# Testing Between the Test Cases: Proving End-to-End Steering in Conditions You Never Drove

arXiv: https://arxiv.org/abs/2609.10951 · HTML: https://mlsanity.com/paper/2609.10951/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 10 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Planning-oriented Autonomous Driving](https://mlsanity.com/paper/2212.10156/) (2022)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Deep Retinex Decomposition for Low-Light Enhancement](https://mlsanity.com/paper/1808.04560/) (2018)
- [VAD: Vectorized Scene Representation for Efficient Autonomous Driving](https://mlsanity.com/paper/2303.12077/) (2023)
- [End-to-end Autonomous Driving: Challenges and Frontiers](https://mlsanity.com/paper/2306.16927/) (2023)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Learning to Drive in a Day](https://mlsanity.com/paper/1807.00412/) (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)
- [Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifiers](https://mlsanity.com/paper/2011.13824/) (2020)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks](https://mlsanity.com/paper/1902.08722/) (2019)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [Uncertainty Quantification with Statistical Guarantees in End-to-End Autonomous Driving Control](https://mlsanity.com/paper/1909.09884/) (2019)
- [Formal Verification of Neural Network Controlled Autonomous Systems](https://mlsanity.com/paper/1810.13072/) (2018)
- [An Analysis of ISO 26262: Using Machine Learning Safely in Automotive Software](https://mlsanity.com/paper/1709.02435/) (2017)
- [ACDC: The Adverse Conditions Dataset with Correspondences for Robust Semantic Driving Scene Perception](https://mlsanity.com/paper/2104.13395/) (2021)
- [NVIDIA OmniDreams: Real-Time Generative World Model for Closed-Loop Autonomous Vehicle Simulation](https://mlsanity.com/paper/2606.03159/) (2026)
- [SDP-CROWN: Efficient Bound Propagation for Neural Network Verification with Tightness of Semidefinite Programming](https://mlsanity.com/paper/2506.06665/) (2025)
- [Building a Credible Case for Safety: Waymo's Approach for the Determination of Absence of Unreasonable Risk](https://mlsanity.com/paper/2306.01917/) (2023)
- [Bootstrapping confidence in future safety based on past safe operation](https://mlsanity.com/paper/2110.10718/) (2021)
- [Open Challenges in the Formal Verification of Autonomous Driving](https://mlsanity.com/paper/2411.14520/) (2024)
- [Automating Automotive Software Development: A Synergy of Generative AI and Model-Based Methods](https://mlsanity.com/paper/2505.02500/) (2025)
- [Understanding Adversarial Transferability in Vision-Language Models for Autonomous Driving: A Cross-Architecture Analysis](https://mlsanity.com/paper/2604.27414/) (2026)

## Built on by (most cited first, 1 of 1)

- [Certified Mechanistic Edits: Behavioral Guarantees for Skill Removal and Preservation](https://mlsanity.com/paper/2610.03502/) (2026)

## Abstract (arXiv)

AI-based automated vehicle testing is challenging because a model that passes every test condition can still fail in the real world. Formal verification offers a way to directly address this gap. On a simulated highway and an arterial road we trained two small end-to-end steering networks each in CARLA, one on clear conditions alone and one on clear, fog, night and low sun. All four models were driven against a 2.19 ft lane-departure budget. Without driving again, we used bound propagation, a formal method that reads the trained weights, to compute how far steering can drift at every disturbance strength between two captured images. One calculation covers more than a campaign could drive: on the arterial it spans 133 poses, where ten intensities each would be 10^133 combinations, in minutes on one GPU. Not only did formal verification find conditions that broke the clear-trained policy without simulation testing, it provided some preliminary evidence for potential failures between the test cases. Our overall conclusion is that formal verification is a viable complement to simulation, and could be adopted as a part of verification and validation for automated driving.