Research and Learning Notes

This page is a collection of research or learning notes.

Applied Algebraic

This is the lecture notes on CS7343 – Applied Algebraic, Fall 2023 in Shanghai Jiao Tong University.

Approximate Counting and Sampling

The followings are the research notes on the topic of approximate counting and sampling.

• Basic Models
  • $k$-heights Models
  • Monomer-dimer Models
  • Six-vertex Models
• State of the Art:
  • Canonical Paths, Multi-commodity Flows and Windability
  • Path Coupling
• Advance Topics (MCMC 2.0):
  • Local-to-global Frameworks: High-Dimensional Expander
  • Local-to-global Frameworks: Localization Schemes

Combinatorics and Graph Theory

The followings are the notes on the topic of combinatorics and graph theory.

• Christoffel-Darboux Identity:
  • Christoffel-Darboux Identity of the Independence Polynomial
• Non-backtracking Matrix (Hashimoto Matrix)
• Notes on Random Graph Theory

Optimization

This is the lecture notes on CS2910: Optimization, Summer 2023 in Zhiyuan College, Shanghai Jiao Tong University, instructed by Yunwei Ren.

• The Basic Parts:
  • Lecture 01. Convex Sets and Functions
  • Lecture 02. Gradient Descent
  • Lecture 03. Duality
  • Lecture 04. Mirror Descent
  • Lecture 05. Stochastic Gradient Descent
  • Lecture 06. Proximal Gradient Descent
  • Lecture 07. Distributed Optimization and ADMM
  • Lecture 08. Escaping Saddle Points
  • Lecture 09. Momentum
  • Lecture 10. Bayesian Optimization
  • Lecture 11. Pre-conditioned Gradient Descent
• Advanced Lectures:
  • Lecture A. Optimal Transport
  • Lecture B. Wasserstein Gradient Flow
  • Lecture C. Mean-Field Networks

If you find some typos or faults, or have some suggestions, please feel free to contact me.