Temporal Graph Neural Networks

Updated 1 December 2025

Temporal Graph Neural Networks are neural architectures that fuse graph topology with temporal evolution, enabling dynamic predictions across time-variant data.
They employ techniques such as memory modules, event-driven message passing, and temporal attention to capture and propagate time-dependent features.
TGNNs show improved performance in tasks like link prediction, dynamic node classification, and session-based recommendation, offering scalable and efficient real-time inference.

Temporal Graph Neural Networks (TGNNs) are a class of neural architectures designed to capture both the topological structure and temporal dynamics of graph-structured data that evolves over time. TGNNs generalize Graph Neural Networks (GNNs) by jointly modeling spatial (graph) dependencies and temporal evolution, supporting discrete-time snapshots, event-based dynamics, and heterogeneous or continuously evolving entity and relation sets. Applications of TGNNs span dynamic recommendation, traffic forecasting, knowledge graphs, temporal link and node prediction, and session-based modeling.

1. Foundational Models and Temporal Graph Formalism

A temporal graph is characterized by a sequence of time-stamped interactions or snapshots. The representation varies by regime:

Snapshot-based: The data is a sequence of graphs $\{G^{(1)},\ldots,G^{(T)}\}$ , each a static graph at discrete time $t$ ; $G^{(t)}=(V^{(t)},E^{(t)},X^{(t)})$ (Bonner et al., 2018).
Continuous-Time/Event-based (CTDG): The graph is a chronologically ordered sequence of events $\mathcal{G} = \{ (u,v,t,e_{uv}(t)) \}$ , where each event encodes a node/edge operation at time $t$ (Rossi et al., 2020, Petrović et al., 4 Jun 2024).

Key tasks include temporal link prediction, dynamic node classification, and spatio-temporal forecasting.

Canonical TGNN Frameworks

Temporal Graph Networks (TGN) provide a generic, inductive event-based TGNN framework, combining node-wise memory modules, event-driven message-passing, and flexible embedding/readout operators (identity, time-projection, graph-sum, graph-attention) (Rossi et al., 2020). The message-store, memory-update, and embedding/read functions can recover models such as TGAT, JODIE, and DyRep as special cases.
Temporal Graph Offset Reconstruction shifts the autoencoding target to future adjacency, training encoders to predict $\widehat{A}^{(t+\Delta)}$ from the present, which introduces explicit temporal robustness (Bonner et al., 2018).

2. Model Architectures and Temporal Mechanisms

TGNNs realize the interplay between temporal and spatial (graph-topological) complexities through various architectural paradigms:

Memory-Augmented and Message-Passing Designs

TGN (Rossi et al., 2020) maintains per-node memory $s_i(t)$ updated at every event, with messages generated via prior state, edge features, and inter-event time. Updating is handled by a learnable unit (e.g., GRU), and embeddings can be computed on-the-fly or after graph-based attention.
Trajectory Encoding TGN (TETGN) introduces a parallel trajectory stream: each node maintains a learnable temporal position (ID), propagated via exponential decay and message passing. This reconciles the expressivity of non-anonymous (ID-based) and anonymous (structure-only) temporal models for improved transductive and inductive performance (Xiong et al., 15 Apr 2025).

Attention-Based and Sequence-Modeling Approaches

Temporal Graph Attention (TGAT, TGNN-Transformer) utilizes attention over temporal neighborhoods, combining node/edge features with functional or learnable time encodings (Huang et al., 9 Sep 2024). TF-TGN adapts the Transformer decoder (with causal masking, suffix infilling, and self-loop attention) for TGNNs, allowing efficient exploitation of optimized Transformer codebases for scalable training (Huang et al., 9 Sep 2024).
TempoKGAT enhances temporal GAT by combining time-decaying kernels with selective (top- $k$ ) neighbor aggregation, where attention is further modulated by age/time and explicit edge weights for robust pattern discovery in spatio-temporal data (Sasal et al., 29 Aug 2024).

ODE-Based and Continuous-Time Models

Continuous Temporal Graph Networks (CTGN) parameterize node evolution over time intervals as neural ODEs: embeddings evolve according to $dz_u/d\tau = f_\theta(z_u, \{z_v\}, \tau)$ , integrating memory, GAT-based encoding, and interaction durations for continuous evolution (Guo et al., 2022).
TGNN4I addresses irregular sampling by combining a piecewise-constant ODE (exponential/periodic decay) with a GNN-augmented GRU at observation times, supporting partial and asynchronous node observations (Oskarsson et al., 2023).

