# Safety verification of Neural-Network-based controllers: a set invariance approach

arXiv: https://arxiv.org/abs/2312.11352 · HTML: https://mlsanity.com/paper/2312.11352/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Dec 2023.

## Built on by (most cited first, 4 of 4)

- [Certified Robust Invariant Polytope Training in Neural Controlled ODEs](https://mlsanity.com/paper/2408.01273/) (2024)
- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Bridging Robustness and Generalization Against Word Substitution Attacks in NLP via the Growth Bound Matrix Approach](https://mlsanity.com/paper/2507.10330/) (2025)
- [Safe Deep Reinforcement Learning for Energy-Efficient HVAC Control in Multi-Zone Residential Buildings](https://mlsanity.com/paper/2608.17235/) (2026)

## Abstract (arXiv)

This paper presents a novel approach to ensure the safety of continuous-time linear dynamical systems controlled by a neural network (NN) based state-feedback. Our method capitalizes on the use of continuous piece-wise affine (PWA) activation functions (e.g. ReLU) which render the NN a PWA continuous function. By computing the affine regions of the latter and applying Nagumo's theorem, a subset of boundary points can effectively verify the invariance of a potentially non-convex set. Consequently, an algorithm that partitions the state space in affine regions is proposed. The scalability of our approach is thoroughly analyzed, and extensive tests are conducted to validate its effectiveness.