mlsanityData to 7 Oct 2026

On Lipschitz Bounds of General Convolutional Neural Networks

arXiv 1808.01415 ↗First posted 4 Aug 2018cs.IT cs.CV math.ITcited by 29

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Abstract (arXiv)

Many convolutional neural networks (CNNs) have a feed-forward structure. In this paper, a linear program that estimates the Lipschitz bound of such CNNs is proposed. Several CNNs, including the scattering networks, the AlexNet and the GoogleNet, are studied numerically and compared to the theoretical bounds. Next, concentration inequalities of the output distribution to a stationary random input signal expressed in terms of the Lipschitz bound are established. The Lipschitz bound is further used to establish a nonlinear discriminant analysis designed to measure the separation between features of different classes.

Key facts. Cited by 29 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Aug 2018.

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Citing papers per year: 2021: 11; 2022: 5; 2023: 7; 2024: 3; 2025: 0; 2026: 3.

29 papers.

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  1. 2021Globally-Robust Neural Networkscited by 106
  2. 2023When Deep Learning Meets Polyhedral Theory: A Surveycited by 39
  3. 2021Learning Frequency Domain Approximation for Binary Neural Networkscited by 38
  4. 2021CLIP: Cheap Lipschitz Training of Neural Networkscited by 29
  5. 2022Group-invariant max filteringcited by 18
  6. 2021Convergence of Deep ReLU Networkscited by 14
  7. 2021Analytical bounds on the local Lipschitz constants of ReLU networkscited by 12
  8. 2021Connections between Numerical Algorithms for PDEs and Neural Networkscited by 10
  9. 2024Fair Bilevel Neural Network (FairBiNN): On Balancing fairness and accuracy via Stackelberg Equilibriumcited by 9
  10. 2023Importance of Smoothness Induced by Optimizers in FL4ASR: Towards Understanding Federated Learning for End-to-End ASRcited by 8
  11. 2021Convergence Guarantees for Deep Epsilon Greedy Policy Learningcited by 6
  12. 2021What training reveals about neural network complexitycited by 5
17 more
  1. 2023Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widthscited by 5
  2. 2023Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equationcited by 5
  3. 2022Stability of the scattering transform for deformations with minimal regularitycited by 3
  4. 2022On the sensitivity of pose estimation neural networks: rotation parameterizations, Lipschitz constants, and provable boundscited by 2
  5. 2022On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networkscited by 2
  6. 2023Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction using the Local Lipschitzcited by 2
  7. 2024Analyzing Neural Network Robustness Using Graph Curvaturecited by 2
  8. 2021Generalized moduli of continuity under irregular or random deformations via multiscale analysiscited by 1
  9. 2021GraN-GAN: Piecewise Gradient Normalization for Generative Adversarial Networkscited by 1
  10. 2023Transferability of Convolutional Neural Networks in Stationary Learning Taskscited by 1
  11. 2024Lipschitz-Driven Noise Robustness in VQ-AE for High-Frequency Texture Repair in ID-Specific Talking Headscited by 1
  12. 2026Tight Long-Term Tail Decay of (Clipped) SGD in Non-Convex Optimizationcited by 1
  13. 2021On the Robustness and Generalization of Deep Learning Driven Full Waveform Inversioncited by 0
  14. 2022Optimal Transport for Super Resolution Applied to Astronomy Imagingcited by 0
  15. 2023Promoting Fairness in GNNs: A Characterization of Stabilitycited by 0
  16. 2026Optimizing Server Placement for Vertical Federated Learning in Dynamic Edge/Fog Networkscited by 0
  17. 2026General Quantification of Covariate and Concept Shiftscited by 0