mlsanityData to 7 Oct 2026

Provable Lipschitz Certification for Generative Models

arXiv 2107.02732 ↗First posted 6 Jul 2021cs.LG stat.MLcited by 7

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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.

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

Builds on

15 of 20 references.

References · 15

  1. 2013Auto-Encoding Variational Bayescited by 3,980
  2. 2015Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networkscited by 2,048
  3. 2017Provable defenses against adversarial examples via the convex outer adversarial polytopecited by 564
  4. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  5. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  6. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  7. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  8. 2020Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifierscited by 183
  9. 2017Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulationcited by 182
  10. 2018Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approachcited by 181
  11. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  12. 2020Lipschitz constant estimation of Neural Networks via sparse polynomial optimizationcited by 87
3 more
  1. 2020Verification of Deep Convolutional Neural Networks Using ImageStarscited by 75
  2. 2019Provable Certificates for Adversarial Examples: Fitting a Ball in the Union of Polytopescited by 25
  3. 2020Deep Neural Networks with Trainable Activations and Controlled Lipschitz Constantcited by 25

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 3; 2024: 0; 2025: 0; 2026: 1.

7 papers.

  1. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  2. 2022Zonotope Domains for Lagrangian Neural Network Verificationcited by 5
  3. 2023Statistically Optimal Generative Modeling with Maximum Deviation from the Empirical Distributioncited by 3
  4. 2023Evaluating the diversity and utility of materials proposed by generative modelscited by 2
  5. 2022A Domain-Theoretic Framework for Robustness Analysis of Neural Networkscited by 0
  6. 2023Functional trustworthiness of AI systems by statistically valid testingcited by 0
  7. 2026Geometric Decoupling: Diagnosing the Structural Instability of Latentcited by 0