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Article overview
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Non-Deterministic Learning Dynamics in Large Neural Networks due to Structural Data Bias | H.C. Rae
; J.A.F. Heimel
; A.C.C. Coolen
; | Date: |
13 Jul 2000 | Journal: | J.Phys.A. 33 (2000) 8703-8722 | Subject: | Disordered Systems and Neural Networks | cond-mat.dis-nn | Abstract: | We study the dynamics of on-line learning in large perceptrons, for the case of training sets with a structural bias of the input vectors, by deriving exact and closed macroscopic dynamical laws using non-equilibrium statistical mechanical tools. In sharp contrast to the more conventional theories developed for homogeneously distributed or only weakly biased data, these laws are found to describe a non-trivial and persistently non-deterministic macroscopic evolution, and a generalisation error which retains both stochastic and sample-to-sample fluctuations, even for infinitely large networks. Furthermore, for the standard error-correcting microscopic algorithms (such as the perceptron learning rule) one obtains learning curves with distinct bias-induced phases. Our theoretical predictions find excellent confirmation in numerical simulations. | Source: | arXiv, cond-mat/0007232 | Services: | Forum | Review | PDF | Favorites |
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