# Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generation

arXiv: https://arxiv.org/abs/2604.21556 · HTML: https://mlsanity.com/paper/2604.21556/

## 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 (most cited first, 15 of 15)

- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Marabou 2.0: A Versatile Formal Analyzer of Neural Networks](https://mlsanity.com/paper/2401.14461/) (2024)
- [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)
- [POLAR: A Polynomial Arithmetic Framework for Verifying Neural-Network Controlled Systems](https://mlsanity.com/paper/2106.13867/) (2021)
- [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)
- [Statistical Guarantees for the Robustness of Bayesian Neural Networks](https://mlsanity.com/paper/1903.01980/) (2019)
- [Neural Network Repair with Reachability Analysis](https://mlsanity.com/paper/2108.04214/) (2021)
- [PROVEN: Certifying Robustness of Neural Networks with a Probabilistic Approach](https://mlsanity.com/paper/1812.08329/) (2018)
- [Adversarial Robustness Certification for Bayesian Neural Networks](https://mlsanity.com/paper/2306.13614/) (2023)
- [Probabilistic Verification of ReLU Neural Networks via Characteristic Functions](https://mlsanity.com/paper/2212.01544/) (2022)
- [Probabilistic Reach-Avoid for Bayesian Neural Networks](https://mlsanity.com/paper/2310.01951/) (2023)

## 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.