Propagation ofInterval Belief Structures andImprecise Copulas for~Neural Network Verification

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.

State-of-the-art neural network verifiers use the branch-and-bound procedure as their core solving mechanism. We introduce an inprocessing framework for neural network verification driven by the lookahead procedure. Under this framework, lookahead derives new lemmas over the phases of unstable ReLUs, which are collected into an implication graph that is used to prune the search space and vivify boolean cuts. We instantiate the framework in two state-of-the-art verifiers, Marabou and $α$-$β$-CROWN, and demonstrate that it improves performance in both, proving up to 34% more instances unsatisfiable.

Verification of neural networks against relational specifications, such as global robustness, is crucial for safety-critical applications of cyber-physical systems (CPS), given their increasing adoption of AI components. Compared to simple trace properties (e.g., local robustness), verifying relational specifications requires reasoning about the relationship between multiple network inferences, which brings significant technical challenges. Existing research has explored abstraction techniques based on sound and convex over-approximation of neural network outputs; however, since these approaches are inherently incomplete and may raise false alarms, they further underscore the need of effective abstraction refinement. In this paper, we propose a branch-and-bound (BaB) framework to mitigate the issue, which iteratively splits the problem until all sub-problems are verified. Specifically, our BaB framework features splitting of relational neurons rather than individual neurons as prior works do, and as the core of our technique, we devise a relational neuron selection strategy based on the dual formulation of the verification problem, which allows us to efficiently select the (most likely) optimal relational neuron that maximizes the refinement brought by problem splitting. We evaluate SaBRe on 817 verification problems across ACAS Xu, MNIST-F, MNIST-C, CIFAR and GTSRB. The results show that SaBRe outperforms different baseline approaches, in terms of the number of solved instances and verification efficiency, which demonstrates the effectiveness of our proposed techniques.