Genetic Algorithms and Neural Networks: Making Use of Parameter Space Symmetries

A functional equivalence of feed-forward 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 leads to further open problems.