Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

MiS Preprint
113/2014

Deep Narrow Boltzmann Machines are Universal Approximators

Guido Montúfar

Abstract

We show that deep narrow Boltzmann machines are universal approximators of probability distributions on the activities of their visible units, provided they have sufficiently many hidden layers, each containing the same number of units as the visible layer. Besides from this existence statement, we provide upper and lower bounds on the sufficient number of layers and parameters. These bounds show that deep narrow Boltzmann machines are at least as compact universal approximators as restricted Boltzmann machines and narrow sigmoid belief networks, with respect to the currently available bounds for those models.

Received:
Nov 14, 2014
Published:
Nov 20, 2014

Related publications

inBook
2015 Repository Open Access
Guido Montúfar

Deep narrow Boltzmann machines are universal approximators

In: Third international conference on learning representations - ICLR 2015 : May 7-9 2015, San Diego, CA. USA
San Diego : ICLR, 2015.