  Adversarial attacks against machine learning models are a rather hefty
obstacle to our increasing reliance on these models. Due to this, provably
robust (certified) machine learning models are a major topic of interest.
Lipschitz continuous models present a promising approach to solving this
problem. By leveraging the expressive power of a variant of neural networks
which maintain low Lipschitz constants, we prove that three layer neural
networks using the FullSort activation function are Universal Lipschitz
function Approximators (ULAs). This both explains experimental results and
paves the way for the creation of better certified models going forward. We
conclude by presenting experimental results that suggest that ULAs are a not
just a novelty, but a competitive approach to providing certified classifiers,
using these results to motivate several potential topics of further research.
