Analytic Solutions to the Formation of Feature-Analysing Cells of a Three-Layer Feedforward Visual Information Processing Neural Net

Analytic solutions to the information-theoretic evolution equation of the connection strength of a three-layer feedforward neural net for visual information processing are presented. The results are (1) the receptive fields of the feature-analysing cells correspond to the eigenvector of the maximum eigenvalue of the Fredholm integral equation of the first kind derived from the evolution equation of the connection strength; (2) a symmetry-breaking mechanism (parity-violation) has been identified to be responsible for the changes of the morphology of the receptive field; (3) the conditions for the formation of different morphologies are explicitly identified.