~/tedtes/writing/math-foundations-for-reasoning-models

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Embeddings and Representation

Token

A token is the discrete unit a model receives after text has been split into processable pieces.

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Token

Definition

A token is a discrete unit used by a model.

For text, a token may be:

a word
a part of a word
a punctuation mark
a space-like pattern

A token is not always the same as a word.

A token is the model's discrete input unit.


Why Tokens Are Needed

Raw text must be converted into units before a model can process it.

Simple flow:

text -> tokens -> token IDs -> embeddings

The token step turns continuous-looking text into a sequence of discrete pieces.

Tokenization makes text countable and addressable by the model.


Token vs Symbol

A token is a kind of symbol inside the model's input system.

It is distinguishable from other tokens.

Example:

token A != token B

But being distinguishable is not enough.

The token must later become an embedding to participate in neural computation.

Tokens distinguish input pieces; embeddings make them computable.


Token Sequence

Models usually receive a sequence of tokens.

Example:

text:
"the cat slept"

tokens:
[the, cat, slept]

Actual tokenization may split differently depending on the tokenizer.

The key idea is that text becomes an ordered list of discrete units.

A token sequence is the structured input a language model operates on.


Token Is Not The Final Representation

A token is an input unit.

It is not yet a rich model representation.

The next steps are:

token -> token ID -> embedding -> contextual representation

Each step makes the input more usable for computation.

A token starts the representation process; it does not finish it.


Final Summary

  • A token is a discrete model input unit.
  • Tokens are not always words.
  • Text is converted into a sequence of tokens.
  • Tokens are distinguishable symbols.
  • Token IDs identify tokens.
  • Embeddings turn tokens into numerical representations.

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Continue the series.

Token ID