Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generation

• URL: http://arxiv.org/abs/2604.21556v1
• Date: Thu, 23 Apr 2026 11:31:06 GMT
• Title: Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generation
• Abstract summary: We propose a novel neural network probabilistic verification framework which computes a guaranteed range for the safe probability.<n>The accuracy and efficiency of our approach are evaluated on various benchmarks including ACAS Xu and a rocket lander controller.
• Score: 10.859851140571045
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• On the Probabilistic Learnability of Compact Neural Network Preimage Bounds [71.59148070050212]
  In this work, we adopt a novel probabilistic perspective, aiming to deliver solutions with high-confidence guarantees and bounded error.<n>We introduce $textbfR$andom $textbfF$orest $textbfPro$perty $textbfVe$rifier ($texttRF-ProVe$), a method that exploits an ensemble of randomized decision trees to generate candidate input regions satisfying a desired output property.<n>Our theoretical derivations offer formal statistical guarantees on region purity and global coverage, providing a practical, scalable solution for computing
  arXiv  Detail & Related papers  (2025-11-10T16:56:51Z)
• Exact characterization of ε-Safe Decision Regions for exponential family distributions and Multi Cost SVM approximation [2.225810431340323]
  We introduce a formal definition of epsilon-Safe Decision Region, a subset of the input space in which the prediction of a target (safe) class is probabilistically guaranteed.<n>Inspired by this limitation, we developed Multi Cost SVM, an SVM based algorithm that approximates the safe region and is also able to handle unbalanced data.
  arXiv  Detail & Related papers  (2025-01-29T16:14:35Z)
• Tractable Function-Space Variational Inference in Bayesian Neural Networks [72.97620734290139]
  A popular approach for estimating the predictive uncertainty of neural networks is to define a prior distribution over the network parameters. We propose a scalable function-space variational inference method that allows incorporating prior information. We show that the proposed method leads to state-of-the-art uncertainty estimation and predictive performance on a range of prediction tasks.
  arXiv  Detail & Related papers  (2023-12-28T18:33:26Z)
• Enumerating Safe Regions in Deep Neural Networks with Provable Probabilistic Guarantees [86.1362094580439]
  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. 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.
  arXiv  Detail & Related papers  (2023-08-18T22:30:35Z)
• Bayesian Safety Validation for Failure Probability Estimation of Black-Box Systems [34.61865848439637]
  Estimating the probability of failure is an important step in the certification of safety-critical systems. This work frames the problem of black-box safety validation as a Bayesian optimization problem. The algorithm is designed to search for failures, compute the most-likely failure, and estimate the failure probability over an operating domain.
  arXiv  Detail & Related papers  (2023-05-03T22:22:48Z)
• Semantic Strengthening of Neuro-Symbolic Learning [85.6195120593625]
  Neuro-symbolic approaches typically resort to fuzzy approximations of a probabilistic objective. We show how to compute this efficiently for tractable circuits. We test our approach on three tasks: predicting a minimum-cost path in Warcraft, predicting a minimum-cost perfect matching, and solving Sudoku puzzles.
  arXiv  Detail & Related papers  (2023-02-28T00:04:22Z)
• The #DNN-Verification Problem: Counting Unsafe Inputs for Deep Neural Networks [94.63547069706459]
  #DNN-Verification problem involves counting the number of input configurations of a DNN that result in a violation of a safety property. We propose a novel approach that returns the exact count of violations. We present experimental results on a set of safety-critical benchmarks.
  arXiv  Detail & Related papers  (2023-01-17T18:32:01Z)
• Reliability analysis of discrete-state performance functions via adaptive sequential sampling with detection of failure surfaces [0.0]
  The paper presents a new efficient and robust method for rare event probability estimation. The method can estimate the probabilities of multiple failure types. It can accommodate this information to increase the accuracy of the estimated probabilities.
  arXiv  Detail & Related papers  (2022-08-04T05:59:25Z)
• Handling Epistemic and Aleatory Uncertainties in Probabilistic Circuits [18.740781076082044]
  We propose an approach to overcome the independence assumption behind most of the approaches dealing with a large class of probabilistic reasoning. We provide an algorithm for Bayesian learning from sparse, albeit complete, observations. Each leaf of such circuits is labelled with a beta-distributed random variable that provides us with an elegant framework for representing uncertain probabilities.
  arXiv  Detail & Related papers  (2021-02-22T10:03:15Z)
• Improving Uncertainty Calibration via Prior Augmented Data [56.88185136509654]
  Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. They are often overconfident in their predictions, which leads to inaccurate and miscalibrated probabilistic predictions. We propose a solution by seeking out regions of feature space where the model is unjustifiably overconfident, and conditionally raising the entropy of those predictions towards that of the prior distribution of the labels.
  arXiv  Detail & Related papers  (2021-02-22T07:02:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.