We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynam-ics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equa...

In the Hopfield model the ability of the network to generalization is studied in the case of the network trained by one input image (the standard).

In this research paper, the problem of minimization 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....

In the Hopfield Neural Network (HNN), each neuron is connected to every other neuron. Thereby, the HNN causes high cost to generate the network in terms of implementation. Small World Hopfield Neural Network (SWHNN) improves ability for transmission by introducing the shortcut connections into the sparse regular network. However the storage ability of the SWHNN decreases for associative memory ...

This paper presents some new implementations of parallel Hopfield neural network model -Cauchy machineon Graphic Processor Units (GPU). The main operators in the parallel Hopfield neural work are loaded into RGBA textures so that input calculation, output update and terminal condition check are implemented by fragment processors on GPU. In addition, the matrix-vector multiplication is realized ...

The extended Hopfield neural network proposed by Abe et al. for solving combinatorial optimization problems with equality and/or inequality constraints has the drawback of being frequently stabilized in states with neurons of ambiguous classification as active or inactive. We introduce in the model a competitive activation mechanism and we derive a new expression of the penalty energy allowing ...

Matt Stowe and Subhash Kak . Abstract: This paper examines the memory capacity of generalized neural networks. Hopfield networks trained with a variety of learning techniques are investigated for their capacity both for binary and non-binary alphabets. It is shown that the capacity can be much increased when multilevel inputs are used. New learning strategies are proposed to increase Hopfield n...

In this paper, a new approach based on Artificial Neural Networks to solve the robot motion planning problem is presented. For this purpose, a Hopfield Neural Network is used in a certain constraint satisfaction problem of the robot motion planning in conjunction with fuzzy modeling of the real robot’s environment so that the energy of a state can be interpreted as the extent to which a hypothe...

In this paper, a novel color image hiding technique using spread grey-based competitive Hopfield neural network (SGHNN) and Hadamard Transform (HT) digital watermarking is proposed. The goal is to offer secure communications in the internet through compress the original color image and embedded into another disguise color image. Our method includes a spread-unsupervised competitive Hopfield neu...

In this paper, we derive a sufficient condition for asymptotic stability of the zero solution of delay-difference control system of Hopfield neural networks in terms of certain matrix inequalities by using a discrete version of the Lyapunov second method. The result is applied to obtain new asymptotic stability condition for some class of delay-difference control system such as delay-difference...