A New Look at the Spin Glass Problem from a Deep Learning Perspective

Abstract

Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method.

P-Adic Statistical Field Theory and Deep Belief Networks

“…Finally, we want to mention that the literature about statistical mechanics and machine learning is enormous; see, e.g., [54]- [55], and the references therein. To the best of our knowledge, our results are new and complementary to the ones available in the literature.…”