# On the Perils of Cascading Robust Classifiers

arXiv: https://arxiv.org/abs/2206.00278 · HTML: https://mlsanity.com/paper/2206.00278/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 34 references that are in the map.
- First posted on arXiv 1 Jun 2022.

## Builds on (most cited first, 22 of 22)

- [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)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networks](https://mlsanity.com/paper/1702.01135/) (2017)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [Efficient Neural Network Robustness Certification with General Activation Functions](https://mlsanity.com/paper/1811.00866/) (2018)
- [On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models](https://mlsanity.com/paper/1810.12715/) (2018)
- [Certified Defenses against Adversarial Examples](https://mlsanity.com/paper/1801.09344/) (2018)
- [Towards Fast Computation of Certified Robustness for ReLU Networks](https://mlsanity.com/paper/1804.09699/) (2018)
- [Improving Adversarial Robustness via Promoting Ensemble Diversity](https://mlsanity.com/paper/1901.08846/) (2019)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (2018)
- [Adversarial Examples Are a Natural Consequence of Test Error in Noise](https://mlsanity.com/paper/1901.10513/) (2019)
- [Globally-Robust Neural Networks](https://mlsanity.com/paper/2102.08452/) (2021)
- [DVERGE: Diversifying Vulnerabilities for Enhanced Robust Generation of Ensembles](https://mlsanity.com/paper/2009.14720/) (2020)
- [Improving Adversarial Robustness of Ensembles with Diversity Training](https://mlsanity.com/paper/1901.09981/) (2019)
- [On the Certified Robustness for Ensemble Models and Beyond](https://mlsanity.com/paper/2107.10873/) (2021)
- [EMPIR: Ensembles of Mixed Precision Deep Networks for Increased Robustness against Adversarial Attacks](https://mlsanity.com/paper/2004.10162/) (2020)
- [Provable Certificates for Adversarial Examples: Fitting a Ball in the Union of Polytopes](https://mlsanity.com/paper/1903.08778/) (2019)
- [Fast Geometric Projections for Local Robustness Certification](https://mlsanity.com/paper/2002.04742/) (2020)
- [Voting based ensemble improves robustness of defensive models](https://mlsanity.com/paper/2011.14031/) (2020)
- [Enhancing Certifiable Robustness via a Deep Model Ensemble](https://mlsanity.com/paper/1910.14655/) (2019)
- [Boosting Barely Robust Learners: A New Perspective on Adversarial Robustness](https://mlsanity.com/paper/2202.05920/) (2022)

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

- [Building Production-Ready Probes For Gemini](https://mlsanity.com/paper/2601.11516/) (2026)

## Abstract (arXiv)

Ensembling certifiably robust neural networks is a promising approach for improving the certified robust accuracy of neural models. Black-box ensembles that assume only query-access to the constituent models (and their robustness certifiers) during prediction are particularly attractive due to their modular structure. Cascading ensembles are a popular instance of black-box ensembles that appear to improve certified robust accuracies in practice. However, we show that the robustness certifier used by a cascading ensemble is unsound. That is, when a cascading ensemble is certified as locally robust at an input x (with respect to ε), there can be inputs x' in the ε-ball centered at x, such that the cascade's prediction at x' is different from x and thus the ensemble is not locally robust. Our theoretical findings are accompanied by empirical results that further demonstrate this unsoundness. We present cascade attack (CasA), an adversarial attack against cascading ensembles, and show that: (1) there exists an adversarial input for up to 88% of the samples where the ensemble claims to be certifiably robust and accurate; and (2) the accuracy of a cascading ensemble under our attack is as low as 11% when it claims to be certifiably robust and accurate on 97% of the test set. Our work reveals a critical pitfall of cascading certifiably robust models by showing that the seemingly beneficial strategy of cascading can actually hurt the robustness of the resulting ensemble. Our code is available at urlhttps://github.com/TristaChi/ensembleKW.