Smoothed Embeddings for Certified Few-Shot Learning

Mikhail Pautov, Olesya Kuznetsova, Nurislam Tursynbek, Aleksandr Petiushko, Ivan Oseledets

Keywords: Certified robustness, randomized smoothing, few-shot learning

Abstract: 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 class prototypes. In this work, we extend randomized smoothing to few-shot learning models that map inputs to normalized embeddings. We provide analysis of the Lipschitz continuity of such models and derive a 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.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2202.01186/code)