  To evaluate the robustness of non-classifier models, we propose probabilistic
local equivalence, based on the notion of randomized smoothing, as a way to
quantitatively evaluate the robustness of an arbitrary function. In addition,
to understand the effect of adversarial training on non-classifiers and to
investigate the level of robustness that can be obtained without degrading
performance on the training distribution, we apply Fast is Better than Free
adversarial training together with the TRADES robust loss to the training of an
instance segmentation network. In this direction, we were able to achieve a
symmetric best dice score of 0.85 on the TuSimple lane detection challenge,
outperforming the standardly-trained network's score of 0.82. Additionally, we
were able to obtain an F-measure of 0.49 on manipulated inputs, in contrast to
the standardly-trained network's score of 0. We show that probabilisitic local
equivalence is able to successfully distinguish between standardly-trained and
adversarially-trained models, providing another view of the improved robustness
of the adversarially-trained models.
