Machine de Boltzmann restreinte

Résumé

En apprentissage automatique, la machine de Boltzmann restreinte est un type de réseau de neurones artificiels pour l'apprentissage non supervisé. Elle est couramment utilisée pour avoir une estimation de la distribution probabiliste d'un jeu de données. Elle a initialement été inventée sous le nom de Harmonium en 1986 par Paul Smolenski. Les machine de Boltzmann restreinte rentre dans le cadre des modèles graphiques et des modèles à base d'énergie. Description Dans sa forme la plus simple, une machine de Boltzmann est composée d'une couche de neurones qui reçoit l'entrée, ainsi que d'une couche de neurones cachée. Si on suppose que les neurones d'une même couche sont indépendants entre eux, on appelle cette configuration une machine de Boltzmann restreinte (RBM). vignette|Machine de Boltzmann Restreinte On définit l'énergie pour une configuration de donnée de la manière suivante : E = -\left(\sum_{i,j} w_{ij} , x_i , h_j + \sum_i b_i , x_i + \sum_j c_j h_j \

Source officielle

https://fr.wikipedia.org/wiki/Machine_de_Boltzmann_restreinte

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Parallel retrieval of correlated patterns: From Hopfield networks to Boltzmann machines

Andrea De Antoni

In this work, we first revise some extensions of the standard Hopfield model in the low storage limit, namely the correlated attractor case and the multitasking case recently introduced by the authors. The former case is based on a modification of the Hebbian prescription, which induces a coupling between consecutive patterns and this effect is tuned by a parameter a. In the latter case, dilution is introduced in pattern entries, in such a way that a fraction d of them is blank. Then, we merge these two extensions to obtain a system able to retrieve several patterns in parallel and the quality of retrieval, encoded by the set of Mattis magnetizations {m(mu)}, is reminiscent of the correlation among patterns. By tuning the parameters d and a, qualitatively different outputs emerge, ranging from highly hierarchical to symmetric. The investigations are accomplished by means of both numerical simulations and statistical mechanics analysis, properly adapting a novel technique originally developed for spin glasses, i.e. the Hamilton-Jacobi interpolation, with excellent agreement. Finally, we show the thermodynamical equivalence of this associative network with a (restricted) Boltzmann machine and study its stochastic dynamics to obtain even a dynamical picture, perfectly consistent with the static scenario earlier discussed. (c) 2012 Elsevier Ltd. All rights reserved.

Elsevier2013

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Preconditioned Spectral Descent for Deep Learning

Volkan Cevher, Edo Collins, Ya-Ping Hsieh

Deep learning presents notorious computational challenges. These challenges in- clude, but are not limited to, the non-convexity of learning objectives and estimat- ing the quantities needed for optimization algorithms, such as gradients. While we do not address the non-convexity, we present an optimization solution that exploits the so far unused “geometry” in the objective function in order to best make use of the estimated gradients. Previous work attempted similar goals with precon- ditioned methods in the Euclidean space, such as L-BFGS, RMSprop, and ADA- grad. In stark contrast, our approach combines a non-Euclidean gradient method with preconditioning. We provide evidence that this combination more accurately captures the geometry of the objective function compared to prior work. We theo- retically formalize our arguments and derive novel preconditioned non-Euclidean algorithms. The results are promising in both computational time and quality when applied to Restricted Boltzmann Machines, Feedforward Neural Nets, and Convolutional Neural Nets.

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Restricted Boltzmann machines in quantum physics

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