Randomized smoothing is considered to be the state-of-the-art provable defense against adversarial perturbations. However, it heavily exploits the fact that classifiers map input objects to class probabilities and do not focus on the ones that learn a metric space in which classification is performed by computing distances to embeddings of classes prototypes. In this work, we extend randomized smoothing to few-shot learning models that map inputs to normalized embeddings. We provide analysis of Lipschitz continuity of such models and derive robustness certificate against $\ell_2$-bounded perturbations that may be useful in few-shot learning scenarios. Our theoretical results are confirmed by experiments on different datasets.

翻译：随机平滑被认为是最先进的对抗性扰动防御。 但是,它大量利用了一个事实,即分类者将输入对象映射成分级概率,而不是侧重于那些通过计算距离进行分类的计量空间到分类原型嵌入空间。在这项工作中,我们将随机平滑推广到几张将输入映射成正常嵌入的微小学习模型上。我们对这种模型的利普施奇茨连续性进行了分析,并用$@ell_2$在几近的学习情景中可能有用的强力测试。我们的理论结果得到了不同数据集实验的证实。