# Reachability Analysis and Safety Verification of Neural Feedback Systems via Hybrid Zonotopes

arXiv: https://arxiv.org/abs/2210.03244 · HTML: https://mlsanity.com/paper/2210.03244/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2022.

## Built on by (most cited first, 5 of 5)

- [Hybrid Zonotopes Exactly Represent ReLU Neural Networks](https://mlsanity.com/paper/2304.02755/) (2023)
- [Provably-Safe Neural Network Training Using Hybrid Zonotope Reachability Analysis](https://mlsanity.com/paper/2501.13023/) (2025)
- [Automated Reachability Analysis of Neural Network-Controlled Systems via Adaptive Polytopes](https://mlsanity.com/paper/2212.07553/) (2022)
- [Compression Repair for Feedforward Neural Networks Based on Model Equivalence Evaluation](https://mlsanity.com/paper/2402.11737/) (2024)
- [Efficient Reachability Analysis for Convolutional Neural Networks Using Hybrid Zonotopes](https://mlsanity.com/paper/2503.10840/) (2025)

## Abstract (arXiv)

Hybrid zonotopes generalize constrained zonotopes by introducing additional binary variables and possess some unique properties that make them convenient to represent nonconvex sets. This paper presents novel hybrid zonotope-based methods for the reachability analysis and safety verification of neural feedback systems. Algorithms are proposed to compute the input-output relationship of each layer of a feedforward neural network, as well as the exact reachable sets of neural feedback systems. In addition, a sufficient and necessary condition is formulated as a mixed-integer linear program to certify whether the trajectories of a neural feedback system can avoid unsafe regions. The proposed approach is shown to yield a formulation that provides the tightest convex relaxation for the reachable sets of the neural feedback system. Complexity reduction techniques for the reachable sets are developed to balance the computation efficiency and approximation accuracy. Two numerical examples demonstrate the superior performance of the proposed approach compared to other existing methods.