# Efficient Safety Verification of Autonomous Vehicles with Neural Network Operator

arXiv: https://arxiv.org/abs/2512.04557 · HTML: https://mlsanity.com/paper/2512.04557/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in End-to-end system architecture, one of 9 directions in End-to-end autonomous driving.
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 4 Dec 2025.

## Placed in

- End-to-end autonomous driving / [End-to-end system architecture](https://mlsanity.com/driving/end-to-end-system-architecture/)

## Builds on (most cited first, 11 of 11)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes](https://mlsanity.com/paper/2210.10691/) (2022)
- [On Infusing Reachability-Based Safety Assurance within Planning Frameworks for Human-Robot Vehicle Interactions](https://mlsanity.com/paper/2012.03390/) (2020)
- [A Classification-based Approach for Approximate Reachability](https://mlsanity.com/paper/1803.03237/) (2018)
- [Neural State Classification for Hybrid Systems](https://mlsanity.com/paper/1807.09901/) (2018)
- [Reachability-Based Confidence-Aware Probabilistic Collision Detection in Highway Driving](https://mlsanity.com/paper/2302.07109/) (2023)
- [Formal Certification Methods for Automated Vehicle Safety Assessment](https://mlsanity.com/paper/2202.02818/) (2022)

## Abstract (arXiv)

When autonomous vehicles encounter untrained scenarios, ensuring safety hinges on effective safety verification to prevent accidents stemming from unexpected model decisions. Reachability analysis, a method of safety verification, offers relatively high precision but at the cost of significant computational complexity. Our method leverages end-to-end neural network operators to compute reachable sets, replacing traditional mathematical set operators, thereby achieving higher efficiency in safety verification without substantially compromising accuracy or increasing conservativeness. We define vehicle dynamics on discrete time series and detail the safety verification process and safety standard based on reachable sets. Experimental evaluations conducted in several typical road driving scenarios demonstrate the superior efficiency performance of our proposed operator over classical methods.