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GTIN: A Unified Framework for Joint Event and Time Prediction in Temporal Graphs

This paper proposes a unified mathematical framework, GTIN, for jointly predicting the next event and its occurrence time in temporal graphs, which demonstrates superior performance over existing methods across diverse datasets, particularly in handling irregular patterns and complex temporal dependencies.

Original authors: Mohammad Ostadmohammadi, Sepehr Kazemi, Hamid R. Rabiee

Published 2026-08-17

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CC BY 4.0

Original authors: Mohammad Ostadmohammadi, Sepehr Kazemi, Hamid R. Rabiee

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the digital age, our world is increasingly mapped as a series of connections. Every message sent, every transaction made, and every post shared creates a link between two points in a vast, shifting network. For decades, scientists have studied these networks, known as graphs, to understand how information and influence flow. However, traditional methods often treated these connections as static snapshots, freezing a moment in time and ignoring the fact that relationships are constantly evolving. More recent approaches have begun to account for time, treating the network as a living stream of events. Yet, a significant gap remained: while researchers could predict when an event might happen or where it might occur, few models could reliably forecast both the timing and the specific nature of the next interaction simultaneously, especially when looking at the network as a whole rather than just a small neighborhood of connections.

A team of researchers at Sharif University of Technology has addressed this challenge by developing a new framework called the Global Temporal Interaction Network, or GTIN. Their work moves beyond the limitations of looking at isolated parts of a network. Instead of focusing only on the immediate neighbors of a specific connection, this new system analyzes the entire graph to understand the global rhythm of activity. The researchers trained their model to answer three fundamental questions about the future of a network: where will the next event happen, when will it occur, and what will that event look like? By treating the entire network as a single, interconnected system, the model captures complex patterns that smaller, localized approaches miss, such as how a burst of activity in one part of a system can ripple through to influence events elsewhere.

To test their ideas, the researchers applied GTIN to a variety of real-world and simulated environments. They examined datasets representing human interactions, including edits made to Wikipedia pages, discussions on the Reddit platform, and private messages exchanged among university students. In each case, the model was asked to predict the very next interaction that would take place. The results were striking. On the Wikipedia dataset, the model's predictions for the timing of the next edit were significantly more accurate than those of previous leading methods, reducing the error rate from over eleven seconds to just under ten. On the Reddit dataset, which features a much denser and faster stream of interactions, the improvement was even more dramatic, with the new model cutting the prediction error in half compared to the next best approach. The system also proved effective in predicting which specific connection would be used next, successfully identifying the correct path for the next event in a significant portion of cases.

The researchers also tested the model on synthetic data designed to mimic different types of temporal behavior, ranging from random, independent events to highly clustered bursts of activity. In every scenario, the new framework outperformed existing techniques. This consistency suggests that the model is not just memorizing specific patterns but has learned a robust way to understand how time and structure interact within a network. A key insight from their analysis is that the model's advantage becomes most apparent when looking at events that are surrounded by less immediate activity. In these quieter moments, the ability to draw information from the broader, global history of the network—rather than just the immediate past of a single connection—provides a crucial edge in making accurate predictions.

Recognizing that analyzing massive networks can be computationally expensive, the team also developed a method to make the system more efficient without sacrificing too much accuracy. They introduced a process that breaks the large network into smaller, balanced pieces, analyzes each piece separately, and then reassembles the findings. This approach reduced the time required to train and run the model by more than half on the largest datasets, making it feasible to apply these techniques to even larger, real-world systems. While the model currently treats all connections as similar, the researchers acknowledge that future versions could be refined to distinguish between different types of interactions, such as a financial transaction versus a social greeting. For now, however, this work establishes a powerful new foundation for understanding the dynamic pulse of complex systems, offering a clearer view of what happens next in our interconnected world.

Technical Summary: GTIN – A Unified Framework for Joint Event and Time Prediction in Temporal Graphs

1. Problem Definition

The paper addresses the challenge of predicting future events in dynamic systems modeled as temporal graphs. Unlike traditional static graph models or existing temporal graph approaches that often focus on localized subgraphs or specific edge histories, this work targets a unified prediction task. The objective is to jointly estimate three critical components of the next event in a temporal graph:

Location ( $c$ ): Which edge (interaction pair) will be active next?
Time ( $t$ ): When will this event occur?
Features ( $W$ ): What are the attributes of this event?

The authors argue that existing methods, such as Temporal Graph Neural Networks (TGNNs) and Temporal Point Processes (TPPs), often fail to utilize the global structural context, relying instead on limited temporal windows or local node neighborhoods. This limitation hinders the ability to capture complex, long-range temporal dependencies and irregular event patterns inherent in real-world systems like social networks, financial transactions, and communication logs.

2. Methodology: Global Temporal Interaction Network (GTIN)

The proposed solution, GTIN, is a unified mathematical framework that treats the entire graph structure as a single entity for prediction, rather than aggregating independent edge predictions.

2.1. Mathematical Formulation

The problem is framed using Marked Point Processes. The history of the graph up to time $t$ , denoted as $\mathcal{H}(t)$ , consists of a sequence of triplets $(t_i, W_i, c_i)$ representing time, features, and the specific edge index. The goal is to maximize the likelihood of the next event triplet $\mathcal{H}(t, 1)$ given the history $\mathcal{H}(t)$ .

The likelihood is decomposed into three conditional probabilities:
$P(\hat{c}, \hat{t}, \hat{W} | \mathcal{H}(t)) = P(\hat{c}|\mathcal{H}(t)) \cdot P(\hat{t}|\hat{c}, \mathcal{H}(t)) \cdot P(\hat{W}|\hat{t}, \hat{c}, \mathcal{H}(t))$

This decomposition allows the model to sequentially predict the edge location, the occurrence time, and the event features.

