Haldane bundles: a dataset for learning to predict the Chern number of line bundles on the torus

Cody Tipton, Elizabeth Coda, Davis Brown, Alyson Bittner, Jung Lee, Grayson Jorgenson, Tegan Emerson, Henry Kvinge
Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, PMLR 228:55-74, 2024.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v228-tipton24a, title = {Haldane bundles: a dataset for learning to predict the Chern number of line bundles on the torus}, author = {Tipton, Cody and Coda, Elizabeth and Brown, Davis and Bittner, Alyson and Lee, Jung and Jorgenson, Grayson and Emerson, Tegan and Kvinge, Henry}, booktitle = {Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations}, pages = {55--74}, year = {2024}, editor = {Sanborn, Sophia and Shewmake, Christian and Azeglio, Simone and Miolane, Nina}, volume = {228}, series = {Proceedings of Machine Learning Research}, month = {16 Dec}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v228/main/assets/tipton24a/tipton24a.pdf}, url = {https://proceedings.mlr.press/v228/tipton24a.html}, 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.} }
Endnote
%0 Conference Paper %T Haldane bundles: a dataset for learning to predict the Chern number of line bundles on the torus %A Cody Tipton %A Elizabeth Coda %A Davis Brown %A Alyson Bittner %A Jung Lee %A Grayson Jorgenson %A Tegan Emerson %A Henry Kvinge %B Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations %C Proceedings of Machine Learning Research %D 2024 %E Sophia Sanborn %E Christian Shewmake %E Simone Azeglio %E Nina Miolane %F pmlr-v228-tipton24a %I PMLR %P 55--74 %U https://proceedings.mlr.press/v228/tipton24a.html %V 228 %X 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.
APA
Tipton, C., Coda, E., Brown, D., Bittner, A., Lee, J., Jorgenson, G., Emerson, T. & Kvinge, H.. (2024). Haldane bundles: a dataset for learning to predict the Chern number of line bundles on the torus. Proceedings of the 2nd NeurIPS Workshop on Symmetry and Geometry in Neural Representations, in Proceedings of Machine Learning Research 228:55-74 Available from https://proceedings.mlr.press/v228/tipton24a.html.

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