Optical implementation of probabilistic graphical models

We are investigating the use of optics to solve highly connected graphical models by probabilistic inference, and more specifically the sum-product message passing algorithm. We are examining the fundamental limit of size and power requirement according to the best multiplexing strategy we have found. For a million nodes, and an alphabet of a hundred, we found that the minimum size for the optical implementation is 10mm3, and the lowest bound for the power is 200 watts for operation at the shot noise limit. The various functions required for the algorithm to be operational are presented and potential implementations are discussed. These include a vector matrix multiplication using spectral hole burning, a logarithm carried out with two photon absorption, an exponential performed with saturable absorption, a normalization executed with an thermo-optics interferometer, and a wavelength remapping accomplished with a pump-probe amplifier.