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Posts
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portfolio
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publications
Simpler Grassmannian optimization
Published in arXiv, 2020
A simpler model for optimization on Grassmannian manifolds. A follow-up paper deals with the flag manifolds.
Recommended citation: Lai, Zehua, Lek-Heng Lim, and Ke Ye. "Simpler Grassmannian optimization." arXiv e-prints (2020): arXiv-2009.13502 https://arxiv.org/pdf/2009.13502.pdf
Recht-Ré noncommutative arithmetic-geometric mean conjecture is false
Published in ICML, 2020
The noncommutative arithmetic-geometric mean inequality is false.
Recommended citation: 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. http://proceedings.mlr.press/v119/lai20a/lai20a.pdf
Haagerup Bound for Quaternionic Grothendieck Inequality
Published in arXiv, 2022
A generalization of Haagerup method to Grothendieck Inequality for quaternions.
Recommended citation: Shmuel Friedland, Zehua Lai, and Lek-Heng Lim. "Haagerup Bound for Quaternionic Grothendieck Inequality." arXiv e-prints (2021): arXiv-2212.00208. https://arxiv.org/abs/2212.00208
Simpler Flag Optimization
Published in arXiv, 2022
An extension of previous simpler Grassmannian optimization paper.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Simpler Flag Optimization." arXiv e-prints (2021): arXiv-2212.00212 https://arxiv.org/pdf/2212.00212.pdf
Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent
Published in preprint, 2022
Statistical inference for contextual bandits.
Recommended citation: Chen, Xi, Zehua Lai, He Li, and Yichen Zhang. "Online Statistical Inference for Contextual Bandits via Stochastic Gradient Descent." preprints (2022) http://laizehua.github.io/files/bandit.pdf
Online Statistical Inference for Stochastic Optimization via Kiefer-Wolfowitz Methods
Published in Journal of the American Statistical Association, 2023
Statistical inference in gradient free methods.
Recommended citation: 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
Published in Computational Optimization and Applications, 2024
A stochastic generalization of Steffensen method.
Recommended citation: 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
Published in arXiv, 2025
Splines are important in transformers.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Yucong Liu. "Attention is a smoothed cubic spline." arXiv e-prints (2024): arXiv-2408.09624 https://www.arxiv.org/pdf/2408.09624
Euclidean distance degree in manifold optimization
Published in SIAM Journal on Optimization, 2025
Compute EDD of important manifolds.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Euclidean distance degree in manifold optimization." SIAM Journal on Optimization, Volume 35, Issue 4, (2025) https://epubs.siam.org/doi/full/10.1137/25M1735032
Simple matrix expressions for the curvatures of Grassmannian
Published in Foundations of Computational Mathematics, 2025
Compute differential geometry quantity in the Grassmannian.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Simple matrix expressions for the curvatures of Grassmannian." Foundations of Computational Mathematics, (2025) https://link.springer.com/article/10. 1007/s10208-025-09723-9
Stiefel optimization is NP-hard
Published in Optimization Letters, 2025
NP-hardness of linear optimization over Stiefel
Recommended citation: Zehua Lai, Lek-Heng Lim, and Tianyun Tang. "Stiefel optimization is NP-hard." Optimization Letters (to appear). https://arxiv.org/pdf/2507.02839
Pierce-Birkhoff conjecture is true for splines
Published in arXiv, 2025
Pierce-Birkhoff conjecture is true for splines
Recommended citation: Zehua Lai, and Lek-Heng Lim. "Pierce-Birkhoff conjecture is true for splines." arXiv e-prints (2025): arXiv-2507.07976 https://arxiv.org/abs/2507.07976
talks
Stochastic Steffensen Method
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Recht-Re Noncommutative Arithmetic-Geometric Mean Conjecture is False
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My first virtual presentation is here!
Simpler Grassmannian Optimization
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Simpler Grassmannian optimization
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Attention is a cubic spline
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Attention is a cubic spline
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Attention is a cubic spline
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Attention is a cubic spline
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Attention is a cubic spline
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Attention is a cubic spline
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Attention is a cubic spline
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Check the videos here
The Expressive Strength of Relu Transformers
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teaching
Teaching in Uchicago
Graduate courses, University of Chicago, 2018
Spring 2022, STAT 28000 Optimization, Teaching Assistant
Teaching in UTAustin
Undergraduate courses, University of Texas at Austin, 2023
Spring 2024, Probability I 53860, Instructor