Research Report CS-RR-271

Simon Clippingdale and R.G. Wilson, Self-Similar Neural Networks Based On A Kohonen Learning Rule (October 1, 1994).

Abstract

One of the most striking features about the perceptual machinery of mammals is its regularity of structure. This is particularly evident in the mammalian visual system, as the work pioneered by Hubel and Wiesel has demonstrated. The likely source of this regularity is the visual stimulus, which does not change randomly from instant to instant, but is affected primarily by motions of both the animal and objects in the environment. These motions induce structured changes in the visual stimulus, which might well be expected to have a significant effect in shaping the structure of the visual machinery, whether through individual plasticity or longer-term genetic changes. The work reported in this paper is an investigation of the structures that may evolve in a simple artificial neural network driven not by random changes of input pattern, but directly by transformations which are themselves related to transformations of the input signal through an analysis of motion-prediction error. Results are presented which demonstrate that such networks can evolve a remarkable degree of regularity which reflects the underlying symmetry group of the transformations, both in one and two dimensions. An appropriate and visually plausible choice of transformation group can lead to the development of foveal structures in two-dimensional networks. We also present some preliminary results on parameterised function spaces which support the general conclusion that global structure bearing a considerable resemblance to that found in the mammalian visual system can evolve as the result of a simple learning rule in networks driven by transformations similar to those typically encountered in vision.

S.C. Clippingdale and R.G. Wilson, "Self-Similar Neural Networks Based on a Kohonen Learning Rule", Neural Networks 9(5) pp. 747-763 (1996)