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 ...

The Hopfield model in a transverse field is investigated in order to clarify how quantum fluctuations affect the macroscopic behavior of neural networks. Using the Trotter decomposition and the replica method, we find that the α (the ratio of the number of stored patterns to the system size)-∆ (the strength of the transverse field) phase diagram of this model in the ground state resembles the α...

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...

The Hopfield model neural net has attracted much recent attention. One use of the Hopfield net is as a highly parallel content-addressable memory, where retrieval is possible although the input is corrupted by noise. For binary input patterns, an alternate approach is to compute Hamming distances between the input pattern and each of the stored patterns and retrieve that stored pattern with min...

In this paper, artificial neural networks for solving multiobjective optimization problems have been considered. The Tank-Hopfield model for linear programming has been extended, and then the neural model for finding Pareto-optimal solutions in the linear multi-criterion optimization problem with continuous decision variables has been discussed. Furthermore, the model for solving quasi-quadrati...

In 1973, the phenomenon of long-term potentiation (LTP) was discovered. The study of LTP is now a small industry within the field of neuroscience. Among the various forms of LTP, those that depend on the NMDA subtype of glutamate receptor are regarded as “Hebbian.” These forms depend on temporal contiguity of presynaptic and postsy­ naptic activity. The requirement of temporal contiguity is exp...

Drawing important ideas from several sources, the idea of associative memory from psychology (Kohonen, 1977), the idea of Hebbian adaptation from neurophysiology (Hebb, 1949), the idea of neuron as a thresholding device from prior modeling work (McCulloch & Pitts, 1943) etc., Hopfield presented an elegant model of associative memory storage and retrieval in the brain (Hopfield, 1982; Hopfield, ...

A model of neurons with CHN (Continuous Hysteresis Neurons) for the Hopfield neural networks is studied. We prove theoretically that the emergent collective properties of the original Hopfield neural networks also are present in the Hopfield neural networks with continuous hysteresis neurons. The network architecture is applied to the N-Queens problem and results of computer simulations are pre...

We investigate the retrieval phase diagrams of an asynchronous fully-connected attractor network with non-monotonic transfer function by means of a mean-field approximation. We find for the noiseless zero-temperature case that this non-monotonic Hopfield network can store more patterns than a network with monotonic transfer function investigated by Amit et al. Properties of retrieval phase diag...

We summarize the Storkey Learning Rules for the Hopfield Model, and evaluate performance relative to other learning rules. Hopfield Models are normally used for auto-association, and Storkey Learning Rules have been found to have good balance between local learning and capacity. In this paper we outline different learning rules and summarise capacity results. Hopfield networks are related to Bo...