Whitening Improves Robustness to Spurious Correlations in Linear Probes

Abstract

Deep neural networks tend to rely on simple features that may be spurious and thus fail to generalize. We study this problem in the setting of linear probes, where a (generalized) linear model is fitted on the representations of a (pretrained) model. We use the connection of these models to the max-margin classifier, and show they favor directions associated with large eigenvalues of the covariance matrix. Whitening removes this preference by equalizing the eigenvalues of the covariance matrix. This observation motivates whitening as a preprocessing step that can reduce reliance on spurious correlations without requiring prior knowledge of their presence or labeled data. We examine the effect of whitening on a synthetic data-generating process and standard spurious correlation benchmarks, and find that it improves robustness. We also find that whitening can improve robustness when added to existing approaches.