Phase transitions in soft-committee machines

Details Phase transitions in soft-committee machines Phase transitions in soft-committee machines

1998-05-15

arxiv.org/abs/cond-mat/9805182v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

8 pages, 4 figures

Scientific paper

10.1209/epl/i1998-00466-6

Equilibrium statistical physics is applied to layered neural networks with differentiable activation functions. A first analysis of off-line learning in soft-committee machines with a finite number (K) of hidden units learning a perfectly matching rule is performed. Our results are exact in the limit of high training temperatures. For K=2 we find a second order phase transition from unspecialized to specialized student configurations at a critical size P of the training set, whereas for K > 2 the transition is first order. Monte Carlo simulations indicate that our results are also valid for moderately low temperatures qualitatively. The limit K to infinity can be performed analytically, the transition occurs after presenting on the order of N K examples. However, an unspecialized metastable state persists up to P= O (N K^2).

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