Research Initiation Award: Comparisons of Deterministic/ Stochastic Neural Network Computing for Solving NP-Complete Problems

本文主要研究了一种基于神经网络的高度并行分布式处理系统。所研究的神经网络利用了分散控制的柯西机爬坡能力和Hopfield网络的快速收敛特性。能量代价函数的重新表述和神经网络的适当权值是减小局部极小值的关键。许多用于解决np完全问题的神经网络采用梯度下降算法。虽然收敛速度快，但系统很容易陷入局部极小值。采用模拟退火的神经网络得到了较好的结果，但收敛速度很慢。该算法利用了Hopfield网络的快速收敛性和Boltzmann机器的爬坡性，由s型神经元和随机突触连接组成。这样的研究将进一步加深我们在将神经网络映射到VLSI方面的知识，并产生更有效的学习算法。因此，强烈建议提供支持。

This research focuses on studying a highly parallel distributed processing system based on neural networks with and without simulated annealing. The neural network under investigation takes advantage of the hill-climbing capability of Cauchy machines with decentralized control and the fast convergence property of Hopfield networks. A reformulation of an energy cost function and appropriate weights of the neural network are crucial to reducing local minima. Many neural networks used in solving NP-complete problems apply a gradient descent algorithm. Although convergence is fast, it is very easy for the system to be trapped in a local minimum. Neural networks employing simulated annealing give better results but converge very slowly. The proposed Gaussian machine, which is composed of sigmoid neurons and stochastic synaptic links, takes advantage of the fast convergence property of the Hopfield network and the hill-climbing property of the Boltzmann machine. Such a study will further our knowledge in mapping neural networks to VLSI and result in more efficient learning algorithms. Support is, therefore, highly recommended.