In this research paper, the problem of existence of the associative memory synthesized by Hopfield is addressed and solved. Using Hadamard matrix of suitable dimension, an algorithm to synthesize real valued Hopfield neural network is discussed. The problem of existence and synthesis of a certain complex Hopfield neural network is addressed and solved. Also, synthesis of real and complex Hopfie...

An approach is proposed to the Hopfield model where the mean-field treatment is made for a given set of stored patterns (sample) and then the statistical average over samples is taken. This corresponds to the approach made by Thouless, Anderson and Palmer (TAP) to the infinite-range model of spin glasses. Taking into account the fact that in the Hopfield model there exist correlations between d...

The consequences of imposing a sign constraint on the standard Hopfield architecture associative memory model, trained using perceptron like learning rules, is examined. Such learning rules have been shown to have capacity of at most half of their unconstrained versions. This paper reports experimental investigations into the consequences of constraining the sign of the network weights in terms...

Networks of coupled periodic oscillators (similar to the Kuramoto model) have been proposed as models of associative memory. However, error-free retrieval states of such oscillatory networks are typically unstable, resulting in a near zero capacity. This puts the networks at disadvantage as compared with the classical Hopfield network. Here we propose a simple remedy for this undesirable proper...

This paper presents an improved approach for enhancing the performance of doing logic programming in Hopfield neural network. Generally Hopfield networks are suitable for solving combinatorial optimization problems. In spite of usefulness of Hopfield neural networks they have limitations; one of the most concerning drawbacks is that sometimes the solutions are local minimum instead of global mi...

This paper presents a novel approach to the emulation of locomotor central pattern generators (CPGs) of legged animals. Based on Scheduling by Multiple Edge Reversal (SMER), a simple but powerful distributed algorithm, it is shown how oscillatory building blocks (OBBs) can be created and how OBB-based networks can be implemented as asymmetric Hopfield-like neural networks for the generation of ...

This paper proposes an augmented Lagrange Hopfield network (ALHN) for combined heat and power economic dispatch (CHPED) problem. The ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian relaxation. In the proposed ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagran...

This paper considers the use of discrete Hopfield neural networks for solving school timetabling problems. Two alternative formulations are provided for the problem: a standard Hopfield-Tank approach, and a more compact formulation which allows the Hopfield network to be competitive with swapping heuristics. It is demonstrated how these formulations can lead to different results. The Hopfield n...

After the original work of Hopfield and Tank, a lot of modified Hopfield neural network models have been proposed for combinatorial optimization problems. Recently, a positively selffeedbacked Hopfield neural network architecture was proposed by Li et al. and successfully applied to crossbar switching problem. In this paper, we analysis the dynamics of the positively self-feedbacked Hopfield ne...

This paper presents a theoretical analysis on the asymptotic memory capacity of the generalized Hopfield network. The perceptron learning scheme is proposed to store sample patterns as the stable states in a generalized Hopfield network. We have obtained that …n 2 1† and 2n are a lower and an upper bound of the asymptotic memory capacity of the network of n neurons, respectively, which shows th...