Inference Time Scaling
Monte Carlo, control, and sequential methods that convert additional inference computation into reliable accuracy gains.
Read more →Scientific Computing and Learning
Yiping Lu
I am a tenure-track assistant professor at Beijing International Center for Mathematical Research, Peking University.
I develop mathematical foundations and scalable algorithms at the intersection of machine learning, numerical computation, applied probability, and scientific discovery.
Current position
Assistant Professor · BICMR · PKU
Research
Scaling laws for learning and inference
Methods
Machine Learning Theory · Applied Probability · Computational Math
Education
Stanford PhD · PKU BS
Community
PKU SCALE Lab
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.
OpportunitiesResearch directions
How can learning systems scale reliably?
My work treats scaling as a mathematical question about representation, geometry, simulation, and resource allocation rather than an empirical slogan.
Scientific Machine Learning
Structure preserving learning for PDEs, operator learning, uncertainty quantification, and simulation calibrated correction.
Read more →Optimization and Reliability
Width and depth stable optimization geometry, predictable hyperparameter transfer, and robust learning algorithms.
Read more →Agentic Mathematical Reasoning
Representations and search procedures that help AI systems discover, verify, and communicate mathematical structure.
Read more →Selected work
Recent research signals
A selection spanning probability, generative inference, scientific machine learning, and large scale optimization.
Signed BAR Conjecture
Uniqueness in the Harrison–Reiman class and a completely S class obstruction for a longstanding problem in reflected Brownian motion.
Paper ↗URGE
Unbiased derivative free inference time scaling for diffusion models through sequential Monte Carlo on path measures.
Paper ↗MOGA
Matrix operator norm geometry explains width scaling, row and column normalization, and hyperparameter transfer.
Paper ↗Simulation Calibrated Scientific ML
Inference time defect correction improves high dimensional PDE solvers without retraining the learned model.
Paper ↗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.
Paper ↗Fragility of Interpolators
Heavy tailed risk and high dimensional large deviations reveal failure modes hidden by benign average case behavior.
Paper ↗Research arc
From structure to scalable computation
Each project moves through the same loop: expose structure, convert it into an algorithm, and test whether scaling becomes predictable.
Step 01
Find the mathematical structure
Start from PDEs, stochastic processes, control, geometry, or algebra.
Step 02
Design the representation
Choose coordinates and operators that preserve the structure that matters.
Step 03
Build a scalable algorithm
Use randomization, optimization, and simulation to turn theory into computation.
Step 04
Prove and measure reliability
Connect finite computation to accuracy, stability, and resource scaling.