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Spectral dynamics of learning in restricted Boltzmann machines

Publicated to:Epl. 119 (6): 60001- - 2017-09-01 119(6), DOI: 10.1209/0295-5075/119/60001

Authors: Decelle, A; Fissore, G; Furtlehner, C

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Abstract

The restricted Boltzmann machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical observations, we propose a generic statistical ensemble for the weight matrix of the RBM and characterize its mean evolution. This let us show how in the linear regime, in which the RBM is found to operate at the beginning of the training, the statistical properties of the data drive the selection of the unstable modes of the weight matrix. A set of equations characterizing the non-linear regime is then derived, unveiling in some way how the selected modes interact in later stages of the learning procedure and defining a deterministic learning curve for the RBM. Copyright (C) EPLA, 2017

Keywords

ModelNeural-networks

Quality index

Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal Epl due to its progression and the good impact it has achieved in recent years, according to the agency WoS (JCR), it has become a reference in its field. In the year of publication of the work, 2017, it was in position 36/78, thus managing to position itself as a Q2 (Segundo Cuartil), in the category Physics, Multidisciplinary. Notably, the journal is positioned en el Cuartil Q2 para la agencia Scopus (SJR) en la categoría Physics and Astronomy (Miscellaneous).

From a relative perspective, and based on the normalized impact indicator calculated from World Citations provided by WoS (ESI, Clarivate), it yields a value for the citation normalization relative to the expected citation rate of: 1.12. This indicates that, compared to works in the same discipline and in the same year of publication, it ranks as a work cited above average. (source consulted: ESI Nov 14, 2024)

Specifically, and according to different indexing agencies, this work has accumulated citations as of 2025-06-03, the following number of citations:

  • WoS: 27

Impact and social visibility

From the perspective of influence or social adoption, and based on metrics associated with mentions and interactions provided by agencies specializing in calculating the so-called "Alternative or Social Metrics," we can highlight as of 2025-06-03:

  • The use, from an academic perspective evidenced by the Altmetric agency indicator referring to aggregations made by the personal bibliographic manager Mendeley, gives us a total of: 32.
  • The use of this contribution in bookmarks, code forks, additions to favorite lists for recurrent reading, as well as general views, indicates that someone is using the publication as a basis for their current work. This may be a notable indicator of future more formal and academic citations. This claim is supported by the result of the "Capture" indicator, which yields a total of: 32 (PlumX).

With a more dissemination-oriented intent and targeting more general audiences, we can observe other more global scores such as:

  • The Total Score from Altmetric: 5.95.
  • The number of mentions on the social network Facebook: 3 (Altmetric).
  • The number of mentions on the social network X (formerly Twitter): 10 (Altmetric).

Leadership analysis of institutional authors

This work has been carried out with international collaboration, specifically with researchers from: France.

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: First Author (DECELLE, AURELIEN FABRICE) .

the author responsible for correspondence tasks has been DECELLE, AURELIEN FABRICE.