Verifying Global Neural Network Specifications using Hyperproperties

TL;DR

This paper introduces a hyperproperty formalism for verifying global neural network specifications, enabling guarantees like monotonicity and Lipschitz continuity across all inputs, thus broadening the scope of neural network verification.

Contribution

It presents a novel formalism for expressing and verifying global specifications, extending existing neural network verification methods to cover all potential inputs.

Findings

Verification of global specifications is feasible with current methods.

The formalism can express properties like monotonicity and fairness.

Extends guarantees beyond local robustness to all inputs.

Abstract

Current approaches to neural network verification focus on specifications that target small regions around known input data points, such as local robustness. Thus, using these approaches, we can not obtain guarantees for inputs that are not close to known inputs. Yet, it is highly likely that a neural network will encounter such truly unseen inputs during its application. We study global specifications that - when satisfied - provide guarantees for all potential inputs. We introduce a hyperproperty formalism that allows for expressing global specifications such as monotonicity, Lipschitz continuity, global robustness, and dependency fairness. Our formalism enables verifying global specifications using existing neural network verification approaches by leveraging capabilities for verifying general computational graphs. Thereby, we extend the scope of guarantees that can be provided using existing methods. Recent success in verifying specific global specifications shows that attaining strong guarantees for all potential data points is feasible.