Learning a spin glass: determining Hamiltonians from metastable states

TL;DR

This paper investigates how to infer the Hamiltonian of a fully connected Ising Spin Glass from measurements of its local minima, extending learning theory to complex spin systems and analyzing the effectiveness of various algorithms.

Contribution

It introduces a framework for learning Hamiltonians from metastable states in spin glasses, bridging neural network learning theory with statistical physics.

Findings

Analytical and simulation results on learning curves

Comparison of different algorithms for Hamiltonian inference

Insights into the complexity of learning in rugged energy landscapes

Abstract

We study the problem of determining the Hamiltonian of a fully connected Ising Spin Glass of $N$ units from a set of measurements, whose sizes needs to be ${\cal O}(N^2)$ bits. The student-teacher scenario, used to study learning in feed-forward neural networks, is here extended to spin systems with arbitrary couplings. The set of measurements consists of data about the local minima of the rugged energy landscape. We compare simulations and analytical approximations for the resulting learning curves obtained by using different algorithms.