  We study layered neural networks of rectified linear units (ReLU) in a
modelling framework for stochastic training processes. The comparison with
sigmoidal activation functions is in the center of interest. We compute typical
learning curves for shallow networks with K hidden units in matching student
teacher scenarios. The systems exhibit sudden changes of the generalization
performance via the process of hidden unit specialization at critical sizes of
the training set. Surprisingly, our results show that the training behavior of
ReLU networks is qualitatively different from that of networks with sigmoidal
activations. In networks with K >= 3 sigmoidal hidden units, the transition is
discontinuous: Specialized network configurations co-exist and compete with
states of poor performance even for very large training sets. On the contrary,
the use of ReLU activations results in continuous transitions for all K: For
large enough training sets, two competing, differently specialized states
display similar generalization abilities, which coincide exactly for large
networks in the limit K to infinity.
