Smallest neural network to learn the Ising criticality
Abstract
Learning with an artificial neural network encodes the system behavior in a feedforward function with a number of parameters optimized by datadriven training. An open question is whether one can minimize the network complexity without loss of performance to reveal how and why it works. Here we investigate the learning of the phase transition in the Ising model and find that having two hidden neurons can be enough for an accurate prediction of critical temperature. We show that the networks learn the scaling dimension of the order parameter while being trained as a phase classifier, demonstrating how the machine learning exploits the Ising universality to work for different lattices of the same criticality within a single set of trainings in one lattice geometry.
 Publication:

Physical Review E
 Pub Date:
 August 2018
 DOI:
 10.1103/PhysRevE.98.022138
 arXiv:
 arXiv:1804.02171
 Bibcode:
 2018PhRvE..98b2138K
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 Phys. Rev. E 98, 022138 (2018)