# Probabilistic Robustness Analysis in High Dimensional Space: Application to Semantic Segmentation Network

arXiv: https://arxiv.org/abs/2509.11838 · HTML: https://mlsanity.com/paper/2509.11838/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 54 references that are in the map.
- First posted on arXiv 15 Sep 2025.

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

- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [The Cityscapes Dataset for Semantic Urban Scene Understanding](https://mlsanity.com/paper/1604.01685/) (2016)
- [Deep High-Resolution Representation Learning for Visual Recognition](https://mlsanity.com/paper/1908.07919/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Adversarial Machine Learning at Scale](https://mlsanity.com/paper/1611.01236/) (2016)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adversarial Examples for Semantic Segmentation and Object Detection](https://mlsanity.com/paper/1703.08603/) (2017)
- [NNV: The Neural Network Verification Tool for Deep Neural Networks and Learning-Enabled Cyber-Physical Systems](https://mlsanity.com/paper/2004.05519/) (2020)
- [Safe Planning in Dynamic Environments using Conformal Prediction](https://mlsanity.com/paper/2210.10254/) (2022)
- [Strong mixed-integer programming formulations for trained neural networks](https://mlsanity.com/paper/1811.08359/) (2018)
- [Robust Validation: Confident Predictions Even When Distributions Shift](https://mlsanity.com/paper/2008.04267/) (2020)
- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)
- [Verification of Deep Convolutional Neural Networks Using ImageStars](https://mlsanity.com/paper/2004.05511/) (2020)
- [The Fifth International Verification of Neural Networks Competition (VNN-COMP 2024): Summary and Results](https://mlsanity.com/paper/2412.19985/) (2024)
- [Conformal Prediction Regions for Time Series using Linear Complementarity Programming](https://mlsanity.com/paper/2304.01075/) (2023)
- [Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planes](https://mlsanity.com/paper/2501.00200/) (2024)
- [Formal Verification and Control with Conformal Prediction](https://mlsanity.com/paper/2409.00536/) (2024)
- [A DPLL(T) Framework for Verifying Deep Neural Networks](https://mlsanity.com/paper/2307.10266/) (2023)
- [GSmooth: Certified Robustness against Semantic Transformations via Generalized Randomized Smoothing](https://mlsanity.com/paper/2206.04310/) (2022)
- [Forking Uncertainties: Reliable Prediction and Model Predictive Control with Sequence Models via Conformal Risk Control](https://mlsanity.com/paper/2310.10299/) (2023)
- [Enumerating Safe Regions in Deep Neural Networks with Provable Probabilistic Guarantees](https://mlsanity.com/paper/2308.09842/) (2023)
- [Verifiably Robust Conformal Prediction](https://mlsanity.com/paper/2405.18942/) (2024)
- [Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inference](https://mlsanity.com/paper/2309.09187/) (2023)
- [Spinal cord gray matter segmentation using deep dilated convolutions](https://mlsanity.com/paper/1710.01269/) (2017)
- [Statistical Reachability Analysis of Stochastic Cyber-Physical Systems under Distribution Shift](https://mlsanity.com/paper/2407.11609/) (2024)
- [Computing the Approximate Convex Hull in High Dimensions](https://mlsanity.com/paper/1603.04422/) (2016)
- [Adaptive Hierarchical Certification for Segmentation using Randomized Smoothing](https://mlsanity.com/paper/2402.08400/) (2024)
- [Probabilistic reachable and invariant sets for linear systems with correlated disturbance](https://mlsanity.com/paper/2004.06960/) (2020)

## Built on by (most cited first, 3 of 3)

- [Fast and Flexible Robustness Certificates for Semantic Segmentation](https://mlsanity.com/paper/2512.06010/) (2025)
- [Towards Verified and Targeted Explanations through Formal Methods](https://mlsanity.com/paper/2604.14209/) (2026)
- [NNV3: Expanding Neural Network Verification to New Architectures and Domains](https://mlsanity.com/paper/2609.30050/) (2026)

## Abstract (arXiv)

Semantic segmentation networks (SSNs) are central to safety-critical applications such as medical imaging and autonomous driving, where robustness under uncertainty is essential. However, existing probabilistic verification methods often fail to scale with the complexity and dimensionality of modern segmentation tasks, producing guarantees that are overly conservative and of limited practical value. We propose a probabilistic verification framework that is architecture-agnostic and scalable to high-dimensional input-output spaces. Our approach employs conformal inference (CI), enhanced by a novel technique that we call the clipping block, to provide provable guarantees while mitigating the excessive conservatism of prior methods. Experiments on large-scale segmentation models across CamVid, OCTA-500, Lung Segmentation, and Cityscapes demonstrate that our framework delivers reliable safety guarantees while substantially reducing conservatism compared to state-of-the-art approaches on segmentation tasks. We also provide a public GitHub repository (https://github.com/Navidhashemicodes/SSNReachCLPSurrogate) for this approach, to support reproducibility.