Xingyu YangRESEARCH NOTES · AI · MATH · LINGUISTICS

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  • Category Theory
  • Topology
  • Abstract Algebra
  • Information Theory
  • Linear Algebra
  • Calculus
  • Computational Mathematics
  • Probability and Statistics
  • Discrete Mathematics
  • Mathematical Foundations
  • Direct Preference Optimization
  • Group Relative Policy Optimization
  • Proximal Policy Optimization
  • Why I Believe Linguistics Is Still Part of My Study in AI, Math, and CS
  • Reinforcement Learning, from First Principles
  • Policies as Probability Distributions
  • Planning with a Known Model
  • Return, Value, and the Bellman Equation
  • The Markov Ladder
  • The Reinforcement Learning Problem
  • Policy Gradient
  • Learning as Approximation
  • My Personal AI Workbench: How I Split Work Between Codex, Hermes, Obsidian, and CC Switch
  • From Noise to Images: A Short History of Diffusion Models
  • Artificial Intelligence
  • From Words to Attention: How I Learned to See Transformers
  • Self-Hosted AI Gateway for Unified LLM Access
  • OpenCode as an Early Multi-Agent Workbench
  • Abstraction of Data Types: From Interfaces to Algebraic Data Types
  • Functional Programming Basics with Cons Lists
  • Programming Languages
  • Weak Law of Large Numbers
  • Moment Generating Functions
  • Expectation and Variance
  • Probability Distributions
  • Mathematical Foundations of Memory Address Mapping: From C Pointers to General Theory
  • Generalizing Graph Search to State Space Search
  • Random Variable
  • Mathematics
  • Parallel Computing
  • Algorithm Complexity
  • The First API Boundary I Had to Understand
  • Computer Systems
  • Integrating Development Environments Between NixOS and macOS
  • Why This Site Exists
  • Algorithm & Data Structure
  • Relations and Order
  • Boolean Algebra and Logic
  • Number Systems, Algorithms, and Recursion
  • Counting and Probability Axioms
  • Inequalities
  • Mathematical Induction
  • Indirect Proof
  • Proof by Cases
  • Direct Proof
  • Converse, Inverse, and Contrapositive
  • Propositions and Axiomatic Systems
  • Number Theory and Cryptography
  • Stochastic Processes
  • Limit Theory in Probability
  • Joint Cumulative Distributions
  • Continuous Distributions
  • Conditional Probability and Independence
  • Sets, Functions, Sequences, and Summation
  • Graph Theory
  • Complex Numbers
  • Category Theory Fundamentals
  • Introductory Topology
  • Basics of Abstract Algebra
  • Information Theory Foundations
  • Statistics: Foundations and Inference
  • Linear Algebra: Core Topics
  • Multivariable Calculus
  • Infinite Series
  • Differential Equations
  • Integral Calculus
  • Differential Calculus
  • Limits and Continuity
  • Abstract and Piecewise Functions
  • Function Monotonicity, Parity, and Periodicity
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