Directional-Unit Boltzmann Machines
Abstract
We present a general formulation for a network of stochastic di(cid:173) rectional 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 approxima(cid:173) tion to a stochastic DUBM, the phase component of a unit's state represents its mean direction, and the magnitude component spec(cid:173) ifies the degree of certainty associated with this direction. This combination of a value and a certainty provides additional repre(cid:173) sentational power in a unit. We describe a learning algorithm and simulations that demonstrate a mean-field DUBM'S ability to learn interesting mappings.
Cite
Text
Zemel et al. "Directional-Unit Boltzmann Machines." Neural Information Processing Systems, 1992.Markdown
[Zemel et al. "Directional-Unit Boltzmann Machines." Neural Information Processing Systems, 1992.](https://mlanthology.org/neurips/1992/zemel1992neurips-directionalunit/)BibTeX
@inproceedings{zemel1992neurips-directionalunit,
title = {{Directional-Unit Boltzmann Machines}},
author = {Zemel, Richard S. and Williams, Christopher K. I. and Mozer, Michael},
booktitle = {Neural Information Processing Systems},
year = {1992},
pages = {172-179},
url = {https://mlanthology.org/neurips/1992/zemel1992neurips-directionalunit/}
}