  Successful adoption of deep learning (DL) in the wild requires models to be:
(1) compact, (2) accurate, and (3) robust to distributional shifts.
Unfortunately, efforts towards simultaneously meeting these requirements have
mostly been unsuccessful. This raises an important question: Is the inability
to create Compact, Accurate, and Robust Deep neural networks (CARDs)
fundamental? To answer this question, we perform a large-scale analysis of
popular model compression techniques which uncovers several intriguing
patterns. Notably, in contrast to traditional pruning approaches (e.g., fine
tuning and gradual magnitude pruning), we find that "lottery ticket-style"
approaches can surprisingly be used to produce CARDs, including binary-weight
CARDs. Specifically, we are able to create extremely compact CARDs that,
compared to their larger counterparts, have similar test accuracy and matching
(or better) robustness -- simply by pruning and (optionally) quantizing.
Leveraging the compactness of CARDs, we develop a simple domain-adaptive
test-time ensembling approach (CARD-Decks) that uses a gating module to
dynamically select appropriate CARDs from the CARD-Deck based on their
spectral-similarity with test samples. The proposed approach builds a "winning
hand'' of CARDs that establishes a new state-of-the-art (on RobustBench) on
CIFAR-10-C accuracies (i.e., 96.8% standard and 92.75% robust) and CIFAR-100-C
accuracies (80.6% standard and 71.3% robust) with better memory usage than
non-compressed baselines (pretrained CARDs and CARD-Decks available at
https://github.com/RobustBench/robustbench). Finally, we provide theoretical
support for our empirical findings.
