【报告摘要】Recently, the double descent phenomenon has been widely observed, where the generalization error first   decreases, then increases, and surprisingly decreases again as model size grows. While a growing body of theoretical work has sought to explain this behavior,   the underlying mechanism of this phenomenon remains unclear. Motivated by the double ascent behavior observed in high-dimensional hypothesis tests and linear regression,   we establish a connection between the occurrence of double descent and the generalized inverse of the sample covariance matrix. Leveraging  random matrix theory, we provide a mechanistic understanding of the double descent/ascent phenomenon through    the convergence of the eigenvalues of the sample covariance matrix. Building on this insight, we propose a regularization method to eliminate the double ascent phenomenon so that the generalization error always   decreases as model size grows, and demonstrate its effectiveness through simulation studies.

【报告人简介】郑术蓉，东北师范大学教授。主要研究方向为：大维随机矩阵理论及高维统计分析。曾在统计学顶级期刊 Annals of Statistics , Journal of the American Statistical Association, Biometrika 等上发表多篇与大维随机矩阵理论相关的学术论文。现任 Statistica Sinica, Journal of Business & Economic Statistics, Journal of Multivariate Analysis 等6个学术期刊编委。