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. We introduce IoUCert, a novel formal verification framework designed specifically to overcome these bottlenecks in foundational anchor-based object detection architectures. Focusing on the object localisation component in single-object settings, we propose a coordinate transformation that enables our algorithm to circumvent precision-degrading relaxations of non-linear box prediction functions. This allows us to optimise bounds directly with respect to the anchor box offsets which enables a novel Interval Bound Propagation method that derives optimal IoU bounds. We demonstrate that our method enables, for the first time, the robustness verification of realistic, anchor-based models including SSD, YOLOv2, and YOLOv3 variants against various input perturbations.
@article{arxiv.2603.03043,
title = {IoUCert: Robustness Verification for Anchor-based Object Detectors},
author = {Benedikt Brückner and Alejandro J. Mercado and Yanghao Zhang and Panagiotis Kouvaros and Alessio Lomuscio},
journal= {arXiv preprint arXiv:2603.03043},
year = {2026}
}