Optimal Capacity of the Blume-Emery-Griffiths perceptron

A Blume-Emery-Griffiths perceptron model is introduced and its optimal capacity is calculated within the replica-symmetric Gardner approach, as a function of the pattern activity and the imbedding stability parameter. The stability of the replica-symmetric approximation is studied via the analogue of the Almeida-Thouless line. A comparison is made with other three-state perceptrons.Comment: 10 pages, 8 figure

GUÍA DE EVALUACIÓN DEL APRENDIZAJE DE ECONOMÍA AGROPECUARIA

GUÍA DE EVALUACIÓN DEL APRENDIZAJ

A spherical Hopfield model

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics 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 equations for the order parameters and effective correlation and response function typical for neural networks. The stationary limit corresponds to the thermodynamic results. Numerical calculations illustrate our findings.Comment: 9 pages Latex including 3 eps figures, Addition of an author in the HTML-abstract unintentionally forgotten, no changes to the manuscrip