ID and OOD Performance Are Sometimes Inversely Correlated on Real-world Datasets

Context. Several studies have compared the in-distribution (ID) and out-ofdistribution (OOD) performance of models in computer vision and NLP. They report a frequent positive correlation and some surprisingly never even observe an inverse correlation indicative of a necessary trade-off. The possibility of inverse patterns is important to determine whether ID performance can serve as a proxy for OOD generalization capabilities. Findings. This paper shows with multiple datasets that inverse correlations between ID and OOD performance do happen in real-world data -not only in theoretical worst-case settings. We also explain theoretically how these cases can arise even in a minimal linear setting, and why past studies could miss such cases due to a biased selection of models. Implications. Our observations lead to recommendations that contradict those found in much of the current literature. • High OOD performance sometimes requires trading off ID performance. • Focusing on ID performance alone may not lead to optimal OOD performance. It may produce diminishing (eventually negative) returns in OOD performance. • In these cases, studies on OOD generalization that use ID performance for model selection (a common recommended practice) will necessarily miss the bestperforming models, making these studies blind to a whole range of phenomena.