Data augmentation (DA) is a powerful workhorse for bolstering performance in modern machine learning. Specific augmentations like translations and scaling in computer vision are traditionally believed to improve generalization by generating new (artificial) data from the same distribution. However, this traditional viewpoint does not explain the success of prevalent augmentations in modern machine learning (e.g. randomized masking, cutout, mixup), that greatly alter the training data distribution. In this work, we develop a new theoretical framework to characterize the impact of a general class of DA on underparameterized and overparameterized linear model generalization. Our framework reveals that DA induces implicit spectral regularization through a combination of two distinct effects: a) manipulating the relative proportion of eigenvalues of the data covariance matrix in a training-data-dependent manner, and b) uniformly boosting the entire spectrum of the data covariance matrix through ridge regression. These effects, when applied to popular augmentations, give rise to a wide variety of phenomena, including discrepancies in generalization between over-parameterized and under-parameterized regimes and differences between regression and classification tasks. Our framework highlights the nuanced and sometimes surprising impacts of DA on generalization, and serves as a testbed for novel augmentation design.

翻译：数据增强是现代机器学习中提升性能的强大工具。传统观点认为，计算机视觉中的平移与缩放等特定增强方法，通过从相同分布生成新（人工）数据来改善泛化。然而，这种传统视角无法解释现代机器学习中流行的增强方法（如随机掩码、裁剪、混合）的成功，这些方法会显著改变训练数据分布。本文提出新的理论框架，刻画通用类数据增强对欠参数化与过参数化线性模型泛化能力的影响。该框架揭示，数据增强通过两种不同效应的组合诱发隐式谱正则化：a) 以训练数据依赖的方式操纵数据协方差矩阵特征值的相对比例，b) 通过岭回归统一增强数据协方差矩阵的完整频谱。将这些效应应用于流行增强方法时，会产生丰富多样的现象，包括过参数化与欠参数化场景下的泛化差异，以及回归任务与分类任务之间的特性差异。本文框架不仅揭示了数据增强对泛化能力产生的微妙且有时令人惊讶的影响，更为新型增强方法设计提供了测试基准。