Simpler Grassmannian optimization
Lai, Zehua, Lek-Heng Lim, and Ke Ye. "Simpler Grassmannian optimization." arXiv preprint arXiv:2009.13502 (2020).
CV
pdf version here
Employment
- Since 2023, R. H. Bing Instructor of Mathematics, University of Texas at Austin, Austin, TX
Education
- 2018-2023, Ph.D. in Computational and Applied Mathematics, University of Chicago, Chicago, IL.
- 2014-2018, B.A. in Mathematics, B.A. in Economics and Finance, Tsinghua University, Beijing, China.
Publications
Recht-Ré noncommutative arithmetic-geometric mean conjecture is false
Lai, Zehua, and Lek-Heng Lim. "Recht-Ré noncommutative arithmetic-geometric mean conjecture is false." In International Conference on Machine Learning, pp. 5608-5617. PMLR, 2020.
Haagerup Bound for Quaternionic Grothendieck Inequality
Shmuel Friedland, Zehua Lai, and Lek-Heng Lim. "Haagerup Bound for Quaternionic Grothendieck Inequality." arXiv e-prints (2021): arXiv-2212.00208.
Simpler Flag Optimization
Zehua Lai, Lek-Heng Lim, and Ke Ye. "Simpler Flag Optimization." arXiv e-prints (2021): arXiv-2212.00212.
Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent
Chen, Xi, Zehua Lai, He Li, and Yichen Zhang. "Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent." preprints (2022).
Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods
Chen, Xi, Zehua Lai, He Li, and Yichen Zhang. "Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods." Journal of the American Statistical Association，(2023),https://doi.org/10.1080/01621459.2023.2296703.
Stochastic Steffensen Method
Minda Zhao, Zehua Lai, and Lek-Heng Lim. "Stochastic Steffensen Method." Computational Optimization and Applications, (2024), https://doi.org/10.1007/s10589-024-00583-7.
Attention is a smoothed cubic spline
Zehua Lai, Lek-Heng Lim, and Yucong Liu. "Attention is a smoothed cubic spline." arXiv e-prints (2024): arXiv-2408.09624.
Euclidean distance degree in manifold optimization
Zehua Lai, Lek-Heng Lim, and Ke Ye. "Euclidean distance degree in manifold optimization." arXiv e-prints (2025): arXiv-2502.10336.
Simple matrix expressions for the curvatures of Grassmannian
Zehua Lai, Lek-Heng Lim, and Ke Ye. "Simple matrix expressions for the curvatures of Grassmannian." arXiv e-prints (2024): arXiv-2406.11821.
Grassmannian optimization is NP-hard
Zehua Lai, Lek-Heng Lim, and Ke Ye. "Grassmannian optimization is NP-hard." arXiv e-prints (2024): arXiv-2406.19377.
