Classifying topological sector via machine learning

TL;DR

This paper demonstrates that a convolutional neural network can accurately estimate the topological charge in SU(3) Yang-Mills configurations from topological charge density data, revealing insights into feature detection across dimensions.

Contribution

It introduces a machine learning approach to estimate topological charge and investigates the role of data dimensionality in neural network performance.

Findings

Neural network estimates Q with high accuracy at small flow time.

Dimensional reduction does not significantly affect estimation accuracy.

Neural network does not rely on high-dimensional features for Q estimation.

Abstract

We employ a machine learning technique for an estimate of the topological charge $Q$ of gauge configurations in SU(3) Yang-Mills theory in vacuum. As a first trial, we feed the four-dimensional topological charge density with and without smoothing into the convolutional neural network and train it to estimate the value of $Q$. We find that the trained neural network can estimate the value of $Q$ from the topological charge density at small flow time with high accuracy. Next, we perform the dimensional reduction of the input data as a preprocessing and analyze lower dimensional data by the neural network. We find that the accuracy of the neural network does not have statistically-significant dependence on the dimension of the input data. From this result we argue that the neural network does not find characteristic features responsible for the determination of $Q$ in the higher dimensional space.