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Doctoral Thesis
DOI
https://doi.org/10.11606/T.54.1988.tde-09042007-154549
Document
Author
Full name
Jose Fernando Fontanari
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1988
Supervisor
Committee
Koberle, Roland (President)
Felicio, Jose Roberto Drugowich de
Oliveira, Paulo Murilo Castro de
Onuchic, Jose Nelson
Theumann, Walter Karl
Title in Portuguese
Processamento de informações em redes de neurônios sincronas
Keywords in Portuguese
Mecânica estatística
Memória associativa
Redes neurais
Vidros de spin
Abstract in Portuguese
Vidros de spins são sistemas extremamente complexos caracterizados por um número enorme de estados estáveis e meta estáveis. Se identificarmos cada um desses estados com uma informação memorizada, esses sistemas podem ser utilizados como memórias associativas ou endereçáveis por conteúdo. O modelo de vidro de spins passa então a ser chamado de rede de neurônios. Neste trabalho estudamos a termodinâmica e alguns aspectos dinâmicos de uma rede de neurônios com processamento paralelo ou síncrono - o Modelo de Little de memória associativa - no regime em que o número de informações memorizadas p cresce como p = αN, onde N é o número de neurônios. Usando a teoria simétrica em relação às réplicas obtemos o diagrama de fases no espaço de parâmetros do modelo no qual incluímos um termo de autointeração dos neurônios.A riqueza do diagrama de fases que possui uma superfície de pontos tricríticos é devida à competição entre os dois regimes assintóticos da dinâmica síncrona: pontos fixos e ciclos de período dois.
Title in English
Information processing in synchronous neural networks
Keywords in English
Associative memory
Neural networks
Spin glasses
Statistical mechanics
Abstract in English
Spin glasses are very complex systems characterized by a huge number of stable and metastable states. If we identify each state with a memorized information then spin glasses may be used as associative or content addressable memories. This spin glass model is then called a neural network. In this work we study the thermodynamics and some dynamical aspects of a neural network with parallel or synchronous processing - Little's model of associative memory -in the regime where the number of memorized informations p grows as p = αN, where N is the number of neurons. Using the replica symmetric theory we determine the phase diagram in the space of the model's parameters, in which we include a neural self interaction term. The richness of the phase diagram which possesses a surface of tricritical points is due to the competition between the two asymptotic dynamical behaviours of the synchronous dynamics: fixed points and cycles of lenght two.
 
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Fontanari.pdf (3.53 Mbytes)
Publishing Date
2007-04-10
 
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