The Little-Hopfield model on a Random Graph

We study the Hopfield model on a random graph in scaling regimes where the average number of connections per neuron is a finite number and where the spin dynamics is governed by a synchronous execution of the microscopic update rule (Little-Hopfield model).We solve this model within replica symmetry and by using bifurcation analysis we prove that the spin-glass/paramagnetic and the retrieval/paramagnetictransition lines of our phase diagram are identical to those of sequential dynamics.The first-order retrieval/spin-glass transition line follows by direct evaluation of our observables using population dynamics. Within the accuracy of numerical precision and for sufficiently small values of the connectivity parameter we find that this line coincides with the corresponding sequential one. Comparison with simulation experiments shows excellent agreement.Comment: 14 pages, 4 figure

Storage of Natural Language Sentences in a Hopfield Network

This paper look at how the Hopfield neural network can be used to store and recall patterns constructed from natural language sentences. As a pattern recognition and storage tool, the Hopfield neural network has received much attention. This attention however has been mainly in the field of statistical physics due to the model's simple abstraction of spin glass systems. A discussion is made of the differences, shown as bias and correlation, between natural language sentence patterns and the randomly generated ones used in previous experiments. Results are given for numerical simulations which show the auto-associative competence of the network when trained with natural language patterns.Comment: latex, 10 pages with 2 tex figures and a .bib file, uses nemlap.sty, to appear in Proceedings of NeMLaP-

Intelligent search for distributed information sources using heterogeneous neural networks

As the number and diversity of distributed information sources on the Internet exponentially increase, various search services are developed to help the users to locate relevant information. But they still exist some drawbacks such as the difficulty of mathematically modeling retrieval process, the lack of adaptivity and the indiscrimination of search. This paper shows how heteroge-neous neural networks can be used in the design of an intelligent distributed in-formation retrieval (DIR) system. In particular, three typical neural network models - Kohoren's SOFM Network, Hopfield Network, and Feed Forward Network with Back Propagation algorithm are introduced to overcome the above drawbacks in current research of DIR by using their unique properties. This preliminary investigation suggests that Neural Networks are useful tools for intelligent search for distributed information sources

The Relativistic Hopfield network: rigorous results

The relativistic Hopfield model constitutes a generalization of the standard Hopfield model that is derived by the formal analogy between the statistical-mechanic framework embedding neural networks and the Lagrangian mechanics describing a fictitious single-particle motion in the space of the tuneable parameters of the network itself. In this analogy the cost-function of the Hopfield model plays as the standard kinetic-energy term and its related Mattis overlap (naturally bounded by one) plays as the velocity. The Hamiltonian of the relativisitc model, once Taylor-expanded, results in a P-spin series with alternate signs: the attractive contributions enhance the information-storage capabilities of the network, while the repulsive contributions allow for an easier unlearning of spurious states, conferring overall more robustness to the system as a whole. Here we do not deepen the information processing skills of this generalized Hopfield network, rather we focus on its statistical mechanical foundation. In particular, relying on Guerra's interpolation techniques, we prove the existence of the infinite volume limit for the model free-energy and we give its explicit expression in terms of the Mattis overlaps. By extremizing the free energy over the latter we get the generalized self-consistent equations for these overlaps, as well as a picture of criticality that is further corroborated by a fluctuation analysis. These findings are in full agreement with the available previous results.Comment: 11 pages, 1 figur