Categorial approach to machine learning

W.C. Hoffman (1970, 1985) has demonstrated the utility of mathematical category theory in explaining the functions of the multiple topographic maps in the cortex. After some mathematical preliminaries, the authors describe the Hoffman model in more detail. A comparison to other current theories follows and then an application to learning in machine vision is presented. Two otherwise unsolvable problems are treated by supplementing perceptrons with prolongations. Hoffman proposed that the brain used prolongations of the symmetry groups of visual perception. The first problem is the XOR problem and the second is ASCII character recognition. In each case, prolonged images of the original image are added to the perceptron´s input set. This addition transforms these linearly inseparable problems into separable ones. This is a general result. Any recognition problem becomes linearly separable, and hence perception solvable, by sufficient prolongation