REPRESENTATIONS · SIMILARITY · SEARCH Embeddings, From a list of numbers to a useful neighbor. Five short chapters, one small map you can change.
Start reading → Query and passage vectors Hand-authored vectors A through E. Query [1.638, 1.147], direction 35 degrees, length 2. E ranks first at 0.999. Scoring rule: cosine. The geometry lab in chapter 3 explains the scores. 0 1 1 2 2 3 3 x₁ x₂ A B C D E q 35° · length 2.0 A hand-authored map. The chapters explain what its geometry can—and cannot—tell you.
Start with basic ML and arithmetic. We will introduce vectors, norms and similarity as we need them. No model download, paid API, or prior linear-algebra course required.
01 A place in space An embedding turns an input into coordinates. The useful part is what those coordinates let us compare.
↗ 02 Learning the map Training gives a representation a purpose. It does not label every axis with a concept.
↗ 03 What “near” means The same points can produce different winners. A similarity rule decides what counts.
↗ 04 From query to results A search system uses vectors to choose candidates. The passage—not its coordinate—is what the reader needs.
↗ 05 What a vector cannot say A representation is useful because it preserves selected relationships. It is limited for the same reason.
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