Lipschitz neural networks are dense in the set of all Lipschitz functions

This note shows that, for a fixed Lipschitz constant $L > 0$, one layer neural networks that are $L$-Lipschitz are dense in the set of all $L$-Lipschitz functions with respect to the uniform norm on bounded sets.

stat.ML cs.LG math.NA Neural Networks and Applications Control Systems and Identification Face and Expression Recognition Mathematics Computer Science

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