# An Ensemble Approach Towards Adversarial Robustness

arXiv: https://arxiv.org/abs/2106.05996 · HTML: https://mlsanity.com/paper/2106.05996/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 25 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 18 of 18)

- [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)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Obfuscated Gradients Give a False Sense of Security: Circumventing Defenses to Adversarial Examples](https://mlsanity.com/paper/1802.00420/) (2018)
- [Robustness May Be at Odds with Accuracy](https://mlsanity.com/paper/1805.12152/) (2018)
- [Provable defenses against adversarial examples via the convex outer adversarial polytope](https://mlsanity.com/paper/1711.00851/) (2017)
- [On Adaptive Attacks to Adversarial Example Defenses](https://mlsanity.com/paper/2002.08347/) (2020)
- [Adversarial Examples Are Not Easily Detected: Bypassing Ten Detection Methods](https://mlsanity.com/paper/1705.07263/) (2017)
- [Decision-Based Adversarial Attacks: Reliable Attacks Against Black-Box Machine Learning Models](https://mlsanity.com/paper/1712.04248/) (2017)
- [Generating Natural Language Adversarial Examples](https://mlsanity.com/paper/1804.07998/) (2018)
- [Audio Adversarial Examples: Targeted Attacks on Speech-to-Text](https://mlsanity.com/paper/1801.01944/) (2018)
- [Formal Guarantees on the Robustness of a Classifier against Adversarial Manipulation](https://mlsanity.com/paper/1705.08475/) (2017)
- [Scaling provable adversarial defenses](https://mlsanity.com/paper/1805.12514/) (2018)
- [Towards the first adversarially robust neural network model on MNIST](https://mlsanity.com/paper/1805.09190/) (2018)
- [L2-Nonexpansive Neural Networks](https://mlsanity.com/paper/1802.07896/) (2018)
- [Neural Belief Reasoner](https://mlsanity.com/paper/1909.04719/) (2019)

## Abstract (arXiv)

It is a known phenomenon that adversarial robustness comes at a cost to natural accuracy. To improve this trade-off, this paper proposes an ensemble approach that divides a complex robust-classification task into simpler subtasks. Specifically, fractal divide derives multiple training sets from the training data, and fractal aggregation combines inference outputs from multiple classifiers that are trained on those sets. The resulting ensemble classifiers have a unique property that ensures robustness for an input if certain don't-care conditions are met. The new techniques are evaluated on MNIST and Fashion-MNIST, with no adversarial training. The MNIST classifier has 99% natural accuracy, 70% measured robustness and 36.9% provable robustness, within L2 distance of 2. The Fashion-MNIST classifier has 90% natural accuracy, 54.5% measured robustness and 28.2% provable robustness, within L2 distance of 1.5. Both results are new state of the art, and we also present new state-of-the-art binary results on challenging label-pairs.