mlsanityData to 7 Oct 2026

Probabilistic Robustness in Deep Learning: A Concise yet Comprehensive Guide

arXiv 2502.14833 ↗First posted 20 Feb 2025cs.LGcited by 6

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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.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 38 of its 57 references that are in the map. First posted on arXiv 20 Feb 2025.

Builds on

38 of 57 references.

References · 38

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  11. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  12. 2021Recent Advances in Adversarial Training for Adversarial Robustnesscited by 276
26 more
  1. 2016Safety Verification of Deep Neural Networkscited by 262
  2. 2018Reachability Analysis of Deep Neural Networks with Provable Guaranteescited by 93
  3. 2018A Statistical Approach to Assessing Neural Network Robustnesscited by 54
  4. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 41
  5. 2019Robustness of Neural Networks: A Probabilistic and Practical Approachcited by 38
  6. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 36
  7. 2022Probabilistically Robust Learning: Balancing Average- and Worst-case Performancecited by 36
  8. 2020Scalable Quantitative Verification For Deep Neural Networkscited by 31
  9. 2022SAFARI: Versatile and Efficient Evaluations for Robustness of Interpretabilitycited by 28
  10. 2023Stable Diffusion is Unstablecited by 27
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  12. 2020A Safety Framework for Critical Systems Utilising Deep Neural Networkscited by 19
  13. 2022PRoA: A Probabilistic Robustness Assessment against Functional Perturbationscited by 19
  14. 2021CC-Cert: A Probabilistic Approach to Certify General Robustness of Neural Networkscited by 18
  15. 2019Statistically Robust Neural Network Classificationcited by 16
  16. 2021Reliability Assessment and Safety Arguments for Machine Learning Components in System Assurancecited by 16
  17. 2019Assessing the Safety and Reliability of Autonomous Vehicles from Road Testingcited by 15
  18. 2021Assessing the Reliability of Deep Learning Classifiers Through Robustness Evaluation and Operational Profilescited by 11
  19. 2024ProTIP: Probabilistic Robustness Verification on Text-to-Image Diffusion Models against Stochastic Perturbationcited by 10
  20. 2020Assessing Safety-Critical Systems from Operational Testing: A Study on Autonomous Vehiclescited by 9
  21. 2022Hierarchical Distribution-Aware Testing of Deep Learningcited by 8
  22. 2023What, Indeed, is an Achievable Provable Guarantee for Learning-Enabled Safety Critical Systemscited by 6
  23. 2024Trustworthy Text-to-Image Diffusion Models: A Timely and Focused Surveycited by 6
  24. 2025Where AI Assurance Might Go Wrong: Initial lessons from engineering of critical systemscited by 3
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 3.

6 papers.

  1. 2025PRBench: A Standardized Probabilistic Robustness Benchmarkcited by 1
  2. 2025Non-Parametric Probabilistic Robustness: A Conservative Risk Estimator under Unknown Perturbation Distributionscited by 1
  3. 2025Deep Learning Perspective of Scene Understanding in Autonomous Robotscited by 0
  4. 2026Probabilistic Robustness in Medical Image Classificationcited by 0
  5. 2026Probabilistic Robustness-driven Universal Adversarial Perturbations with Explainability against Deep Reinforcement Learning-based Intrusion Detection Systemcited by 0
  6. 2026Probabilistic Adversarial Trainingcited by 0