Outputs (6)

Polytopes and machine learning (2023)
Journal Article
Bao, J., He, Y.-H., Hirst, E., Hofscheier, J., Kasprzyk, A., & Majumder, S. (2023). Polytopes and machine learning. International Journal of Data Science in the Mathematical Sciences, 1(2), 181-211. https://doi.org/10.1142/S281093922350003X

We introduce machine learning methodology to the study of lattice polytopes. With supervised learning techniques, we predict standard properties such as volume, dual volume, reflexivity, etc, with accuracies up to 100%. We focus on 2d polygons and 3d... Read More about Polytopes and machine learning.

Machine learning detects terminal singularities (2023)
Presentation / Conference Contribution
Kasprzyk, A. M., Coates, T., & Veneziale, S. (2023, December). Machine learning detects terminal singularities. Presented at 37th Conference on Neural Information Processing Systems (NeurIPS 2023), New Orleans, USA

Algebraic varieties are the geometric shapes defined by systems of polynomial equations; they are ubiquitous across mathematics and science. Amongst these algebraic varieties are Q-Fano varieties: positively curved shapes which have Q-factorial termi... Read More about Machine learning detects terminal singularities.

The Rapid Rise of Generative AI: Assessing risks to safety and security (2023)
Report
Janjeva, A., Harris, A., Mercer, S., Kasprzyk, A., & Gausen, A. (2023). The Rapid Rise of Generative AI: Assessing risks to safety and security. Alan Turing Institute

This CETaS Research Report presents the findings from a major project exploring the implications of generative AI for national security. It is based on extensive engagement with more than 50 experts across government, academia, industry, and civil so... Read More about The Rapid Rise of Generative AI: Assessing risks to safety and security.

Machine learning the dimension of a Fano variety (2023)
Journal Article
Kasprzyk, A. M., Coates, T., & Veneziale, S. (2023). Machine learning the dimension of a Fano variety. Nature Communications, 14, Article 5526. https://doi.org/10.1038/s41467-023-41157-1

Fano varieties are basic building blocks in geometry – they are ‘atomic pieces’ of mathematical shapes. Recent progress in the classification of Fano varieties involves analysing an invariant called the quantum period. This is a sequence of integers... Read More about Machine learning the dimension of a Fano variety.

Machine Learning: The Dimension of a Polytope (2023)
Book Chapter
Coates, T., Hofscheier, J., & Kasprzyk, A. M. (2023). Machine Learning: The Dimension of a Polytope. In Machine Learning in Pure Mathematics and Theoretical Physics (85-104). World Scientific. https://doi.org/10.1142/9781800613706_0003

We use machine learning to predict the dimension of a lattice polytope directly from its Ehrhart series. This is highly effective, achieving almost 100% accuracy. We also use machine learning to recover the volume of a lattice polytope from its Ehrha... Read More about Machine Learning: The Dimension of a Polytope.

Toric Sarkisov Links of Toric Fano Varieties (2023)
Presentation / Conference Contribution
Brown, G., Buczyński, J., & Kasprzyk, A. (2019, April). Toric Sarkisov Links of Toric Fano Varieties. Presented at Birational Geometry, Kähler–Einstein Metrics and Degenerations, Moscow, Shanghai and Pohang

We explain a web of Sarkisov links that overlies the classification of Fano weighted projective spaces in dimensions 3 and 4, extending results of Prokhorov.