On Continuity of Robust and Accurate Classifiers

Summary

This research paper argues that the continuity of a classifier, rather than robustness and accuracy themselves, is what conflicts with them in many scenarios. The authors introduce a framework for studying harmonic and holomorphic hypotheses in learning theory terms and report empirical evidence that continuous hypotheses underperform discontinuous ones on some common machine learning tasks. They explain adversarial examples as a conflict between continuity and uniform convergence to a discontinuous function.

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