Genetic algorithms and neural networks: making use of parameter space symmetries

A functional equivalence of feedforward networks has been proposed to reduce the search space of learning algorithms. The description of equivalence classes has been used to introduce a unique parametrization property and consequently the so-called canonical parameterizations as representatives of functional equivalence classes. A novel genetic learning algorithm for neural networks that outperforms standard genetic learning has been proposed based on these results. In this paper we summarize previous results and present a geometrical approach that illustrates the situation and also leads to further open problems