Writing

Information Geometry & Natural Gradients

Statistical Manifolds, the Fisher Information Metric, and the geometry of optimization.

2026-01-13

A rigorous treatment of discrete-time martingales. Filtrations, Doob's Theorems, Optional Stopping, and concentration inequalities.

2026-01-05

Spectral Kernels, Posterior Geometry, and the connection to Reproducing Kernel Hilbert Spaces.

2025-08-15

High-dimensional loss landscapes, the Kac-Rice formula, and why gradients avoid local minima.

2025-07-28

The Duality of Regularity. Moore-Aronszajn, Mercer's Theorem, and the Sobolev connection.

2025-07-12

Minimal sufficiency, the Fisher Information, and the geometry of lossless compression.

2025-06-30

Universality in the spectrum of noise. The Stieltjes Transform, Free Probability, and the BBP Phase Transition.

2025-06-21

Why high-dimensional space is mostly surface. Levy's Lemma, Log-Sobolev Inequalities, and Matrix Concentration.

2025-06-15

Transforming integration into optimization. The Evidence Lower Bound (ELBO), Natural Gradients, and Stein Variational Gradient Descent.

2025-05-20

The PDE perspective on Optimal Transport. The Benamou-Brenier formula, Otto Calculus, and the JKO scheme.

2025-05-15

Symplectic structure, Shadow Hamiltonians, and the preservation of phase space volume. Why Leapfrog is symplectic.

2025-04-10

Why the sample mean is inadmissible in high dimensions. Shrinkage, Admissibility, and the James-Stein Estimator.

2025-04-01

Convergence rates for the Central Limit Theorem. Edgeworth expansions, Stein's Method, and dependence on dimension.

2025-03-18

Monge, Kantorovich, and the Geometry of Measures. Duality, Sinkhorn, and Brenier's Theorem.

2025-02-12