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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
84/2020

Natural Wake-Sleep Algorithm

Csongor Varady, Nihat Ay, Riccardo Volpi and Luigi Malagò

Abstract

The benefits of using the natural gradient are well known in a wide range of optimization problems. However, for the training of common neural networks the resulting increase in computational complexity sets a limitation to its practical application. Helmholtz Machines are a particular type of generative model composed of two Sigmoid Belief Networks (SBNs), acting as an encoder and a decoder, commonly trained using the Wake-Sleep (WS) algorithm and its reweighted version RWS. For SBNs, it has been shown how the locality of the connections in the graphical structure induces sparsity in the Fisher information matrix. The resulting block diagonal structure can be efficiently exploited to reduce the computational complexity of the Fisher matrix inversion and thus compute the natural gradient exactly, without the need of approximations. We present a geometric adaptation of well-known methods from the literature, introducing the Natural Wake-Sleep (NWS) and the Natural Reweighted Wake-Sleep (NRWS) algorithms. We present an experimental analysis of the novel geometrical algorithms based on the convergence speed and the value of the log-likelihood, both with respect to the number of iterations and the time complexity and demonstrating improvements on these aspects over their respective non-geometric baselines.

Received:
Aug 21, 2020
Published:
Aug 21, 2020
Keywords:
natural gradient, Helmholtz machines, wake-sleep algorithm, Sigmoid Belief Networks, Generative Models

Related publications

inJournal
2022 Repository Open Access
Csongor Várady, Riccardo Volpi, Luigi Malagò and Nihat Ay

Natural reweighted wake-sleep

In: Neural networks, 155 (2022), pp. 574-591