Cognithesis — an instrument for curiosity

cognithesis.← Return to the engine

Origin

The making of this little machine.

Opening the notebook.

A place for research notes, experiments, and the questions worth following.

1 min

The Allegory of the Manifold

Pollen grains, electron spheres, and the dodecahedron Plato saved for last: what embedding spaces, unlearning, and enterprise data chaos have in common — the dents are the meaning.

17 min

The Emperor's Gradient

Gradient descent locates a point in D-dimensional space using one reference point and a direction — the mathematical equivalent of GPS triangulation with a single satellite and a compass. Everyone's been too polite to mention it.

17 min

This Theory Is Not Incorrect

I trained a network by mostly telling it what it wasn't. It learned better, faster. Then I pulled the geometry back out.

7 min

The Purloined Position

Sinusoidal positional encoding assumes your data lives in a queue. Data lineage lives in a DAG. The fix was hiding in spectral graph theory the whole time — in plain sight, on the mantelpiece.

18 min

The Only Thing I Know Is Everything

Language models cannot say 'I don't know' because nothing in their training ever taught them where their knowledge ends — and preference tuning buried the exit. Fixing it means making uncertainty legible.

12 min

HIDRA: Attention Is a Search Problem

An old theory paper, dusted off: replace quadratic attention with exact k-NN retrieval, and let a router decide where to look. Untested, unrepented.

6 min