The Langevin method in the statistical dynamics of learning
- 7 August 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (15) , L763-L766
- https://doi.org/10.1088/0305-4470/23/15/012
Abstract
The statistical dynamics of learning in the presence of noise has been treated recently by Hertz, Krogh and Thorbergson (1989) using a Langevin model. Fluctuations introduced by this model into the space orthogonal to the space of patterns are shown to influence the dynamics of learning in a spurious way. This is avoided in the new Langevin model in which the noise is introduced directly into the cost function by using randomly modulated training patterns. Correspondingly a new kind of response function is defined. Unconstrained learning and learning under constrained thermal fluctuations are discussed as examples. Explicit expressions-e.g. for the learning time-are found to differ substantially from those given by Hertz et al.Keywords
This publication has 2 references indexed in Scilit:
- Phase transitions in simple learningJournal of Physics A: General Physics, 1989
- Learning in Neural Networks: Solvable DynamicsEurophysics Letters, 1989