  The last six years have witnessed significant progress in adversarially
robust deep learning. As evidenced by the CIFAR-10 dataset category in
RobustBench benchmark, the accuracy under $\ell_\infty$ adversarial
perturbations improved from 44\% in \citet{Madry2018Towards} to 71\% in
\citet{peng2023robust}. Although impressive, existing state-of-the-art is still
far from satisfactory. It is further observed that best-performing models are
often very large models adversarially trained by industrial labs with
significant computational budgets. In this paper, we aim to understand: ``how
much longer can computing power drive adversarial robustness advances?" To
answer this question, we derive \emph{scaling laws for adversarial robustness}
which can be extrapolated in the future to provide an estimate of how much cost
we would need to pay to reach a desired level of robustness. We show that
increasing the FLOPs needed for adversarial training does not bring as much
advantage as it does for standard training in terms of performance
improvements. Moreover, we find that some of the top-performing techniques are
difficult to exactly reproduce, suggesting that they are not robust enough for
minor changes in the training setup. Our analysis also uncovers potentially
worthwhile directions to pursue in future research. Finally, we make our
benchmarking framework (built on top of \texttt{timm}~\citep{rw2019timm})
publicly available to facilitate future analysis in efficient robust deep
learning.
