Self-similarity in neural networks driven by transformations

There have been several studies of neural networks whose response properties approximate those found in mammalian visual systems. Most of these have been concerned with the evolution of single units or small sets of units having receptive field profiles which are eigenvectors of an appropriately defined energy function, such as the covariance function of the input vectors. While studies of individual units are important, one of the most striking features of the visual system is its global structure, represented by the so called retinotopic maps found at all levels of the system studied so far: at each level there is a regular mapping of the input which preserves the 2-D topology of the visual stimulus. Similar organization occurs for other perceptual modalities. It would be of some interest, therefore, to uncover the perceptual rules underlying this high degree of ordering. The work reported here is aimed at establishing how such structure might emerge and what its perceptual function may be. The key to this work, unlike most other work in the area, is the role that motion plays in defining the structure. This leads to a concept of self-similarity which bears some resemblance to that used in defining fractal sets