# IoUCert: Robustness Verification for Anchor-based Object Detectors

arXiv: https://arxiv.org/abs/2603.03043 · HTML: https://mlsanity.com/paper/2603.03043/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 83 references that are in the map.
- First posted on arXiv 3 Mar 2026.

## Builds on (most cited first, 30 of 47)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [A Survey on Deep Learning in Medical Image Analysis](https://mlsanity.com/paper/1702.05747/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Bridging the Gap Between Anchor-based and Anchor-free Detection via Adaptive Training Sample Selection](https://mlsanity.com/paper/1912.02424/) (2019)
- [Object Detection in 20 Years: A Survey](https://mlsanity.com/paper/1905.05055/) (2019)
- [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)
- [YOLOv6: A Single-Stage Object Detection Framework for Industrial Applications](https://mlsanity.com/paper/2209.02976/) (2022)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [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)
- [Formal Security Analysis of Neural Networks using Symbolic Intervals](https://mlsanity.com/paper/1804.10829/) (2018)
- [Semidefinite relaxations for certifying robustness to adversarial examples](https://mlsanity.com/paper/1811.01057/) (2018)
- [OTA: Optimal Transport Assignment for Object Detection](https://mlsanity.com/paper/2103.14259/) (2021)
- [Efficient Formal Safety Analysis of Neural Networks](https://mlsanity.com/paper/1809.08098/) (2018)
- [Adversarial Sensor Attack on LiDAR-based Perception in Autonomous Driving](https://mlsanity.com/paper/1907.06826/) (2019)
- [Probabilistic Anchor Assignment with IoU Prediction for Object Detection](https://mlsanity.com/paper/2007.08103/) (2020)
- [An approach to reachability analysis for feed-forward ReLU neural networks](https://mlsanity.com/paper/1706.07351/) (2017)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [General Cutting Planes for Bound-Propagation-Based Neural Network Verification](https://mlsanity.com/paper/2208.05740/) (2022)
- [Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programming](https://mlsanity.com/paper/1903.01287/) (2019)
- [Complete Verification via Multi-Neuron Relaxation Guided Branch-and-Bound](https://mlsanity.com/paper/2205.00263/) (2022)
- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)

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

- [Certified Training for Convolutional Perturbations](https://mlsanity.com/paper/2607.18195/) (2026)

## Abstract (arXiv)

While formal robustness verification has seen significant success in image classification, scaling these guarantees to object detection remains notoriously difficult due to complex non-linear coordinate transformations and Intersection-over-Union (IoU) metrics. As a fundamental step towards verifying complete detection pipelines, we introduce IoUCert, a novel formal verification framework designed specifically to overcome these core mathematical bottlenecks. By isolating the object localisation task in single-object settings, we propose a coordinate transformation that circumvents precision-degrading relaxations of non-linear box prediction functions. This approach allows us to optimise bounds directly with respect to anchor box offsets, enabling a novel Interval Bound Propagation method that derives optimal IoU bounds. We demonstrate that IoUCert enables, for the first time, the robustness verification of foundational, anchor-based architectures including tractable variants of SSD, YOLOv2, and YOLOv3 against various input perturbations, providing a rigorous theoretical basis for future end-to-end detector verification.