# Unsupervised learning using topological data augmentation

## TL;DR

This paper introduces a novel unsupervised deep learning method that employs topological data augmentation to classify quantum systems based on their topological indices with high accuracy.

## Contribution

The paper proposes a new unsupervised learning protocol using topological data augmentation to identify topological indices in quantum systems.

## Key findings

- Achieves near 100% classification accuracy
- Successfully classifies objects outside training regime
- Demonstrates effectiveness on 1d and 2d insulators

## Abstract

Unsupervised machine learning is a cornerstone of artificial intelligence as it provides algorithms capable of learning tasks, such as classification of data, without explicit human assistance. We present an unsupervised deep learning protocol for finding topological indices of quantum systems. The core of the proposed scheme is a 'topological data augmentation' procedure that uses seed objects to generate ensembles of topologically equivalent data. Such data, assigned with dummy labels, can then be used to train a neural network classifier for sorting arbitrary objects into topological equivalence classes. Our protocol is explicitly illustrated on 2-band insulators in 1d and 2d, characterized by a winding number and a Chern number respectively. By using the augmentation technique also in the classification step we can achieve accuracy arbitrarily close to 100% even for objects with indices outside the training regime.