Interpreting machine learning functions as physical observables

TL;DR

This paper introduces a novel approach to interpret neural network functions as physical observables, enabling the application of statistical-mechanical methods to analyze phase transitions without prior symmetry knowledge.

Contribution

It presents a new framework that treats machine learning functions as physical observables, facilitating the study of phase transitions and order-disorder phenomena in physical systems.

Findings

Applied histogram reweighting and finite-size scaling to neural network outputs.

Demonstrated inducing phase transitions via predictive functions as conjugate variables.

No prior symmetry knowledge needed for the analysis.

Abstract

We propose to interpret machine learning functions as physical observables, opening up the possibility to apply "standard" statistical-mechanical methods to outputs from neural networks. This includes histogram reweighting and finite-size scaling, to analyse phase transitions quantitatively. In addition we incorporate predictive functions as conjugate variables coupled to an external field within the Hamiltonian of a system, allowing to induce order-disorder phase transitions in a novel manner. A noteworthy feature of this approach is that no knowledge of the symmetries in the Hamiltonian is required.