Talks
On Matrix Arithmetic-Geometric Mean Inequality and Noncommutative Positivstellensatz
Talk at Seminar, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing， China
On Matrix Arithmetic-Geometric Mean Inequality and Noncommutative Positivstellensatz
Talk at AMS Fall Central Sectional Meeting, Special Session on Applications of Algebra and Geometry, University of Wisconsin-Madison, Madison, Madison, US
Stochastic Steffensen Method
Talk at International Conference on Data Science, Fudan University, Shanghai， China
Recht-Re Noncommutative Arithmetic-Geometric Mean Conjecture is False
Talk at 37th International Conference on Machine Learning, Online
Recht-Re Noncommutative Arithmetic-Geometric Mean Conjecture is False
Talk at Algebraic Statistics Online Seminar, Online
Recht-Re Noncommutative Arithmetic-Geometric Mean Conjecture is False
Talk at Sanya Workshop on Algebraic Geometry and Machine Learning, Online
Recht-Re Noncommutative Arithmetic-Geometric Mean Conjecture is False
Talk at UCSD Optimization and Data Science Seminar, Online
Online Statistical Inference for Gradient-free Stochastic Optimization
Talk at CAM Student Seminar, Online
Noncommutative positivstellensatz and stochastic gradient descent
Talk at 4th Annual Meeting of the Texas Louisiana Section, South Padre Island, US
Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods
Talk at AMS Spring Central Sectional Meeting, Special Session on Mathematical Foundation of Data Science in Scientific Computing, Online
Simpler Grassmannian Optimization
Talk at AMS Spring Central Sectional Meeting, Special Session on Numerical Linear Algebra, Online
Simpler Grassmannian optimization
Talk at Joint Mathematics Meetings, International Linear Algebra Society Special Session on Matrix Analysis and Applications, Online
Embedding models for Grassmannians and flag manifolds
Talk at The 2nd Young Topologist Seminar-BIMSA, Online
Central limit theorems for stochastic optimization
Talk at Center for Computational and Applied Mathematics Seminar, Purdue University, West Lafayette, IN
Central limit theorems for stochastic optimization
Talk at Seminar, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China
Optimization on Grassmannian and Flag manifolds
Talk at SIAM Conference on Applied Algebraic Geometry, Eindhoven University of Technology, Eindhoven, Netherlands
Central limit theorems for stochastic optimization
Talk at Applied Mathematics Seminar, University of Texas at Austin, Austin, TX
Central limit theorems for stochastic optimization
Talk at Workshop on Statistical Machine Learning for High Dimensional Data, Institute for Mathematical Sciences, National University of Singapore, Singapore
Tensor Products of Reproducing Kernel Banach Spaces
Talk at 2024 Workshop: Matrices and Operators, The Department of Mathematics and Statistics, University of Nevada, Reno, NV
Attention is a cubic spline
Talk at Applied Algebra Seminar, The Department of Mathematics, University of Wisconsin, Madison, WI
Attention is a cubic spline
Talk at Math Machine Learning seminar, Max Planck Institute for Mathematics in the Sciences/UCLA, Online
Attention is a cubic spline
Talk at 7th Annual Meeting of SIAM Conference Texas-Louisiana Section, Baylor University, Waco, TX
Attention is a cubic spline
Talk at Math and Data Seminar, The Department of Mathematics, University of Missouri, Columbia, MO
Attention is a cubic spline
Talk at AMS Special Session on Topological, Algebraic, and Geometric Methods for Safe, Robust, and Explainable Machine Learning, Joint Mathematics Meeting, Seattle, WA
Attention is a cubic spline
Talk at The 1st International Conference on Data Analytics and Topology, Online
Attention is a cubic spline
Talk at Mathematics in Deep Learning Workshop, University of Texas at Austin, Austin, TX
Teaching
Service
Organizer
- Jun 2025, ILAS 2025 Conference, Minisymposium on Advances in Matrix Manifold Optimization
- May 2021, SIAM LA21 Minisymposium on Linear Algebra and Differential Geometry
- Jun 2019, RTG Summer Lectures 2019 on Numerical Methods in Data Science and Deep Neural Networks, http://www.stat.uchicago.edu/events/rtg/
Referee
- Annals of Statistics
- Applied Numerical Mathematics
- Arnold Mathematical Journal
- BIT Numerical Mathematics
- Computational Geometry: Theory and Applications
- Conference on Neural Information Processing Systems
Foundations of Computational Mathematics
- IEEE Journal of Selected Topics in Signal Processing
- International Conference on Learning Representations
- International Conference on Machine Learning
- Journal of Machine Learning Research
- Journal of Mathematical Physics
- Journal of Scientific Computing
- Journal of Symbolic Computation
- Linear Algebra and its Applications
- Linear and Multilinear Algebra
- Mathematics of Operations Research
- Mathematical Programming (2024 Meritorious Service Award)
- Numerical Algorithms
- Numerical Linear Algebra with Applications
- Optimization Methods and Software
- SIAM Journal on Optimization
- Transactions on Mathematical Software
- Vietnam Journal of Mathematics