–15

Detailed Settings for Effectiveness Evaluation

• Table 8 reports transductive Average Precision under random, historical, and inductive negative sampling, with best and second-best results marked.The supplied caption identifies the table's scope but does not provide cell values.Source: Table 8 · p. 15

Inductive Negative Sampling

• Inductive negatives are edges first seen during evaluation that appeared before the current batch but are absent from it; random negatives fill any shortfall.The task is to determine whether such edges recur at subsequent timestamps.Source: §A.3 · p. 15

Detailed Settings for Robustness Evaluation

• Robustness is tested on Wikipedia and Can. Parl. by training on clean transductive data and corrupting a fraction of input features only during evaluation.Noise rates range from 0.1 to 0.6, with 0 denoting the clean setting and shared corruption seeds across methods.Source: §A.3 · p. 15

A.4 ADDITIONAL EXPERIMENTAL RESULTS

• Tables 8 and 9 report Average Precision for transductive and new-node inductive link prediction, while Figure 8 compares AUC-ROC with training time across 12 datasets.Figures 6 and 7 show latent alignment with and without the predictive objective on Wikipedia and UCI, respectively.Source: §A.4 · p. 15, Figure 6 · p. 16, Figure 7 · p. 16

A.5 ALGORITHM DETAILS

• The appendix identifies Algorithm 1 as representation construction, Algorithm 2 as dual-level predictive training, and Algorithm 3 as link inference without the target branch.The supplied passages describe the algorithms' roles rather than their complete procedures.Source: §A.5 · p. 17

A.6 HISTORICAL REPRESENTATION CONSTRUCTION

• Historical node contexts use the preceding W−1 snapshots, while exact-time relation representations additionally use the strict event prefix H<τ.Bin-level representations depend only on the snapshot context; exact-time representations also depend on events before the query time.Source: §A.6 · p. 17

A.7 DUAL-LEVEL PREDICTIVE TRAINING

• Dual-level training uses online parameters and EMA target parameters, with candidate groups kept intact within minibatches; sampled negatives enter only link and ranking losses.Node and relation targets use observed interactions, and relation targets do not receive explicit target-snapshot pair statistics.Source: §A.7 · pp. 17–18
• For node classification, the relation predictor, event-history branch, link scorer, and relation loss are disabled.The node predictor maps the node context to its prediction target.Source: §A.7 · p. 18

A.8 LINK INFERENCE

• At link inference, the target encoders and predictive losses are removed, and queries use only historical snapshots and events strictly before query time.The prediction score is computed from the resulting historical relation representation.Source: §A.8 · p. 18

B. COMPUTATIONAL COMPLEXITY

• Historical snapshot encodings and node contexts are shared across candidates, whereas relation contexts, relation signatures, and event-history features are pair-conditioned.The computational analysis defines snapshot, candidate, and relation-context quantities and describes sparse neighborhood pooling and node updates.Source: B COMPUTATIONAL COMPLEXITY · p. 18, §B.1 · p. 19

B.2 RELATION-CENTRIC CONTEXT SELECTION; B.3 NODE-RELATION PATH SIGNATURES; B.4 EXACT-TIME EVENT-HISTORY QUERIES

• Relation-context pooling is bounded by budget B, second-order signatures scale with the number of historical increments, and strict-prefix queries use binary search in O(log M).Partial top-B selection reduces sorting to O(Cj log B); node signatures are shared and relation signatures are pair-conditioned.Source: §B.2 · p. 20, §B.3 · p. 20, §B.4 · p. 20

B.5 PREDICTION HEADS AND TRAINING OBJECTIVE

• Endpoint transformation, relation encoding, fusion, prediction, and link scoring cost O(Pd^2), while pointwise losses cost O(Pd) and groupwise ranking costs at most O(P log P).Variance penalties cost O(P+d); covariance terms are omitted when a level has fewer than two prediction vectors.Source: §B.5 · p. 21

B.6 TRAINING-TIME OVERHEAD

• Training additionally encodes the target snapshot and constructs positive relation targets, with the EMA update independent of graph size and candidate count.Each group-preserving minibatch re-encodes historical and target snapshots after its parameter update; inference can reuse historical representations across candidate minibatches.Source: §B.6 · p. 21

B.7 MEMORY COMPLEXITY

• Inference memory includes historical context, node and relation representations, and candidate-dependent storage; training adds target embeddings, activations, covariance matrices, gradients, and optimizer states.The stated inference expression excludes model parameters and the persistent event-history index; relation-centric modeling is bounded by B, and the target branch is training-only.Source: §B.7 · p. 21

C PROOFS AND TECHNICAL DERIVATIONS

• The appendix establishes that snapshot views do not generally identify pairwise interaction multiplicity, second-order signatures capture temporal order beyond first-order summaries, and deployed scoring depends on historical context and the strict event prefix.These properties address snapshot information loss, path ordering, and the inputs used by the deployed scorer.Source: C PROOFS AND TECHNICAL DERIVATIONS · p. 21

C.1 NON-IDENTIFIABILITY OF PAIRWISE INTERACTION MULTIPLICITY

• Identical snapshot views can arise from streams with arbitrarily different directed-pair multiplicities when snapshots omit pair-resolved statistics.The stated construction allows the multiplicity difference to be any integer k ≥ 1.Source: §C.1 · pp. 21–22

C.2 ORDER SENSITIVITY OF THE SECOND-ORDER SIGNATURE

• First-order signatures collapse two-step orderings; second-order signatures distinguish them exactly when increments are non-collinear, but are not fully injective for longer paths.Distinct longer paths may still share the same truncated second-order signature.Source: §C.2 · pp. 22–23

C.3 PREFIX OF THE DEPLOYED SCORER

• With fixed learned parameters and an offline partition, identical historical snapshot contexts and strict prefixes yield identical deployed scores; target-bin data may still affect training.At inference, the target snapshot encoder and target-snapshot representations are not scoring inputs.Source: §C.3 · p. 23