Dynamical and Stationary Properties of On-line Learning from Finite Training Sets

Details Dynamical and Stationary Properties of On-line Learning from Finite Training Sets Dynamical and Stationary Properties of On-line Learning from Finite Training Sets

2002-08-29

arxiv.org/abs/cond-mat/0208578v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

30 pages, 4 figures

Scientific paper

10.1103/PhysRevE.67.011906

The dynamical and stationary properties of on-line learning from finite training sets are analysed using the cavity method. For large input dimensions, we derive equations for the macroscopic parameters, namely, the student-teacher correlation, the student-student autocorrelation and the learning force uctuation. This enables us to provide analytical solutions to Adaline learning as a benchmark. Theoretical predictions of training errors in transient and stationary states are obtained by a Monte Carlo sampling procedure. Generalization and training errors are found to agree with simulations. The physical origin of the critical learning rate is presented. Comparison with batch learning is discussed throughout the paper.

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