# On Lipschitz Bounds of General Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1808.01415 · HTML: https://mlsanity.com/paper/1808.01415/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Aug 2018.

## Built on by (most cited first, 29 of 29)

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- [Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths](https://mlsanity.com/paper/2306.01692/) (2023)
- [Multi-Grade Deep Learning for Partial Differential Equations with Applications to the Burgers Equation](https://mlsanity.com/paper/2309.07401/) (2023)
- [Stability of the scattering transform for deformations with minimal regularity](https://mlsanity.com/paper/2205.11142/) (2022)
- [On the sensitivity of pose estimation neural networks: rotation parameterizations, Lipschitz constants, and provable bounds](https://mlsanity.com/paper/2203.09937/) (2022)
- [On the Shift Invariance of Max Pooling Feature Maps in Convolutional Neural Networks](https://mlsanity.com/paper/2209.11740/) (2022)
- [Uncertainty Estimation and Out-of-Distribution Detection for Deep Learning-Based Image Reconstruction using the Local Lipschitz](https://mlsanity.com/paper/2305.07618/) (2023)
- [Analyzing Neural Network Robustness Using Graph Curvature](https://mlsanity.com/paper/2410.19607/) (2024)
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- [GraN-GAN: Piecewise Gradient Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/2111.03162/) (2021)
- [Transferability of Convolutional Neural Networks in Stationary Learning Tasks](https://mlsanity.com/paper/2307.11588/) (2023)
- [Lipschitz-Driven Noise Robustness in VQ-AE for High-Frequency Texture Repair in ID-Specific Talking Heads](https://mlsanity.com/paper/2410.00990/) (2024)
- [Tight Long-Term Tail Decay of (Clipped) SGD in Non-Convex Optimization](https://mlsanity.com/paper/2602.05657/) (2026)
- [On the Robustness and Generalization of Deep Learning Driven Full Waveform Inversion](https://mlsanity.com/paper/2111.14220/) (2021)
- [Optimal Transport for Super Resolution Applied to Astronomy Imaging](https://mlsanity.com/paper/2202.05354/) (2022)
- [Promoting Fairness in GNNs: A Characterization of Stability](https://mlsanity.com/paper/2309.03648/) (2023)
- [Optimizing Server Placement for Vertical Federated Learning in Dynamic Edge/Fog Networks](https://mlsanity.com/paper/2605.09813/) (2026)
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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.