Przemysław R. Grzybowski

Przemysław R. Grzybowski, Antoni Jankiewicz, Eloy Piñol et al.

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.

Alejandro Pozas-Kerstjens, Gorka Muñoz-Gil, Eloy Piñol et al.

We introduce a new family of energy-based probabilistic graphical models for efficient unsupervised learning. Its definition is motivated by the control of the spin-glass properties of the Ising model described by the weights of Boltzmann machines. We use it to learn the Bars and Stripes dataset of various sizes and the MNIST dataset, and show how they quickly achieve the performance offered by standard methods for unsupervised learning. Our results indicate that the standard initialization of Boltzmann machines with random weights equivalent to spin-glass models is an unnecessary bottleneck in the process of training. Furthermore, this new family allows for very easy access to low-energy configurations, which points to new, efficient training algorithms. The simplest variant of such algorithms approximates the negative phase of the log-likelihood gradient with no Markov chain Monte Carlo sampling costs at all, and with an accuracy sufficient to achieve good learning and generalization.