Neural networks successfully capture the computational power of the human brain for many tasks. Similarly inspired by the brain architecture, Nearest Neighbor (NN) representations is a novel approach of computation. We establish a firmer correspondence between NN representations and neural networks. Although it was known how to represent a single neuron using NN representations, there were no results even for small depth neural networks. Specifically, for depth-2 threshold circuits, we provide explicit constructions for their NN representation with an explicit bound on the number of bits to represent it. Example functions include NN representations of convex polytopes (AND of threshold gates), IP2, OR of threshold gates, and linear or exact decision lists.

翻译：神经网络成功捕捉了人脑在许多任务中的计算能力。同样受大脑架构启发，最近邻（NN）表示是一种新颖的计算方法。我们建立了NN表示与神经网络之间更紧密的对应关系。尽管已知如何用NN表示单个神经元，但即使对于小深度神经网络此前也没有相关结果。具体而言，对于深度为2的阈值电路，我们提供了其NN表示的显式构造，并给出了表示所需比特数的显式界限。示例函数包括凸多面体（阈值门与运算）、IP2、阈值门或运算以及线性或精确决策列表的NN表示。