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LipBaB: Computing exact Lipschitz constant of ReLU networks

arXiv 2105.05495 ↗First posted 12 May 2021cs.LG cs.DScited by 16

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Abstract (arXiv)

The Lipschitz constant of neural networks plays an important role in several contexts of deep learning ranging from robustness certification and regularization to stability analysis of systems with neural network controllers. Obtaining tight bounds of the Lipschitz constant is therefore important. We introduce LipBaB, a branch and bound framework to compute certified bounds of the local Lipschitz constant of deep neural networks with ReLU activation functions up to any desired precision. We achieve this by bounding the norm of the Jacobians, corresponding to different activation patterns of the network caused within the input domain. Our algorithm can provide provably exact computation of the Lipschitz constant for any p-norm.

Key facts. Cited by 16 papers in the map (data through 7 Oct 2026). Builds on 14 of its 15 references that are in the map. First posted on arXiv 12 May 2021.

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14 of 15 references.

References · 14

  1. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,618
  2. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 413
  3. 2018Invertible Residual Networkscited by 364
  4. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  5. 2019Residual Flows for Invertible Generative Modelingcited by 256
  6. 2018Towards Fast Computation of Certified Robustness for ReLU Networkscited by 254
  7. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
  8. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  9. 2018Evaluating the Robustness of Neural Networks: An Extreme Value Theory Approachcited by 181
  10. 2020The Lipschitz Constant of Self-Attentioncited by 171
  11. 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
  12. 2016Robust Large Margin Deep Neural Networkscited by 117
2 more
  1. 2020Exactly Computing the Local Lipschitz Constant of ReLU Networkscited by 102
  2. 2020Lipschitz constant estimation of Neural Networks via sparse polynomial optimizationcited by 87

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 3; 2024: 2; 2025: 4; 2026: 3.

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  1. 2022Efficiently Computing Local Lipschitz Constants of Neural Networks via Bound Propagationcited by 45
  2. 2024Gradient-Regularized Out-of-Distribution Detectioncited by 13
  3. 2021GoTube: Scalable Stochastic Verification of Continuous-Depth Modelscited by 12
  4. 2025Parameterized Hardness of Zonotope Containment and Neural Network Verificationcited by 4
  5. 2024Policy Verification in Stochastic Dynamical Systems Using Logarithmic Neural Certificatescited by 3
  6. 2025Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsificationcited by 3
  7. 2021An automatic differentiation system for the age of differential privacycited by 2
  8. 2023Adversarial Sample Detection Through Neural Network Transport Dynamicscited by 1
  9. 2025ECLipsE-Gen-Local: Efficient Compositional Local Lipschitz Estimates for Deep Neural Networkscited by 1
  10. 2026ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networkscited by 1
  11. 2022A Domain-Theoretic Framework for Robustness Analysis of Neural Networkscited by 0
  12. 2023Verifying Global Neural Network Specifications using Hyperpropertiescited by 0
4 more
  1. 2023Robustness Analysis of Continuous-Depth Models with Lagrangian Techniquescited by 0
  2. 2025Exploration Behavior of Untrained Policiescited by 0
  3. 2026Demystifying Lipschitz verification: positive matrices, negative resultscited by 0
  4. 2026LiD-GLM: Lipschitz-constrained Deep Generalized Linear Modelscited by 0