# Convex neural network synthesis for robustness in the 1-norm

arXiv: https://arxiv.org/abs/2405.19029 · HTML: https://mlsanity.com/paper/2405.19029/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 27 references that are in the map.
- First posted on arXiv 29 May 2024.

## Builds on (most cited first, 17 of 17)

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Training robust neural networks using Lipschitz bounds](https://mlsanity.com/paper/2005.02929/) (2020)
- [Direct Parameterization of Lipschitz-Bounded Deep Networks](https://mlsanity.com/paper/2301.11526/) (2023)
- [Recurrent Equilibrium Networks: Flexible Dynamic Models with Guaranteed Stability and Robustness](https://mlsanity.com/paper/2104.05942/) (2021)
- [Deep Equilibrium Approaches to Diffusion Models](https://mlsanity.com/paper/2210.12867/) (2022)
- [A Quantitative Geometric Approach to Neural-Network Smoothness](https://mlsanity.com/paper/2203.01212/) (2022)
- [Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2203.11812/) (2022)
- [Sparse Polynomial Optimisation for Neural Network Verification](https://mlsanity.com/paper/2202.02241/) (2022)
- [Synthesis of Stabilizing Recurrent Equilibrium Network Controllers](https://mlsanity.com/paper/2204.00122/) (2022)
- [Linear systems with neural network nonlinearities: Improved stability analysis via acausal Zames-Falb multipliers](https://mlsanity.com/paper/2103.17106/) (2021)
- [Stability of Non-linear Neural Feedback Loops using Sum of Squares](https://mlsanity.com/paper/2204.03913/) (2022)
- [Bounding the difference between model predictive control and neural networks](https://mlsanity.com/paper/2204.06486/) (2022)
- [Robust error bounds for quantised and pruned neural networks](https://mlsanity.com/paper/2012.00138/) (2020)
- [Reduced-Order Neural Network Synthesis with Robustness Guarantees](https://mlsanity.com/paper/2102.09284/) (2021)
- [Mapping back and forth between model predictive control and neural networks](https://mlsanity.com/paper/2404.12030/) (2024)

## Abstract (arXiv)

With neural networks being used to control safety-critical systems, they increasingly have to be both accurate (in the sense of matching inputs to outputs) and robust. However, these two properties are often at odds with each other and a trade-off has to be navigated. To address this issue, this paper proposes a method to generate an approximation of a neural network which is certifiably more robust. Crucially, the method is fully convex and posed as a semi-definite programme. An application to robustifying model predictive control is used to demonstrate the results. The aim of this work is to introduce a method to navigate the neural network robustness/accuracy trade-off.