mlsanityData to 14 Oct 2026

Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generation

arXiv 2604.21556 ↗First posted 23 Apr 2026cs.AI cs.SEcited by 0

Not on the map. Why?

Abstract (arXiv)

The problem of probabilistic verification of a neural network investigates the probability of satisfying the safe constraints in the output space when the input is given by a probability distribution. It is significant to answer this problem when the input is affected by disturbances often modeled by probabilistic variables. In the paper, we propose a novel neural network probabilistic verification framework which computes a guaranteed range for the safe probability by efficiently finding safe and unsafe probabilistic hulls. Our approach consists of three main innovations: (1) a state space subdivision strategy using regression trees to produce probabilistic hulls, (2) a boundary-aware sampling method which identifies the safety boundary in the input space using samples that are later used for building regression trees, and (3) iterative refinement with probabilistic prioritization for computing a guaranteed range for the safe probability. The accuracy and efficiency of our approach are evaluated on various benchmarks including ACAS Xu and a rocket lander controller. The result shows an obvious advantage over the state of the art.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 15 of its 22 references that are in the map. First posted on arXiv 23 Apr 2026.

Builds on

15 of 22 references.

References · 15

  1. 2020Knowledge Distillation: A Surveycited by 1,603
  2. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 744
  3. 2021Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verificationcited by 228
  4. 2024Marabou 2.0: A Versatile Formal Analyzer of Neural Networkscited by 81
  5. 2018A Statistical Approach to Assessing Neural Network Robustnesscited by 54
  6. 2022Adversarial Robustness of Deep Neural Networks: A Survey from a Formal Verification Perspectivecited by 42
  7. 2021POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systemscited by 39
  8. 2021How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Reviewcited by 39
  9. 2019Robustness of Neural Networks: A Probabilistic and Practical Approachcited by 38
  10. 2019Statistical Guarantees for the Robustness of Bayesian Neural Networkscited by 35
  11. 2021Neural Network Repair with Reachability Analysiscited by 19
  12. 2018PROVEN: Certifying Robustness of Neural Networks with a Probabilistic Approachcited by 10
3 more
  1. 2023Adversarial Robustness Certification for Bayesian Neural Networkscited by 7
  2. 2022Probabilistic Verification of ReLU Neural Networks via Characteristic Functionscited by 5
  3. 2023Probabilistic Reach-Avoid for Bayesian Neural Networkscited by 5

Built on by

Not cited yet.