Elenco seminari del ciclo di seminari
“DEEP LEARNING ARTIFICIAL AND STATISTICAL MECHANICS”

Abstract In this talk we introduce a new variational approach to a class mean-field models, the so called bipartite spin models. In this framework the set of spins is divided in two groups and the interaction links only spins belonging to different groups. We start with the bipartite Curie-Weiss model showing how this approach leads to two equivalent variational representations of the limiting pressure density of the model.

The inverse problem is tested for a class of statistical mechanics mean-field models: the Curie-Weiss model together with its multi-species version and the monomer-dimer model with attractive interaction. In particular, we show that the inversion is obtained by analytically identifying the model parameters in terms of the correlation functions. Moreover, we show that the robustness of the inversion procedure depends on the knowledge of the phase space of the system.

In the first part of this talk we review the main definitions, concepts and classical results on neural networks, distinguishing between the two principal cognitive tasks, i.e., "learning" and "retrieval". Focusing on the latter, the Hopfield model is probably the one most extensively investigated, although it exhibits an intrinsic capacity limit (in terms of the ratio between the amount P of stored patterns and the network size N) far below the theoretical known bound. In this talk we will show that this limit can be improved by means of “unlearning” iterations which mimic unconscious mechanisms taking place during the REM phase of mammals.

Belief Propagation (BP) is an iterative message passing algorithm that can be used to derive marginal probabilities on a system within the Bethe-Peierls approximation. It is not well understood how this deep learning method is able to learn and how it doesn't get trapped in configurations with low computational performance. Since we aim to classify the congestion situations, we analyze the fundamental diagram of traffic which gives a relation between the traffic flow and the traffic density. A traffic congestion occurs when the density of the road grows up and the flow decreases. In order to predict congestion situations, we train the BP neural network using binarized vectors obtained by the processing of the fundamental diagram. We apply our method to real data which have been recorded by traffic detectors provided by Emilia Romagna region.