Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

SGOOD: Substructure-enhanced Graph-Level Out-of-Distribution Detection

Zhihao Ding, Jieming Shi, Shiqi Shen, Xuequn Shang, Jiannong Cao, Zhipeng Wang, Zhi Gong

TL;DR

SGOOD tackles graph-level out-of-distribution detection by harnessing task-agnostic substructures. It builds a per-graph super graph of substructures and applies a two-level GIN-based encoding to fuse substructure information into graph representations, complemented by substructure-preserving augmentations and a two-stage training objective that blends contrastive and supervised learning. The method is theoretically more expressive than 1&2-WL and empirically outperforms 11 baselines across 8 real-world datasets on OOD metrics, while maintaining strong ID performance. This approach offers a principled, scalable way to detect OOD graphs by preserving meaningful substructure semantics, with practical implications for safety-critical domains.

Abstract

Graph-level representation learning is important in a wide range of applications. Existing graph-level models are generally built on i.i.d. assumption for both training and testing graphs. However, in an open world, models can encounter out-of-distribution (OOD) testing graphs that are from different distributions unknown during training. A trustworthy model should be able to detect OOD graphs to avoid unreliable predictions, while producing accurate in-distribution (ID) predictions. To achieve this, we present SGOOD, a novel graph-level OOD detection framework. We find that substructure differences commonly exist between ID and OOD graphs, and design SGOOD with a series of techniques to encode task-agnostic substructures for effective OOD detection. Specifically, we build a super graph of substructures for every graph, and develop a two-level graph encoding pipeline that works on both original graphs and super graphs to obtain substructure-enhanced graph representations. We then devise substructure-preserving graph augmentation techniques to further capture more substructure semantics of ID graphs. Extensive experiments against 11 competitors on numerous graph datasets demonstrate the superiority of SGOOD, often surpassing existing methods by a significant margin. The code is available at https://github.com/TommyDzh/SGOOD.

SGOOD: Substructure-enhanced Graph-Level Out-of-Distribution Detection

TL;DR

SGOOD tackles graph-level out-of-distribution detection by harnessing task-agnostic substructures. It builds a per-graph super graph of substructures and applies a two-level GIN-based encoding to fuse substructure information into graph representations, complemented by substructure-preserving augmentations and a two-stage training objective that blends contrastive and supervised learning. The method is theoretically more expressive than 1&2-WL and empirically outperforms 11 baselines across 8 real-world datasets on OOD metrics, while maintaining strong ID performance. This approach offers a principled, scalable way to detect OOD graphs by preserving meaningful substructure semantics, with practical implications for safety-critical domains.

Abstract

Graph-level representation learning is important in a wide range of applications. Existing graph-level models are generally built on i.i.d. assumption for both training and testing graphs. However, in an open world, models can encounter out-of-distribution (OOD) testing graphs that are from different distributions unknown during training. A trustworthy model should be able to detect OOD graphs to avoid unreliable predictions, while producing accurate in-distribution (ID) predictions. To achieve this, we present SGOOD, a novel graph-level OOD detection framework. We find that substructure differences commonly exist between ID and OOD graphs, and design SGOOD with a series of techniques to encode task-agnostic substructures for effective OOD detection. Specifically, we build a super graph of substructures for every graph, and develop a two-level graph encoding pipeline that works on both original graphs and super graphs to obtain substructure-enhanced graph representations. We then devise substructure-preserving graph augmentation techniques to further capture more substructure semantics of ID graphs. Extensive experiments against 11 competitors on numerous graph datasets demonstrate the superiority of SGOOD, often surpassing existing methods by a significant margin. The code is available at https://github.com/TommyDzh/SGOOD.
Paper Structure (19 sections, 3 theorems, 8 equations, 7 figures, 11 tables)

This paper contains 19 sections, 3 theorems, 8 equations, 7 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. The SGOOD Method
  4. Substructure-Enhanced Graph Encoding
  5. Substructure-Preserving Augmentations
  6. Model Training and OOD Scoring
  7. Two-stage model training
  8. Graph-level OOD scoring
  9. Theoretical Analysis
  10. Experiments
  11. Experimental Setup
  12. Datasets.
  13. Baselines.
  14. Evaluation and Implementation.
  15. Overall Performance
  16. ...and 4 more sections

Key Result

Proposition 3.2

When the GNNs adopted in SGOOD are with sufficient number of layers, and the $f_{\text{POOL}}$ function in Eq.eq:node_pool and $f_{\text{OUT}}$ function in Eq.eq:sub_pool are injective, then SGOOD is strictly more expressive than 1&2-WL.

Figures (7)

  • Figure 1: Substructure-enhanced graph-level OOD detection
  • Figure 2: The SGOOD framework.
  • Figure 3: ID and OOD score distributions, with the dotted line indicating the mean of ID/OOD scores.
  • Figure 4: OOD detection performance of SGOOD by AUROC (%) when the number of pretraining epochs $T_{PT}$ varies from 0 to 200, with colored area representing standard deviation.
  • Figure 5: OOD detection results of SGOOD by AUROC (%) when the weight of the contrastive loss $\alpha$ varies from 0 to 1, with the colored area representing standard deviation.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Definition 3.1: A Super Graph of Substructures
  • Proposition 3.2
  • Lemma 3.3
  • Definition 3.4: 2-regular graph
  • Lemma 3.5