  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.
