Verification of Neural Networks' Global Robustness

TL;DR

This paper introduces VHAGaR, a novel verifier for global robustness of neural networks, providing tighter bounds and significantly faster performance than existing methods, thereby enhancing safety guarantees.

Contribution

The work proposes a new global robustness property and an efficient verifier, VHAGaR, that improves accuracy and speed over prior global robustness verification techniques.

Findings

VHAGaR reduces the average gap to 1.9 compared to 154.7 by existing verifiers.

VHAGaR is 130.6 times faster than previous global robustness verifiers.

Leveraging dependencies and adversarial attacks enhances VHAGaR's speed by 78.6 times.

Abstract

Neural networks are successful in various applications but are also susceptible to adversarial attacks. To show the safety of network classifiers, many verifiers have been introduced to reason about the local robustness of a given input to a given perturbation. While successful, local robustness cannot generalize to unseen inputs. Several works analyze global robustness properties, however, neither can provide a precise guarantee about the cases where a network classifier does not change its classification. In this work, we propose a new global robustness property for classifiers aiming at finding the minimal globally robust bound, which naturally extends the popular local robustness property for classifiers. We introduce VHAGaR, an anytime verifier for computing this bound. VHAGaR relies on three main ideas: encoding the problem as a mixed-integer programming and pruning the search space by identifying dependencies stemming from the perturbation or the network's computation and generalizing adversarial attacks to unknown inputs. We evaluate VHAGaR on several datasets and classifiers and show that, given a three hour timeout, the average gap between the lower and upper bound on the minimal globally robust bound computed by VHAGaR is 1.9, while the gap of an existing global robustness verifier is 154.7. Moreover, VHAGaR is 130.6x faster than this verifier. Our results further indicate that leveraging dependencies and adversarial attacks makes VHAGaR 78.6x faster.