# Lipschitz constant estimation for 1D convolutional neural networks

arXiv: https://arxiv.org/abs/2211.15253 · HTML: https://mlsanity.com/paper/2211.15253/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 28 Nov 2022.

## Builds on (most cited first, 10 of 10)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [1D Convolutional Neural Networks and Applications: A Survey](https://mlsanity.com/paper/1905.03554/) (2019)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Lipschitz constant estimation of Neural Networks via sparse polynomial optimization](https://mlsanity.com/paper/2004.08688/) (2020)
- [Lipschitz Certificates for Layered Network Structures Driven by Averaged Activation Operators](https://mlsanity.com/paper/1903.01014/) (2019)
- [Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks](https://mlsanity.com/paper/2204.00846/) (2022)
- [Neural network training under semidefinite constraints](https://mlsanity.com/paper/2201.00632/) (2022)
- [Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativity](https://mlsanity.com/paper/2111.12906/) (2021)

## Built on by (most cited first, 13 of 13)

- [Direct Parameterization of Lipschitz-Bounded Deep Networks](https://mlsanity.com/paper/2301.11526/) (2023)
- [ECLipsE: Efficient Compositional Lipschitz Constant Estimation for Deep Neural Networks](https://mlsanity.com/paper/2404.04375/) (2024)
- [Lipschitz-bounded 1D convolutional neural networks using the Cayley transform and the controllability Gramian](https://mlsanity.com/paper/2303.11835/) (2023)
- [Lipschitz constant estimation for general neural network architectures using control tools](https://mlsanity.com/paper/2405.01125/) (2024)
- [Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activations](https://mlsanity.com/paper/2401.14033/) (2024)
- [Convolutional Neural Networks as 2-D systems](https://mlsanity.com/paper/2303.03042/) (2023)
- [State space representations of the Roesser type for convolutional layers](https://mlsanity.com/paper/2403.11938/) (2024)
- [A Complete Set of Quadratic Constraints for Repeated ReLU and Generalizations](https://mlsanity.com/paper/2407.06888/) (2024)
- [LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers](https://mlsanity.com/paper/2410.22258/) (2024)
- [Improved Scalable Lipschitz Bounds for Deep Neural Networks](https://mlsanity.com/paper/2503.14297/) (2025)
- [RobustNeuralNetworks.jl: a Package for Machine Learning and Data-Driven Control with Certified Robustness](https://mlsanity.com/paper/2306.12612/) (2023)
- [ECLipsE-Gen-Local: Efficient Compositional Local Lipschitz Estimates for Deep Neural Networks](https://mlsanity.com/paper/2510.05261/) (2025)
- [ExLipBaB: Exact Lipschitz Constant Computation for Piecewise Linear Neural Networks](https://mlsanity.com/paper/2602.15499/) (2026)

## Abstract (arXiv)

In this work, we propose a dissipativity-based method for Lipschitz constant estimation of 1D convolutional neural networks (CNNs). In particular, we analyze the dissipativity properties of convolutional, pooling, and fully connected layers making use of incremental quadratic constraints for nonlinear activation functions and pooling operations. The Lipschitz constant of the concatenation of these mappings is then estimated by solving a semidefinite program which we derive from dissipativity theory. To make our method as efficient as possible, we exploit the structure of convolutional layers by realizing these finite impulse response filters as causal dynamical systems in state space and carrying out the dissipativity analysis for the state space realizations. The examples we provide show that our Lipschitz bounds are advantageous in terms of accuracy and scalability.