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Redundancy-Aware Test-Time Graph Out-of-Distribution Detection

Yue Hou, He Zhu, Ruomei Liu, Yingke Su, Junran Wu, Ke Xu

TL;DR

This paper tackles graph out-of-distribution detection under test-time constraints by introducing RedOUT, a redundancy-aware framework that decouples essential information from redundant structure. Central to RedOUT is ReGIB, which splits the representation into an essential view realized via a coding-tree with minimized structural entropy and a redundant portion to be discarded, with tractable upper and lower bounds guiding optimization. A dual-loss objective combines a contrastive term and a conditional redundancy-eliminated term, enabling effective OOD scoring without retraining the pre-trained GNN. Empirical results across 10 OOD pairs and anomaly-detection tasks show consistent gains over state-of-the-art baselines, with notable improvements on molecular datasets, and analyses reveal the method's robustness and its reliance on an appropriate coding-tree height and loss trade-off.

Abstract

Distributional discrepancy between training and test data can lead models to make inaccurate predictions when encountering out-of-distribution (OOD) samples in real-world applications. Although existing graph OOD detection methods leverage data-centric techniques to extract effective representations, their performance remains compromised by structural redundancy that induces semantic shifts. To address this dilemma, we propose RedOUT, an unsupervised framework that integrates structural entropy into test-time OOD detection for graph classification. Concretely, we introduce the Redundancy-aware Graph Information Bottleneck (ReGIB) and decompose the objective into essential information and irrelevant redundancy. By minimizing structural entropy, the decoupled redundancy is reduced, and theoretically grounded upper and lower bounds are proposed for optimization. Extensive experiments on real-world datasets demonstrate the superior performance of RedOUT on OOD detection. Specifically, our method achieves an average improvement of 6.7%, significantly surpassing the best competitor by 17.3% on the ClinTox/LIPO dataset pair.

Redundancy-Aware Test-Time Graph Out-of-Distribution Detection

TL;DR

This paper tackles graph out-of-distribution detection under test-time constraints by introducing RedOUT, a redundancy-aware framework that decouples essential information from redundant structure. Central to RedOUT is ReGIB, which splits the representation into an essential view realized via a coding-tree with minimized structural entropy and a redundant portion to be discarded, with tractable upper and lower bounds guiding optimization. A dual-loss objective combines a contrastive term and a conditional redundancy-eliminated term, enabling effective OOD scoring without retraining the pre-trained GNN. Empirical results across 10 OOD pairs and anomaly-detection tasks show consistent gains over state-of-the-art baselines, with notable improvements on molecular datasets, and analyses reveal the method's robustness and its reliance on an appropriate coding-tree height and loss trade-off.

Abstract

Distributional discrepancy between training and test data can lead models to make inaccurate predictions when encountering out-of-distribution (OOD) samples in real-world applications. Although existing graph OOD detection methods leverage data-centric techniques to extract effective representations, their performance remains compromised by structural redundancy that induces semantic shifts. To address this dilemma, we propose RedOUT, an unsupervised framework that integrates structural entropy into test-time OOD detection for graph classification. Concretely, we introduce the Redundancy-aware Graph Information Bottleneck (ReGIB) and decompose the objective into essential information and irrelevant redundancy. By minimizing structural entropy, the decoupled redundancy is reduced, and theoretically grounded upper and lower bounds are proposed for optimization. Extensive experiments on real-world datasets demonstrate the superior performance of RedOUT on OOD detection. Specifically, our method achieves an average improvement of 6.7%, significantly surpassing the best competitor by 17.3% on the ClinTox/LIPO dataset pair.
Paper Structure (53 sections, 17 theorems, 93 equations, 27 figures, 10 tables, 2 algorithms)

This paper contains 53 sections, 17 theorems, 93 equations, 27 figures, 10 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Notations and Preliminaries
  3. Methodology
  4. The Principle of ReGIB
  5. Redundancy-eliminated Essential Information.
  6. ReGIB Principle Instantiation
  7. Coding Tree Construction (Instantiation for $G^*$).
  8. Representing Learning on Essential Information.
  9. Instantiation for $I(f(G^*); f(G))$.
  10. Instantiation for $I(f(G^*); f(G)|\tilde{Y})$.
  11. Optimization.
  12. Experiment
  13. Performance on OOD Detection
  14. Performance on Anomaly Detection
  15. Ablation Study
  16. ...and 38 more sections

Key Result

Proposition 1

[yshift=-0em]below,leftI1Eq. eq:low-GG and eq:ins-CL[yshift=-0em]below,leftI2Eq. eq:up-CRI and eq:ins-CRI

Figures (27)

  • Figure 1: (a) A schema comparison. (b) A toy example of distinctive components within test graphs. (c) Scoring distributions before/after structural entropy (abbr. SE) minimization.
  • Figure 2: Overview of the overall framework of RedOUT and proposed ReGIB. (a) the ReGIB principle and its bounds. (b) obtained by minimizing structural entropy of graph $G$, coding tree $T$ serves as an instantiation of the essential view. (c) message passing and aggregating on graph are under the guidance of the coding tree.
  • Figure 3: Comparison between the basic GIB and proposed ReGIB. Note ReGIB balances signals $\textcircled{1}, \textcircled{2}$ with optimal $f(G^*)$ to capture the essential information and discard redundancy.
  • Figure 4: Scalability of coding tree construction on Erdős-Rényi graphs with $|\mathcal{E}|=2|\mathcal{V}|$.
  • Figure 5: The natural hierarchy of graph.
  • ...and 22 more figures

Theorems & Definitions (38)

  • Proposition 1: Lower Bound of $I(f(G^*); \tilde{Y})$
  • Definition 3.1: Redundancy-aware Graph Information Bottleneck
  • Proposition 2: Lower Bound of $I(f(G^*); f(G))$
  • Proposition 3: Upper Bound of $I(f(G^*); f(G)|\tilde{Y})$
  • Definition 3.2
  • Theorem 3.3
  • Proposition 4: Upper Bound of $I(G^*;f(G^*))$
  • Theorem 3.4
  • Theorem 3.5: Bounds of Redundant and Essential Information
  • Definition C.1: Informational Divergence
  • ...and 28 more