# Adaptive Hierarchical Certification for Segmentation using Randomized Smoothing

arXiv: https://arxiv.org/abs/2402.08400 · HTML: https://mlsanity.com/paper/2402.08400/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 35 references that are in the map.
- First posted on arXiv 13 Feb 2024.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [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)
- [Deep High-Resolution Representation Learning for Human Pose Estimation](https://mlsanity.com/paper/1902.09212/) (2019)
- [COCO-Stuff: Thing and Stuff Classes in Context](https://mlsanity.com/paper/1612.03716/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Segmentation Transformer: Object-Contextual Representations for Semantic Segmentation](https://mlsanity.com/paper/1909.11065/) (2019)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [A Convex Relaxation Barrier to Tight Robustness Verification of Neural Networks](https://mlsanity.com/paper/1902.08722/) (2019)
- [Maximum Resilience of Artificial Neural Networks](https://mlsanity.com/paper/1705.01040/) (2017)
- [Deep Hierarchical Semantic Segmentation](https://mlsanity.com/paper/2203.14335/) (2022)
- [CNN-based Segmentation of Medical Imaging Data](https://mlsanity.com/paper/1701.03056/) (2017)
- [Object detection via a multi-region & semantic segmentation-aware CNN model](https://mlsanity.com/paper/1505.01749/) (2015)
- [Detection as Regression: Certified Object Detection by Median Smoothing](https://mlsanity.com/paper/2007.03730/) (2020)
- [Scalable Certified Segmentation via Randomized Smoothing](https://mlsanity.com/paper/2107.00228/) (2021)
- [Instance-Level Segmentation for Autonomous Driving with Deep Densely Connected MRFs](https://mlsanity.com/paper/1512.06735/) (2015)
- [Wasserstein Smoothing: Certified Robustness against Wasserstein Adversarial Attacks](https://mlsanity.com/paper/1910.10783/) (2019)
- [A Brief Survey and an Application of Semantic Image Segmentation for Autonomous Driving](https://mlsanity.com/paper/1808.08413/) (2018)
- [Center Smoothing: Certified Robustness for Networks with Structured Outputs](https://mlsanity.com/paper/2102.09701/) (2021)

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

- [Certified Circuits: Stability Guarantees for Mechanistic Circuits](https://mlsanity.com/paper/2602.22968/) (2026)
- [Pixel-level Certified Explanations via Randomized Smoothing](https://mlsanity.com/paper/2506.15499/) (2025)
- [Probabilistic Robustness Analysis in High Dimensional Space: Application to Semantic Segmentation Network](https://mlsanity.com/paper/2509.11838/) (2025)

## Abstract (arXiv)

Certification for machine learning is proving that no adversarial sample can evade a model within a range under certain conditions, a necessity for safety-critical domains. Common certification methods for segmentation use a flat set of fine-grained classes, leading to high abstain rates due to model uncertainty across many classes. We propose a novel, more practical setting, which certifies pixels within a multi-level hierarchy, and adaptively relaxes the certification to a coarser level for unstable components classic methods would abstain from, effectively lowering the abstain rate whilst providing more certified semantically meaningful information. We mathematically formulate the problem setup, introduce an adaptive hierarchical certification algorithm and prove the correctness of its guarantees. Since certified accuracy does not take the loss of information into account for coarser classes, we introduce the Certified Information Gain (CIG) metric, which is proportional to the class granularity level. Our extensive experiments on the datasets Cityscapes, PASCAL-Context, ACDC and COCO-Stuff demonstrate that our adaptive algorithm achieves a higher CIG and lower abstain rate compared to the current state-of-the-art certification method. Our code can be found here: https://github.com/AlaaAnani/adaptive-certify.