We study the asymptotic overfitting behavior of interpolation with minimum
norm ($\ell_2$ of the weights) two-layer ReLU networks for noisy univariate
regression. We show that overfitting is tempered for the $L_1$ loss, and any
$L_p$ loss for $p<2$, but catastrophic for $p\geq 2$.

研究了使用最小范数两层 ReLU 网络进行有噪单变量回归时的渐近过拟合行为，发现对于 L1 损失和 p<2 的任何 Lp 损失缓解了过拟合，但对于 p≥2 却是灾难性的。

使用浅层单变量 ReLU 网络的噪声插值学习

Noisy Interpolation Learning with Shallow Univariate ReLU Networks

This paper considers the fundamental limit of compressed sensing for i.i.d.
signal distributions and i.i.d. Gaussian measurement matrices. Its main
contribution is a rigorous characterization of the asymptotic mutual
information (MI) and minimum mean-square error (MMSE) in this setting. Under
mild technical conditions, our results show that the limiting MI and MMSE are
equal to the values predicted by the replica method from statistical physics.
This resolves a well-known problem that has remained open for over a decade.

本文考虑了压缩感知在独立同分布信号分布和独立同分布高斯测量矩阵情况下的基本限制，并在温和技术条件下严格描述了其渐近互信息和最小均方误差。结果表明，极限互信息和最小均方误差等于统计物理学中复制方法预测的值。这解决了一个长达十年的已知问题。