提出二维ReLU网络的显式积分表示，实现低维无关误差逼近。
Explicit integral representations and quantitative bounds for two-layer ReLU networks
- 用调和延拓与投影构造改进型ReLU积分表示
- 在L²(D)下误差不依赖维度和次数，仅与系数和分布有关
- 关联指数核再生核希尔伯特空间，简化表示更优
本文提出一种构造二维ReLU网络显式积分表示的方法，可为任意多元多项式提供相对简洁的表达。针对一种经过优化的ReLU积分表示（涉及调和延拓与投影），给出了定量误差界。该界表明，函数在$L^{2}(/mathcal{D})$范数下的逼近误差不显式依赖于输入维度或多项式次数，而仅取决于其单项式展开的系数及分布$/mathcal{D}$。此外，论文还揭示了该表示与指数核$K(x,y)=\exp\left(\left\langle x,y\right\rangle \right)$对应的再生核希尔伯特空间（RKHS）之间的联系，并提出一种更简单的积分表示形式——额外乘以一个固定函数，具有更优的定量误差界。
原文摘要 · Abstract (English)
An approach to construct explicit integral representations for two-layer ReLU networks is presented, which provides relatively simple representations for any multivariate polynomial. Quantitative bounds are provided for a particular, sharpened ReLU integral representation, which involves a harmonic extension and a projection. The bounds demonstrate that functions can be approximated with $L^{2}(\mathcal{D})$ errors that do not depend explicitly on dimension or degree, but rather the coefficients of their monomial expansions and the distribution $\mathcal{D}$. We also present a connection to the RKHS of the exponential kernel $K(x,y)=\exp\left(\left\langle x,y\right\rangle \right)$, and a very simple integral representation involving additionally multiplication via a fixed function which has better quantitative bounds.
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