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Equilibrium states of large layered neural networks with differentiableactivation function and a single, linear output unit are investigated using thereplica formalism. The quenched free energy of a student network with a verylarge number of hidden units learning a rule of perfectly matching complexityis calculated analytically. The system undergoes a first order phase transitionfrom unspecialized to specialized student configurations at a critical size ofthe training set. Computer simulations of learning by stochastic gradientdescent from a fixed training set demonstrate that the equilibrium resultsdescribe quantitatively the plateau states which occur in practical trainingprocedures at sufficiently small but finite learning rates.Comment: 11 pages, 4 figure

Statistical physics and practical training of soft-committee machines