Embeddings and similarity search

Embeddings turn text into points so that similar meanings land close together. Search is finding the nearest points.

The idea

An embedding model turns a piece of text into a list of numbers (a vector) that captures its meaning. Texts with similar meaning get similar vectors, so they sit close together. To search, embed the query with the same model, compare it with every stored vector using cosine similarity (the angle between them), and keep the top few. It finds matches by meaning, not by shared words. Here the vectors have only 2 numbers so we can draw them; real ones have hundreds or thousands.

Code

public static float Cosine(float[] a, float[] b)
{
    float dot = 0, na = 0, nb = 0;
    for (int i = 0; i < a.Length; i++)
    {
        dot += a[i] * b[i];
        na += a[i] * a[i];
        nb += b[i] * b[i];
    }
    return dot / (MathF.Sqrt(na) * MathF.Sqrt(nb));
}

public static async Task<List<string>> SearchAsync(
    IEmbedder embedder,
    List<(string Text, float[] Vector)> index,
    string query)
{
    float[] q = await embedder.EmbedAsync(query);
    var scored = index
        .Select(d => (d.Text, Score: Cosine(q, d.Vector)))
        .OrderByDescending(x => x.Score);
    return scored.Take(3).Select(x => x.Text).ToList();
}

Tips

• Interview line: "Embeddings map text to vectors where closeness means semantic similarity. Cosine similarity compares direction, so vector length does not matter."
• Always embed the query with the same model that embedded the documents, otherwise the numbers are not comparable.
• Scanning every vector is fine for thousands of items. For millions, use a vector database or an approximate nearest neighbour index.
• Similar is not the same as correct. The top match might be on the right topic and still not contain the answer.

In the .NET library

Store vectors as float[] (or ReadOnlyMemory<float>) and keep the embedding call behind an interface like IEmbedder so you can swap models, cache results, and unit test the search with a fake embedder.