Mingsong Yan
Visiting Assistant Professor
Department of Mathematics
University of California, Santa Barbara
Email: mingsongyan at ucsb dot edu
About
I am a Visiting Assistant Professor in the Department of Mathematics at the University of California, Santa Barbara, where I work with Prof. Sui Tang. At UCSB, I also co-mentor undergraduate and graduate students with Prof. Tang and organize the Applied Math/PDE/Data Science Seminar.
I received my Ph.D. in Computational and Applied Mathematics from Old Dominion University in 2024 under the supervision of Prof. Yuesheng Xu. My dissertation was titled Deep Learning in Reproducing Kernel Banach Spaces. Previously, I earned my B.S. through the Tang Aoqing Honors Program in Mathematics at Jilin University in China in 2018.
Research
My research focuses on the mathematical foundations of efficient and interpretable machine learning. Using tools from optimization, functional analysis, probability, and dynamical systems, I study how mathematical structure shapes representation, approximation, convergence, stability, and transferability in modern learning models.
My work centers on two closely connected themes:
Interpretability
- In-context learning: Studying how transformers learn from examples in context, with a focus on their connections to kernel ridge regression and iterative algorithms.
- Function spaces: Studying hypothesis spaces and representer theorems for deep learning.
Efficiency
- Low-rank structure in LLMs: Exploring low-rank structure in LLM activations to guide architecture design and improve pretraining efficiency.
- Size transferability: Understanding when Neural ODEs trained on small graphs can transfer to larger, structurally similar graphs, reducing the need for expensive training on large graphs.
- Sparse optimization: Developing sparse regularization methods and algorithms for signal and image processing and deep learning, aiming to improve computational efficiency and reconstruction or prediction accuracy.
See Publications for the complete list of papers.
Selected Awards and Grants
- Mochizuki Memorial Instructor Award, Department of Mathematics, UC Santa Barbara — June 2026.
- AMS–Simons Travel Grant — July 2025–June 2027.