# Luke Chen

Thanks for stopping by!

I am a Mathematics PhD Student at KAIST, where I’m very fortunate to be advised by Youngjoon Hong in the Machine Learning and Scientific Computing Lab, and to have my research supported by the KAIST Presidential PhD Fellowship. Recently I’ve been working on improving the theoretical foundations of diffusion models, focusing on sampling efficiency. Also, I’ve been exploring the combination of approaches from graph representation learning and diffusion to generate desirable neural network parameters.

My research interests include:

- Diffusion Models in General Geometric Spaces
- Image & Video Processing
- High-Dimensional Statistics
- Optimization on Manifolds (e.g. Riemannian, Finslerian)
- Dynamical Systems Analysis of Optimization Methods

Previously, I graduated from UC Berkeley with High Honors with majors from the Mathematics Department and Electrical Engineering and Computer Science Department, where I had the pleasure of being advised by Bruno Olshausen and Jack Gallant in the Berkeley Artificial Intelligence Research Lab. There I worked on theoretical visual neuroscience and unsupervised learning methods for computer vision. I was also an undergrad research intern at UC Irvine.

After graduating and before beginning my PhD, I worked as a machine learning engineer, where I learned more about how to deploy machine learning in production-quality software, and how to engineer scalable data pipelines.

Besides my research interests, I also find the applications of functional analysis to machine learning interesting.

In my free time (which is kind of nonexistent nowadays) my hobbies are swimming and cooking. Recently I’ve been into Italian recipes!

If you’re interested in what I do and want to chat, you’re welcome to email me!

# News

For Summer 2025, I will be a research intern supervised by Arun Ross at the iPRoBe Lab working on using Riemannian Diffusion Models and Geometry Processing for Biometrics!

Paper accepted to ICPRAI 2024!

# Resources

## Mathematics/Statistics Notes

Functional Analysis Lecture Notes PDF

High-Dimensional Statistics and the Johnson-Lindenstrauss Embedding PDF

VC Dimension and Glivenko-Cantelli Theorem PDF

Stochastic Processes: PDF

Measure Theory and Lebesgue Integration: PDF

## Course Notes

- EE222: Nonlinear Systems: Analysis, Stability and Control (UC Berkeley Graduate Course)
EECS 225A: Statistical Signal Processing (UC Berkeley Graduate Course): PDF

- STAT 210A: Theoretical/Mathematical Statistics (UC Berkeley Graduate Course): PDF

# Awards

- KAIST Presidential PhD Fellowship: Awarded by KAIST to Top PhD Applicant by Department
- Regents’ and Chancellors’ Scholar: Awarded to Top 1.5% of Incoming UC Berkeley Undergraduates
- Regents’ and Chancellors’ Research Scholarship: UC Berkeley
- UC Berkeley Deans’ Honors List
- UC Berkeley Undergraduate Research Fellowship
- Summer Undergraduate Research Fellowship: The Rose Hills Foundation, UC Berkeley ($5000)
- Upsilon Pi Epsilon National Computer Science Honors Society: UC Berkeley Chapter
- UC Berkeley Mathematics Major Departmental Honors