Transformers Explained: Attention, QKV, and Why LLMs Work

The 2017 paper Attention Is All You Need replaced recurrence with self-attention — and modern AI was born. No RNN loops. No convolutions over sequences. Just matrices.

Self-attention in one paragraph

Each token asks every other token: "How relevant are you to me?" That relevance is a learned attention score, computed from three projections:

• Query (Q) — what am I looking for?
• Key (K) — what do I contain?
• Value (V) — what information do I pass if selected?

# Scaled dot-product attention
scores = (Q @ K.T) / sqrt(d_k)
weights = softmax(scores)
output = weights @ V

The sqrt(d_k) scaling prevents softmax from saturating when dimensions grow large.

Multi-head attention

One attention pattern isn't enough. Multi-head attention runs parallel attention "heads" — each learning different relationships (syntax, coreference, long-range deps):

MultiHead(Q, K, V) = Concat(head_1, ..., head_h) @ W_O
where head_i = Attention(Q @ W_Qi, K @ W_Ki, V @ W_Vi)

Positional encoding

Attention is permutation-invariant — it doesn't know word order. Transformers inject positional encodings (sinusoidal or learned) so "dog bites man" ≠ "man bites dog".

Encoder vs decoder

GPT is a decoder-only stack: causal masking ensures token i never peeks at token i+1.

Why it scales

Attention is O(n²) in sequence length — expensive, but embarrassingly parallel on GPUs. That parallelism, plus scaling data and parameters, is why trillion-parameter models became feasible.

Practical intuition

Think of attention as a dynamic routing table. Each token broadcasts a query; others respond with keys; values flow proportional to match strength. No explicit graph — the network learns the wiring.

That's the entire revolution in one mechanism.