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 an 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.