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

arXiv: https://arxiv.org/abs/2312.04600 · HTML: https://mlsanity.com/paper/2312.04600/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 22 references that are in the map.
- First posted on arXiv 6 Dec 2023.

## Builds on (most cited first, 6 of 6)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Bundle Networks: Fiber Bundles, Local Trivializations, and a Generative Approach to Exploring Many-to-one Maps](https://mlsanity.com/paper/2110.06983/) (2021)
- [FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundles](https://mlsanity.com/paper/2206.06513/) (2022)
- [Fiber Bundle Morphisms as a Framework for Modeling Many-to-Many Maps](https://mlsanity.com/paper/2203.08189/) (2022)

## Built on by (most cited first, 1 of 1)

- [Adjusted Cup-Product Neural Layer](https://mlsanity.com/paper/2606.13568/) (2026)

## Abstract (arXiv)

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.