Provable Lipschitz Certification for Generative Models

TL;DR

This paper introduces a scalable method to upper bound the Lipschitz constant of generative models by layerwise convex approximations, enabling efficient estimation for large neural networks like VAEs and DCGANs.

Contribution

It proposes a novel layerwise convex approximation technique using zonotopes for Lipschitz estimation, improving scalability and tightness over previous methods.

Findings

Provides tight Lipschitz bounds for small networks

Scales to large generative models like VAE and DCGAN

Outperforms prior zonotope-based methods

Abstract

We present a scalable technique for upper bounding the Lipschitz constant of generative models. We relate this quantity to the maximal norm over the set of attainable vector-Jacobian products of a given generative model. We approximate this set by layerwise convex approximations using zonotopes. Our approach generalizes and improves upon prior work using zonotope transformers and we extend to Lipschitz estimation of neural networks with large output dimension. This provides efficient and tight bounds on small networks and can scale to generative models on VAE and DCGAN architectures.