LOTOS: Layer-wise Orthogonalization for Training Robust Ensembles

TL;DR

This paper introduces LOTOS, a novel ensemble training method that promotes orthogonality among model transformations to improve robustness against adversarial attacks, outperforming existing techniques.

Contribution

LOTOS is a new training paradigm that enhances ensemble robustness by orthogonalizing model sub-spaces, counteracting the transferability increase caused by low Lipschitz constants.

Findings

Increases robust accuracy of ResNet-18 ensembles by 6 percentage points against black-box attacks.

Combines with prior methods to improve robust accuracy by 10.7 percentage points.

Theoretically shows that small $k$ suffices for convolutional layers, with negligible computational overhead.

Abstract

Transferability of adversarial examples is a well-known property that endangers all classification models, even those that are only accessible through black-box queries. Prior work has shown that an ensemble of models is more resilient to transferability: the probability that an adversarial example is effective against most models of the ensemble is low. Thus, most ongoing research focuses on improving ensemble diversity. Another line of prior work has shown that Lipschitz continuity of the models can make models more robust since it limits how a model's output changes with small input perturbations. In this paper, we study the effect of Lipschitz continuity on transferability rates. We show that although a lower Lipschitz constant increases the robustness of a single model, it is not as beneficial in training robust ensembles as it increases the transferability rate of adversarial examples across models in the ensemble. Therefore, we introduce LOTOS, a new training paradigm for ensembles, which counteracts this adverse effect. It does so by promoting orthogonality among the top-$k$ sub-spaces of the transformations of the corresponding affine layers of any pair of models in the ensemble. We theoretically show that $k$ does not need to be large for convolutional layers, which makes the computational overhead negligible. Through various experiments, we show LOTOS increases the robust accuracy of ensembles of ResNet-18 models by $6$ percentage points (p.p) against black-box attacks on CIFAR-10. It is also capable of combining with the robustness of prior state-of-the-art methods for training robust ensembles to enhance their robust accuracy by $10.7$ p.p.