Smallest Neural Network to Learn the Ising Criticality

TL;DR

This paper demonstrates that a neural network with only two hidden neurons can accurately learn and predict the critical temperature of the Ising model, revealing minimal complexity needed for phase transition learning.

Contribution

It shows that a neural network with just two hidden neurons can effectively learn the Ising phase transition and exploits universality to generalize across different lattices.

Findings

Two hidden neurons suffice for accurate critical temperature prediction.

The network learns the scaling dimension of the order parameter.

The approach exploits Ising universality across lattice types.

Abstract

Learning with an artificial neural network encodes the system behavior in a feed-forward function with a number of parameters optimized by data-driven 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.