Speaker: Mustafa Hajij, Santa Clara UniversityTitle: Algebraically-Informed Deep Networks (AIDN): A Deep Learning Approach to Represent Algebraic StructuresDate: 04/13/2021Time: 2:50 PM - 3:40 PMPlace: Online (virtual meeting) (Virtual Meeting Link)Contact: Honghao Gao (gaohongh@msu.edu)

One of the central problems in the interface of deep learning and mathematics is that of building learning systems that can automatically uncover underlying mathematical laws from observed data. In this work, we make one step towards building a bridge between algebraic structures and deep learning, and introduce\textbf {AIDN},\textit {Algebraically-Informed Deep Networks}.\textbf {AIDN} is a deep learning algorithm to represent any finitely-presented algebraic object with a set of deep neural networks. The deep networks obtained via\textbf {AIDN} are\textit {algebraically-informed} in the sense that they satisfy the algebraic relations of the presentation of the algebraic structure that serves as the input to the algorithm. Our proposed network can robustly compute linear and non-linear representations of most finitely-presented algebraic structures such as groups, associative algebras, and Lie algebras. We evaluate our proposed approach and demonstrate its applicability to algebraic and geometric objects that are significant in low-dimensional topology. In particular, we study solutions for the Yang-Baxter equations and their applications on braid groups. Further, we study the representations of the Temperley-Lieb algebra. Finally, we show, using the Reshetikhin-Turaev construction, how our proposed deep learning approach can be utilized to construct new link invariants. We believe the proposed approach would tread a path toward a promising future research in deep learning applied to algebraic and geometric structures.

Department of Mathematics

Michigan State University

619 Red Cedar Road

C212 Wells Hall

East Lansing, MI 48824

Phone: (517) 353-0844

Fax: (517) 432-1562

- People
- All
- Regular Faculty
- Postdocs
- Fixed Term/Visiting Faculty
- Specialists and Instructors
- Adjunct Faculty
- Emeriti
- Graduate Students
- Teaching Assistants
- Staff
- Administration
- Diversity, Equity, Inclusiveness
- Faculty Honors

- Research
- Faculty Research Interests
- Seminars
- Seminars by Week
- Geometry & Topology
- MCIAM
- MathSciNet
- Institute of Mathematical Physics
- Math Library
- Phillips Lecture

- Undergraduate
- Undergraduate Program
- Class Pages
- Student Portal
- Webwork
- Math Learning Center
- Actuarial Science
- Advising Information
- Override Request
- Math Placement Service
- Herzog Competition
- Scholarships
- Exchange Program
- Sample Finals
- Multicultural Center Feasibility