2.2. Model Architecture

GTIN employs a Message Passing Framework where edges in the original graph are treated as nodes in a transformed "line graph." Neighboring edge-nodes are those sharing a common endpoint in the original graph.

Edge Embeddings: Each edge $n$ maintains an embedding $h_n(t)$ that aggregates temporal information from its own history and the histories of neighboring edges.
$h_n(t) = \text{COMB}\left( \text{AGG}\{\Phi(t^j_i, W^j_i) | t^j_i \leq t, j \in \mathcal{N}(n)\}, \Phi(t^n_i, W^n_i) \right)$
Here, $\text{COMB}$ utilizes a self-attention mechanism, and $\text{AGG}$ is a learnable linear transformation.
Temporal Encoding: To handle continuous time without discretization, the model uses a harmonic time encoder (similar to GNPP), mapping timestamps to high-dimensional vectors using learnable frequency parameters. This captures short-term recency, long-term dependencies, and periodicity.
Global Graph Representation: The global state of the graph at time $t$ is computed as a weighted sum of all edge embeddings:
$h_G(t) = \sum_{n=1}^{N} w_n h_n(t)$
This global embedding $h_G(t)$ serves as the context for predicting the next event, ensuring that the prediction considers the entire graph's temporal state.

2.3. Prediction Heads

The model utilizes three distinct heads based on the global and local embeddings:

Edge Prediction (Classification): Uses a softmax over all candidate edges to predict $c_i$ .
Time Prediction (Regression): Models the time distribution as a Gaussian $\mathcal{N}(\mu_t, \sigma_t^2)$ , predicting both mean and variance to quantify uncertainty.
Feature Prediction (Regression): Models event features as a multivariate normal distribution, conditioned on the predicted edge, time, and global history.

The training objective minimizes the negative log-likelihood, which is the sum of classification loss, time prediction loss, and feature prediction loss.

2.4. Scalability Extension (DGI + Clustering)

To address computational complexity on large graphs, the authors propose an extension using Deep Graph Infomax (DGI) and Balanced K-means Clustering:

DGI: Learns unsupervised node embeddings that preserve mutual information between local patches and the global graph context.
Balanced Clustering: Partitions the graph into approximately equal-sized subgraphs.
Hierarchical Prediction: The pipeline constructs a new "super graph" where each subgraph is treated as a super-node. This super graph is fed into the algorithm to detect in which cluster the next event occurs. Once the target cluster is identified, the corresponding subgraph is fed into the event prediction module, where both the next event type and its occurrence time are jointly predicted using the temporal model. This enables parallel processing and significantly reduces training and inference time.

3. Key Contributions

The paper highlights three primary contributions:

Global Event-Time Prediction Framework: A model that jointly predicts the next event's location, timing, and features by analyzing the entire graph structure, moving beyond reliance on local neighborhoods.
Hierarchical Scalability: A mechanism to efficiently partition and process graphs of any size while maintaining temporal dependencies, facilitating training on large-scale datasets.
Feature-Level Event Forecasting: The capability to estimate event attributes (features) alongside structural and temporal predictions, providing a more comprehensive forecasting capability.

4. Experimental Results

The authors evaluated GTIN on three real-world datasets (Wikipedia, Reddit, CollegeMsg) and three synthetic datasets (Hawkes-negative, Hawkes-positive, Poisson).

Performance: GTIN consistently outperformed baselines including TGAT, TGN, DyRep, and Neural Point Process models (THP, SAHP, NNPP).
- On the Wikipedia dataset, GTIN achieved an RMSE of 10.6, significantly lower than TGN (23.81) and TGAT (37.66).
- On the Reddit dataset, GTIN achieved an RMSE of 0.51, nearly halving the error of the next best model (GNPP at 1.08).
- On synthetic datasets, GTIN reduced error rates by 8–70% compared to the strongest baseline (GNPP), particularly excelling in datasets with strong self-exciting behaviors (Hawkes-positive).
Location Prediction: The model demonstrated strong performance in predicting the correct edge (Hits@10 and MRR), validating the effectiveness of the global context integration.
Scalability: The DGI-based pipeline reduced training time by 52–68% and inference time by 50–66% across datasets, with only a marginal increase in RMSE, confirming a favorable trade-off between accuracy and efficiency.
Ablation Studies: Removing the attention mechanism resulted in consistent performance drops, confirming that attention is crucial for weighting informative neighbors. Analysis of "neighboring-edge activity" showed that GTIN's advantage is most pronounced for events surrounded by low local activity, proving its ability to leverage global information where local history is sparse.

5. Significance and Limitations

Significance:
The paper claims that GTIN provides a robust foundation for temporal event prediction by unifying structural and temporal modeling. Its ability to handle irregular event patterns and complex dependencies makes it superior to methods restricted to local windows. The framework is presented as a versatile architecture capable of adapting to diverse dynamic environments, from dense social interactions to sparse communication networks.

Limitations:
The authors explicitly acknowledge two main limitations:

Homogeneity Assumption: The model treats all edges as equivalent, ignoring specific edge types or contextual relationships (e.g., distinguishing between different types of financial transactions).
Exclusion of Node Features: The current implementation does not incorporate node-specific attributes (e.g., user demographics), potentially missing valuable predictive signals available in metadata-rich datasets.

The paper concludes that while GTIN advances the state of the art, future work should focus on incorporating heterogeneous edge types, node attributes, and distributed computing mechanisms to further enhance scalability and accuracy in sparse interaction settings.