Raising the Bar in Graph OOD Generalization: Invariant Learning Beyond Explicit Environment Modeling

TL;DR

This paper introduces MPHIL, a novel graph invariant learning method that enhances out-of-distribution generalization by using hyperspherical representations and class prototypes, avoiding explicit environment modeling.

Contribution

The paper proposes MPHIL, a new approach with hyperspherical invariant features and multi-prototype classification, addressing environment modeling and semantic cliff issues in graph OOD generalization.

Findings

Achieves state-of-the-art results on 11 OOD benchmarks.

Outperforms existing methods across diverse graph domains.

Effectively mitigates semantic cliff and environment modeling challenges.

Abstract

Out-of-distribution (OOD) generalization has emerged as a critical challenge in graph learning, as real-world graph data often exhibit diverse and shifting environments that traditional models fail to generalize across. A promising solution to address this issue is graph invariant learning (GIL), which aims to learn invariant representations by disentangling label-correlated invariant subgraphs from environment-specific subgraphs. However, existing GIL methods face two major challenges: (1) the difficulty of capturing and modeling diverse environments in graph data, and (2) the semantic cliff, where invariant subgraphs from different classes are difficult to distinguish, leading to poor class separability and increased misclassifications. To tackle these challenges, we propose a novel method termed Multi-Prototype Hyperspherical Invariant Learning (MPHIL), which introduces two key innovations: (1) hyperspherical invariant representation extraction, enabling robust and highly discriminative hyperspherical invariant feature extraction, and (2) multi-prototype hyperspherical classification, which employs class prototypes as intermediate variables to eliminate the need for explicit environment modeling in GIL and mitigate the semantic cliff issue. Derived from the theoretical framework of GIL, we introduce two novel objective functions: the invariant prototype matching loss to ensure samples are matched to the correct class prototypes, and the prototype separation loss to increase the distinction between prototypes of different classes in the hyperspherical space. Extensive experiments on 11 OOD generalization benchmark datasets demonstrate that MPHIL achieves state-of-the-art performance, significantly outperforming existing methods across graph data from various domains and with different distribution shifts.