What is an LLM¶
An LLM — large language model — is, at heart, a function that maps a sequence of tokens to a probability distribution over the next token. You sample from that distribution, append the result to the input, and call the model again. Everything you see an LLM do — chat, code, reason, use tools — emerges from running this loop millions of times.
The loop¶
flowchart LR
T[Tokens in] --> M[Model]
M --> D[Next-token distribution]
D --> S[Sample one]
S -->|append, repeat| T"Stop" usually means either an end-of-sequence token or a user-specified limit (max_tokens).
A concrete example¶
Given the prefix "The PID controller", the model's next-token distribution might look like:
| Candidate token | Probability |
|---|---|
is |
0.51 |
controls |
0.18 |
was |
0.06 |
adjusts |
0.04 |
| (thousands of others) | … |
The sampler picks one — temperature controls how far down the list it will go — we append it to the prefix, and repeat.
Pretraining vs. post-training¶
- Pretraining. Trillions of tokens of internet text, next-token prediction only. Produces a model that is fluent but wanders, doesn't follow instructions well, and has no stable style.
- Post-training. Supervised fine-tuning on curated examples plus RLHF or DPO. Turns the pretrained base into a model that follows instructions, refuses unsafe requests, and stays on task.
Every model you reach via an API has been post-trained. Access to raw base models is rare outside open-weight releases.
Why "predict the next token" is useful¶
Next-token prediction at scale forces the model to compress the patterns in its training data: syntax, factual associations, code structure, dialog conventions. Asking it to continue a well-framed prompt pulls out those compressed patterns. The cleverness lives in the prompt and the loop around the model, not in a reasoning engine inside the model. That's why the rest of this tutorial spends so much time on how to shape inputs and iterate.