More interestingly, there is a deep connection between the Boltzmann machine and tensor networks of quantum many-body systems. proposed a quantum Boltzmann machine based on the quantum Boltzmann distribution of a quantum Hamiltonian. employed the Thouless–Anderson–Palmer mean-field approximation, used for a spin glass problem, to replace the Gibbs sampling of contrastive-divergence training. Recently, RBMs have gained renewed attention in physics since Carleo and Troyer showed that a quantum many-body state could be efficiently represented by the RBM. Īs its name implies, the RBM is closely connected to physics and they share some important concepts such as entropy, free energy, and so forth. RBMs have been applied widely, for example, in dimensionality reduction, classification, feature learning, pattern recognition, topic modeling, and so on. An RBM is an undirected Markov random field and is considered a basic building block of deep neural networks. RBMs and general Boltzmann machines are described by a probability distribution with parameters, i.e., the Boltzmann distribution. 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.Ī restricted Boltzmann machine (RBM) is a generative probabilistic neural network. 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 demonstrate the growth of the correlation between the visible and hidden layers via the subadditivity of entropies as the training proceeds. 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. In this paper, we analyze the training process of the restricted Boltzmann machine in the context of statistical physics. Given training data, its learning is done by optimizing the parameters of the energy function of the network. A probability of finding the network in a certain configuration is given by the Boltzmann distribution. A restricted Boltzmann machine is a generative probabilistic graphic network.
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