Probabilistic Verification of Neural Networks using Branch and Bound

2024-05-27

arXiv.org

AI Summary

This work addresses probabilistic verification of neural networks—formally certifying probabilistic output properties (e.g., fairness, safety) under given input distributions. Existing methods suffer from low efficiency and a fundamental trade-off between reliability and completeness. To overcome this, we are the first to systematically integrate interval-bound propagation and branch-and-bound—techniques originally developed for deterministic verification—into the probabilistic verification framework. Our approach combines probabilistic interval estimation with heuristic pruning strategies to yield a solver that is efficient, provably reliable, and conditionally complete. Experimental evaluation on multiple benchmarks demonstrates that our method reduces verification time from tens of minutes to tens of seconds, achieving consistent and substantial improvements over state-of-the-art probabilistic verifiers and domain-specific algorithms.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Probabilistic Circuits and Graphical Models
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Probabilistic verification of neural networks is concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification include verifying the demographic parity fairness notion or quantifying the safety of a neural network. We present a new algorithm for the probabilistic verification 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 subsets of probabilistic verification. 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.

Problem

• Neural Networks
• Uncertainty Quantification
• Probabilistic Output

Innovation

• Probabilistic Verification
• Neural Network Outputs
• Efficiency Improvement