Double descent presents a counter-intuitive aspect within the machine learning domain, and researchers have observed its manifestation in various models and tasks. While some theoretical explanations have been proposed for this phenomenon in specific contexts, an accepted theory for its occurring mechanism in deep learning remains yet to be established. In this study, we revisited the phenomenon of double descent and discussed the conditions of its occurrence. This paper introduces the concept of class-activation matrices and a methodology for estimating the effective complexity of functions, on which we unveil that over-parameterized models exhibit more distinct and simpler class patterns in hidden activations compared to under-parameterized ones. We further looked into the interpolation of noisy labelled data among clean representations and demonstrated overfitting w.r.t. expressive capacity. By comprehensively analysing hypotheses and presenting corresponding empirical evidence that either validates or contradicts these hypotheses, we aim to provide fresh insights into the phenomenon of double descent and benign over-parameterization and facilitate future explorations. By comprehensively studying different hypotheses and the corresponding empirical evidence either supports or challenges these hypotheses, our goal is to offer new insights into the phenomena of double descent and benign over-parameterization, thereby enabling further explorations in the field. The source code is available at https://github.com/Yufei-Gu-451/sparse-generalization.git.

该研究重新审视了双下降现象，探讨其发生条件，并引入类激活矩阵的概念和一种估计函数有效复杂性的方法，揭示超参数化模型在隐藏激活中展现出更明显和更简单的类别模式。通过全面分析并提供相应的实证证据来验证或反驳这些假设，旨在为双下降现象和良性超参数化提供新的洞察，并促进未来的探索。

基于类别的激活解读深度双下降之谜