  We investigate the generalization ability of a perceptron with non-monotonic
transfer function of a reversed-wedge type in on-line mode. This network is
identical to a parity machine, a multilayer network. We consider several
learning algorithms. By the perceptron algorithm the generalization error is
shown to decrease by the ${\alpha}^{-1/3}$-law similarly to the case of a
simple perceptron in a restricted range of the parameter $a$ characterizing the
non-monotonic transfer function. For other values of $a$, the perceptron
algorithm leads to the state where the weight vector of the student is just
opposite to that of the teacher. The Hebbian learning algorithm has a similar
property; it works only in a limited range of the parameter. The conventional
AdaTron algorithm does not give a vanishing generalization error for any values
of $a$.We thus introduce a modified AdaTron algorithm which yields a good
performance for all values of $a$. We also investigate the effects of
optimization of the learning rate as well as of the learning algorithm. Both
methods give excellent learning curves proportional to ${\alpha}^{-1}$. The
latter optimization is related to the Bayes statistics and is shown to yield
useful hints to extract maximum amount of information necessary to accelerate
learning processes.
