# Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guide

arXiv: https://arxiv.org/abs/2502.14833 · HTML: https://mlsanity.com/paper/2502.14833/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 57 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 30 of 38)

- [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)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Distillation as a Defense to Adversarial Perturbations against Deep Neural Networks](https://mlsanity.com/paper/1511.04508/) (2015)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Recent Advances in Adversarial Training for Adversarial Robustness](https://mlsanity.com/paper/2102.01356/) (2021)
- [Safety Verification of Deep Neural Networks](https://mlsanity.com/paper/1610.06940/) (2016)
- [Reachability Analysis of Deep Neural Networks with Provable Guarantees](https://mlsanity.com/paper/1805.02242/) (2018)
- [A Statistical Approach to Assessing Neural Network Robustness](https://mlsanity.com/paper/1811.07209/) (2018)
- [Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspective](https://mlsanity.com/paper/2206.12227/) (2022)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [Robustness of Neural Networks: A Probabilistic and Practical Approach](https://mlsanity.com/paper/1902.05983/) (2019)
- [Probabilistically Robust Learning: Balancing Average- and Worst-case Performance](https://mlsanity.com/paper/2202.01136/) (2022)
- [Scalable Quantitative Verification For Deep Neural Networks](https://mlsanity.com/paper/2002.06864/) (2020)
- [SAFARI: Versatile and Efficient Evaluations for Robustness of Interpretability](https://mlsanity.com/paper/2208.09418/) (2022)
- [Stable Diffusion is Unstable](https://mlsanity.com/paper/2306.02583/) (2023)
- [Probabilistically robust conformal prediction](https://mlsanity.com/paper/2307.16360/) (2023)
- [A Safety Framework for Critical Systems Utilising Deep Neural Networks](https://mlsanity.com/paper/2003.05311/) (2020)
- [CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networks](https://mlsanity.com/paper/2109.10696/) (2021)
- [PRoA: A Probabilistic Robustness Assessment against Functional Perturbations](https://mlsanity.com/paper/2207.02036/) (2022)
- [Statistically Robust Neural Network Classification](https://mlsanity.com/paper/1912.04884/) (2019)
- [Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurance](https://mlsanity.com/paper/2112.00646/) (2021)
- [Assessing the Safety and Reliability of Autonomous Vehicles from Road Testing](https://mlsanity.com/paper/1908.06540/) (2019)
- [Assessing the Reliability of Deep Learning Classifiers Through Robustness Evaluation and Operational Profiles](https://mlsanity.com/paper/2106.01258/) (2021)

## Built on by (most cited first, 6 of 6)

- [PRBench: A Standardized Probabilistic Robustness Benchmark](https://mlsanity.com/paper/2511.01724/) (2025)
- [Non-Parametric Probabilistic Robustness: A Conservative Risk Estimator under Unknown Perturbation Distributions](https://mlsanity.com/paper/2511.17380/) (2025)
- [Deep Learning Perspective of Scene Understanding in Autonomous Robots](https://mlsanity.com/paper/2512.14020/) (2025)
- [Probabilistic Robustness in Medical Image Classification](https://mlsanity.com/paper/2607.03797/) (2026)
- [Probabilistic Robustness-driven Universal Adversarial Perturbations with Explainability against Deep Reinforcement Learning-based Intrusion Detection System](https://mlsanity.com/paper/2609.30605/) (2026)
- [Probabilistic Adversarial Training](https://mlsanity.com/paper/2609.39798/) (2026)

## Abstract (arXiv)

Deep learning (DL) has demonstrated significant potential across various safety-critical applications, yet ensuring its robustness remains a key challenge. While adversarial robustness has been extensively studied in worst-case scenarios, probabilistic robustness (PR) offers a more practical perspective by quantifying the likelihood of failures under stochastic perturbations. This paper provides a concise yet comprehensive overview of PR, covering its formal definitions, evaluation and enhancement methods. We introduce a reformulated ''min-max'' optimisation framework for adversarial training specifically designed to improve PR. Furthermore, we explore the integration of PR verification evidence into system-level safety assurance, addressing challenges in translating DL model-level robustness to system-level claims. Finally, we highlight open research questions, including benchmarking PR evaluation methods, extending PR to generative AI tasks, and developing rigorous methodologies and case studies for system-level integration.