Towards Context-Aware Domain Generalization: Representing Environments with Permutation-Invariant Networks

In this work, we show that information about the context of an input $X$ can improve the predictions of deep learning models when applied in new domains or production environments. We formalize the notion of context as a permutation-invariant representation of a set of data points that originate from the same environment/domain as the input itself. These representations are jointly learned with a standard supervised learning objective, providing incremental information about the unknown outcome. Furthermore, we offer a theoretical analysis of the conditions under which our approach can, in principle, yield benefits, and formulate two necessary criteria that can be easily verified in practice. Additionally, we contribute insights into the kind of distribution shifts for which our approach promises robustness. Our empirical evaluation demonstrates the effectiveness of our approach for both low-dimensional and high-dimensional data sets. Finally, we demonstrate that we can reliably detect scenarios where a model is tasked with unwarranted extrapolation in out-of-distribution (OOD) domains, identifying potential failure cases. Consequently, we showcase a method to select between the most predictive and the most robust model, circumventing the well-known trade-off between predictive performance and robustness.