M19 / LABORATORY

Embeddings. Where meaning lives.
Six dimensions, projected to three.

Train a model long enough and similar things end up close together in some high-dimensional space. We can't see 768 dimensions — but we can rotate three. Drag the cube. Find the nearest neighbors. Interpolate.

EXPERIMENT 06.01 · LATENT.SPACE POINTS · 240 DIM · 6 → 3 (PCA) STATUS · REAL-TIME
3D PROJECTION DRAG · ROTATE · SCROLL · ZOOM
PC₁ → PC₂ ↑ PC₃ ⊙ θ 0° · φ 0°
CONFIGURATION
CLUSTERS 4
PTS/CLUSTER 60
SPREAD σ 0.18
AUTO ROTATE 20
SHOW EDGES off
NEAREST NEIGHBORS
Pick a query point to find its k closest neighbors by cosine similarity.
K NEIGHBORS 6
RANKIDCOS-SIM
INTERPOLATION
Walk a line between two latent vectors. Useful for understanding "between-ness" in semantic space.
α 0.50
z = (1 − α) · zA + α · zB
Why this matters → Vector search, recommendation, RAG, clustering — they all live in spaces like this. The trick of modern ML is finding a good projection where "similar" really means "nearby". PCA gives a mathematical optimum; t-SNE and UMAP preserve local neighborhoods at the expense of global structure.