Vectors & the dot product·5 min

What is an embedding?

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An embedding is a list of numbers — a point in a high-dimensional space. A model like all-MiniLM-L6-v2 turns any sentence into 384 numbers; our synthetic corpus uses 64. The magic property is the same either way: sentences that mean similar things land near each other. "vitamin D and infection" sits near a vaccine-efficacy abstract and far from a paper on bridge construction.

One point per document

Why 64 (or 384) dimensions?

It's the model's hidden size after pooling. More dims = more capacity to separate meanings, but more compute per comparison. Real MiniLM uses 384; this course uses 64 so everything stays instant — the math is identical at any width.

A 2-D sketch of the idea (real space is 64-D)

        vaccine•   •infection
                •vitamin-D
   bridges•
   •concrete            •(query: "does vitamin D prevent infection?")

Real space is 64-D (or 384-D), but the intuition is exactly this picture — retrieval is finding the nearest points to the query point. Everything you build in this course is a way to compute and rank that nearness.

You already have these vectors

Doc 0's 64 numbers are sitting in corpus_emb.f32 right now (you just read its norm). By the end of this chapter you'll be able to measure how close any two of them are.

Load the vectors The dot product