Lipschitz neural networks are dense in the set of all Lipschitz functions
arXiv:2009.13881v18 citations
Originality Synthesis-oriented
AI Analysis
This provides a theoretical foundation for using neural networks to approximate Lipschitz functions, which is incremental as it builds on existing density results in approximation theory.
The paper tackles the problem of approximating Lipschitz functions using neural networks, showing that one-layer neural networks with a fixed Lipschitz constant are dense in the set of all Lipschitz functions with that constant under the uniform norm on bounded sets.
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.