Yuxin Chen

I am a Professor of Statistics and Data Science and of Electrical and Systems Engineering at University of Pennsylvania. Before moving to UPenn in 2022, I was an assistant professor of Electrical and Computer Engineering, and an associated faculty member of Computer Science and Applied and Computational Mathematics at Princeton University from 2017 to 2021. Prior to this, I was a postdoc in Statistics at Stanford University from 2015 to 2017, and obtained my Ph.D. in Electrical Engineering at Stanford University in Jan 2015. Contact: 313 Academic Research Building 265 South 37th Street, Philadelphia, PA 19104 Email: yuxinc at wharton dot upenn dot edu

Openings

I'm looking for highly motivated postdocs and Ph. D. students with strong mathematical background and interest in machine learning theory (particularly diffusion models, LLM, and RL), statistics, and optimization.

Recent news

Together with Prof. Qing Qu and Prof. Liyue Shen, we presented a tutorial on diffusion models at ICML 2025. Check out our website. See also [slides of my part]. Together with Prof. Yuejie Chi and Prof. Yuting Wei, we will present a tutorial on reinforcement learning at the 2025 INFORMS Annual Meetings. See the reading material. Our paper on implicit regularization in nonconvex statistical estimation received the SIAM Activity Group on Imaging Science Best Paper Prize (SIAM news). Our paper on MagNet (an ML framework for power magnetics modeling) received the IEEE Transactions on Power Electronics Prize Paper Award (first place). (Project webpage by Prof. Minjie Chen's lab). Our new monograph "Spectral Methods for Data Science: A Statistical Perspective" is published in Foundations and Trends in Machine Learning. See slides for PKU summer school on theoretical statistics.

Topic courses I have developed

• Fall 2023: STAT9910-303: Large-Scale Optimization for Data Science (UPenn)
  

• Spring 2022: STAT991-302: Mathematics of High-Dimensional Data (UPenn)
  

• Fall 2020: ELE520: Mathematics of Data Science (Princeton)
  

Selected recent papers

• Foundations of generative AI

  • G. Li*, Y. Jiao*, Y. Huang, Y. Wei, Y. Chen, “Transformers meet in-context learning: A universal approximation theory,” 2025 (*=equal contributions). [slides]

  • Y. Huang*, Z. Wen, A. Singh, Y. Chi, Y. Chen, “Transformers provably learn chain-of-thought reasoning with length generalization,” NeurIPS 2025 (*=equal contributions).

  • J. Liang, Z. Huang, Y. Chen, “Low-dimensional adaptation of diffusion models: Convergence in total variation,” 2025 (accepted in part to COLT 2025). [slides]

  • Z. Huang, Y. Wei, Y. Chen, “Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality,” Mathematics of Operations Research, 2025+.

  • G. Li, Y. Wei, Y. Chi, Y. Chen, “A sharp convergence theory for the probability flow ODEs of diffusion models,” 2024. [slides]

• Optimization in machine learning

  • J. Ma, Y. Huang, Y. Chi, Y. Chen, “Preconditioning benefits of spectral orthogonalization in Muon,” 2026.

• Statistical inference and learning

  • J. Liang, Z. Ren, Y. Chen, “Optimal training-conditional regret for online conformal prediction,” 2026.

  • Z. Zhang, W. Zhan, Y. Chen, S. S. Du, J. D. Lee, “Optimal multi-distribution learning,” Journal of the ACM, vol. 72, no. 5, pp. 1-71, 2025 (appeared in part in COLT 2024). [slides]

  • Y. Chen, J. Fan, C. Ma, Y. Yan, “Inference and uncertainty quantification for noisy matrix completion,” Proceedings of the National Academy of Sciences (PNAS), vol. 116, no. 46, pp. 22931–22937, Nov. 2019. [ArXiv][PNAS version][slides]

  • Y. Chen, J. Fan, C. Ma, K. Wang, “Spectral method and regularized MLE are both optimal for top-K ranking,” Annals of Statistics, vol. 47, no. 4, pp. 2204-2235, August 2019. [ArXiv][AoS version][slides]

• Foundations of reinforcement learning

  • Z. Zhang, Y. Chen, J. D. Lee, S. S. Du, “Settling the sample complexity of online reinforcement learning,” Journal of the ACM, vol. 72, no. 3, pp. 1-63, 2025 (appeared in part in COLT 2024). [paper][JACM version][slides]

  • G. Li, L. Shi, Y. Chen, Y. Chi, Y. Wei, “Settling the sample complexity of model-based offline reinforcement learning,” Annals of Statistics, vol. 52, no. 1, pp. 233-260, 2024. [paper][AoS version]

  • G. Li, C. Cai, Y. Chen, Y. Wei, Y. Chi, “Is Q-Learning minimax optimal? A tight sample complexity analysis,” Operations Research, vol. 72, no. 1, pp. 203-221, 2024 (appeared in part to ICML 2021). [paper][OR version]

  • G. Li, Y. Wei, Y. Chi, Y. Chen, “Breaking the sample size barrier in model-based reinforcement learning with a generative model,” Operations Research, vol. 72, no. 1, pp. 222-236, 2024 (appeared in part to NeurIPS 2020). [paper][OR version][slides]

• Nonconvex statistical estimation

  • C. Ma, K. Wang, Y. Chi, Y. Chen, “Implicit regularization in nonconvex statistical estimation: Gradient descent converges linearly for phase retrieval, matrix completion, and blind deconvolution,” Foundations of Computational Mathematics, vol. 20, no. 3, pp. 451-632, June 2020 (SIAM Activity Group on Imaging Science Best Paper Prize). [main text][supplement][full paper (Arxiv)][slides]

  • Y. Chen, Y. Chi, J. Fan, C. Ma, “Gradient descent with random initialization: Fast global convergence for nonconvex phase retrieval,” Mathematical Programming, vol. 176, no. 1-2, pp. 5-37, July 2019. [ArXiv][slides]

  • Y. Chen, Y. Chi, J. Fan, C. Ma, Y. Yan, “Noisy matrix completion: Understanding statistical guarantees for convex relaxation via nonconvex optimization,” SIAM Journal on Optimization, vol. 30, no. 4, pp. 3098–3121, October 2020. [ArXiv][slides]

  • Y. Chen and E. J. Candes, “Solving random quadratic systems of equations is nearly as easy as solving linear systems,” Communications on Pure and Applied Mathematics, vol. 70, issue 5, pp. 822-883, May 2017 (ICCM Best Paper Award (Gold Medal), and Finalist for Best Paper Prize for Young Researchers in Continuous Optimization). [slides][website]