# Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting

@article{Koehler2021UniformCO, title={Uniform Convergence of Interpolators: Gaussian Width, Norm Bounds, and Benign Overfitting}, author={Frederic Koehler and Lijia Zhou and Danica J. Sutherland and Nathan Srebro}, journal={ArXiv}, year={2021}, volume={abs/2106.09276} }

We consider interpolation learning in high-dimensional linear regression with Gaussian data, and prove a generic uniform convergence guarantee on the generalization error of interpolators in an arbitrary hypothesis class in terms of the class’s Gaussian width. Applying the generic bound to Euclidean norm balls recovers the consistency result of Bartlett et al. (2020) for minimum-norm interpolators, and confirms a prediction of Zhou et al. (2020) for near-minimal-norm interpolators in the… Expand

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