Machine Learning Theory
Mathematical foundations for optimization, generalization, reasoning, and reliable scaling.
Read direction →BICMR · Peking University
Mathematics for scalable intelligence.
PKU SCALE Lab develops mathematical foundations and scalable algorithms at the intersection of machine learning, applied probability, computational mathematics, and scientific discovery.
QuestionHow can learning and inference scale reliably?
ApproachTheory that predicts algorithmic behavior
SystemsGenerative AI and scientific computing
CommunityStudents and researchers across disciplines
Research directions
Scaling is a mathematical question.
We study how representation, geometry, simulation, and resource allocation determine whether added computation produces reliable gains.
Applied Probability
Sequential Monte Carlo, stochastic simulation, rare events, and high dimensional probability.
Read direction →Computational Mathematics
Randomized numerical algorithms, matrix computation, PDEs, and uncertainty quantification.
Read direction →Scientific and Generative AI
Inference time scaling, scientific machine learning, and AI assisted mathematical discovery.
Read direction →Featured work
Recent research signals.
Current work spans LLM reasoning theory, stochastic networks, generative inference, optimizer geometry, and scientific computing.
On the Power of Approximate Reward Models for Inference Time Scaling
A theory for when approximate rewards make long horizon reasoning computationally tractable.
Paper ↗An AI Assisted Solution to the Signed BAR Conjecture
A resolution of the finite signed uniqueness problem in the Harrison Reiman class and an obstruction beyond it.
Paper ↗Matrix Operator Geometry Aware Optimization
Width stable geometry and transferable learning rates for neural network optimizers.
Paper ↗Derivative Free Inference Time Scaling for Diffusion Models
Sequential Monte Carlo on path measures for additional inference computation.
Paper ↗Physics Informed Inference Time Scaling
Defect correction turns additional simulation into improved high dimensional PDE predictions.
Paper ↗High Dimensional Interpolators Can Be Fragile
Large deviations expose heavy tail risk hidden by benign average performance.
Paper ↗Open opportunities
Work with us.
I am actively recruiting undergraduate students, graduate students, and postdocs to join my research group. Interested candidates are encouraged to email yipinglu [at] bicmr.pku.edu.cn.
See opportunitiesLatest news
From the group.
Selected research and group updates.
Latest writing
From the lab blog.
Research notes, mathematical perspectives, and updates from members of PKU SCALE Lab.
Welcome to the PKU SCALE Lab Blog
A new space for research notes, mathematical perspectives, and updates from our group.
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