Episode 2: Q, K, V — Why 3 Matrices Instead of One?

The million-dollar question

In the previous episode, we said that we "copy the embeddings 3 times". But is that always the case? And why 3 copies?

The short answer

No. Real models use 3 different projection matrices (Wq, Wk, Wv), learned during training.

The 3 roles

Q (Query) = The question

The model projects each word into a space where it phrases its "request". "Bank" produces a Q that means "I'm looking for information about money".

K (Key) = The label

The same word is projected into ANOTHER space to create its label. That label answers: "I'm a word that's about money".

V (Value) = The knowledge

This is what actually gets carried. A 3rd, independent projection where the network stores what is worth passing on.

Why does this separation make learning possible?

If Q and K were identical, the word couldn't tell the difference between searching and being searched for. Concretely, the score matrix would become symmetric: "stole" would give "apple" exactly the same score as "apple" gives "stole". And each word would often get its best score with itself, since the dot product of a vector with itself is large: it would look at itself rather than at the others. By separating them, the model can fine-tune these spaces through backpropagation.

Example: "The banker stole an apple"

• "stole" (Q) queries "apple" (K) → high attention percentage
• In the V of "apple", the network has stored "fruit, red, edible"
• Result: "stole" understands that it stole something edible

A bit of Rust

// Teaching version: Q = K = V
let q = embeddings.clone();
let k = embeddings.clone();
let v = embeddings.clone();

// Real version: 3 projections
// let q = mat_mul(&embeddings, &w_q);
// let k = mat_mul(&embeddings, &w_k);
// let v = mat_mul(&embeddings, &w_v);

Key takeaways

• Q = searches, K = answers, V = carries
• The vectors capture several nuances at the same time