# Towards Formal Verification of Deep Neural Networks for Object Detection

arXiv: https://arxiv.org/abs/2407.01295 · HTML: https://mlsanity.com/paper/2407.01295/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 42 of its 74 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 30 of 42)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [Conformer: Convolution-augmented Transformer for Speech Recognition](https://mlsanity.com/paper/2005.08100/) (2020)
- [ViViT: A Video Vision Transformer](https://mlsanity.com/paper/2103.15691/) (2021)
- [Video Swin Transformer](https://mlsanity.com/paper/2106.13230/) (2021)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Adversarial Patch](https://mlsanity.com/paper/1712.09665/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Towards Stable and Efficient Training of Verifiably Robust Neural Networks](https://mlsanity.com/paper/1906.06316/) (2019)
- [Branch and Bound for Piecewise Linear Neural Network Verification](https://mlsanity.com/paper/1909.06588/) (2019)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [Universal Physical Camouflage Attacks on Object Detectors](https://mlsanity.com/paper/1909.04326/) (2019)
- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)
- [PRIMA: General and Precise Neural Network Certification via Scalable Convex Hull Approximations](https://mlsanity.com/paper/2103.03638/) (2021)
- [An Abstraction-Based Framework for Neural Network Verification](https://mlsanity.com/paper/1910.14574/) (2019)
- [Detection as Regression: Certified Object Detection by Median Smoothing](https://mlsanity.com/paper/2007.03730/) (2020)
- [Towards Formal XAI: Formally Approximate Minimal Explanations of Neural Networks](https://mlsanity.com/paper/2210.13915/) (2022)
- [Towards Scalable Verification of Deep Reinforcement Learning](https://mlsanity.com/paper/2105.11931/) (2021)
- [Verifying Learning-Based Robotic Navigation Systems](https://mlsanity.com/paper/2205.13536/) (2022)
- [Output Range Analysis for Deep Neural Networks](https://mlsanity.com/paper/1709.09130/) (2017)
- [Formally Explaining Neural Networks within Reactive Systems](https://mlsanity.com/paper/2308.00143/) (2023)

## Built on by (most cited first, 4 of 4)

- [SETA: Statistical Fault Attribution for Compound AI Systems](https://mlsanity.com/paper/2601.19337/) (2026)
- [Talking with Verifiers: Automatic Specification Generation for Neural Network Verification](https://mlsanity.com/paper/2603.02235/) (2026)
- [Information Coordination as a Bridge: A Neuro-Symbolic Architecture for Reliable Autonomous Driving Scene Understanding](https://mlsanity.com/paper/2605.04475/) (2026)
- [SoK: Formal Methods for Fact-Checking and Information Integrity](https://mlsanity.com/paper/2609.23239/) (2026)

## Abstract (arXiv)

Deep neural networks (DNNs) are widely used in real-world computer vision applications, yet they remain vulnerable to errors and adversarial attacks. Formal verification offers a systematic approach to identify and mitigate these vulnerabilities, enhancing model robustness and reliability. While most existing verification methods focus on image classification models, this work extends formal verification to the more complex domain of object detection models. We propose a formulation for verifying the robustness of such models and demonstrate how state-of-the-art verification tools, originally developed for classification, can be adapted for this purpose. Through a comprehensive evaluation, we highlight the ability of formal verification to uncover vulnerabilities in object detection models, and derive formal robustness guarantees, underscoring the potential and need to further extend verification efforts in this domain. This work lays the foundation for further research into formal verification of object detection models across a broader range of computer vision applications. Our source code is publicly available online.