# Lipschitz Properties for Deep Convolutional Networks

arXiv: https://arxiv.org/abs/1701.05217 · HTML: https://mlsanity.com/paper/1701.05217/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Jan 2017.

## Built on by (most cited first, 9 of 9)

- [Neural Network Robustness as a Verification Property: A Principled Case Study](https://mlsanity.com/paper/2104.01396/) (2021)
- [Stability of the scattering transform for deformations with minimal regularity](https://mlsanity.com/paper/2205.11142/) (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)
- [Generalized moduli of continuity under irregular or random deformations via multiscale analysis](https://mlsanity.com/paper/2104.11977/) (2021)
- [Lipschitz-Driven Noise Robustness in VQ-AE for High-Frequency Texture Repair in ID-Specific Talking Heads](https://mlsanity.com/paper/2410.00990/) (2024)
- [On the Robustness and Generalization of Deep Learning Driven Full Waveform Inversion](https://mlsanity.com/paper/2111.14220/) (2021)
- [The CAISAR Platform: Extending the Reach of Machine Learning Specification and Verification](https://mlsanity.com/paper/2506.12084/) (2025)
- [A Cycle-Consistency Constrained Framework for Dynamic Solution Space Reduction in Noninjective Regression](https://mlsanity.com/paper/2507.04659/) (2025)

## Abstract (arXiv)

In this paper we discuss the stability properties of convolutional neural networks. Convolutional neural networks are widely used in machine learning. In classification they are mainly used as feature extractors. Ideally, we expect similar features when the inputs are from the same class. That is, we hope to see a small change in the feature vector with respect to a deformation on the input signal. This can be established mathematically, and the key step is to derive the Lipschitz properties. Further, we establish that the stability results can be extended for more general networks. We give a formula for computing the Lipschitz bound, and compare it with other methods to show it is closer to the optimal value.