Projects
Technical Notes.
Disclaimer: These notes may contain errors, and I try to cite every source I consulted while preparing them. Please contact me to correct the errors. Thank you.

Some Notes on Diffusion Models.
This notes were prepared while learning diffusion models from two papers, Ho et al., 2020 (DDPM) and Song et al., 2021 (DDIM). The equations are derived with more details with a consistent notation.
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Results when Sampling from a Normal Distribution.
Started with a sample from $\mathcal{N}(\mu, \sigma^2)$, I filled in the gap of many proofs that are missing in many textbooks:
how to arrive at a $\chi^2$ distribution with proofs of handwavy theorems and lemmas used in textbooks along the way,
how and why to derive $t$distribution and $F$distribution and prove their properties,
how they contribute to inference problems, and how they are related to each other and other distributions (e.g. to $\mathcal{N}(0,1)$ and to $\text{Beta}$).
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(Course Project) LeviCivita Connections, with Kexin Ding, Luke Hammer, Mattie Ji, and Jiayuan Sheng.
Instructor: Prof. Jungang Li, MATH1140: Functions of Several Variables II (Differential Manifolds).
This is the writeup for our final project, where we mainly consulted the book 黎曼几何初步 by 白正国.
notes
Projects

Honors Thesis Project, Exploring Topological Structures in Neural Nets.
Advisor: Prof. Stuart Geman, Reader: Prof. Basilis Gidas
pdf

Emory REU/RET Computational Mathematics for Data Science,
Training Implicit Networks for Image Deblurring using JacobianFree Backpropagation,
with Lisa Zhao and Shuaicheng Tong.
https://arxiv.org/abs/2402.02065
Advisor: Prof. Samy Wu Fung

Brown University Summer Student Research, Exploring Biologically Plausible Mechanisms to Induce Noise Correlations for Learning, with Niloufar Razmi
Advisor: Prof. Matt Nassar
poster

A Review of Publicly Available Geospatial Datasets and Indicators in Support of UNCCD Strategic Objective (SO) 2, with David LopezCarr, Kevin M. Mwenda, Kerry L. Mapes,
Susanne H. Sokolow, and Narcisa G. Pricope.
Advisor: Prof. Kevin M. Mwenda
pdf

Brown University Mathematics Project (BUMP), Randomizing,
with George Daccache and Zhiyuan Zhou.
Ph.D. Student Advisor: Juniper Cocomello.
pdf
github