Design of Energy-Efficient Threshold Circuits Based on Biological Information Processing, and its limitation

本文将阈值电路作为神经网络的理论模型，研究了阈值电路的能量、大小和深度之间的关系。我们得到了以下两个结果：1）证明了计算MOD函数的阈值电路的能量复杂度与电路规模之间存在一个紧密的折衷关系; 2）证明了如果一个函数可以用一个能量复杂度小的阈值电路来计算，那么这个函数也可以用一个深度小的阈值电路来计算。

We consider a threshold circuit as a theoretical model of a neural network, and study a relationship among its energy, size and depth. We obtain the following two results : 1) we prove that there exists a tight tradeoff between energy complexity and size of threshold circuits computing MOD functions ; 2) we prove that if a function can be computed by a threshold circuit of small energy complexity, then the function can be computed by a threshold circuit of small depth, too.