mlsanityData to 7 Oct 2026

Lipschitz constant estimation of Neural Networks via sparse polynomial optimization

arXiv 2004.08688 ↗First posted 18 Apr 2020cs.LG stat.MLcited by 87

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Abstract (arXiv)

We introduce LiPopt, a polynomial optimization framework for computing increasingly tighter upper bounds on the Lipschitz constant of neural networks. The underlying optimization problems boil down to either linear (LP) or semidefinite (SDP) programming. We show how to use the sparse connectivity of a network, to significantly reduce the complexity of computation. This is specially useful for convolutional as well as pruned neural networks. We conduct experiments on networks with random weights as well as networks trained on MNIST, showing that in the particular case of the ℓ_∞-Lipschitz constant, our approach yields superior estimates, compared to baselines available in the literature.

Key facts. Cited by 87 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Apr 2020.

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Citing papers per year: 2021: 13; 2022: 16; 2023: 19; 2024: 19; 2025: 14; 2026: 6.

87 papers.

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  1. 2021Orthogonalizing Convolutional Layers with the Cayley Transformcited by 105
  2. 2023How Does Information Bottleneck Help Deep Learning?cited by 92
  3. 2025Whoever Started the Interference Should End It: Guiding Data-Free Model Merging via Task Vectorscited by 59
  4. 2022Rethinking Lipschitz Neural Networks and Certified Robustness: A Boolean Function Perspectivecited by 48
  5. 2024CViT: Continuous Vision Transformer for Operator Learningcited by 47
  6. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  7. 2023How Smooth Is Attention?cited by 44
  8. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  9. 2024Stable Neural Stochastic Differential Equations in Analyzing Irregular Time Series Datacited by 35
  10. 2024Visual Adversarial Attack on Vision-Language Models for Autonomous Drivingcited by 35
  11. 2023LipsFormer: Introducing Lipschitz Continuity to Vision Transformerscited by 33
  12. 2022LOT: Layer-wise Orthogonal Training on Improving ℓ2 Certified Robustnesscited by 32
38 more
  1. 2021Pay attention to your loss: understanding misconceptions about 1-Lipschitz neural networkscited by 30
  2. 2023Some Fundamental Aspects about Lipschitz Continuity of Neural Networkscited by 25
  3. 2021Learning by Transference: Training Graph Neural Networks on Growing Graphscited by 22
  4. 2021Towards Understanding the Data Dependency of Mixup-style Trainingcited by 19
  5. 2023Efficient Bound of Lipschitz Constant for Convolutional Layers by Gram Iterationcited by 19
  6. 2023Certified Robustness via Dynamic Margin Maximization and Improved Lipschitz Regularizationcited by 19
  7. 2023Fighting Uncertainty with Gradients: Offline Reinforcement Learning via Diffusion Score Matchingcited by 17
  8. 2021LipBaB: Computing exact Lipschitz constant of ReLU networkscited by 16
  9. 2022A Quantitative Geometric Approach to Neural-Network Smoothnesscited by 16
  10. 2023Statistical Guarantees for Variational Autoencoders using PAC-Bayesian Theorycited by 16
  11. 2022Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networkscited by 15
  12. 2022Approximation of Lipschitz Functions using Deep Spline Neural Networkscited by 15
  13. 2022Adaptive Stochastic Variance Reduction for Non-convex Finite-Sum Minimizationcited by 15
  14. 2021Controlling Wasserstein Distances by Kernel Norms with Application to Compressive Statistical Learningcited by 13
  15. 2022Lipschitz constant estimation for 1D convolutional neural networkscited by 13
  16. 2021Analytical bounds on the local Lipschitz constants of ReLU networkscited by 12
  17. 2022Adversarial robustness of sparse local Lipschitz predictorscited by 11
  18. 2022Width is Less Important than Depth in ReLU Neural Networkscited by 10
  19. 2024ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networkscited by 10
  20. 2023Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramiancited by 9
  21. 2024Intriguing Equivalence Structures of the Embedding Space of Vision Transformerscited by 8
  22. 2024Lipschitz constant estimation for general neural network architectures using control toolscited by 8
  23. 2021Provable Lipschitz Certification for Generative Modelscited by 7
  24. 2021Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativitycited by 7
  25. 2022Memory-efficient model-based deep learning with convergence and robustness guaranteescited by 7
  26. 2021Zeroth and First Order Stochastic Frank-Wolfe Algorithms for Constrained Optimizationcited by 6
  27. 2023CertViT: Certified Robustness of Pre-Trained Vision Transformerscited by 6
  28. 2024Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activationscited by 6
  29. 2021What training reveals about neural network complexitycited by 5
  30. 2022Controlling the Complexity and Lipschitz Constant improves polynomial netscited by 5
  31. 2023Cycle Consistency-based Uncertainty Quantification of Neural Networks in Inverse Imaging Problemscited by 4
  32. 2023A Neurosymbolic Approach to the Verification of Temporal Logic Properties of Learning enabled Control Systemscited by 3
  33. 2024Policy Verification in Stochastic Dynamical Systems Using Logarithmic Neural Certificatescited by 3
  34. 2024Disentangling Latent Shifts of In-Context Learning with Weak Supervisioncited by 3
  35. 2022On the sensitivity of pose estimation neural networks: rotation parameterizations, Lipschitz constants, and provable boundscited by 2
  36. 2024A Survey of Neural Network Robustness Assessment in Image Recognitioncited by 2
  37. 2024Provable Bounds on the Hessian of Neural Networks: Derivative-Preserving Reachability Analysiscited by 2
  38. 2024Computable Lipschitz Bounds for Deep Neural Networkscited by 2

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