# Smoothed Embeddings for Certified Few-Shot Learning

arXiv: https://arxiv.org/abs/2202.01186 · HTML: https://mlsanity.com/paper/2202.01186/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 72 references that are in the map.
- First posted on arXiv 2 Feb 2022.

## Builds on (most cited first, 30 of 46)

- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [DeepFool: a simple and accurate method to fool deep neural networks](https://mlsanity.com/paper/1511.04599/) (2015)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Certified Robustness to Adversarial Examples with Differential Privacy](https://mlsanity.com/paper/1802.03471/) (2018)
- [Meta-learning with differentiable closed-form solvers](https://mlsanity.com/paper/1805.08136/) (2018)
- [Mitigating Adversarial Effects Through Randomization](https://mlsanity.com/paper/1711.01991/) (2017)
- [Provably Robust Deep Learning via Adversarially Trained Smoothed Classifiers](https://mlsanity.com/paper/1906.04584/) (2019)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Meta-Dataset: A Dataset of Datasets for Learning to Learn from Few Examples](https://mlsanity.com/paper/1903.03096/) (2019)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Adversarial Examples for Semantic Segmentation and Object Detection](https://mlsanity.com/paper/1703.08603/) (2017)
- [Formal Verification of Piece-Wise Linear Feed-Forward Neural Networks](https://mlsanity.com/paper/1705.01320/) (2017)
- [Certified Adversarial Robustness with Additive Noise](https://mlsanity.com/paper/1809.03113/) (2018)
- [Efficient Decision-based Black-box Adversarial Attacks on Face Recognition](https://mlsanity.com/paper/1904.04433/) (2019)
- [Stochastic Activation Pruning for Robust Adversarial Defense](https://mlsanity.com/paper/1803.01442/) (2018)
- [AdvHat: Real-world adversarial attack on ArcFace Face ID system](https://mlsanity.com/paper/1908.08705/) (2019)
- [Towards Robust Neural Networks via Random Self-ensemble](https://mlsanity.com/paper/1712.00673/) (2017)
- [Making an Invisibility Cloak: Real World Adversarial Attacks on Object Detectors](https://mlsanity.com/paper/1910.14667/) (2019)
- [Randomized Smoothing of All Shapes and Sizes](https://mlsanity.com/paper/2002.08118/) (2020)

## Built on by (most cited first, 6 of 6)

- [The Lipschitz-Variance-Margin Tradeoff for Enhanced Randomized Smoothing](https://mlsanity.com/paper/2309.16883/) (2023)
- [Certification of Speaker Recognition Models to Additive Perturbations](https://mlsanity.com/paper/2404.18791/) (2024)
- [RS-Reg: Probabilistic and Robust Certified Regression Through Randomized Smoothing](https://mlsanity.com/paper/2405.08892/) (2024)
- [FCert: Certifiably Robust Few-Shot Classification in the Era of Foundation Models](https://mlsanity.com/paper/2404.08631/) (2024)
- [Provably Robust Adaptation for Language-Empowered Foundation Models](https://mlsanity.com/paper/2510.08659/) (2025)
- [Contract And Conquer: How to Provably Compute Adversarial Examples for a Black-Box Model?](https://mlsanity.com/paper/2603.10689/) (2026)

## Abstract (arXiv)

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 ℓ2-bounded perturbations that may be useful in few-shot learning scenarios. Our theoretical results are confirmed by experiments on different datasets.