mlsanityData to 14 Oct 2026

Enumerating Safe Regions in Deep Neural Networks with Provable Probabilistic Guarantees

arXiv 2308.09842 ↗First posted 18 Aug 2023cs.LG cs.AIcited by 19

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Abstract (arXiv)

Identifying safe areas is a key point to guarantee trust for systems that are based on Deep Neural Networks (DNNs). To this end, we introduce the AllDNN-Verification problem: given a safety property and a DNN, enumerate the set of all the regions of the property input domain which are safe, i.e., where the property does hold. Due to the #P-hardness of the problem, we propose an efficient approximation method called epsilon-ProVe. Our approach exploits a controllable underestimation of the output reachable sets obtained via statistical prediction of tolerance limits, and can provide a tight (with provable probabilistic guarantees) lower estimate of the safe areas. Our empirical evaluation on different standard benchmarks shows the scalability and effectiveness of our method, offering valuable insights for this new type of verification of DNNs.

Key facts. Cited by 19 papers in the map (data through 14 Oct 2026). Builds on 19 of its 30 references that are in the map. First posted on arXiv 18 Aug 2023.

Builds on

19 of 30 references.

References · 19

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,415
  2. 2013Intriguing properties of neural networkscited by 5,155
  3. 2016Towards Evaluating the Robustness of Neural Networkscited by 2,998
  4. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  5. 2015An Introduction to Convolutional Neural Networkscited by 514
  6. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 228
  7. 2019Algorithms for Verifying Deep Neural Networkscited by 221
  8. 2018Formal Security Analysis of Neural Networks using Symbolic Intervalscited by 185
  9. 2018Efficient Formal Safety Analysis of Neural Networkscited by 165
  10. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 103
  11. 2021The Second International Verification of Neural Networks Competition (VNN-COMP 2021): Summary and Resultscited by 71
  12. 2019Quantitative Verification of Neural Networks And its Security Applicationscited by 56
7 more
  1. 2022Verifying Learning-Based Robotic Navigation Systemscited by 33
  2. 2021Neural Network Repair with Reachability Analysiscited by 19
  3. 2023The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networkscited by 19
  4. 2021Curriculum Learning for Safe Mapless Navigationcited by 11
  5. 2023Safe Deep Reinforcement Learning by Verifying Task-Level Propertiescited by 9
  6. 2023Constrained Reinforcement Learning and Formal Verification for Safe Colonoscopy Navigationcited by 9
  7. 2023Online Safety Property Collection and Refinement for Safe Deep Reinforcement Learning in Mapless Navigationcited by 7

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 7; 2025: 8; 2026: 3.

19 papers.

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  1. 2024Verification-Guided Shielding for Deep Reinforcement Learningcited by 13
  2. 2024Analyzing Adversarial Inputs in Deep Reinforcement Learningcited by 7
  3. 2024ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networkscited by 7
  4. 2024Rigorous Probabilistic Guarantees for Robust Counterfactual Explanationscited by 6
  5. 2024Improving Policy Optimization via varepsilon-Retraincited by 5
  6. 2024Solving Probabilistic Verification Problems of Neural Networks using Branch and Boundcited by 4
  7. 2025Advancing Neural Network Verification through Hierarchical Safety Abstract Interpretationcited by 4
  8. 2025Designing Control Barrier Function via Probabilistic Enumeration for Safe Reinforcement Learning Navigationcited by 3
  9. 2025Probabilistic Robustness Analysis in High Dimensional Space: Application to Semantic Segmentation Networkcited by 3
  10. 2025On the Probabilistic Learnability of Compact Neural Network Preimage Boundscited by 3
  11. 2025Inductive Learning of Robot Task Knowledge from Raw Data and Online Expert Feedbackcited by 2
  12. 2025Probabilistically Tightened Linear Relaxation-based Perturbation Analysis for Neural Network Verificationcited by 2
7 more
  1. 2023Scaling #DNN-Verification Tools with Efficient Bound Propagation and Parallel Computingcited by 1
  2. 2024LEVIS: Large Exact Verifiable Input Spaces for Neural Networkscited by 1
  3. 2025Formal Verification of Variational Quantum Circuitscited by 1
  4. 2025BaB-prob: Branch and Bound with Preactivation Splitting for Probabilistic Verification of Neural Networkscited by 0
  5. 2026Probabilistic Verification of Recurrent Neural Networks for Single and Multi-Agent Reinforcement Learningcited by 0
  6. 2026Verifiable Foundation Models for Robot Safetycited by 0
  7. 2026A Survey on the Verification of Reinforcement Learning Policiescited by 0