Heterogeneous Temporal Models

HTGNN and SE-HTGNN generalize to heterogeneous (multi-type) temporal graphs, employing hierarchical attention over relation types, spatial and temporal slices, and, for SE-HTGNN, LLM-based node type prompting for inductive type-prior knowledge (Fan et al., 2021, Wang et al., 21 Oct 2025). SE-HTGNN further integrates spatial and temporal learning with a dynamic attention mechanism retaining attention histories across time, yielding improved accuracy and 10 $\times$ training speedup (Wang et al., 21 Oct 2025).

3. Temporal Reasoning, Propagation, and Rewiring

Transition and Trajectory Encoders

TIP-GNN encodes personalized neighbor transition structures: for each node, a bilevel graph is constructed—explicit interaction (star) and a directed transition graph among its neighbors (capturing the order of visits). Embeddings propagate through $K$ steps over the transition graph, bilevel attention is applied, and step-wise fusion aggregates the information (Zheng et al., 2023).
TETGN (see above) ensures time-consistent, trajectory-aware node representations via exponential decay of temporal IDs, supporting both discriminative performance for known nodes and generalization to unseen nodes (Xiong et al., 15 Apr 2025).

Graph Rewiring for Temporal Message Passing

TGR introduces temporal graph rewiring for CTDGs: memory vectors are periodically mixed on expander graphs (e.g., Cayley expanders), ensuring constant spectral gap, logarithmic diameter, and eliminating information bottlenecks typical in temporal GNNs (oversquashing, under-reaching, memory staleness) (Petrović et al., 4 Jun 2024). The architecture alternates native TGNN message passing with expander mixing layers. Empirically, TGR yields large gains in mean reciprocal rank (up to 50% on certain TGB benchmarks).

4. Learning Objectives, Evaluation, and Robustness

TGNNs optimize a variety of objectives:

Supervised: Cross-entropy for node classification and binary link prediction, sometimes with mean squared error for regression (Rossi et al., 2020, Fan et al., 2021).
Self-supervised: Temporal offset loss (future adjacency reconstruction), variational objectives (TO-GVAE), neural ODE reconstruction (Bonner et al., 2018, Guo et al., 2022).
Regularization: Time-encoding smoothness, $L_2$ weight decay, dropout, volatility-aware penalties (Guo et al., 2022, Su et al., 10 Dec 2024).

Volatility-Aware Evaluation

Standard metrics such as AP and AU-ROC are instance-based and invariant to the temporal arrangement of errors, thus failing to detect error bursts (volatility clustering) (Su et al., 10 Dec 2024). The Volatility Cluster Statistics (VCS) metric computes the temporal clustering of errors by comparing nearest-neighbor inter-error times to randomly sampled baselines, and can be integrated as a differentiable penalty (VCA) to enforce temporal error uniformity. This regularization halves the VCS (error clustering), minimally reducing AP (accuracy) (Su et al., 10 Dec 2024).

5. Applications, Scalability, and Implementation Considerations

Applications

Temporal link prediction in social, citation, transaction, and online systems (Rossi et al., 2020, Bonner et al., 2018, Zheng et al., 2023).
Dynamic node classification for streaming labeling and evolving categories (Rossi et al., 2020, Fan et al., 2021, Feng et al., 2023).
Session-based recommendation using dynamic session graphs (TempGNN) where per-interaction time is explicitly modeled for next-item prediction; time-scoped node and edge embeddings are fused with item-based features (Oh et al., 2023).
Dynamic object detection in 3D point clouds (autonomous driving) using temporal proposal smoothing (see (Wang et al., 2022)).

Scalability and Efficiency

Memory and sampling: TGN caches per-node memory, supports neighbor sampling by time, and processes batches in an event-driven, parallelizable fashion; message computation, aggregation, and updating can be decoupled for flexibility (Rossi et al., 2020).
Transformer-based acceleration: TF-TGN demonstrates >2 $\times$ end-to-end speedup on billion-edge graphs by leveraging hardware-optimized Transformer kernels (flash-attention), causal masking, and batch parallelism (Huang et al., 9 Sep 2024).
AP-block approaches (TAP-GNN) achieve whole-history aggregation in $O(|E|)$ time per layer—substantially outperforming neighbor-sampling models (TGAT) that scale exponentially with depth—allowing for online low-latency inference (Zheng et al., 2023).

