论文标题
双重下降的简短史无前例
A Brief Prehistory of Double Descent
论文作者
论文摘要
在发人深省的论文[1]中，Belkin等。在现代高复杂学习者的背景下说明并讨论风险曲线的形状。考虑到固定的培训样本量$ n $，此类曲线表明了学习者的风险是其复杂性$ n $的某些（近似）度量的函数。使用$ n $功能的数量，这些曲线也称为特征曲线。 [1]中的一个显着观察是，这些曲线可以显示，他们所谓的，双重下降：随着$ n $的增加，风险最初会降低，最低降低，然后增加，直到$ n $等于$ n $，其中培训数据完美地拟合。增加$ n $的增加，风险降低了第二次也是最后一次，在$ n = n $中造成了峰值。这个双重下降可能会令人惊讶，但与[1]报告相比，历史上没有被忽视。我们的信提请人们注意当代机器学习感兴趣的一些原始的，早期的发现。
In their thought-provoking paper [1], Belkin et al. illustrate and discuss the shape of risk curves in the context of modern high-complexity learners. Given a fixed training sample size $n$, such curves show the risk of a learner as a function of some (approximate) measure of its complexity $N$. With $N$ the number of features, these curves are also referred to as feature curves. A salient observation in [1] is that these curves can display, what they call, double descent: with increasing $N$, the risk initially decreases, attains a minimum, and then increases until $N$ equals $n$, where the training data is fitted perfectly. Increasing $N$ even further, the risk decreases a second and final time, creating a peak at $N=n$. This twofold descent may come as a surprise, but as opposed to what [1] reports, it has not been overlooked historically. Our letter draws attention to some original, earlier findings, of interest to contemporary machine learning.
