Pattern reconstruction with restricted Boltzmann machines – Giuseppe Genovese (University of Zurich)


Aula Magna


A Restricted Boltzmann machine (RBM) is a Gibbs probability distribution of great theoretical and methodological relevance in machine learning. It is defined on a bipartite graph, with one layer (so-called visible) usually made of binary variables encoding the data, and a second ancillary layer (so-called hidden). The RBM retrieves a pattern if any algorithmic search initialised in proximity of the pattern does not end up so far from it. Alternatively, the patterns and the local minima of the energy are close enough. I will present some recent results showing that the ability of a RBM to retrieve a random pattern depends on the choice of the distribution of the hidden layer. Indeed efficient retrieval is possible for distributions with a strict sub-Gaussian decay, while strict super-Gaussian tails give poor performance. The case of Gaussian tail is critical and separates these two regimes.

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