We've discussed how Large Language Models learn from vast amounts of text data. But where exactly does the model store the patterns, grammar rules, facts, and stylistic nuances it picks up during this extensive training process? The answer lies in the model's parameters.

Think of parameters as the internal adjustable "knobs" or configuration settings of the LLM. During training, the model processes the input text and continuously adjusts these parameters to get better at its core task, typically predicting the next word in a sequence. This adjustment process is how the model "learns".

You might be familiar with parameters from simpler mathematical models. For instance, in basic linear regression, we try to find the best line to fit data using an equation like:

y = mx + b

Here, $m$ (the slope) and $b$ (the intercept) are the parameters. The process of "fitting the line" involves finding the optimal values for these two parameters based on the data.

LLMs operate on a similar principle but at an unimaginably larger scale. Instead of just two parameters, they have millions, billions, or even trillions of them. The sheer number of parameters, often denoted by $P$ , is a defining characteristic of LLMs and is directly related to their capabilities.

Why So Many Parameters?

Human language is incredibly rich and complex. Consider everything involved:

Grammar and Syntax: The rules governing sentence structure.
Semantics: The meaning of words and phrases.
Context: How meaning changes based on surrounding text.
Factual Knowledge: Information about the world.
Reasoning: The ability to draw inferences (even if limited).
Style and Tone: Different ways of expressing ideas.

To capture these multifaceted aspects of language learned from petabytes of text data, a model needs an enormous number of parameters. Each parameter contributes a tiny part to the overall representation of language learned by the model. A larger number of parameters generally provides the model with a higher capacity to memorize information and learn intricate patterns from the training data. This is why there's often a correlation between the size of the training dataset and the number of parameters in the model designed to learn from it – you need a large model ( $P$ ) to effectively absorb information from large data.

Approximate parameter counts for different scales of LLMs. Note the logarithmic scale used to display the vast differences.

Once the training phase is complete, these parameters are typically "frozen", meaning their values are fixed. When you provide a prompt to a trained LLM, your input text is processed through the layers of the model. The calculations performed at each step depend on the input data and the fixed values of these learned parameters. The interplay between the input and the billions of parameters ultimately determines the sequence of words the model generates as output.

These parameters are not just a massive, disorganized collection. They are carefully arranged within a specific network structure that allows the model to process language effectively. One of the most important structures enabling modern LLMs is the Transformer architecture, which we will introduce at a high level in the next section.