Lipschitz neural networks are dense in the set of all Lipschitz functions
Not on the map. Why?
Abstract (arXiv)
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.
Key facts. Cited by 6 papers in the map (data through 14 Oct 2026). First posted on arXiv 29 Sep 2020.
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Citing papers per year: 2022: 3; 2023: 1; 2024: 1; 2025: 0; 2026: 1.
6 papers.
- 2022Recurrent Neural Networks and Universal Approximation of Bayesian Filterscited by 5
- 2026Approximation Theory for Lipschitz Continuous Transformerscited by 5
- 2022Detecting data-driven robust statistical arbitrage strategies with deep neural networkscited by 4
- 2024A Wasserstein perspective of Vanilla GANscited by 3
- 2022Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networkscited by 1
- 20231-Lipschitz Neural Networks are more expressive with N-Activationscited by 1
- 2026Approximation Theory for Lipschitz Continuous Transformers17 Feb 2026
- 2024A Wasserstein perspective of Vanilla GANs22 Mar 2024
- 20231-Lipschitz Neural Networks are more expressive with N-Activations10 Nov 2023
- 2022Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks15 Nov 2022
- 2022Recurrent Neural Networks and Universal Approximation of Bayesian Filters1 Nov 2022
- 2022Detecting data-driven robust statistical arbitrage strategies with deep neural networks7 Mar 2022