# Adaptive Adversarial Cross-Entropy Loss for Sharpness-Aware Minimization

arXiv: https://arxiv.org/abs/2406.14329 · HTML: https://mlsanity.com/paper/2406.14329/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 20 Jun 2024.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Accurate, Large Minibatch SGD: Training ImageNet in 1 Hour](https://mlsanity.com/paper/1706.02677/) (2017)
- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima](https://mlsanity.com/paper/1609.04836/) (2016)
- [Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data](https://mlsanity.com/paper/1703.11008/) (2017)
- [Entropy-SGD: Biasing Gradient Descent Into Wide Valleys](https://mlsanity.com/paper/1611.01838/) (2016)
- [A PAC-Bayesian Approach to Spectrally-Normalized Margin Bounds for Neural Networks](https://mlsanity.com/paper/1707.09564/) (2017)
- [ASAM: Adaptive Sharpness-Aware Minimization for Scale-Invariant Learning of Deep Neural Networks](https://mlsanity.com/paper/2102.11600/) (2021)
- [Surrogate Gap Minimization Improves Sharpness-Aware Training](https://mlsanity.com/paper/2203.08065/) (2022)
- [Deep Pyramidal Residual Networks](https://mlsanity.com/paper/1610.02915/) (2016)
- [Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks](https://mlsanity.com/paper/1907.04595/) (2019)
- [Stochastic gradient descent performs variational inference, converges to limit cycles for deep networks](https://mlsanity.com/paper/1710.11029/) (2017)
- [Fisher-Rao Metric, Geometry, and Complexity of Neural Networks](https://mlsanity.com/paper/1711.01530/) (2017)
- [Closing the Generalization Gap of Adaptive Gradient Methods in Training Deep Neural Networks](https://mlsanity.com/paper/1806.06763/) (2018)
- [GA-SAM: Gradient-Strength based Adaptive Sharpness-Aware Minimization for Improved Generalization](https://mlsanity.com/paper/2210.06895/) (2022)
- [Breaking Inter-Layer Co-Adaptation by Classifier Anonymization](https://mlsanity.com/paper/1906.01150/) (2019)
- [PoF: Post-Training of Feature Extractor for Improving Generalization](https://mlsanity.com/paper/2207.01847/) (2022)

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

- [EMASAM: a Computationally Efficient Sharpness-Aware Minimization via EMA-Guided Perturbations](https://mlsanity.com/paper/2608.15105/) (2026)

## Abstract (arXiv)

Recent advancements in learning algorithms have demonstrated that the sharpness of the loss surface is an effective measure for improving the generalization gap. Building upon this concept, Sharpness-Aware Minimization (SAM) was proposed to enhance model generalization and achieved state-of-the-art performance. SAM consists of two main steps, the weight perturbation step and the weight updating step. However, the perturbation in SAM is determined by only the gradient of the training loss, or cross-entropy loss. As the model approaches a stationary point, this gradient becomes small and oscillates, leading to inconsistent perturbation directions and also has a chance of diminishing the gradient. Our research introduces an innovative approach to further enhancing model generalization. We propose the Adaptive Adversarial Cross-Entropy (AACE) loss function to replace standard cross-entropy loss for SAM's perturbation. AACE loss and its gradient uniquely increase as the model nears convergence, ensuring consistent perturbation direction and addressing the gradient diminishing issue. Additionally, a novel perturbation-generating function utilizing AACE loss without normalization is proposed, enhancing the model's exploratory capabilities in near-optimum stages. Empirical testing confirms the effectiveness of AACE, with experiments demonstrating improved performance in image classification tasks using Wide ResNet and PyramidNet across various datasets. The reproduction code is available online