  Randomized Smoothing (RS) is considered the state-of-the-art approach to
obtain certifiably robust models for challenging tasks. However, current RS
approaches drastically decrease standard accuracy on unperturbed data, severely
limiting their real-world utility. To address this limitation, we propose a
compositional architecture, ACES, which certifiably decides on a per-sample
basis whether to use a smoothed model yielding predictions with guarantees or a
more accurate standard model without guarantees. This, in contrast to prior
approaches, enables both high standard accuracies and significant provable
robustness. On challenging tasks such as ImageNet, we obtain, e.g., $80.0\%$
natural accuracy and $28.2\%$ certifiable accuracy against $\ell_2$
perturbations with $r=1.0$. We release our code and models at
https://github.com/eth-sri/aces.
