Developing a Maximum-Entropy Restricted Boltzmann Machine with a Quantum Thermodynamics Formalism

TL;DR

This paper introduces a novel Restricted Boltzmann Machine that employs quantum thermodynamics principles and entropy maximization to model physical systems, demonstrating its effectiveness on the Inverse Ising Problem.

Contribution

It presents a new entropy-based RBM framework incorporating quantum thermodynamics, enabling modeling of complex physical and biological systems.

Findings

Accurately modeled temperature-dependent physical quantities

Achieved results consistent with existing literature

Demonstrated applicability to quantum and biological systems

Abstract

We propose a Restricted Boltzmann Machine (RBM) neural network using a quantum thermodynamics formalism and the maximization of entropy as the cost function for the optimization problem. We verify the possibility of using an entropy maximization approach for modeling physical systems by applying it to the Inverse Ising Problem, which describes a system of interacting spins. The temperature-dependent behaviors of physical quantities, such as magnetization and Gibbs energy, were calculated from the Ising Hamiltonian whose coefficients were obtained through entropy maximization and were found to be in good agreement to literature results. These results suggest that RBM neural networks using the principle of maximum entropy can be applied to modeling physical systems that can be described by discrete states, including fundamental quantum physics such as topological systems, and biological systems such as the correlated spiking of neurons.