Deep neural networks (DNNs) have demonstrated promising results in various
complex tasks. However, current DNNs encounter challenges with
over-parameterization, especially when there is limited training data
available. To enhance the generalization capability of DNNs, the Mixup
technique has gained popularity. Nevertheless, it still produces suboptimal
outcomes. Inspired by the successful Sharpness-Aware Minimization (SAM)
approach, which establishes a connection between the sharpness of the training
loss landscape and model generalization, we propose a new learning framework
called Generalized-Mixup, which combines the strengths of Mixup and SAM for
training DNN models. The theoretical analysis provided demonstrates how the
developed G-Mix framework enhances generalization. Additionally, to further
optimize DNN performance with the G-Mix framework, we introduce two novel
algorithms: Binary G-Mix and Decomposed G-Mix. These algorithms partition the
training data into two subsets based on the sharpness-sensitivity of each
example to address the issue of "manifold intrusion" in Mixup. Both theoretical
explanations and experimental results reveal that the proposed BG-Mix and
DG-Mix algorithms further enhance model generalization across multiple datasets
and models, achieving state-of-the-art performance.

深度神经网络（DNN）面临着超参数化的挑战，特别是在训练数据有限的情况下。为了增强 DNN 的泛化能力，我们提出了一种名为 Generalized-Mixup 的新学习框架，将 Mixup 和 Sharpness-Aware Minimization（SAM）的优势结合起来进行 DNN 模型训练。理论分析表明，开发的 G-Mix 框架可以增强泛化能力。此外，为了进一步优化 DNN 性能，我们引入了两种新算法：Binary G-Mix 和 Decomposed G-Mix。这些算法根据每个示例的锐度敏感性将训练数据划分为两个子集，以解决 Mixup 中 “流形入侵” 的问题。理论解释和实验结果均表明，所提出的 BG-Mix 和 DG-Mix 算法进一步提高了多个数据集和模型的模型泛化能力，实现了最先进的性能。