Universal representation by Boltzmann machines with Regularised Axons
Abstract
It is widely known that Boltzmann machines are capable of representing arbitrary probability distributions over the values of their visible neurons, given enough hidden ones. However, sampling -- and thus training -- these models can be numerically hard. Recently we proposed a regularisation of the connections of Boltzmann machines, in order to control the energy landscape of the model, paving a way for efficient sampling and training. Here we formally prove that such regularised Boltzmann machines preserve the ability to represent arbitrary distributions. This is in conjunction with controlling the number of energy local minima, thus enabling easy \emph{guided} sampling and training. Furthermore, we explicitly show that regularised Boltzmann machines can store exponentially many arbitrarily correlated visible patterns with perfect retrieval, and we connect them to the Dense Associative Memory networks.
Cite
@article{arxiv.2310.14395,
title = {Universal representation by Boltzmann machines with Regularised Axons},
author = {Przemysław R. Grzybowski and Antoni Jankiewicz and Eloy Piñol and David Cirauqui and Dorota H. Grzybowska and Paweł M. Petrykowski and Miguel Ángel García-March and Maciej Lewenstein and Gorka Muñoz-Gil and Alejandro Pozas-Kerstjens},
journal= {arXiv preprint arXiv:2310.14395},
year = {2023}
}
Comments
12 pages. Updated references