Optical computing and higher order associative memories

Citation

Park, Cheol Hoon (1990) Optical computing and higher order associative memories. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/n0ke-5a24. https://resolver.caltech.edu/CaltechETD:etd-05102007-111726

Abstract

Beginning with a discussion of the relationship between degrees of freedom and capacity of the system, the original work on higher order associative memories is described in three aspects, Learning, Capacity, and Generalization for pattern recognition and neural networks with the orthogonalization of binary vectors and the ternarization of weights, and their optical implementations using volume holograms are suggested for optical computing. Selection of terms is considered to satisfy the given conditions. When a simple sum of outer product learning rule is applied, higher order memories become higher order Hopfield-type memories. Their capacities are derived from SNR analyses for both nonzero diagonal and zero diagonal memories. Especially in the case of quadratic and cubic memories, optical implementations are suggested in three elegant ways due to the three-dimensional property of volume holograms. Robustness of higher order associative memories is discussed as a generalization property with consideration of dynamic range in terms of robustness of errors in input (error tolerance) and noise in the system (noise sensitivity). In the case of autoassociation or bidirectional association the energy functions are used to investigate the dynamics that provides a mechanism of escaping the local minima to find global minima.

Algorithmic aspects and architectures of optical computing are discussed in terms of deterministic and random algorithms.

Thesis Files