# SDM: A Powerful Tool for Evaluating Model Robustness

arXiv: https://arxiv.org/abs/2605.20308 · HTML: https://mlsanity.com/paper/2605.20308/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 19 May 2026.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [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)
- [Adversarial examples in the physical world](https://mlsanity.com/paper/1607.02533/) (2016)
- [Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks](https://mlsanity.com/paper/2003.01690/) (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)
- [Minimally distorted Adversarial Examples with a Fast Adaptive Boundary Attack](https://mlsanity.com/paper/1907.02044/) (2019)
- [EAD: Elastic-Net Attacks to Deep Neural Networks via Adversarial Examples](https://mlsanity.com/paper/1709.04114/) (2017)
- [Advances in adversarial attacks and defenses in computer vision: A survey](https://mlsanity.com/paper/2108.00401/) (2021)
- [Adversarial Robustness Limits via Scaling-Law and Human-Alignment Studies](https://mlsanity.com/paper/2404.09349/) (2024)
- [Boosting Adversarial Training via Fisher-Rao Norm-based Regularization](https://mlsanity.com/paper/2403.17520/) (2024)

## Abstract (arXiv)

Gradient-based attacks are important methods for evaluating model robustness. However, since the proposal of APGD, it has been difficult for such methods to achieve significant breakthroughs. To achieve such an effect, we first analyze the issue of "high-loss non-adversarial examples" that degrades attack performance in previous methods, and prove that this issue arises from inappropriate objectives for adversarial example generation. Subsequently, we reconstruct the objective as "maximizing the difference between the non-ground-truth label probability upper bound and the ground-truth label probability", and proposes a novel and powerful gradient-based attack method named Sequential Difference Maximization (SDM). SDM establishes a three-layer optimization framework of "cycle-stage-step". It adopts the negative probability loss function and the Directional Probability Difference Ratio (DPDR) loss function in the initial and subsequent optimization stages, respectively, and approaches the ideal objective of adversarial example generation via stage-wise sequential optimization. Experiments demonstrate that compared with previous state-of-the-art methods, SDM not only achieves stronger attack performance but also exhibits superior cost-effectiveness. The code is available at https://github.com/X-L-Liu/ICML-SDM.