# On Uniform Convergence and Low-Norm Interpolation Learning

@article{Zhou2020OnUC, title={On Uniform Convergence and Low-Norm Interpolation Learning}, author={Lijia Zhou and Dougal J. Sutherland and Nathan Srebro}, journal={ArXiv}, year={2020}, volume={abs/2006.05942} }

We consider an underdetermined noisy linear regression model where the minimum-norm interpolating predictor is known to be consistent, and ask: can uniform convergence in a norm ball, or at least (following Nagarajan and Kolter) the subset of a norm ball that the algorithm selects on a typical input set, explain this success? We show that uniformly bounding the difference between empirical and population errors cannot show any learning in the norm ball, and cannot show consistency for any set… CONTINUE READING

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