# 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.

05/12/2021

### LipBaB: Computing exact Lipschitz constant of ReLU networks

The Lipschitz constant of neural networks plays an important role in sev...
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### Regularisation of Neural Networks by Enforcing Lipschitz Continuity

We investigate the effect of explicitly enforcing the Lipschitz continui...
06/09/2020

### Approximating Lipschitz continuous functions with GroupSort neural networks

Recent advances in adversarial attacks and Wasserstein GANs have advocat...
11/02/2021

### Lipschitz widths

This paper introduces a measure, called Lipschitz widths, of the optimal...
07/19/2021

### Ergodic dynamical systems over the Cartesian power of the ring of p-adic integers

For any 1-lipschitz ergodic map F: ℤ^k_p↦ℤ^k_p, k>1∈ℕ, there are 1-lipsc...
05/24/2021

### Coercivity, essential norms, and the Galerkin method for second-kind integral equations on polyhedral and Lipschitz domains

It is well known that, with a particular choice of norm, the classical d...
08/28/2018

### Lipschitz regularized Deep Neural Networks converge and generalize

Lipschitz regularized neural networks augment the usual fidelity term us...