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Directional-unit boltzmann machines

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 5
PublisherMorgan Kaufmann Publishers Inc.
Pages172-179
Number of pages8
ISBN (Print)1-55860-274-7
Publication statusPublished - 1993

Abstract

We present a general formulation for a network of stochastic directional units. This formulation is an extension of the Boltzmann machine in which the units are not binary, but take on values in a cyclic range, between 0 and 271' radians. The state of each unit in a Directional-Unit Boltzmann Machine (DUBM) is described by a complex variable, where the phase component specifies a direction; the weights are also complex variables. We associate a quadratic energy function, and corresponding probability, with each DUBM configuration. The conditional distribution of a unit's stochastic state is a circular version of the Gaussian probability distribution, known as the von Mises distribution. In a mean-field approximation to a stochastic DUBM, the phase component of a unit's state represents its mean direction, and the magnitude component specifies the degree of certainty associated with this direction. This combination of a value and a certainty provides additional representational power in a unit. We describe a learning algorithm and simulations that demonstrate a mean-field DUBM'S ability to learn interesting mappings.

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