  Classical neural networks achieve only limited convergence in hard problems
such as XOR or parity when the number of hidden neurons is small. With the
motivation to improve the success rate of neural networks in these problems, we
propose a new neural network model inspired by existing neural network models
with so called product neurons and a learning rule derived from classical error
backpropagation, which elegantly solves the problem of mutually exclusive
situations. Unlike existing product neurons, which have weights that are preset
and not adaptable, our product layers of neurons also do learn. We tested the
model and compared its success rate to a classical multilayer perceptron in the
aforementioned problems as well as in other hard problems such as the two
spirals. Our results indicate that our model is clearly more successful than
the classical MLP and has the potential to be used in many tasks and
applications.
