# Verification of Visual Controllers via Compositional Geometric Transformations

arXiv: https://arxiv.org/abs/2507.04523 · HTML: https://mlsanity.com/paper/2507.04523/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 40 references that are in the map.
- First posted on arXiv 6 Jul 2025.

## Builds on (most cited first, 30 of 31)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [Verisig: verifying safety properties of hybrid systems with neural network controllers](https://mlsanity.com/paper/1811.01828/) (2018)
- [TSS: Transformation-Specific Smoothing for Robustness Certification](https://mlsanity.com/paper/2002.12398/) (2020)
- [Neural Network Verification with Branch-and-Bound for General Nonlinearities](https://mlsanity.com/paper/2405.21063/) (2024)
- [Reach-SDP: Reachability Analysis of Closed-Loop Systems with Neural Network Controllers via Semidefinite Programming](https://mlsanity.com/paper/2004.07876/) (2020)
- [Reachability Analysis of Neural Feedback Loops](https://mlsanity.com/paper/2108.04140/) (2021)
- [OVERT: An Algorithm for Safety Verification of Neural Network Control Policies for Nonlinear Systems](https://mlsanity.com/paper/2108.01220/) (2021)
- [Reachable Set Estimation for Neural Network Control Systems: A Simulation-Guided Approach](https://mlsanity.com/paper/2004.12273/) (2020)
- [Reachable Polyhedral Marching (RPM): A Safety Verification Algorithm for Robotic Systems with Deep Neural Network Components](https://mlsanity.com/paper/2011.11609/) (2020)
- [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)
- [Safe Output Feedback Motion Planning from Images via Learned Perception Modules and Contraction Theory](https://mlsanity.com/paper/2206.06553/) (2022)
- [Probably Approximately Correct Vision-Based Planning using Motion Primitives](https://mlsanity.com/paper/2002.12852/) (2020)
- [Toward Certified Robustness Against Real-World Distribution Shifts](https://mlsanity.com/paper/2206.03669/) (2022)
- [Enforcing safety for vision-based controllers via Control Barrier Functions and Neural Radiance Fields](https://mlsanity.com/paper/2209.12266/) (2022)
- [POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled Systems](https://mlsanity.com/paper/2304.01218/) (2023)
- [A Reachability Method for Verifying Dynamical Systems with Deep Neural Network Controllers](https://mlsanity.com/paper/1903.00520/) (2019)
- [One-Shot Reachability Analysis of Neural Network Dynamical Systems](https://mlsanity.com/paper/2209.11827/) (2022)
- [Neural Network Compression of ACAS Xu Early Prototype is Unsafe: Closed-Loop Verification through Quantized State Backreachability](https://mlsanity.com/paper/2201.06626/) (2022)
- [Verifying Low-dimensional Input Neural Networks via Input Quantization](https://mlsanity.com/paper/2108.07961/) (2021)
- [Discovering Closed-Loop Failures of Vision-Based Controllers via Reachability Analysis](https://mlsanity.com/paper/2211.02736/) (2022)
- [System-Level Safety Monitoring and Recovery for Perception Failures in Autonomous Vehicles](https://mlsanity.com/paper/2409.17630/) (2024)
- [Enhancing Safety and Robustness of Vision-Based Controllers via Reachability Analysis](https://mlsanity.com/paper/2410.21736/) (2024)
- [Data-Driven Modeling and Verification of Perception-Based Autonomous Systems](https://mlsanity.com/paper/2312.06848/) (2023)
- [Scenario-based Compositional Verification of Autonomous Systems with Neural Perception](https://mlsanity.com/paper/2504.20942/) (2025)

## Abstract (arXiv)

Perception-based neural network controllers are increasingly used in autonomous systems that rely on visual inputs to operate in the real world. Ensuring the safety of such systems under uncertainty is challenging. Existing verification techniques typically focus on Lp-bounded perturbations in the pixel space, which fails to capture the low-dimensional structure of many real-world effects. In this work, we introduce a novel verification framework for perception-based controllers that can generate outer-approximations of reachable sets through explicitly modeling uncertain observations with geometric perturbations. Our approach constructs a boundable mapping from states to images, enabling the use of state-based verification tools while accounting for uncertainty in perception. We provide theoretical guarantees on the soundness of our method and demonstrate its effectiveness across benchmark control environments. This work provides a principled framework for certifying the safety of perception-driven control systems under realistic visual perturbations.