Neural networks with finitely many fixed weights have the universal approximation property under certain conditions on compact subsets of the d-dimensional Euclidean space, where approximation process is considered. Such conditions were delineated in our paper [26]. But for many compact sets it is impossible to approximate multivariate functions with arbitrary precision and the question on estimation or efficient computation of approximation error arises. This paper provides an explicit formula for the approximation error of single hidden layer neural networks with two fixed weights.

中文翻译：

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固定权值单隐层神经网络的逼近误差

具有有限多个固定权重的神经网络在d维欧几里德空间的紧子集上的某些条件下具有通用逼近性质，其中考虑了逼近过程。我们的论文[26]中描述了此类条件。但对于许多紧集，不可能以任意精度逼近多元函数，并且出现了估计或有效计算逼近误差的问题。本文提供了具有两个固定权重的单隐层神经网络的逼近误差的显式公式。