# Certified geometric robustness -- Super-DeepG

arXiv: https://arxiv.org/abs/2604.24379 · HTML: https://mlsanity.com/paper/2604.24379/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 27 Apr 2026.

## Builds on (most cited first, 10 of 10)

- [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)
- [TSS: Transformation-Specific Smoothing for Robustness Certification](https://mlsanity.com/paper/2002.12398/) (2020)
- [The Fifth International Verification of Neural Networks Competition (VNN-COMP 2024): Summary and Results](https://mlsanity.com/paper/2412.19985/) (2024)
- [Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspective](https://mlsanity.com/paper/2206.12227/) (2022)
- [Scalable Certified Segmentation via Randomized Smoothing](https://mlsanity.com/paper/2107.00228/) (2021)
- [A Review of Formal Methods applied to Machine Learning](https://mlsanity.com/paper/2104.02466/) (2021)
- [Provable Defense Against Geometric Transformations](https://mlsanity.com/paper/2207.11177/) (2022)
- [Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisation](https://mlsanity.com/paper/2408.13140/) (2024)
- [LARD 2.0: Enhanced Datasets and Benchmarking for Autonomous Landing Systems](https://mlsanity.com/paper/2603.26748/) (2026)

## Abstract (arXiv)

Safety-critical applications are required to perform as expected in normal operations. Image processing functions are often required to be insensitive to small geometric perturbations such as rotation, scaling, shearing or translation. This paper addresses the formal verification of neural networks against geometric perturbations on their image dataset. Our method Super-DeepG improves the reasoning used in linear relaxation techniques and Lipschitz optimization, and provides an implementation that leverages GPU hardware. By doing so, Super-DeepG achieves both precision and computational efficiency of robustness certification, to an extent that outperforms prior work. Super-DeepG is shared as an open-source tool on GitHub.