  Reweighting adversarial data during training has been recently shown to
improve adversarial robustness, where data closer to the current decision
boundaries are regarded as more critical and given larger weights. However,
existing methods measuring the closeness are not very reliable: they are
discrete and can take only a few values, and they are path-dependent, i.e.,
they may change given the same start and end points with different attack
paths. In this paper, we propose three types of probabilistic margin (PM),
which are continuous and path-independent, for measuring the aforementioned
closeness and reweighting adversarial data. Specifically, a PM is defined as
the difference between two estimated class-posterior probabilities, e.g., such
the probability of the true label minus the probability of the most confusing
label given some natural data. Though different PMs capture different geometric
properties, all three PMs share a negative correlation with the vulnerability
of data: data with larger/smaller PMs are safer/riskier and should have
smaller/larger weights. Experiments demonstrate that PMs are reliable
measurements and PM-based reweighting methods outperform state-of-the-art
methods.
