Dynamics of Supervised Learning with Restricted Training Sets

Details Dynamics of Supervised Learning with Restricted Training Sets Dynamics of Supervised Learning with Restricted Training Sets

1998-03-05

arxiv.org/abs/cond-mat/9803062v1

Physics

Condensed Matter

Disordered Systems and Neural Networks

36 pages, latex2e, 12 eps figures (to be publ in: Proc Newton Inst Workshop on On-Line Learning '97)

Scientific paper

We study the dynamics of supervised learning in layered neural networks, in the regime where the size $p$ of the training set is proportional to the number $N$ of inputs. Here the local fields are no longer described by Gaussian probability distributions. We show how dynamical replica theory can be used to predict the evolution of macroscopic observables, including the relevant performance measures, incorporating the old formalism in the limit $\alpha=p/N\to\infty$ as a special case. For simplicity we restrict ourselves to single-layer networks and realizable tasks.

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