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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 preprint arXiv:2009.13502 (2020). 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. 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. 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 arXiv, 2025
Compute EDD of important manifolds.
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Euclidean distance degree in manifold optimization." arXiv e-prints (2025): arXiv-2502.10336. https://arxiv.org/pdf/2502.10336
Simple matrix expressions for the curvatures of Grassmannian
Published in arXiv, 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." arXiv e-prints (2024): arXiv-2406.11821. https://arxiv.org/pdf/2406.11821
Grassmannian optimization is NP-hard
Published in arXiv (accepted by SIOPT), 2025
NP-hardness of quadratic optimization over Grassmannian
Recommended citation: Zehua Lai, Lek-Heng Lim, and Ke Ye. "Grassmannian optimization is NP-hard." arXiv e-prints (2024): arXiv-2406.19377. https://arxiv.org/pdf/2406.19377
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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teaching
Teaching in Uchicago
graduate course, University of Chicago, 2019
Spring 2022, STAT 28000 Optimization, Teaching Assistant
Teaching in UTAustin
graduate course, University of Texas at Austin, 2023
Spring 2024, Probability I 53860, Instructor