Lesson 01 — the cost surface of LLMs. A practical first look at what every other lesson on this site will assume you’ve felt for yourself. The mistake nobody catches You’re sitting across from the head of a Maltese SME. They want to deploy an AI chat agent for their customer support. They ask the…

Lesson 02 — what actually happens when a model emits one token. After this lesson you should be able to narrate the forward pass without hand-waving. One token. Seven steps. Every token a large language model produces comes from the same seven-stage pipeline. Skip any one of them and you lose the ability to reason…

Lesson 03 — the difference between “the model said it” and “the model could have said it”. Sampling is where probability becomes language. From logits to a chosen token After the last block of the transformer, the model produces a vector of logits — one real number per token in the vocabulary. They’re unbounded. They…

Lesson 04 — the single most operationally important fact about LLM serving. Most teams discover this the expensive way. Why caching K and V matters To generate token N, self-attention has to read the keys and values of every previous token. Token N+1 needs the same plus one more. Without caching, position N would re-compute…