自监督预训练中相关样本汇聚的统计理论分析

Translation Process: Self-Supervised Learning Abstract

Okay, let's see. My task is to translate this abstract into Simplified Chinese, preserving the technical meaning and format. First, I need to understand the gist. This is about self-supervised learning, data augmentation, and comparing pooling augmentations versus partitioning data. Alright, sounds straightforward enough.

I'll start by segmenting the text and translating each part, paying close attention to the technical terms. "Self-supervised learning" I'll keep as 自监督学习. "Data augmentation," I'll translate as 数据增强. The math notations like $\phi(x)$ and $\cal V$ must be maintained, as these are critical. I see the term "invariant subspace" (不变子空间) is important for downstream tasks. So, the first sentence is about how data augmentation is used to learn a low-complexity invariant subspace.

Next, I see the concept of "pooling augmentations" (增强样本汇集在一起). This seems to be the core idea. The text says there are dependencies between the augmentations of the same data point, but they're pooled anyway. Theoretical works tend to avoid these dependencies, working on subsets of independent data. I have to make sure to capture that nuance. The term "pooling augmentations" I should translate as “汇集增强样本” , and I'll keep “分割基线” for "partitioning baseline."

The text then says we show that pooling is better. "Better" than what? Ah, partitioning the data into independent subsets. That's the baseline. And it looks like the statistical estimation error bounds are never worse for pooling. In fact, in some cases, "naive pooling" leads to "faster rates." Now I need to consider an appropriate Chinese translation for "faster rates", I need to translate it as "更快的收敛速率" because the context is about convergence in terms of the number of augmentations.

Finally, the benefits of pooling are particularly prominent when the correlations between augmentations are mild or help decrease estimation variance. It's about how this all gives us new insights into why pooling augmented samples works in self-supervised pre-training. And it provides an intuition behind using a lot of augmentations. Okay, so that’s a direct translation for the whole paragraph. Time to refine and polish. I'll make sure the flow is natural and technically accurate in Chinese. Math symbols look good. Paragraph breaks are correct. No extraneous commentary is needed, just the translation. Now I'll do a final review.

自监督学习依赖于对无标签数据点 $x$ 进行的所谓数据增强 $φ(x)$——例如掩蔽图像 $x$ 中的随机像素——这些增强应保持 $x$ 的标签不变，且通常用于为下游任务学习一个较低复杂度的不变子空间 $\cal V$。在实践中，尽管同一数据点 $x$ 的不同增强 $φ_l(x), φ_k(x)$ 之间存在明显的相互依赖性，人们仍会将这些增强样本 ${ φ_l(x_i) }$ 汇集在一起以学习 $\cal V$。然而，该领域相关的理论研究通常考虑避开此类依赖性的方法，因此局限于在规模较小的独立数据子集上进行操作。我们在本研究中表明，尽管存在相互依赖性，但相较于将数据划分为独立数据子集的基准方法，将增强样本汇集在一起是一个更优的选择。更具体地说，在估计 $\cal V$ 的背景下，汇集方法的统计估计误差界绝不劣于划分基线，并且在某些情况下——例如在浅层神经网络上基于掩蔽或噪声注入的增强——就增强数量而言，朴素汇集能带来更快的收敛速率。当不同增强 $φ_l(x), φ_k(x)$ 之间的相关性对估计的影响较小，或有助于降低估计方差时，汇集带来的优势尤为显著。因此，该分析为自监督预训练中汇集增强样本的成功提供了新的见解，并为实践中偏好使用大量增强样本的现象提供了直观的理论依据。