After more than a decade of research, there now exist several neural-network techniques for solving NP-hard combinatorial optimization problems. Hopfield networks and self-organizing maps are the two main categories into which most of the approaches can be divided. Criticism of these approaches includes the tendency of the Hopfield network to produce infeasible solutions, and the lack of genera...

In this paper, we present FPGA recurrent neural network systems with learning capability using the simultaneous perturbation learning rule. In the neural network systems, outputs and internal values are represented by pulse train. That is, analog recurrent neural networks with pulse frequency representation are considered. The pulse density representation and the simultaneous perturbation enabl...

In our previous research, we confirmed that the chaotic switching noise generated by the cubic map gained a good performance for solving combinatorial optimization problems when the noise was injected to the Hopfield neural network. However, the reason of the good effect of chaotic switching noise has not been clarified completely. In this study, we investigate the solving ability of Hopfield n...

This paper, written for interdisciplinary audience, presents computational image reconstruction implementable by quantum optics. The input-triggered selection of a high-resolution image among many stored ones, and its reconstruction if the input is occluded or noisy, has been successfully simulated. The original algorithm, based on the Hopfield associative neural net, was transformed in order t...

A hybrid Neural-Genetic algorithm (NG) is presented for FPGA Segmented Channel Routing Problems (FSCRP). The NG algorithm consists in a Hopfield Neural Network (HNN) which manages the problem constraints, hybrided with a Genetic Algorithm (GA) for improving the solutions obtained. Six hard FSCRP instances have been generated in order to test the performance of the NG algorithm. Key-Words: FPGAs...

In this note, I review some basic properties of the Hopfield model. I closely follow Chapter 2 of Herz, Krogh & Palmer (1991) which is an excellent introductory textbook on the theory of neural networks. I motivate the mean field analysis of the stochastic Hopfield model slightly differently than Herz, Krogh & Palmer (1991) and my derivations are a little longer, filling in some of the gaps in ...

In this work, a novel method, based upon Hopfield neural networks, is proposed for parameter estimation in the context of system identification. This subject is a very active field of research, because even when a model of a physical system is available, some parameters may be uncertain or time varying. In our methodology, identification is formulated as an optimization problem, profiting from ...

In this research paper, the problem of optimization of quadratic forms associated with the dynamics of Hopfield-Amari neural network is considered. An elegant (and short) proof of the states at which local/global minima of quadratic form are attained is provided. A theorem associated with local/global minimization of quadratic energy function using the HopfieldAmari neural network is discussed....

It is well known that stability of Hopfield type neural networks plays a very important role in both theoretical research and applications. So, it has been kept on studying in two decades. Stochastic effectiveness to this kind of neural networks has also received a lot of attention (ref. [Liao et al, 1996 A], [Liao et al, 1996 B], [Blythe,S. et al, 2001A] and [Blythe,S. et al, 2001B]). In this ...

J. J. Hopfield, “Neural Networks and Physical Systems with Emergent Collective Computational Abilities,” Proc. Nat. Acad. Sci., USA, vol. 79, pp. 2254-2258, Apr. 1982. R. J. McEliece, et al., “The Capacity of the Hopfield Associative Memory,” IEEE Transactions on Information Theory, vol. T-33, pp. 461-482, 1987. B. L. Montgomery et al., “Evaluation of the use of Hopfield Neural Network Model as...