Below are portions of scribble notes for various topics that I have come across in research that I try to organize and record for future reference.

Mathy Notes
Johnson-Lindenstrauss Lemma

Lemma Statement \[ d() \] bi-Lipschitz statement

Two Proofs for JL Lemma

Proof 1: Original

Proof 2: Dasgupta and Gupta (2002)

Seminal Papers

The Johnson-Lindenstrauss Lemma Is Optimal for Linear Dimensionality Reduction

Optimality of the Johnson-Lindenstrauss Lemma

Interpretability (The "Traditional" Kind)

Integrated Gradients

SHAPley Values

Manifold Learning
Markov Chains
Sum-of-Squares

Reference: Proofs, beliefs, and algorithms through the lens of sum-of-squares (by Boaz Barak and David Steurer)

\(k\)-means++
Neural Tangent Kernels
Positive & Unlabeled (PU) Learning
Kamada-Kawai Formulation of Multi-Dimensional Scaling

Reference: A quasi-polynomial time algorithm for Multi-Dimensional Scaling via LP hierarchies (Bakshi et al., 2023), and conversations with Noah Bergam

Tail Bounds for Matrix Martingales

Reference: Joel Tropp's Papers

Sufficient Statistics
More Empirics-Centered Notes
Flash Attention

Mamba (S4) Model

Other Notes (PDFs)