Weight space structure and the storage capacity of a fully connected committee machine

Autor:	Jong-Hoon Oh, Chulan Kwon, Yuansheng Xiong
Rok vydání:	1997
Předmět:	Combinatorics Discrete mathematics Committee machine Structure (category theory) Order (ring theory) Weight space Limit (mathematics) Representation (mathematics) Mathematics
Zdroj:	Physical Review E. 56:4540-4544
ISSN:	1095-3787 1063-651X
Popis:	We study the storage capacity of a fully connected committee machine with a large number $K$ of hidden nodes. The storage capacity is obtained by analyzing the geometrical structure of the weight space related to the internal representation. By examining the asymptotic behavior of order parameters in the limit of large $K,$ the storage capacity ${\ensuremath{\alpha}}_{c}$ is found to be proportional to $K\sqrt{\mathrm{ln}K}$ up to the leading order. This result satisfies the mathematical bound given by Mitchison and Durbin [Biol. Cybern. 60, 345 (1989)], whereas the replica-symmetric solution in a conventional Gardner approach [Europhys. Lett. 41, 481 (1987); J. Phys. A 21, 257 (1988)] violates this bound.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4cd5ef2de10455e2bf4db498e8d0bcd8 https://doi.org/10.1103/physreve.56.4540 Zobrazit plný text záznamu