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 (β → 0). 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 ≥ 3 the transition is first order. Monte Carlo simulations indicate that our results are also valid for moderately low temperatures qualitatively. The limit K → ∞ can be performed analytically, the transition occurs after presenting on the order of N K/β examples. However, an unspecialized metastable state persists up to P ∝ N K 2 /β.