How Word Embeddings in Large Language Models Are Connected to Information Entropy

Getting your Trinity Audio player ready…

Introduction

Big AI models like ChatGPT work by turning words into numbers—called embeddings—and figuring out how those numbers relate to one another. These numbers help the model understand the meaning of words, sentences, and even long conversations.

At the same time, there’s a deep concept from information theory called entropy. It’s a way to measure uncertainty or surprise. For example, if I flip a fair coin, the outcome is unpredictable—that’s high entropy. But if I always flip heads, that’s low entropy.

This article explains how these two ideas—embeddings and entropy—are connected. We’ll explore what embeddings are, what entropy means, and how these ideas help language models learn, understand, and generate language more effectively.

What Are Word Embeddings?

When a language model reads a sentence, it needs to turn each word into a format it can work with—numbers. That’s what embeddings are: lists of numbers that represent words (or pieces of words). Words with similar meanings have embeddings that are “close together” in this number space.

For example:

“cat” and “dog” might have similar embeddings.
“cat” and “sky” would be far apart.

These embeddings help the model understand context, meaning, and grammar.

What Is Entropy?

Entropy is a measure of how uncertain or unpredictable something is.

A sentence like “The sun rises in the ___” probably ends with “east.” That’s low entropy—very predictable.
But “I saw a ___ at the zoo” could be “lion,” “giraffe,” “penguin”—that’s higher entropy because there are more reasonable options.

In AI, we use entropy to describe how unsure the model is about what comes next in a sentence.

How These Two Ideas Come Together

When a language model is trained, it tries to guess the next word in a sentence. At first, it’s bad at this and makes lots of wrong guesses. Over time, it learns patterns and gets better. In a way, it’s trying to reduce uncertainty—that is, reduce entropy.

The better the model gets, the more certain it becomes about what word should come next, and the less “entropy” there is in its predictions.

Embeddings are a big part of this learning. They help the model organize knowledge about language in a way that reduces confusion.

Embeddings Are Like Compressed Language Knowledge

Think of embeddings like this:

Imagine reading thousands of books and then trying to remember all the important patterns—grammar, meaning, slang, tone—in a way you could use in new conversations. Embeddings do exactly that. They take all that messy language and compress it into neat little vectors that the model can use to make smart guesses.

That’s where entropy comes in. The model wants these embeddings to carry as much useful info as possible, without storing too much noise or irrelevant detail. This balance between keeping the important stuff and throwing away the extra is what entropy helps us measure.

More Entropy Means More Possibility

Some embeddings represent words with very flexible or unclear meanings. Think about a word like “bank.” It could mean:

a place with money
the side of a river
a verb (to bank a plane)

That’s a word with high entropy—lots of possible meanings. Its embedding needs to stay flexible, depending on context.

Meanwhile, a word like “the” almost always works the same way. It has low entropy—the model isn’t confused about it. Its embedding doesn’t need to do much.

How Entropy Helps Understand Embeddings

1. How Much Information Is Stored

By measuring entropy, researchers can estimate how packed with information an embedding is. If an embedding has high entropy, it probably holds lots of possible meanings or features. If it has low entropy, it might be simpler or even repetitive.

2. Whether the Model Is Repeating Itself

Sometimes, different words end up with very similar embeddings, which means the model might be wasting space by storing the same idea multiple times. That’s a kind of redundancy. Measuring entropy helps detect this. If the overall embedding space has low entropy, it might be too repetitive.

3. Which Layers in the Model Do What

LLMs like GPT or BERT have multiple layers—each one refines the embeddings a little more. Some layers expand on the word’s meaning (adding more info), and some compress it (keeping only what’s useful). You can actually measure how entropy changes across the layers.

Usually, early layers add uncertainty (exploring different meanings), and deeper layers reduce it (settling on the right one for the task).

Why This Matters

Understanding What the Model Knows

If we want to know what kinds of knowledge the model has stored, looking at entropy in its embeddings is a good tool. It tells us where the model is flexible, where it’s confident, and what kind of info it’s storing.

Making Models Smaller or Faster

By identifying embeddings that are too detailed or too redundant, we can simplify models. This makes them faster and use less memory, without losing accuracy. Entropy helps guide those decisions.

Making Models More Interpretable

Researchers can use entropy to see which embeddings are doing what. For example:

Are some embeddings mostly storing grammar?
Are others focused on meaning?
Are some overloaded with too many jobs?

Entropy gives a window into these questions.

Wrapping Up

Embeddings are the secret sauce behind powerful language models. They help the AI “understand” language by turning words into rich, flexible mathematical forms. But to manage all this complexity, the model needs to balance detail with simplicity.

That’s where entropy comes in. It tells us how much the model knows, how uncertain it is, and how efficient its memory is.

By studying embeddings and entropy together, we learn how LLMs compress the complexity of human language into something machines can work with—and maybe, even understand.

Let me know if you’d like this in slide format or as a printable handout!