My research combines machine learning theory, numerical computation, and applied probability to develop
mathematical foundations and scalable algorithms for generative AI, with applications to physical AI and scientific discovery.
Current position
Assistant Professor · BICMR · PKU
Join the group
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.
On the Power of Approximate Reward Models for Inference Time Scaling
A theory of when approximate reward models reduce the complexity of long-horizon LLM reasoning from exponential to polynomial through SMC inference-time scaling.
An Unconstrained Layer Peeled Perspective on Neural Collapse
Studies neural collapse through the implicit bias of gradient flow and the optimization geometry of an unconstrained model of features and classifiers.
Numerical differential equations, optimal control, and mean field limits provide principles for neural network architecture, efficient training, and optimization theory.
Interprets neural architectures as numerical discretizations of differential equations and uses linear multistep methods to design more efficient residual networks.
Formulates adversarial training as a differential game and uses Pontryagin’s maximum principle to reduce repeated propagation through the full network.
Develops a continuum model of deep residual networks and establishes optimization guarantees through mean field analysis and overparameterization from depth.
From shared ancestry to independent rejection, from imperfect values to path correction: finite differences and Stein’s identity explain guidance using only function values.
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