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Numerous recent works show that overparameterization implicitly reducesvariance for min-norm interpolators and max-margin classifiers. These findingssuggest that ridge regularization has vanishing benefits in high dimensions. Wechallenge this narrative by showing that, even in the absence of noise,avoiding interpolation through ridge regularization can significantly improvegeneralization. We prove this phenomenon for the robust risk of both linearregression and classification and hence provide the first theoretical result onrobust overfitting.

Interpolation can hurt robust generalization even when there is no noise