Elementary Holograms And Neurocomputer Architecture For Pattern Recognition
Walter Schempp · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
The massively parallel organization principles which distinguish neural systems from the von Neumann architecture of standard digital computer hardware are one of the main reasons for the largely emerging interest in neurocomputers. Based on a unified nilpotent harmonic analysis approach to artificial neural network models implemented with coherent optical, optoelectronic, or analog electronic neurocomputer architectures, the paper establishes a new identity for the matching polynomials of complete bichromatic graphs which connect neurons located in the neural plane. The key idea is to identify in a first step the hologram plane with the three-dimensional Heisenberg nilpotent Lie group quotiented by its one-dimensional center, then to restrict in a second step the holographic transform to the holographic lattices which form two-dimensional pixel arrays inside the hologram plane, and finally to recognize in a third step the hologram plane as a neural plane. The quantum mechanical treatment of optical holography is imperative in microoptics or amacronics since atoms coherently excited by short laser pulses may be as large as some transistors of microelectronic circuits and the pathways between them inside the hybrid VLSI neurochips.