Writing

Blog

Research notes, ideas, and informal writeups on theoretical computer science, algorithms, and machine learning.

Reinforcement Learning: Foundations, Policy Gradients, and REINFORCE

A walkthrough of the fundamental RL algorithms — MDPs, imitation learning, policy gradients, and REINFORCE — with a practical Gymnasium implementation for the Lunar Lander task.

Reinforcement Learning Policy Gradients Deep Learning

Introduction to Flow Matching

Flow matching is a simple, elegant, and remarkably powerful algorithm for generative modeling, drawing connections between ODEs, probability paths, and vector fields.

Generative Modeling Machine Learning Deep Learning

An Introduction to Variational Autoencoders (VAEs)

We detail the mathematical foundations of Variational Autoencoders, outlining the derivation of the ELBO, the reparameterization trick, and neural network parameterization.

Generative Modeling Deep Learning Probability

The Spectral Gap and Cheeger's Inequality

We present a self-contained proof of Cheeger's Inequality for d-regular graphs, relating spectral expansion to edge expansion using Fiedler's Algorithm and the probabilistic method.

Spectral Graph Theory Expander Graphs Algorithms

An Introduction to Expander Graphs

We introduce expander graphs, covering combinatorial definitions, spectral expansion, the Expander Mixing Lemma, and applications to independent sets and diameter bounds.

Expander Graphs Spectral Graph Theory Combinatorics

Anti-Concentration Bounds for Binomial Distributions

We present two anti-concentration bounds for the tails of binomial distributions, including proofs using KL divergence, entropy, and binomial coefficient bounds.

Probability Algorithms Mathematics