# Efficient Reachability Analysis for Convolutional Neural Networks Using Hybrid Zonotopes

arXiv: https://arxiv.org/abs/2503.10840 · HTML: https://mlsanity.com/paper/2503.10840/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 24 references that are in the map.
- First posted on arXiv 13 Mar 2025.

## Builds on (most cited first, 19 of 19)

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Maxout Networks](https://mlsanity.com/paper/1302.4389/) (2013)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [Verification of Deep Convolutional Neural Networks Using ImageStars](https://mlsanity.com/paper/2004.05511/) (2020)
- [The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Results](https://mlsanity.com/paper/2109.00498/) (2021)
- [Reachability Analysis of Neural Feedback Loops](https://mlsanity.com/paper/2108.04140/) (2021)
- [Verifying Controllers with Convolutional Neural Network-based Perception: A Case for Intelligible, Safe, and Precise Abstractions](https://mlsanity.com/paper/2111.05534/) (2021)
- [NNLander-VeriF: A Neural Network Formal Verification Framework for Vision-Based Autonomous Aircraft Landing](https://mlsanity.com/paper/2203.15841/) (2022)
- [Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems](https://mlsanity.com/paper/2209.14076/) (2022)
- [Hybrid zonotopes: a new set representation for reachability analysis of mixed logical dynamical systems](https://mlsanity.com/paper/2106.14831/) (2021)
- [Safety Verification of Neural Feedback Systems Based on Constrained Zonotopes](https://mlsanity.com/paper/2204.00903/) (2022)
- [Fully Automatic Neural Network Reduction for Formal Verification](https://mlsanity.com/paper/2305.01932/) (2023)
- [Reachability Analysis and Safety Verification of Neural Feedback Systems via Hybrid Zonotopes](https://mlsanity.com/paper/2210.03244/) (2022)
- [Reachability Analysis of Convolutional Neural Networks](https://mlsanity.com/paper/2106.12074/) (2021)
- [Backward Reachability Analysis of Neural Feedback Systems Using Hybrid Zonotopes](https://mlsanity.com/paper/2303.10513/) (2023)
- [Hybrid Zonotope-Based Backward Reachability Analysis for Neural Feedback Systems With Nonlinear Plant Models](https://mlsanity.com/paper/2310.06921/) (2023)

## Abstract (arXiv)

Feedforward neural networks are widely used in autonomous systems, particularly for control and perception tasks within the system loop. However, their vulnerability to adversarial attacks necessitates formal verification before deployment in safety-critical applications. Existing set propagation-based reachability analysis methods for feedforward neural networks often struggle to achieve both scalability and accuracy. This work presents a novel set-based approach for computing the reachable sets of convolutional neural networks. The proposed method leverages a hybrid zonotope representation and an efficient neural network reduction technique, providing a flexible trade-off between computational complexity and approximation accuracy. Numerical examples are presented to demonstrate the effectiveness of the proposed approach.