In this paper, typical analog combinatorial optimization approaches, such as Hopfield net, Hopfield-Lagrange net, Maximum entropy approach, Lagrange-Barrier approach, are systematically examined from the perspective of learning distribution. The minimization of a combinatorial cost is turned into a procedure of learning a simple distribution to approximate the Gibbs distribution induced from th...

This paper discusses the implementation of Hopfield neural networks for solving constraint satisfaction problems using field programmable gate arrays (FPGAs). It discusses techniques for formulating such problems as discrete neural networks, and then it describes the N-Queen problem using this formulation. Finally results will be presented which compare the computation times for the custom comp...

In this paper, based on linear matrix inequality (LMI), by using Lyapunov functional theory, the exponential stability criterion is obtained for a class of uncertain Takagi-Sugeno fuzzy Hopfield neural networks (TSFHNNs) with time delays. Here we choose a generalized Lyapunov functional and introduce a parameterized model transformation with free weighting matrices to it, these techniques lead ...

In this paper, we present a FPGA Hopfield Neural Network system with learning capability using the simultaneous perturbation learning rule. In the neural network, outputs and internal values are represented by pulse train. That is, analog Hopfield Neural Network with pulse frequency representation is considered. The pulse density representation and the simultaneous perturbation enable the syste...

This work evaluates two artificial intelligence techniques for file distribution in Grid environments. These techniques are used to access data on independent servers in parallel, in order to improve the performance and maximize the throughput rate. In this work, genetic algorithms and Hopfield neural networks are the techniques used to solve the problem. Both techniques are evaluated for effic...

Previous derivation of the Thouless-Anderson-Palmer (TAP) equations for the Hopfield model by the cavity method yielded results that were inconsistent with those of the perturbation theory as well as the results derived by the replica theory of the model. Here we present a derivation of the TAP equation for the Hopfield model by the cavity method and show that it agrees with the form derived by...

We study generalized restricted Boltzmann machines with generic priors for units and weights, interpolating between Boolean and Gaussian variables. We present a complete analysis of the replica symmetric phase diagram of these systems, which can be regarded as generalized Hopfield models. We underline the role of the retrieval phase for both inference and learning processes and we show that ret...

The Little-Hopfield network is an auto-associative computational model of neural memory storage and retrieval. This model is known to robustly store collections of randomly generated binary patterns as stable-points of the network dynamics. However, the number of binary memories so storable scales linearly in the number of neurons, and it has been a longstanding open problem whether robust expo...

This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This...

This work studies the influence of random noise in the application of Hopfield networks to combinatorial optimization. It has been suggested that the Abe formulation, rather than the original Hopfield formulation, is better suited to optimization, but the eventual presence of noise in the connection weights of this model has not been considered up to now. This consideration leads to a model tha...