~/writing/math-foundations-for-reasoning-models $ ls
Embeddings and Representation
Token ID
A token ID is a consistent integer label that identifies a token and selects its embedding.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Token ID
Definition
A token ID is a number assigned to a token.
Simple form:
token -> token ID
Example:
"cat" -> 4821
The exact number depends on the tokenizer.
A token ID is a stable label for a token.
Token ID Is Identity, Not Meaning
The number itself does not carry meaning by size.
Example:
ID 100 is not "less meaningful" than ID 9000
ID 9000 is not "larger in meaning" than ID 100
The ID is mainly an index.
It tells the system which token is present.
Token ID number value is not semantic value.
Why Token IDs Are Needed
Computers need discrete identifiers to store and retrieve token information.
Simple flow:
token -> ID -> embedding table lookup
The ID allows the model to find the embedding associated with that token.
Token IDs connect tokens to embedding rows.
Consistency Matters
The same tokenizer must map tokens consistently.
Example:
"cat" -> 4821
If the same token mapped to different IDs unpredictably, the model could not use its learned embeddings reliably.
Consistent token IDs preserve stable reference.
Token ID vs Embedding
A token ID identifies.
An embedding represents.
token ID:
which token is this?
embedding:
how should the model compute with this token?
The ID is discrete.
The embedding is numerical and transformable.
The ID selects the representation; it is not the representation itself.
Final Summary
- A token ID is a number assigned to a token.
- It identifies the token consistently.
- The number's magnitude does not define meaning.
- Token IDs are used to look up embeddings.
- Token ID and embedding are different concepts.
~/writing/math-foundations-for-reasoning-models $ open
Continue the series.
Token Embedding