Inferring effective couplings with restricted Boltzmann machines
Aurélien Decelle, Cyril Furtlehner, Alfonso De Jesús Navas Gómez, Beatriz Seoane
SciPost Phys. 16, 095 (2024) · published 5 April 2024
- doi: 10.21468/SciPostPhys.16.4.095
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Abstract
Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a neural network. We address here the challenge of understanding the physical interpretation of such models. In this study, we propose a simple solution by implementing a direct mapping between the Restricted Boltzmann Machine and an effective Ising spin Hamiltonian. This mapping includes interactions of all possible orders, going beyond the conventional pairwise interactions typically considered in the inverse Ising (or Boltzmann Machine) approach, and allowing the description of complex datasets. Earlier works attempted to achieve this goal, but the proposed mappings were inaccurate for inference applications, did not properly treat the complexity of the problem, or did not provide precise prescriptions for practical application. To validate our method, we performed several controlled inverse numerical experiments in which we trained the RBMs using equilibrium samples of predefined models with local external fields, 2-body and 3-body interactions in different sparse topologies. The results demonstrate the effectiveness of our proposed approach in learning the correct interaction network and pave the way for its application in modeling interesting binary variable datasets. We also evaluate the quality of the inferred model based on different training methods.
Cited by 1
Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 1 Université Paris-Saclay / University of Paris-Saclay
- 2 Universidad Complutense de Madrid / Complutense University of Madrid
- Banco Santander
- Comunidad de Madrid
- Ministerio de Economía y Competitividad (MINECO) (through Organization: Ministerio de Economía, Industria y Competitividad / Ministry of Economy, Industry and Competitiveness [MINECO])