FLINT Lab @ SJTU [中文]
Theory that sparks practice
Foundations of Learning in Nonlinear Transformations
We are a research group led by Fanghui Liu at Shanghai Jiao Tong University, based at the Institute of Natural Sciences and the School of Mathematical Sciences.
We study the mathematical foundations of learning with nonlinear models, connecting approximation, optimization, and generalization to the design and understanding of modern learning systems. Our focus is learning efficiency: understanding nonlinearity mathematically, and using that understanding to develop precise and efficient learning methods.
[People] · [Open Positions] · [Publications]
Research Interests
Our research brings together learning theory and the mechanisms of large language models, with two closely related directions:
Learning theory and nonlinear approximation
What can nonlinear models represent and learn, and at what statistical and computational cost?
High-dimensional approximation, generalization, and function spaces.
Computational–statistical gaps and learning efficiency.
Generalization under scaling and effective model capacity.
Understanding large language models
How do training, fine-tuning, and reasoning work, and how can their mechanisms guide better methods?
Pre-training scaling laws, training dynamics, and stability.
Fine-tuning: when, where, and how much to adapt.
Reasoning, Lean formalization, and AI for machine learning theory.
Selected Research and Projects
A starting point for our research, drawing on work by Fanghui Liu and collaborators. For the complete list, please refer to Publications.
Learning theory and nonlinear approximation.
[JMLR’24], [NeurIPS’25].
Function-space perspectives on approximation and learning.
From theory to fine-tuning.
[ICML’25 Oral].
Connecting mathematical understanding with efficient adaptation of large language models.
Reasoning and formalization.
[ICLR’26], [ICML’26], [StatsMLlib].
Research-level reasoning and formal foundations for probability, statistics, and machine learning in Lean.
People and Open Positions
Meet our people and explore opportunities to work on the foundations and practice of modern learning. Please see Open Positions for current opportunities and application information.