Finite size effects in neural networks

Laura Viana; Arnulfo Castellanos; A. C.C. Coolen

doi:10.1007/BFb0098196

Finite size effects in neural networks

Laura Viana, Arnulfo Castellanos, A. C.C. Coolen

Departamento de Física

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

1 Cita (Scopus)

Resumen

In this paper we give an overview of a recently developed theory [1, 2] which allows for calculating finite size corrections to the dynamical equations describing the dynamics of separable Neural Networks, away from saturation. According to this theory, finite size effects are described by a linear-noise Fokker Planck equation for the fluctuations (corresponding to an Ornstein-Uhlenbeck process), whose solution is characterized by the first two moments. The theory is applied to a particular problem in which detailed balance does not hold.

Idioma original	Inglés
Título de la publicación alojada	Foundations and Tools for Neural Modeling - International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Proceedings
Editores	José Mira, Juan V. Sánchez-Andrés
Editorial	Springer Verlag
Páginas	393-400
Número de páginas	8
ISBN (versión impresa)	3540660690, 9783540660699
DOI	https://doi.org/10.1007/BFb0098196
Estado	Publicada - 1999
Evento	5th International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999 - Alicante, Espana Duración: 2 jun. 1999 → 4 jun. 1999

Serie de la publicación

Nombre	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volumen	1606
ISSN (versión impresa)	0302-9743
ISSN (versión digital)	1611-3349

Conferencia

Conferencia	5th International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999
País/Territorio	Espana
Ciudad	Alicante
Período	2/06/99 → 4/06/99

Nota bibliográfica

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.

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10.1007/BFb0098196

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Viana, L., Castellanos, A., & Coolen, A. C. C. (1999). Finite size effects in neural networks. En J. Mira, & J. V. Sánchez-Andrés (Eds.), Foundations and Tools for Neural Modeling - International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Proceedings (pp. 393-400). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1606). Springer Verlag. https://doi.org/10.1007/BFb0098196

Viana, Laura ; Castellanos, Arnulfo ; Coolen, A. C.C. / Finite size effects in neural networks. Foundations and Tools for Neural Modeling - International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Proceedings. editor / José Mira ; Juan V. Sánchez-Andrés. Springer Verlag, 1999. pp. 393-400 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "In this paper we give an overview of a recently developed theory [1, 2] which allows for calculating finite size corrections to the dynamical equations describing the dynamics of separable Neural Networks, away from saturation. According to this theory, finite size effects are described by a linear-noise Fokker Planck equation for the fluctuations (corresponding to an Ornstein-Uhlenbeck process), whose solution is characterized by the first two moments. The theory is applied to a particular problem in which detailed balance does not hold.",

author = "Laura Viana and Arnulfo Castellanos and Coolen, {A. C.C.}",

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Viana, L, Castellanos, A & Coolen, ACC 1999, Finite size effects in neural networks. En J Mira & JV Sánchez-Andrés (eds.), Foundations and Tools for Neural Modeling - International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1606, Springer Verlag, pp. 393-400, 5th International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Alicante, Espana, 2/06/99. https://doi.org/10.1007/BFb0098196

Finite size effects in neural networks. / Viana, Laura; Castellanos, Arnulfo; Coolen, A. C.C.
Foundations and Tools for Neural Modeling - International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Proceedings. ed. / José Mira; Juan V. Sánchez-Andrés. Springer Verlag, 1999. p. 393-400 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1606).

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

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AB - In this paper we give an overview of a recently developed theory [1, 2] which allows for calculating finite size corrections to the dynamical equations describing the dynamics of separable Neural Networks, away from saturation. According to this theory, finite size effects are described by a linear-noise Fokker Planck equation for the fluctuations (corresponding to an Ornstein-Uhlenbeck process), whose solution is characterized by the first two moments. The theory is applied to a particular problem in which detailed balance does not hold.

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Viana L, Castellanos A, Coolen ACC. Finite size effects in neural networks. En Mira J, Sánchez-Andrés JV, editores, Foundations and Tools for Neural Modeling - International Work-Conference on Artificial and Natural Neural Networks, IWANN 1999, Proceedings. Springer Verlag. 1999. p. 393-400. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/BFb0098196

Finite size effects in neural networks

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