Details

Autor(en) / Beteiligte

• Oh, Sangchul
• Baggag, Abdelkader
• Nha, Hyunchul

Titel

Entropy, Free Energy, and Work of Restricted Boltzmann Machines

Ist Teil von

• Entropy (Basel, Switzerland), 2020-05, Vol.22 (5), p.538

Ort / Verlag

MDPI

Erscheinungsjahr

2020

Link zum Volltext

Quelle

EZB Electronic Journals Library

Beschreibungen/Notizen

• A restricted Boltzmann machine is a generative probabilistic graphic network. A probability of finding the network in a certain configuration is given by the Boltzmann distribution. Given training data, its learning is done by optimizing the parameters of the energy function of the network. In this paper, we analyze the training process of the restricted Boltzmann machine in the context of statistical physics. As an illustration, for small size bar-and-stripe patterns, we calculate thermodynamic quantities such as entropy, free energy, and internal energy as a function of the training epoch. We demonstrate the growth of the correlation between the visible and hidden layers via the subadditivity of entropies as the training proceeds. Using the Monte-Carlo simulation of trajectories of the visible and hidden vectors in the configuration space, we also calculate the distribution of the work done on the restricted Boltzmann machine by switching the parameters of the energy function. We discuss the Jarzynski equality which connects the path average of the exponential function of the work and the difference in free energies before and after training.