  The reliability of neural networks is essential for their use in
safety-critical applications. Existing approaches generally aim at improving
the robustness of neural networks to either real-world distribution shifts
(e.g., common corruptions and perturbations, spatial transformations, and
natural adversarial examples) or worst-case distribution shifts (e.g.,
optimized adversarial examples). In this work, we propose the Decision Region
Quantification (DRQ) algorithm to improve the robustness of any differentiable
pre-trained model against both real-world and worst-case distribution shifts in
the data. DRQ analyzes the robustness of local decision regions in the vicinity
of a given data point to make more reliable predictions. We theoretically
motivate the DRQ algorithm by showing that it effectively smooths spurious
local extrema in the decision surface. Furthermore, we propose an
implementation using targeted and untargeted adversarial attacks. An extensive
empirical evaluation shows that DRQ increases the robustness of adversarially
and non-adversarially trained models against real-world and worst-case
distribution shifts on several computer vision benchmark datasets.
