Solving Probabilistic Verification Problems of Neural Networks using Branch and Bound

TL;DR

This paper introduces a branch and bound algorithm for probabilistic neural network verification that significantly improves efficiency over existing methods, with proven soundness and completeness under certain conditions.

Contribution

The paper presents a novel branch and bound approach leveraging bound propagation for probabilistic verification, outperforming existing algorithms in speed and accuracy.

Findings

Reduces verification times from tens of minutes to seconds.

Outperforms existing probabilistic verification algorithms.

Proves soundness and conditional completeness of the method.

Abstract

Probabilistic verification problems of neural networks are concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification problems include verifying the demographic parity fairness notion or quantifying the safety of a neural network. We present a new algorithm for solving probabilistic verification problems of neural networks based on an algorithm for computing and iteratively refining lower and upper bounds on probabilities over the outputs of a neural network. By applying state-of-the-art bound propagation and branch and bound techniques from non-probabilistic neural network verification, our algorithm significantly outpaces existing probabilistic verification algorithms, reducing solving times for various benchmarks from the literature from tens of minutes to tens of seconds. Furthermore, our algorithm compares favourably even to dedicated algorithms for restricted probabilistic verification problems. We complement our empirical evaluation with a theoretical analysis, proving that our algorithm is sound and, under mildly restrictive conditions, also complete when using a suitable set of heuristics.