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UniDyG: A Unified and Effective Representation Learning Approach for Large Dynamic Graphs

Yuanyuan Xu, Wenjie Zhang, Xuemin Lin, Ying Zhang

TL;DR

UniDyG tackles the challenge of learning unified representations for both continuous-time and discrete-time dynamic graphs by shifting to the frequency domain and introducing Fourier Graph Attention (FGAT). FGAT captures local neighbor interactions and global structural evolution via complex-valued projections and frequency-domain aggregation, while FGAT_N adds an energy-gated filter to suppress temporal noise. The paper proves Lipschitz continuity and universal approximation properties for FGAT, and presents a unified training pipeline with neighbor sampling and edge-based mini-batching to avoid information leakage. Empirically, UniDyG achieves significant performance gains (average improvements around 14–24% over baselines) and demonstrates strong robustness to noise and scalability on nine dynamic-graph benchmarks. Overall, UniDyG offers a principled, scalable, and robust framework for joint CTDG/DTDG learning with practical impact on complex time-evolving networks.

Abstract

Dynamic graphs are formulated in continuous-time or discrete-time dynamic graphs. They differ in temporal granularity: Continuous-Time Dynamic Graphs (CTDGs) exhibit rapid, localized changes, while Discrete-Time Dynamic Graphs (DTDGs) show gradual, global updates. This difference leads to isolated developments in representation learning for each type. To advance representation learning, recent research attempts to design a unified model capable of handling both CTDGs and DTDGs. However, it typically focuses on local dynamic propagation for temporal structure learning in the time domain, failing to accurately capture the structural evolution associated with each temporal granularity. In addition, existing works-whether specific or unified-often overlook the issue of temporal noise, compromising the model robustness and effectiveness. To better model both types of dynamic graphs, we propose UniDyG, a unified and effective representation learning approach, which scales to large dynamic graphs. We first propose a novel Fourier Graph Attention (FGAT) mechanism that can model local and global structural correlations based on recent neighbors and complex-number selective aggregation, while theoretically ensuring consistent representations of dynamic graphs over time. Based on approximation theory, we demonstrate that FGAT is well-suited to capture the underlying structures in CTDGs and DTDGs. We further enhance FGAT to resist temporal noise by designing an energy-gated unit, which adaptively filters out high-frequency noise according to the energy. Last, we leverage our FGAT mechanisms for temporal structure learning and employ the frequency-enhanced linear function for node-level dynamic updates, facilitating the generation of high-quality temporal embeddings. Extensive experiments show that our UniDyG achieves an average improvement of 14.4% over sixteen baselines across nine dynamic graphs.

UniDyG: A Unified and Effective Representation Learning Approach for Large Dynamic Graphs

TL;DR

UniDyG tackles the challenge of learning unified representations for both continuous-time and discrete-time dynamic graphs by shifting to the frequency domain and introducing Fourier Graph Attention (FGAT). FGAT captures local neighbor interactions and global structural evolution via complex-valued projections and frequency-domain aggregation, while FGAT_N adds an energy-gated filter to suppress temporal noise. The paper proves Lipschitz continuity and universal approximation properties for FGAT, and presents a unified training pipeline with neighbor sampling and edge-based mini-batching to avoid information leakage. Empirically, UniDyG achieves significant performance gains (average improvements around 14–24% over baselines) and demonstrates strong robustness to noise and scalability on nine dynamic-graph benchmarks. Overall, UniDyG offers a principled, scalable, and robust framework for joint CTDG/DTDG learning with practical impact on complex time-evolving networks.

Abstract

Dynamic graphs are formulated in continuous-time or discrete-time dynamic graphs. They differ in temporal granularity: Continuous-Time Dynamic Graphs (CTDGs) exhibit rapid, localized changes, while Discrete-Time Dynamic Graphs (DTDGs) show gradual, global updates. This difference leads to isolated developments in representation learning for each type. To advance representation learning, recent research attempts to design a unified model capable of handling both CTDGs and DTDGs. However, it typically focuses on local dynamic propagation for temporal structure learning in the time domain, failing to accurately capture the structural evolution associated with each temporal granularity. In addition, existing works-whether specific or unified-often overlook the issue of temporal noise, compromising the model robustness and effectiveness. To better model both types of dynamic graphs, we propose UniDyG, a unified and effective representation learning approach, which scales to large dynamic graphs. We first propose a novel Fourier Graph Attention (FGAT) mechanism that can model local and global structural correlations based on recent neighbors and complex-number selective aggregation, while theoretically ensuring consistent representations of dynamic graphs over time. Based on approximation theory, we demonstrate that FGAT is well-suited to capture the underlying structures in CTDGs and DTDGs. We further enhance FGAT to resist temporal noise by designing an energy-gated unit, which adaptively filters out high-frequency noise according to the energy. Last, we leverage our FGAT mechanisms for temporal structure learning and employ the frequency-enhanced linear function for node-level dynamic updates, facilitating the generation of high-quality temporal embeddings. Extensive experiments show that our UniDyG achieves an average improvement of 14.4% over sixteen baselines across nine dynamic graphs.

Paper Structure

This paper contains 33 sections, 2 theorems, 20 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Works
  3. Representation Learning on Dynamic Graphs
  4. Frequency-enhanced Representation Learning
  5. Preliminary and Background
  6. Dynamic Graphs
  7. Unified Format for CTDGs and DTDGs
  8. Unified Problem Definition
  9. Discrete Fourier Transform
  10. The Proposed Fourier Graph Attention
  11. Motivation
  12. Formulation of Fourier Graph Attention
  13. Theoretical Analysis for Our FGAT
  14. Further Optimization
  15. The Proposed UniDyG
  16. ...and 18 more sections

Key Result

Theorem 1

The Fourier Graph Attention (FGAT) mechanism is Lipschitz continuous with respect to time translations in the input signals. That is, there exists a constant $L > 0$ such that for any two timestamps $t$ and $t'$, the output representations satisfy: where $\left\|\cdot\right\|$ is the norm and $|\cdot|$ denotes the absolute value.

Figures (5)

  • Figure 1: Visualization of selected edge attributes and timestamps in two domains on Wikipedia and BitcoinAlpha datasets.
  • Figure 2: The overview of the proposed UniDyG. Given input from CTDG or DTDG in (a), it converts the input into a unified format, together with data splits. (b) presents a temporal dynamic model, while (c) shows structure learning using our Fourier graph attention mechanisms. In (d), our adaptive FGAT is illustrated, and (e) highlights downstream tasks.
  • Figure 3: Performance Comparison between our UniDyG and baselines on two CTDGs and two DTDGs. The horizontal axis shows the overall training time. The vertical axis shows AUC results.
  • Figure 4: Robustness evaluation with different level noise in terms of AUC over CTDGs and DTDGs.
  • Figure 5: The heatmap values in AUC (%) of UniDyG across different parameter settings.

Theorems & Definitions (6)

  • Definition 1: Continuous-Time Dynamic Graph (CTDG)
  • Definition 2: Discrete-Time Dynamic Graph (DTDG)
  • Theorem 1: Temporal Coherence
  • Proof 1
  • Theorem 2: Universal Approximation
  • Proof 2