# Machine Learning of Explicit Order Parameters: From the Ising Model to SU(2) Lattice Gauge Theory

## TL;DR

This paper introduces a machine learning pipeline that reconstructs explicit order parameters from neural network decision functions, successfully applied to the Ising model and SU(2) lattice gauge theory, without prior knowledge of the Hamiltonian.

## Contribution

It presents a novel method to extract explicit order parameters from neural networks in phase classification tasks, applicable to complex physical systems.

## Key findings

- Successfully deduced known order parameters from neural network decision functions.
- Applicable to both classical and quantum lattice models.
- Enabled detection of phase transitions without prior physical knowledge.

## Abstract

We present a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The procedure is embedded into a pipeline of machine learning algorithms able to detect the existence of different phases of matter, to determine the position of phase transitions and to find explicit expressions of the physical quantities by which the algorithm distinguishes between phases. We assume no prior knowledge about the Hamiltonian or the order parameters except Monte Carlo-sampled configurations. The method is applied to the Ising Model and SU(2) lattice gauge theory. In both systems we deduce the explicit expressions of the known order parameters from the decision functions of the neural networks.