Embedding

Definition

An embedding is a numerical representation of a discrete item.

Simple form:

discrete item -> numerical representation

For example:

token -> embedding

The embedding gives the model something it can compare, transform, and pass through layers.

An embedding makes a discrete item operable inside neural computation.

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Why Embeddings Are Needed

A token by itself is a symbol.

A model needs a representation it can compute with.

Example:

"cat" -> token ID -> embedding

The embedding is not the original text.

It is the model's numerical representation of that token.

Embeddings connect symbolic input to numerical computation.

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Embedding Is Not Meaning Itself

An embedding can contain useful learned patterns.

But it is not human meaning directly stored in a vector.

It is a representation shaped by training.

Example:

training objective pushes representations to become useful

Useful does not always mean perfectly meaningful or correct.

Embedding meaning is model-relative, not inherent.

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Embedding As A Lookup

One common way to produce embeddings is with a lookup table.

Simple form:

token ID -> row in embedding table -> embedding vector

The token ID selects the representation.

The embedding vector carries the information used by the model.

The ID finds the embedding; the embedding does the representational work.

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What An Embedding Enables

Once a token has an embedding, the model can apply operations such as:

comparison
attention
weighted mixing
layer transformation
prediction

This is why embeddings are a bridge between tokens and neural networks.

Embeddings turn symbols into transformable representations.

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Final Summary

• An embedding is a numerical representation of a discrete item.
• It makes tokens computable by neural layers.
• It is not human meaning directly.
• It is shaped by training.
• A token ID often selects an embedding from a table.
• Embeddings provide the material that attention and later layers transform.