15m: KV Cache from scratch: Why K and V but never Q

​Something interesting: every LLM caches K and V at inference time, but never Q. Most explanations stop at "you don't need the old queries" without showing why. I worked the whole thing out from a 1-layer, single-head transformer. The smallest setup where the logic is actually visible.

• ​why most of a transformer runs per-token, and attention is the only place tokens mix

• ​working backwards from the output to find the minimum you need to predict the next token

• ​why old keys and values don't change when you append a token (and old queries become useless)