Other 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.
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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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Honors Thesis Project, Exploring Topological Structures in Neural Nets.
Advisor: Prof. Stuart Geman, Reader: Prof. Basilis Gidas
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Brown University Summer Student Research, Exploring Biologically Plausible Mechanisms to Induce Noise Correlations for Learning, with Niloufar Razmi
Advisor: Prof. Matt Nassar
poster
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(Course Project) Levi-Civita 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 write-up for our final project, where we mainly consulted the book 黎曼几何初步 by 白正国.
notes
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Brown University Mathematics Project (BUMP), Randomizing,
with George Daccache and Zhiyuan Zhou.
Ph.D. Student Advisor: Juniper Cocomello.
pdf
github
