Projects
A selection of projects in mathematics, machine learning, and computation.
The Natural Geometry of Learning
The Natural Geometry of Learning is an expository blog series exploring how probability, information, transport, and modern machine learning are tied together by geometry. It begins with Fisher information as the local geometry of statistical distinguishability, Wasserstein distance as the geometry of spatial displacement, and KL divergence as the asymmetric geometry of inference. It then develops Schrödinger bridges as stochastic paths between distributions, Hodge decomposition as the algebra of learned flows, and natural gradient as the computational expression of information geometry. The goal is not to propose a new theory, but to synthesize a fragmented landscape into a coherent map for students and practitioners interested in geometric approaches to learning. Once the series is complete, I plan to revise it into a PDF booklet.
Machine Learning Experiments
Experiments, implementations, and technical explorations.
Notes and Derivations
Mathematical notes that may later become essays or papers.