  Adversarial robustness often comes at the cost of degraded accuracy, impeding
the real-life application of robust classification models. Training-based
solutions for better trade-offs are limited by incompatibilities with
already-trained high-performance large models, necessitating the exploration of
training-free ensemble approaches. Observing that robust models are more
confident in correct predictions than in incorrect ones on clean and
adversarial data alike, we speculate amplifying this "benign confidence
property" can reconcile accuracy and robustness in an ensemble setting. To
achieve so, we propose "MixedNUTS", a training-free method where the output
logits of a robust classifier and a standard non-robust classifier are
processed by nonlinear transformations with only three parameters, which are
optimized through an efficient algorithm. MixedNUTS then converts the
transformed logits into probabilities and mixes them as the overall output. On
CIFAR-10, CIFAR-100, and ImageNet datasets, experimental results with custom
strong adaptive attacks demonstrate MixedNUTS's vastly improved accuracy and
near-SOTA robustness -- it boosts CIFAR-100 clean accuracy by 7.86 points,
sacrificing merely 0.87 points in robust accuracy.
