This paper presents two simple optimization techniques based on combining the Langevin Equation with the Hopfield Model. Proposed models referred as Stochastic Model (SM) and Pulsed Noise Model (PNM) can be viewed as straightforward stochastic extensions of the Hopfield optimization network. Both models follow the idea of Stochastic Neural Network [14] and Diffusion Machine [23]. They differ fo...

Although Hopfield neural network is one of the most commonly used neural network models for auto-association and optimization tasks, it has several limitations. For example, it is well known that Hopfield neural networks has limited stored patterns, local minimum problems, limited noise ratio, retrieve reverse value of pattern, and shifting and scaling problems. This research will propose multi...

Although Hopfield neural network is one of the most commonly used neural network models for auto-association and optimization tasks, it has several limitations. For example, it is well known that Hopfield neural networks has limited stored patterns, local minimum problems, limited noise ratio, retrieve reverse value of pattern, and shifting and scaling problems. This research will propose multi...

Recurrent neural networks (RNN) have traditionally been of great interest for their capacity to store memories. In past years, several works have been devoted to determine the maximum storage capacity of RNN, especially for the case of the Hopfield network, the most popular kind of RNN. Analyzing the thermodynamic limit of the statistical properties of the Hamiltonian corresponding to the Hopfi...

Recently, a large number of neural networks models have been proposed and studied extensively since Hopfield constructed a simplified neural network. In most networks however, it is usually expected that time delays exist during the processing and transmission of signals. In general, delay-differential equations exhibit much more complicated dynamics than ordinary differential equations since a...

The information capacity of Kanerva's Sparse, Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used here, it is shown that tire total information stored in these systems is proportional to the number connections in the network. The proportionality constant is the same for the SDM and Hopfield-type models independent of the particular model, or...

This pape.r shows that contrastive Hebbian, the algorithm used in mean field learning, can be applied to any continuous Hopfield model. This implies that non-logistic activation functions as well as self connections are allowed. Contrary to previous approaches, the learning algorithm is derived without considering it a mean field approximation to Boltzmann machine learning. The paper includes a...