At its heart, a Large Language Model generating text is performing a highly sophisticated version of a prediction task. Imagine you're typing a text message, and your phone suggests the next word. LLMs operate on a similar principle, but on a massive scale and with much greater contextual understanding.

The fundamental idea is predicting the next token (which often corresponds to a word or part of a word) in a sequence. Given a sequence of preceding tokens, often called the context, the model calculates the probability distribution over its entire vocabulary for what the very next token should be.

How Prediction Works Sequentially

Think of it like building a sentence one piece at a time.

Input Context: The model receives an initial sequence of tokens. This could be the prompt you provide, or the text it has generated so far. For example, the context might be the tokens representing "The cat sat on the".
Probability Calculation: Based on this context, the model analyzes the patterns it learned during training. It then calculates the probability for every possible token in its vocabulary appearing next. It might determine:
- Probability of "mat" is 0.6 (or 60%)
- Probability of "roof" is 0.2 (or 20%)
- Probability of "chair" is 0.1 (or 10%)
- Probability of "computer" is 0.0001 (or 0.01%)
- ...and so on for thousands of other possible tokens. Mathematically, you can think of this as the model estimating $P(\text{next_token} | \text{context})$ .
Token Selection: The model needs to choose the next token. The simplest strategy is often greedy decoding, where it just picks the token with the highest probability (in our example, "mat"). More complex strategies might involve sampling from the top few most probable tokens to introduce variability, but the core idea remains rooted in these calculated probabilities.
Update Context: The selected token ("mat") is appended to the sequence. The context now becomes "The cat sat on the mat".
Repeat: The process repeats. The model takes the new, longer context ("The cat sat on the mat") and predicts the next token after that (perhaps "and"), calculates probabilities, selects the token, and appends it again.

This cycle continues, adding one token at a time, until the model reaches a stopping condition, such as generating a predefined end-of-sequence token or fulfilling the length requirement specified in the prompt.

The process of text generation involves iteratively predicting the next token based on the current context, appending the chosen token, and repeating the cycle.

The Basis for Prediction: Training Data

How does the model "know" that "mat" is more likely than "computer" after "The cat sat on the"? This knowledge comes entirely from the massive amounts of text data it was trained on. During training, the model learned statistical relationships between tokens. It saw countless examples of sequences like "sat on the mat," "sat on the chair," and very few (if any) like "sat on the computer." This exposure allows it to build an internal representation of language patterns, which it uses to make these predictions.

While we often simplify this by talking about predicting the "next word," remember from the previous section that LLMs actually operate on tokens. The principle is the same, but the units being predicted might be whole words, parts of words, or punctuation, depending on the tokenization method used.

This sequential, probability-driven prediction mechanism is the fundamental operational principle behind how LLMs generate coherent and contextually relevant text. The quality and sophistication of the predictions depend heavily on the model's architecture, the size of its training dataset, and the number of parameters it has, which we will touch upon next.