# Phase transition encoded in neural network

## TL;DR

This paper demonstrates that neural networks trained to predict temperature in Ising/Potts models inherently encode phase transition information in their parameters, revealing how physical phenomena are captured by learned features.

## Contribution

It shows that neural networks trained for temperature prediction automatically learn and encode phase transition information without explicit supervision.

## Key findings

- Weights in trained networks contain phase transition information.
- Networks learn different physical quantities depending on training quality.
- Critical temperature can be identified from network parameters.

## Abstract

We discuss an aspect of neural networks for the purpose of phase transition detection. To this end, we first train the neural network by feeding Ising/Potts configurations with labels of temperature so that it can predict the temperature of input. We do not explicitly supervise whether the configurations are in ordered/disordered phase. Nevertheless, we can identify the critical temperature from the parameters (weights and biases) of trained neural network. We attempt to understand how temperature-supervised neural networks capture the information of phase transition by paying attention to what quantities they learn. Our detailed analyses reveal that they learn different physical quantities depending on how well they are trained. Main observation in this study is how the weights in the trained neural-network can have information of the phase transition in addition to temperature.