Phase transitions in soft-committee machines
Institut für Theoretische Physik, Julius-Maximilians-Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany
Accepted: 31 August 1998
Equilibrium statistical physics is applied to the off-line training of layered neural networks with differentiable activation functions. A first analysis of soft-committee machines with an arbitrary number (K) of hidden units and continuous weights 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 the transition is first order. The limit can be performed analytically, the transition occurs after presenting on the order of examples. However, an unspecialized metastable state persists up to .
PACS: 87.10.+e – General, theoretical, and mathematical biophysics (including logic of biosystems, quantum biology, and relevant aspects of thermodynamics, information theory, cybernetics, and bionics) / 07.05.Mh – Neural networks, fuzzy logic, artificial intelligence / 05.90.+m – Other topics in statistical physics and themodynamics
© EDP Sciences, 1998