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Efficient and Effective Implicit Dynamic Graph Neural Network

Yongjian Zhong, Hieu Vu, Tianbao Yang, Bijaya Adhikari

TL;DR

This work introduces IDGNN, the first implicit graph neural network designed for dynamic graphs, with a theoretical guarantee of a fixed-point representation. To overcome the computational bottlenecks of implicit differentiation, the authors reformulate training as a bilevel optimization and develop a single-loop algorithm that uses moving-average estimates to approximate hypergradients, achieving up to 1600x speedups. Empirical results across multiple regression and classification tasks show IDGNN outperforming state-of-the-art baselines while effectively mitigating oversmoothing and capturing long-range temporal dependencies. The approach offers practical benefits for dynamic graph learning, balancing predictive performance with scalability and efficiency.

Abstract

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting. In this paper, we present Implicit Dynamic Graph Neural Network (IDGNN) a novel implicit neural network for dynamic graphs which is the first of its kind. A key characteristic of IDGNN is that it demonstrably is well-posed, i.e., it is theoretically guaranteed to have a fixed-point representation. We then demonstrate that the standard iterative algorithm often used to train implicit models is computationally expensive in our dynamic setting as it involves computing gradients, which themselves have to be estimated in an iterative manner. To overcome this, we pose an equivalent bilevel optimization problem and propose an efficient single-loop training algorithm that avoids iterative computation by maintaining moving averages of key components of the gradients. We conduct extensive experiments on real-world datasets on both classification and regression tasks to demonstrate the superiority of our approach over the state-of-the-art baselines. We also demonstrate that our bi-level optimization framework maintains the performance of the expensive iterative algorithm while obtaining up to \textbf{1600x} speed-up.

Efficient and Effective Implicit Dynamic Graph Neural Network

TL;DR

This work introduces IDGNN, the first implicit graph neural network designed for dynamic graphs, with a theoretical guarantee of a fixed-point representation. To overcome the computational bottlenecks of implicit differentiation, the authors reformulate training as a bilevel optimization and develop a single-loop algorithm that uses moving-average estimates to approximate hypergradients, achieving up to 1600x speedups. Empirical results across multiple regression and classification tasks show IDGNN outperforming state-of-the-art baselines while effectively mitigating oversmoothing and capturing long-range temporal dependencies. The approach offers practical benefits for dynamic graph learning, balancing predictive performance with scalability and efficiency.

Abstract

Implicit graph neural networks have gained popularity in recent years as they capture long-range dependencies while improving predictive performance in static graphs. Despite the tussle between performance degradation due to the oversmoothing of learned embeddings and long-range dependency being more pronounced in dynamic graphs, as features are aggregated both across neighborhood and time, no prior work has proposed an implicit graph neural model in a dynamic setting. In this paper, we present Implicit Dynamic Graph Neural Network (IDGNN) a novel implicit neural network for dynamic graphs which is the first of its kind. A key characteristic of IDGNN is that it demonstrably is well-posed, i.e., it is theoretically guaranteed to have a fixed-point representation. We then demonstrate that the standard iterative algorithm often used to train implicit models is computationally expensive in our dynamic setting as it involves computing gradients, which themselves have to be estimated in an iterative manner. To overcome this, we pose an equivalent bilevel optimization problem and propose an efficient single-loop training algorithm that avoids iterative computation by maintaining moving averages of key components of the gradients. We conduct extensive experiments on real-world datasets on both classification and regression tasks to demonstrate the superiority of our approach over the state-of-the-art baselines. We also demonstrate that our bi-level optimization framework maintains the performance of the expensive iterative algorithm while obtaining up to \textbf{1600x} speed-up.
Paper Structure (24 sections, 5 theorems, 16 equations, 4 figures, 8 tables, 1 algorithm)

This paper contains 24 sections, 5 theorems, 16 equations, 4 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. Preliminaries
  5. Implicit Model for Dynamic Graphs
  6. Training
  7. SGD with Implicit Differentiation
  8. Efficient Update via Bilevel Optimization
  9. Experiments
  10. Datasets
  11. Regression
  12. Classification
  13. Long-range Dependency and Oversmoothing
  14. Efficiency
  15. Complexity
  16. ...and 9 more sections

Key Result

theorem 1

For any element-wise non-expansive function $\sigma(\cdot)$, the coupled equilibrium equations in (sys) have a unique fixed point solution if $\|\mathcal{M}\|_{op}< 1$, where $\mathcal{M}$ define as and $\|\mathcal{M}\|_{op}$ is the operator norm of $\mathcal{M}$, which is the largest absolute eigenvalue. Furthermore, this is equivalent to $\|M^t\|_{op}< 1$ for any $t=1,...,T$.

Figures (4)

  • Figure 1: Model overview. This figure indicates the forward process of our model.
  • Figure 2: The left and middle are accuracy and loss curves when using 10 layers. The x-axis is epochs, and the y-axis is accuracy and cross entropy loss, respectively. The right plot represents the accuracy results of all baselines under different layer settings.
  • Figure 3: The embedding visualization of our method and TGCN
  • Figure 4: Additional result.

Theorems & Definitions (6)

  • theorem 1
  • theorem 2
  • Remark 1
  • lemma 1
  • lemma 2
  • theorem 2