Hopfield J J, Tank D W
Biol Cybern. 1985;52(3):141-52. doi: 10.1007/BF00339943.
Highly-interconnected networks of nonlinear analog neurons are shown to be extremely effective in computing. The networks can rapidly provide a collectively-computed solution (a digital output) to a problem on the basis of analog input information. The problems to be solved must be formulated in terms of desired optima, often subject to constraints. The general principles involved in constructing networks to solve specific problems are discussed. Results of computer simulations of a network designed to solve a difficult but well-defined optimization problem--the Traveling-Salesman Problem--are presented and used to illustrate the computational power of the networks. Good solutions to this problem are collectively computed within an elapsed time of only a few neural time constants. The effectiveness of the computation involves both the nonlinear analog response of the neurons and the large connectivity among them. Dedicated networks of biological or microelectronic neurons could provide the computational capabilities described for a wide class of problems having combinatorial complexity. The power and speed naturally displayed by such collective networks may contribute to the effectiveness of biological information processing.
高度互联的非线性模拟神经元网络在计算方面显示出极高的效率。这些网络能够基于模拟输入信息迅速为一个问题提供集体计算出的解决方案（数字输出）。待解决的问题必须依据期望的最优解来表述，且常常受到约束条件的限制。文中讨论了构建用于解决特定问题的网络所涉及的一般原则。给出了一个旨在解决一个困难但定义明确的优化问题——旅行商问题——的网络的计算机模拟结果，并用以说明这些网络的计算能力。在仅几个神经时间常数的时间内就能集体计算出该问题的良好解决方案。计算的有效性既涉及神经元的非线性模拟响应，也涉及它们之间的高度连接性。生物或微电子神经元的专用网络可为具有组合复杂性的广泛一类问题提供所述的计算能力。此类集体网络自然展现出的能力和速度可能有助于生物信息处理的有效性。
