Abstract: The paper presents mathematical and empirical results of the behavior of a new multidimensional neural computing paradigm called multidimensional holographic associative computing (MHAC). MHAC can be potentially used for high density associative storage and retrieval of image information. Unlike conventional neural computing, each morsel of information in MHAC is presented as a complex vector in a multidimensional unit spherical space. Each of the individual phases of the vector enumerates a value of the information. The magnitude of the vector represents the associated confidence in the information. In contrast, the conventional neural computing operates only on the notion of confidence. The proposed multidimensional generalization demonstrates significant improvement in associative storage capacity without the loss of generalization space. Virtually, unlimited pattern associations can be enfolded over a single holographic memory substrate by higher order encoding. In addition, its well-structured computation, simultaneous multi-channel learning, and single step non- iterative retrieval promise highly scalable parallelism. The paper presents the theory of operation of MHAC that is founded on the generalized holographic principles and multidimensional Hebbian learning. The paper also presents analytical as well as empirical evidence from computer simulation supporting the superior performance of MHAC cells.!6
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