# Provable Lipschitz Certification for Generative Models

arXiv: https://arxiv.org/abs/2107.02732 · HTML: https://mlsanity.com/paper/2107.02732/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 6 Jul 2021.

## Builds on (most cited first, 15 of 15)

- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Lipschitz regularity of deep neural networks: analysis and efficient estimation](https://mlsanity.com/paper/1805.10965/) (2018)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approach](https://mlsanity.com/paper/1801.10578/) (2018)
- [Exactly Computing the Local Lipschitz Constant of ReLU Networks](https://mlsanity.com/paper/2003.01219/) (2020)
- [Lipschitz constant estimation of Neural Networks via sparse polynomial optimization](https://mlsanity.com/paper/2004.08688/) (2020)
- [Verification of Deep Convolutional Neural Networks Using ImageStars](https://mlsanity.com/paper/2004.05511/) (2020)
- [Provable Certificates for Adversarial Examples: Fitting a Ball in the Union of Polytopes](https://mlsanity.com/paper/1903.08778/) (2019)
- [Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constant](https://mlsanity.com/paper/2001.06263/) (2020)

## Built on by (most cited first, 7 of 7)

- [Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagation](https://mlsanity.com/paper/2210.07394/) (2022)
- [Zonotope Domains for Lagrangian Neural Network Verification](https://mlsanity.com/paper/2210.08069/) (2022)
- [Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distribution](https://mlsanity.com/paper/2307.16422/) (2023)
- [Evaluating the diversity and utility of materials proposed by generative models](https://mlsanity.com/paper/2309.12323/) (2023)
- [A Domain-Theoretic Framework for Robustness Analysis of Neural Networks](https://mlsanity.com/paper/2203.00295/) (2022)
- [Functional trustworthiness of AI systems by statistically valid testing](https://mlsanity.com/paper/2310.02727/) (2023)
- [Geometric Decoupling: Diagnosing the Structural Instability of Latent](https://mlsanity.com/paper/2604.18804/) (2026)

## Abstract (arXiv)

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.