# Machine-Learning Mathematical Structures

@article{He2022MachineLearningMS, title={Machine-Learning Mathematical Structures}, author={Yang-Hui He}, journal={ArXiv}, year={2022}, volume={abs/2101.06317} }

We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from different fields ranging from geometry to representation theory, from combinatorics to number theory, we present a comparative study of the accuracies on different problems. The paradigm should be useful for conjecture formulation, finding more efficient methods of…

## 12 Citations

### SC-Square: Future Progress with Machine Learning?

- Computer Science
- 2022

This extended abstract, to accompany a keynote talk at the 2021 SC-Square Workshop, survey recent work on the use of Machine Learning technology to improve algorithms of interest to SC- Square.

### Towards Understanding Grokking: An Effective Theory of Representation Learning

- Computer ScienceArXiv
- 2022

This study provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

### Machine Learning Algebraic Geometry for Physics

- Computer Science
- 2022

A chapter contribution to the book Machine learning and Algebraic Geometry, edited by A. Kasprzyk et al.

### Cluster Algebras: Network Science and Machine Learning

- Mathematics, Computer ScienceArXiv
- 2022

Network analysis methods are applied to the exchange graphs for cluster algebras of varying mutation types and indicates that when the graphs are represented without identifying by permutation equivalence between clusters an elegant symmetry emerges in the quiver exchange graph embedding.

### Machine learning Calabi-Yau hypersurfaces

- Mathematics, Computer SciencePhysical Review D
- 2022

This work revisits the classic database of weighted-Ps which admit Calabi-Yau 3-fold hypersurfaces equipped with a diverse set of tools from the machine-learning toolbox and identifies a previously unnoticed clustering in the Calabi/Yau data.

### Advancing mathematics by guiding human intuition with AI

- Mathematics, Computer ScienceNature
- 2021

This work proposes a process of using machine learning to discover potential patterns and relations between mathematical objects, understanding them with attribution techniques and using these observations to guide intuition and propose conjectures, and demonstrates its successful application to current research questions in distinct areas of pure mathematics.

### Polytopes and Machine Learning

- Computer Science
- 2021

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…

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