The relationship between the number of training data points, the number of parameters, and the generalization capabilities has been widely studied. Previous work has shown that double descent can occur in the over-parameterized regime, and believe that the standard bias-variance trade-off holds in the under-parameterized regime. These works provide multiple reasons for the existence of the peak. We postulate that the location of the peak depends on the technical properties of both the spectrum as well as the eigenvectors of the sample covariance. We present two simple examples that provably exhibit double descent in the under-parameterized regime and do not seem to occur for reasons provided in prior work.

翻译：训练数据点数量、参数数量与泛化能力之间的关系已被广泛研究。先前工作表明双下降现象可能出现在过参数化区域，并认为标准偏差-方差权衡在欠参数化区域成立。这些研究为峰值的存在提供了多种解释。我们假设峰值的位置取决于样本协方差矩阵谱特征与特征向量的技术特性。我们提出两个简单示例，可证明在欠参数化区域出现双下降现象，且其成因似乎无法用现有理论解释。