On topology, size and generalization of non-linear feed-forward neural networks

The use of similarity transforms in the design and the interpretation of feed-forward neural networks is proposed. The method is based on the so-called Buckingham-Theorem or Pi-Theorem and is valid for all neural network function approximation problems which belong to the class of dimensionally homogeneous equations. The new design method allows the a priori determination of a minimal topology size of the first and last network layer. Finally, the correct and unique pointwise generalization capability of the new so-called similarity network topology is proved and illustrated using two examples.