# Is Certifying ℓp Robustness Still Worthwhile?

arXiv: https://arxiv.org/abs/2310.09361 · HTML: https://mlsanity.com/paper/2310.09361/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 93 of its 117 references that are in the map.
- First posted on arXiv 13 Oct 2023.

## Builds on (most cited first, 30 of 93)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [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)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Universal and Transferable Adversarial Attacks on Aligned Language Models](https://mlsanity.com/paper/2307.15043/) (2023)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Jailbroken: How Does LLM Safety Training Fail?](https://mlsanity.com/paper/2307.02483/) (2023)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (2020)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Adversarial Examples Are Not Bugs, They Are Features](https://mlsanity.com/paper/1905.02175/) (2019)
- [AugMix: A Simple Data Processing Method to Improve Robustness and Uncertainty](https://mlsanity.com/paper/1912.02781/) (2019)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Ensemble Adversarial Training: Attacks and Defenses](https://mlsanity.com/paper/1705.07204/) (2017)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Aligning AI With Shared Human Values](https://mlsanity.com/paper/2008.02275/) (2020)
- [Square Attack: a query-efficient black-box adversarial attack via random search](https://mlsanity.com/paper/1912.00049/) (2019)
- [RobustBench: a standardized adversarial robustness benchmark](https://mlsanity.com/paper/2010.09670/) (2020)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [On Evaluating Adversarial Robustness](https://mlsanity.com/paper/1902.06705/) (2019)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Adversarially Robust Generalization Requires More Data](https://mlsanity.com/paper/1804.11285/) (2018)
- [Do Adversarially Robust ImageNet Models Transfer Better?](https://mlsanity.com/paper/2007.08489/) (2020)
- [Are aligned neural networks adversarially aligned?](https://mlsanity.com/paper/2306.15447/) (2023)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)

## Built on by (most cited first, 1 of 1)

- [Towards Generalized Certified Robustness with Multi-Norm Training](https://mlsanity.com/paper/2410.03000/) (2024)

## Abstract (arXiv)

Over the years, researchers have developed myriad attacks that exploit the ubiquity of adversarial examples, as well as defenses that aim to guard against the security vulnerabilities posed by such attacks. Of particular interest to this paper are defenses that provide provable guarantees against the class of ℓp-bounded attacks. Certified defenses have made significant progress, taking robustness certification from toy models and datasets to large-scale problems like ImageNet classification. While this is undoubtedly an interesting academic problem, as the field has matured, its impact in practice remains unclear, thus we find it useful to revisit the motivation for continuing this line of research. There are three layers to this inquiry, which we address in this paper: (1) why do we care about robustness research? (2) why do we care about the ℓp-bounded threat model? And (3) why do we care about certification as opposed to empirical defenses? In brief, we take the position that local robustness certification indeed confers practical value to the field of machine learning. We focus especially on the latter two questions from above. With respect to the first of the two, we argue that the ℓp-bounded threat model acts as a minimal requirement for safe application of models in security-critical domains, while at the same time, evidence has mounted suggesting that local robustness may lead to downstream external benefits not immediately related to robustness. As for the second, we argue that (i) certification provides a resolution to the cat-and-mouse game of adversarial attacks; and furthermore, that (ii) perhaps contrary to popular belief, there may not exist a fundamental trade-off between accuracy, robustness, and certifiability, while moreover, certified training techniques constitute a particularly promising way for learning robust models.