6. Recent Advances and Challenges

Several advances and open challenges have emerged:

Modeling irregular and partially observed time series: Continuous-time TGNNs enable forecasting at arbitrary times, supporting non-uniform and missing observation scenarios (TGNN4I) (Oskarsson et al., 2023).
Open-set and continual learning: OTGNet disentangles class-related and class-agnostic information, preventing representational collapse and catastrophic forgetting as new classes emerge (Feng et al., 2023).
Explainability: Post-hoc explainers for TGNNs (Bayesian network–based) extract dominant time-period-specific dependency patterns, significantly enhancing interpretability for practitioners in domains such as traffic forecasting (He et al., 2022).

7. Benchmarks, Empirical Results, and Model Comparisons

TGNNs have been evaluated across temporal benchmarks including Wikipedia, Reddit, LastFM, OGBN-MAG, COVID-19 (epidemic forecast), and TGB (large-scale event streams). Empirically:

TGN-attention achieves up to 98.7% AP on Reddit link prediction, outperforming all baselines (Rossi et al., 2020).
HTGNN and SE-HTGNN set new state-of-the-art AUCs on OGBN-MAG for heterogeneous temporal graphs, with SE-HTGNN yielding a 10 $\times$ runtime reduction (Fan et al., 2021, Wang et al., 21 Oct 2025).
TDE-GNN, learning high-order temporal dependencies, improves node classification on non-homophilic graphs (e.g., Squirrel: 78.5% vs 71.0% for first-order models) (Eliasof et al., 20 Jan 2024).
TIP-GNN shows up to 7.2% accuracy gain on temporal link prediction over prior state-of-the-art (Zheng et al., 2023).
TETGN bridges inductive and transductive performance, outperforming both anonymous and non-anonymous TGNNs on link prediction and node classification (Xiong et al., 15 Apr 2025).
TGR provides up to 6% mean reciprocal rank gain at 10% extra runtime via expander graph rewiring (Petrović et al., 4 Jun 2024).
TF-TGN achieves 2–3 $\times$ training speedup with comparable or superior dynamic link prediction accuracy to TGN/TGAT/APAN (Huang et al., 9 Sep 2024).

References

Model / Paper	arXiv ID
Temporal Graph Offset Reconstruction	(Bonner et al., 2018)
Temporal Graph Networks (TGN)	(Rossi et al., 2020)
HTGNN (Heterogeneous Temporal Graph NN)	(Fan et al., 2021)
Transition Propagation GNN (TIP-GNN)	(Zheng et al., 2023)
Trajectory Encoding TGN (TETGN)	(Xiong et al., 15 Apr 2025)
Simple and Efficient HTGNN (SE-HTGNN)	(Wang et al., 21 Oct 2025)
Temporal Aggregation and Propagation GNN (TAP-GNN)	(Zheng et al., 2023)
Continuous Temporal Graph Networks (CTGN)	(Guo et al., 2022)
Temporal Graph Neural Networks for Irregular Data	(Oskarsson et al., 2023)
TempoKGAT	(Sasal et al., 29 Aug 2024)
Temporal Graph Rewiring (TGR)	(Petrović et al., 4 Jun 2024)
Temporal-Aware Evaluation (VCS)	(Su et al., 10 Dec 2024)
Retroffiting TGN with Transformer (TF-TGN)	(Huang et al., 9 Sep 2024)
TempGNN (session-based)	(Oh et al., 2023)
Who Should I Engage (MTGN, missing-event aware)	(Liu et al., 2023)
On the Temporal Domain of DE-GNN (TDE-GNN)	(Eliasof et al., 20 Jan 2024)
An Explainer for TGNNs	(He et al., 2022)
Towards Open Temporal Graph Neural Networks (OTGNet)	(Feng et al., 2023)

This structured overview synthesizes the state of the art in Temporal Graph Neural Networks, reflecting their mathematical underpinnings, model innovations, learning objectives, evaluation protocols, and empirical results as established in recent literature.