Modul: MAT971 Stochastische Prozesse

## Reconstruction of a random pattern with restricted Boltzmann machines

Talk by Dr. Giuseppe Genovese

**Date:** 16.03.22 **Time:** 17.15 - 18.15 **Room:** Y27H12

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). One says that the RBM retrieves a pattern, if any algorithmic search initialised in proximity of it will not end up so far (or 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 (of which the Hopfield model is a special case) is critical and separates these two regimes.