Research notes

Blogs

Learning, optimization, and generation through geometry. Concrete examples, visual explanations, and a closer look at when the methods help.

Visual guide · 10 min + coordinate explorer

Homeomorphism Methods

One change of coordinates, three uses: move from a simple ball to a feasible set, then explore prediction recovery, optimization, and constrained sampling.

Read the visual guide
Visual guide · 15 min + interactive examples

Hard-Constrained Machine Learning

From constrained prediction to constrained generation: use a budget triangle to compare penalties, projection, and feasible coordinates, then follow constraints into diffusion and flow sampling.

Read the visual guide