How many hidden neurons are needed to recognize a symmetrical pattern ?

Abstract

We study the detection of axial symetries in binary images with artificial layered neural networks, trained with the backpropagation rule. The number of hidden neurons necessary to classify correctly images is almost independant from the images' size. We show experimental results obtained with different networks, and we note that only a few hidden neurons are really usefull. These neurons are caracterised by the regular spatial structure of their input weights. We then propose a new and more efficient training algorithm that yields networks with the minimum number of neurons necessary to perform the classification. In the last part, we take up the theoretical analysis of this problem that leads to an interesting superior limit for the number of hidden neurons needed for its solution.