Convergence Experiments Of Hopfield Networks With Serial And Parallel Operation Modes

Neural network algorithms come from highly idealized neuron models,and the use of neural networks for research has become more and more successful and popular.For many applications,neural network-based algorithms are considered the preferred method.Since the synchronous parallel processing capability of the chip in the physical system has advantages in time,considering that the neural network also has the capability of group computing problems,its synchronous parallel processing capability is also our research hotspot.The Hopfield network is based on Hebb's rule and is a dynamic or cyclic network with memory function.Because it is closely related to the statistical physics of spin glass,it is highly concerned by physicists,which also makes it possible to carry out precise mathematical understanding.Hopfield network is an important foundation for the development of computer science.Discrete Hopfield neural networks have two operating modes: serial and parallel.Under the same problem,there are few studies on the performance comparison of these two operating modes.In this regard,this paper uses two operating modes of the discrete Hopfield network to solve the image restoration and traveling salesman problem(TSP),aiming to obtain the relative performance comparison results of the two operating modes on each problem.In the TSP problem,different city sizes will affect the results of the implementation of the network.In order to reduce the computational complexity,the number of cities is set to 10,and the location information of the cities is randomly selected on the grid.After 30 runs,the convergence rate and running time of the two methods are compared..The convergence rate of the serial mode is 80%;the convergence rate of the parallel mode is 26.6%.In the case of convergence,the average time of the serial mode is 5.7901 s,and the average time of the parallel mode is 2.8299 s.It can be seen that the serial mode is about twice as long as the parallel mode..Numerical experiment results show that there is a trade-off between the convergence domain and the running time.The serial convergence rate is high but the running time is long,while the parallel convergence rate is low but the running time is short.For the problem of image restoration,images in different environments and different levels of noise processing will affect the restoration results of the Hopfield network.This is mainly to understand the performance of the two operating modes of the discrete Hopfield network.The image data uses a binary image,and the image is two-valued.Various methods of noise processing(local noise and complete noise)adjust the appropriate threshold parameters according to the image restoration effect.The recovery results show that the two operating modes can restore the image.The number of iterations required in parallel mode is less than 10,and the number of iterations required in serial mode is more than 3000.The greater the degree of image interference by noise,the required number of iterations more.