A geometrical approach to neural network design

A geometrical method for deriving the topology of a neural net is proposed. Instead of making use of learning algorithms, the pattern space is analyzed. The method is outlined for a neural net which performs a binary representation of an analog sensory input. This leads to a geometrical determination of the structure of the neural net, i.e. its layers, weights, and thresholds; no learning is necessary. It is shown that the number of layers and neurons in a feedforward MLP specialized to A/D conversion can be reduced considerably by introducing feedback. The geometrical approach turns out to provide various alternatives for the design of such a net. The results obtained strongly support the view that geometrical analysis of the pattern structure to be recognized helps avoid unnecessary learning.<>