# Transductive Robust Learning Guarantees

arXiv: https://arxiv.org/abs/2110.10602 · HTML: https://mlsanity.com/paper/2110.10602/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 20 Oct 2021.

## Builds on (most cited first, 14 of 14)

- [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)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Unlabeled Data Improves Adversarial Robustness](https://mlsanity.com/paper/1905.13736/) (2019)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Are Labels Required for Improving Adversarial Robustness?](https://mlsanity.com/paper/1905.13725/) (2019)
- [Rademacher Complexity for Adversarially Robust Generalization](https://mlsanity.com/paper/1810.11914/) (2018)
- [VC Classes are Adversarially Robustly Learnable, but Only Improperly](https://mlsanity.com/paper/1902.04217/) (2019)
- [Adversarial examples from computational constraints](https://mlsanity.com/paper/1805.10204/) (2018)
- [Beyond Perturbations: Learning Guarantees with Arbitrary Adversarial Test Examples](https://mlsanity.com/paper/2007.05145/) (2020)
- [Black-box Certification and Learning under Adversarial Perturbations](https://mlsanity.com/paper/2006.16520/) (2020)
- [Adversarial Risk Bounds via Function Transformation](https://mlsanity.com/paper/1810.09519/) (2018)
- [Minimax Lower Bounds for Realizable Transductive Classification](https://mlsanity.com/paper/1602.03027/) (2016)
- [Towards Adversarial Robustness via Transductive Learning](https://mlsanity.com/paper/2106.08387/) (2021)

## Built on by (most cited first, 10 of 10)

- [Cross-Entropy Loss Functions: Theoretical Analysis and Applications](https://mlsanity.com/paper/2304.07288/) (2023)
- [Self-Training: A Survey](https://mlsanity.com/paper/2202.12040/) (2022)
- [Adversarially Robust Learning: A Generic Minimax Optimal Learner and Characterization](https://mlsanity.com/paper/2209.07369/) (2022)
- [A Characterization of Semi-Supervised Adversarially-Robust PAC Learnability](https://mlsanity.com/paper/2202.05420/) (2022)
- [Adversarially Robust Learning with Tolerance](https://mlsanity.com/paper/2203.00849/) (2022)
- [Adversarially Robust PAC Learnability of Real-Valued Functions](https://mlsanity.com/paper/2206.12977/) (2022)
- [Robust Empirical Risk Minimization with Tolerance](https://mlsanity.com/paper/2210.00635/) (2022)
- [PAC Learning is just Bipartite Matching (Sort of)](https://mlsanity.com/paper/2502.00607/) (2025)
- [Two Heads are Actually Better than One: Towards Better Adversarial Robustness via Transduction and Rejection](https://mlsanity.com/paper/2305.17528/) (2023)
- [Adversarially Robust PAC Learning with Optimal VC Rates](https://mlsanity.com/paper/2609.24260/) (2026)

## Abstract (arXiv)

We study the problem of adversarially robust learning in the transductive setting. For classes H of bounded VC dimension, we propose a simple transductive learner that when presented with a set of labeled training examples and a set of unlabeled test examples (both sets possibly adversarially perturbed), it correctly labels the test examples with a robust error rate that is linear in the VC dimension and is adaptive to the complexity of the perturbation set. This result provides an exponential improvement in dependence on VC dimension over the best known upper bound on the robust error in the inductive setting, at the expense of competing with a more restrictive notion of optimal robust error.