MPHIL: Multi-Prototype Hyperspherical Invariant Learning for Graph Out-of-Distribution Generalization

Xu Shen, Yixin Liu, Yili Wang, Rui Miao, Yiwei Dai, Shirui Pan, Xin Wang

Keywords: graph out-of-distribution generalization, invariant learning, hyperspherical space

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) invariant learning in hyperspherical space, enabling robust invariant feature extraction and prototypical learning in a highly discriminative space, and (2) class prototypes as intermediate variables, which eliminate the need for explicit environment modeling in GIL and mitigate the semantic cliff issue through multi-prototype-based classification. 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. The source code of MPHIL is available at https://anonymous.4open.science/r/MPHIL-23C0/.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 2359