# Sequential Difference Maximization: Generating Adversarial Examples via Multi-Stage Optimization

arXiv: https://arxiv.org/abs/2509.00826 · HTML: https://mlsanity.com/paper/2509.00826/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 20 references that are in the map.
- First posted on arXiv 31 Aug 2025.

## Builds on (most cited first, 7 of 7)

- [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)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Towards Evaluating the Robustness of Neural Networks](https://mlsanity.com/paper/1608.04644/) (2016)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Boosting Adversarial Training via Fisher-Rao Norm-based Regularization](https://mlsanity.com/paper/2403.17520/) (2024)

## Abstract (arXiv)

Efficient adversarial attack methods are critical for assessing the robustness of computer vision models. In this paper, we reconstruct the optimization objective for generating adversarial examples as "maximizing the difference between the non-true labels' probability upper bound and the true label's probability," and propose a gradient-based attack method termed Sequential Difference Maximization (SDM). SDM establishes a three-layer optimization framework of "cycle-stage-step." The processes between cycles and between iterative steps are respectively identical, while optimization stages differ in terms of loss functions: in the initial stage, the negative probability of the true label is used as the loss function to compress the solution space; in subsequent stages, we introduce the Directional Probability Difference Ratio (DPDR) loss function to gradually increase the non-true labels' probability upper bound by compressing the irrelevant labels' probabilities. Experiments demonstrate that compared with previous SOTA methods, SDM not only exhibits stronger attack performance but also achieves higher attack cost-effectiveness. Additionally, SDM can be combined with adversarial training methods to enhance their defensive effects. The code is available at https://github.com/X-L-Liu/SDM.