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Temporal Generalization Estimation in Evolving Graphs

Bin Lu, Tingyan Ma, Xiaoying Gan, Xinbing Wang, Yunqiang Zhu, Chenghu Zhou, Shiyu Liang

TL;DR

This work tackles temporal generalization estimation for graphs that evolve over time, showing that representation distortion is unavoidable under graph evolution. It introduces Smart, a self-supervised baseline that adaptively refines feature extractors through structure and feature reconstruction to minimize information loss after deployment. Theoretical analysis on BA graphs and extensive experiments on four real-world evolving graphs demonstrate that Smart outperforms linear baselines and DoC, often approaching a supervised upper bound, with ablations underscoring the critical role of reconstruction. The approach provides a practical, annotation-efficient means to monitor and predict GNN generalization in rapidly changing networks, with broad implications for dynamically evolving systems such as citation networks and social graphs.

Abstract

Graph Neural Networks (GNNs) are widely deployed in vast fields, but they often struggle to maintain accurate representations as graphs evolve. We theoretically establish a lower bound, proving that under mild conditions, representation distortion inevitably occurs over time. To estimate the temporal distortion without human annotation after deployment, one naive approach is to pre-train a recurrent model (e.g., RNN) before deployment and use this model afterwards, but the estimation is far from satisfactory. In this paper, we analyze the representation distortion from an information theory perspective, and attribute it primarily to inaccurate feature extraction during evolution. Consequently, we introduce Smart, a straightforward and effective baseline enhanced by an adaptive feature extractor through self-supervised graph reconstruction. In synthetic random graphs, we further refine the former lower bound to show the inevitable distortion over time and empirically observe that Smart achieves good estimation performance. Moreover, we observe that Smart consistently shows outstanding generalization estimation on four real-world evolving graphs. The ablation studies underscore the necessity of graph reconstruction. For example, on OGB-arXiv dataset, the estimation metric MAPE deteriorates from 2.19% to 8.00% without reconstruction.

Temporal Generalization Estimation in Evolving Graphs

TL;DR

This work tackles temporal generalization estimation for graphs that evolve over time, showing that representation distortion is unavoidable under graph evolution. It introduces Smart, a self-supervised baseline that adaptively refines feature extractors through structure and feature reconstruction to minimize information loss after deployment. Theoretical analysis on BA graphs and extensive experiments on four real-world evolving graphs demonstrate that Smart outperforms linear baselines and DoC, often approaching a supervised upper bound, with ablations underscoring the critical role of reconstruction. The approach provides a practical, annotation-efficient means to monitor and predict GNN generalization in rapidly changing networks, with broad implications for dynamically evolving systems such as citation networks and social graphs.

Abstract

Graph Neural Networks (GNNs) are widely deployed in vast fields, but they often struggle to maintain accurate representations as graphs evolve. We theoretically establish a lower bound, proving that under mild conditions, representation distortion inevitably occurs over time. To estimate the temporal distortion without human annotation after deployment, one naive approach is to pre-train a recurrent model (e.g., RNN) before deployment and use this model afterwards, but the estimation is far from satisfactory. In this paper, we analyze the representation distortion from an information theory perspective, and attribute it primarily to inaccurate feature extraction during evolution. Consequently, we introduce Smart, a straightforward and effective baseline enhanced by an adaptive feature extractor through self-supervised graph reconstruction. In synthetic random graphs, we further refine the former lower bound to show the inevitable distortion over time and empirically observe that Smart achieves good estimation performance. Moreover, we observe that Smart consistently shows outstanding generalization estimation on four real-world evolving graphs. The ablation studies underscore the necessity of graph reconstruction. For example, on OGB-arXiv dataset, the estimation metric MAPE deteriorates from 2.19% to 8.00% without reconstruction.
Paper Structure (45 sections, 2 theorems, 36 equations, 14 figures, 10 tables, 1 algorithm)

This paper contains 45 sections, 2 theorems, 36 equations, 14 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Notations
  4. Problem Formulation
  5. Unavoidable Representation Distortion as Graph Evolves
  6. Methodology
  7. A Naive Way of Estimating Generalization Loss
  8. Information Loss by Representation Distortions
  9. Smart: Self-supervised teMporAl geneRalization esTimation
  10. A Closer Look at Barabási–Albert Random Graph
  11. Experiments on Real-World Evolving Graphs
  12. Experiment Settings
  13. Datasets.
  14. Evaluation Metrics.
  15. Experiment Configurations.
  16. ...and 30 more sections

Key Result

Theorem 1

If $\theta$ is the vectorization of the parameter set $\{(a_j,W_j,b_j)\}_{j=1}^{N}$ and its $i$-th coordinate $\theta_i$ is drawn from the uniform distribution $U(\theta_i^*,\xi)$ centering at the $i$-th coordinate of the vector $\theta_i^*$, the expected deviation $\ell_\tau(i)$ of the perturbed GC where the set $\mathcal{N}_0(i)$ denotes the neighborhood set of the node $i$ at time $0$, $\beta$

Figures (14)

  • Figure 1: GNN performance continues to decline with the rapid growth over 30 years.
  • Figure 2: Illustration for generalization estimation.
  • Figure 3: Test loss changes over time of 30 pre-trained GNN checkpoints on OGB-arXiv dataset.
  • Figure 4: Overview of our proposed Smart for generalization estimation in evolving graph.
  • Figure 5: Experimental results of Smart and its variation on BA random graph.
  • ...and 9 more figures

Theorems & Definitions (4)

  • Theorem 1
  • Theorem 2
  • proof
  • proof