Robustness issues arise in a variety of forms and are studied through multiple lenses in the machine learning literature. Neural networks lack adversarial robustness -- they are vulnerable to adversarial examples that through small perturbations to inputs cause incorrect predictions. Further, trust is undermined when models give miscalibrated or unstable uncertainty estimates, i.e. the predicted probability is not a good indicator of how much we should trust our model and could vary greatly over multiple independent runs. In this paper, we study the connection between adversarial robustness, predictive uncertainty (calibration) and model uncertainty (stability) on multiple classification networks and datasets. We find that the inputs for which the model is sensitive to small perturbations (are easily attacked) are more likely to have poorly calibrated and unstable predictions. Based on this insight, we examine if calibration and stability can be improved by addressing those adversarially unrobust inputs. To this end, we propose Adversarial Robustness based Adaptive Label Smoothing (AR-AdaLS) that integrates the correlations of adversarial robustness and uncertainty into training by adaptively softening labels conditioned on how easily it can be attacked by adversarial examples. We find that our method, taking the adversarial robustness of the in-distribution data into consideration, leads to better calibration and stability over the model even under distributional shifts. In addition, AR-AdaLS can also be applied to an ensemble model to achieve the best calibration performance.
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