HYPO: Hyperspherical Out-of-Distribution Generalization

Out-of-distribution (OOD) generalization is critical for machine learning models deployed in the real world. However, achieving this can be fundamentally challenging, as it requires the ability to learn invariant features across different domains or environments. In this paper, we propose a novel framework HYPO (HYPerspherical OOD generalization) that provably learns domain-invariant representations in a hyperspherical space. In particular, our hyperspherical learning algorithm is guided by intra-class variation and inter-class separation principles--ensuring that features from the same class (across different training domains) are closely aligned with their class prototypes, while different class prototypes are maximally separated. We further provide theoretical justifications on how our prototypical learning objective improves the OOD generalization bound. Through extensive experiments on challenging OOD benchmarks, we demonstrate that our approach outperforms competitive baselines and achieves superior performance. Deploying machine learning models in real-world settings presents a critical challenge of generalizing under distributional shifts. These shifts are common due to mismatches between the training and test data distributions. For instance, in autonomous driving, a model trained on in-distribution (ID) data collected under sunny weather conditions is expected to perform well in out-of-distribution (OOD) scenarios, such as rain or snow. This underscores the importance of the OOD generalization problem, which involves learning a predictor that can generalize across all possible environments, despite being trained on a finite subset of training environments. A plethora of OOD generalization algorithms has been developed in recent years (Zhou et al., 2022), where a central theme is to learn domain-invariant representations--features that are consistent and meaningful across different environments (domains) and can generalize to the unseen test environment. Recently, Ye et al. (2021) theoretically showed that the OOD generalization error can be bounded in terms of intra-class variation and inter-class separation.