Haldane Bundles: A Dataset for Learning to Predict the Chern Number of Line Bundles on the Torus

Published: 29 Nov 2023, Last Modified: 29 Nov 2023NeurReps 2023 PosterEveryoneRevisionsBibTeX
Submission Track: Proceedings
Keywords: Benchmark datasets, vector bundles, characteristic classes, topological insulators
TL;DR: We introduce a benchmark dataset to develop machine learning approaches to predicting characteristic classes of vector bundles
Abstract: Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the *Haldane bundle dataset*, which consists of synthetically generated complex line bundles on the $2$-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes.
Submission Number: 5