外積を利用した3次元連想記憶

概要

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Several models of high dimensional neural networks have been proposed. Complex neural networks are two dimensional neural networks. They has been investigated more than other high dimensional neural networks. Three-dimensional neural networks are Nitta’s 3D model, a model using quaternion numbers and an exterior model. Nitta’s 3D model and the model using quaternion numbers have rotational properties. The inherent properties of exterior model, however, have not been clearfied. We propose Hopfield network using exterior product to investigate exterior model. Real and complex numbers holds commutative and connection laws, but exterior product does not. Therefore it can not use similar discussions. In this paper, we show that the learning method similar to hebbian rule is useful.
2004-01-01