The Sparse, Distributed Memory (SDM) model (Kanerva. 1984) is compared to Hopfield-type, neural-network models. A mathematical framework for cornporing the two models is developed, and the capacity of each model is investigated. The capacity of the SDM can be increased independent of the dimension of the stored vectors, whereas the Hopfield capacity is limited to a fraction of this dimension. T...

Many difficult combinatorial optimization problems arising from science and technology are often difficult to solve exactly. Hence a great number of approximate algorithms for solving combinatorial opthintion problems have been developed [lo], [IS]. Hopfield and Tank applied the continuowtime, continuous-output Hopfield neural network (CTCGH?W) to TSP, thereby initialing a new approach to optim...

In the present paper, an effort has been made for storing and recalling images with Hopfield Neural Network Model of auto-associative memory. Images are stored by calculating a corresponding weight matrix. Thereafter, starting from an arbitrary configuration, the memory will settle on exactly that stored image, which is nearest to the starting configuration in terms of Hamming distance. Thus gi...

In this paper, a new Hopfield-model net based on fuzzy possibilistic reasoning is proposed for the classification of multispectral images. The main purpose is to modify the Hopfield network embedded with fuzzy possibilistic -means (FPCM) method to construct a classification system named fuzzy-possibilistic Hopfield net (FPHN). The classification system is a paradigm for the implementation of fu...

This paper surveys two advanced associative memory models[8][5]. The first model was derived from the projection on a closed convex set spanned by patterns. The second model was derived from training weights to improve the error tolerance of the Hopfield network. Both models are designed to resolve the insufficiencies of the Hopfield network. These insufficiencies are loading capacity, limit cy...

Unsupervised learning in a generalized Hopfield associative-memory network is investigated in this work. First, we prove that the (generalized) Hopfield model is equivalent to a semi-restricted Boltzmann machine with a layer of visible neurons and another layer of hidden binary neurons, so it could serve as the building block for a multilayered deep-learning system. We then demonstrate that the...

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...

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...

Since McCulloch and Pitts’ seminal work (McCulloch & Pitts, 1943), several models of discrete neural networks have been proposed, many of them presenting the ability of assigning a discrete value (other than unipolar or bipolar) to the output of a single neuron. These models have focused on a wide variety of applications. One of the most important models was developed by J. Hopfield in (Hopfiel...