  Certified robustness guarantee gauges a model's robustness to test-time
attacks and can assess the model's readiness for deployment in the real world.
In this work, we critically examine how the adversarial robustness guarantees
from randomized smoothing-based certification methods change when
state-of-the-art certifiably robust models encounter out-of-distribution (OOD)
data. Our analysis demonstrates a previously unknown vulnerability of these
models to low-frequency OOD data such as weather-related corruptions, rendering
these models unfit for deployment in the wild. To alleviate this issue, we
propose a novel data augmentation scheme, FourierMix, that produces
augmentations to improve the spectral coverage of the training data.
Furthermore, we propose a new regularizer that encourages consistent
predictions on noise perturbations of the augmented data to improve the quality
of the smoothed models. We find that FourierMix augmentations help eliminate
the spectral bias of certifiably robust models enabling them to achieve
significantly better robustness guarantees on a range of OOD benchmarks. Our
evaluation also uncovers the inability of current OOD benchmarks at
highlighting the spectral biases of the models. To this end, we propose a
comprehensive benchmarking suite that contains corruptions from different
regions in the spectral domain. Evaluation of models trained with popular
augmentation methods on the proposed suite highlights their spectral biases and
establishes the superiority of FourierMix trained models at achieving
better-certified robustness guarantees under OOD shifts over the entire
frequency spectrum.
