Shizhou Xu

Hi — I’m Shizhou Xu

I am a Postdoctoral Scholar in Mathematics at UC Davis, working with Prof. Thomas Strohmer on the mathematical foundations of machine learning. I earned my Ph.D. in Applied Mathematics (UC Davis, 2024), where my dissertation studied fairness in machine learning via optimal transport.

Starting in 2026, I will join Stanford University and SLAC National Accelerator Laboratory to work on mathematical foundation of deep learning and AI methods for computational quantum physics.

My research develops provable learning principles， linking stochastic dynamics, information theory, and optimal transport， to understand and design modern ML systems with theoretical guarantees and practical impact.

Research Publications CV GitHub LinkedIn

News

  • 2026 — Joining Stanford University / SLAC National Accelerator Laboratory (mathematical foundation of deep learning and AI methods for computational quantum physics).
  • Accepted (Nature Machine Intelligence, 2026) — Multi-Scale Enhancement for Full Spectrum Neural Representations (Yuan Ni, Zhantao Chen, Shizhou Xu, Cheng Peng, Rajan Plumley, Chun Hong Yoon, Jana B. Thayer, Joshua J. Turner).

Research overview

My work asks: What mathematical objects, limits, and invariances explain—and improve—modern machine learning?
I develop theory and algorithms that translate structure (geometry, dynamics, and information constraints) into principled objectives and provable guarantees, with an emphasis on methods that also perform well in practice.

Research themes (foundations)

  • Learning under information constraints: information-theoretic formulations for unlearning, privacy, and fairness, and sharp trade-offs between utility and constraints.
  • Dynamics and optimization of deep learning: stochastic dynamical systems viewpoints for training stability, implicit regularization, and generalization.
  • Optimal transport for learning: OT as a tool for representation learning, geometry-aware regularization, and generative modeling.
  • Statistical foundations: uncertainty quantification, identifiability, and reliable evaluation.

What I build (for industry + academic audiences)

  • Theory → algorithms: proofs that lead to implementable objectives/regularizers.
  • Reliable ML systems: methods designed for robustness, auditability, and constraint satisfaction.
  • Scientific ML: learning pipelines for multimodal scientific data and inverse problems.

Selected publications

  • Yuan Ni, Zhantao Chen, Shizhou Xu, Cheng Peng, Rajan Plumley, Chun Hong Yoon, Jana B. Thayer, Joshua J. Turner.
    Detail Across Scales: Multi-Scale Enhancement for Full Spectrum Neural Representations.
    Nature Machine Intelligence (Accepted, 2026).

  • Shizhou Xu, Thomas Strohmer.
    Fair Data Representation for Machine Learning at the Pareto Frontier. JMLR (2023).
    [PDF]

  • Shizhou Xu, Thomas Strohmer.
    On the (In)Compatibility between Individual and Group Fairness. Minor Revision (SIMODS).
    [Preprint]

  • Shizhou Xu, Thomas Strohmer.
    WHOMP: Improving Upon Randomized Controlled Trials via Wasserstein Homogeneity. Under review (JASA).
    [Preprint]

  • Shizhou Xu, Thomas Strohmer.
    Machine Unlearning via Information-Theoretic Regularization. Under review (Mathematical Foundations of Machine Learning).
    [Preprint]

Full list: /publications/

Impact & translation (selected)

  • Patent pending (LLM unlearning): marginal-information regularization for selective forgetting and controllable fine-tuning.
  • External adoption / guidance: my work on fairness mitigation and OT-based trial design has been recommended in guidance by the Alan Turing Institute.

Industry experience

  • Goldman Sachs — Quantitative Strategy (Intern): risk analytics and margin call analysis (quantitative modeling; validation; large-scale data pipelines).

Talks (selected)

  • 2026 — Talks to appear at AIM Workshop @ Caltech (Fairness and Foundations in ML) and the Joint Mathematics Meetings (JMM).
  • 2025 — Invited/selected talks: University of Utah Applied Mathematics Seminar, INFORMS Annual Meeting, SLAC Users Meeting (Stanford).
  • 2025 — CPAL Spotlight Track and ICLR Workshop presentation on WHOMP.
  • 2024 — Presented at ICML 2024 and CMO–BIRS (Casa Matemática Oaxaca / Banff International Research Station).

Honors & Awards (selected)

  • 2024 — Yueh-Jing Lin Scholarship (UC Davis) for excellence in research.
  • 2019 — School of Engineering Scholarship (NYU) for excellence in research.

Professional service

  • Reviewer: ICML, NeurIPS, SIAM Journal on Mathematics of Data Science, PRX.
  • Teaching: MAT 127C (the last real analysis series course for math-major undergraudates at UC Davis, Summer 2025).

Contact

Email: shzxu@ucdavis.edu
CV: /files/CV.pdf · Publications: /publications/ · Research: /research/