Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generation

2026-04-23

AI Summary

This work addresses the problem of verifying the safety of neural networks under randomly perturbed inputs by proposing an efficient probabilistic verification framework. The approach integrates regression tree-guided state space partitioning, boundary-aware sampling, and probabilistic convex hull construction, complemented by an iterative refinement mechanism with probabilistic prioritization to compute a guaranteed probability interval that the network’s output satisfies given safety constraints. Experimental evaluations on standard benchmarks—including the ACAS Xu airborne collision avoidance system and rocket landing controllers—demonstrate that the proposed method significantly outperforms existing techniques in both verification accuracy and computational efficiency.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Stochastic Optimization
• Natural Language Processing: Safety and Robustness

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

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.

Problem

• probabilistic verification
• neural networks
• safe probability
• probabilistic hulls
• input uncertainty

Innovation

• probabilistic verification
• probabilistic hull
• regression trees
• boundary-aware sampling
• iterative refinement