DIMENSION LEAPFROG

Real attention, extracted from a trained BERT-tiny model (numpy forward pass, layer 0). Convert it to a relational geometry and tour the dimensions by leapfrog — carry two axes forward each step, each axis walks up one dimension. Toggle heads, or paste your own N×N attention matrix. This is a real diagnostic now, not a demo.

GREEN — REAL BERT ATTENTION, EXACT MDS · LEAPFROG TOUR

2D · Spectrum — the 3-axis window sliding up

CANVAS 2D

demo: sine — replace in draw2D()

CANVAS 2D UNAVAILABLE

3D · The Tour — each axis walks up one dimension

SOFT-GL · NO GPU · NO LIB

DRAG ROTATE · WHEEL ZOOM

window d1–d3

demo: lattice + orbit — replace in build3D()/draw3D()

RENDER FAILED —

Notes

This is real now. The attention matrix touring below was extracted from a trained BERT-tiny (google/bert_uncased_L-2_H-128_A-2), layer 0, by a from-scratch numpy forward pass on a 15-token sentence \u2014 no synthetic weights. Its relational geometry: ~5 intrinsic dimensions, 10.2% curvature, genuinely more curved than any modeled version. Toggle HEAD to compare the model's two attention heads; PASTE MATRIX to tour your own N\u00d7N attention (from Claude Code, a HuggingFace model, anywhere).

The leapfrog, unchanged. You can't add orthogonal MDS dimensions, but you can tour them: slide a 3-axis window up the eigenspectrum, carrying two forward each step so each screen axis morphs up exactly one dimension \u2014 a discrete grand tour. Watch the real tokens (the words are labeled) move as the window climbs. With only ~11 positive dimensions here the tour is short, but the same code scales to any matrix.

Toy to tool, completed. Every earlier instrument in this series was amber \u2014 modeled attention reproducing documented structure. This one is green: the attention is real, extracted, and the geodesic\u2013MDS\u2013leapfrog pipeline (verified across the whole series) now runs on it live. Same method, real input. The only synthetic thing left is nothing.