unigram

A bijective codec between bytes and words that cost exactly one LLM token.

The same four bytes, twice:

hex      a14ed61a                                            6 tokens
unigram  people error social career                          4 tokens

The same sixteen:

hex      8623a771b764ce50bb85371ff65aebe9                   21 tokens
unigram  login city population income question head season
         example region location count century update
         football task table                                16 tokens

Now corrupt one character of each.

hex      a14ed61a  ->  a14ed61b     still a valid digest, and nothing can tell

unigram  people error social career  ->  people errer social career
         Err(UnknownWord { position: 1, word: "errer" })

That is the whole pitch. Machine identifiers are routinely handed to a language model and asked back — an acknowledgement token, a digest, a correlation id — and hex is the worst available carrier for that trip. It is expensive, because a hex run shreds into a fragment every character or two under every tokenizer. And it is silently fragile, because every character is drawn from the same sixteen, so every corruption of a hex digest is another hex digest.

Using it

let words = unigram::encode(&[0x3d, 0x9a, 0x00, 0xff]);
assert_eq!(words, "department number access world");
assert_eq!(unigram::decode(&words)?, vec![0x3d, 0x9a, 0x00, 0xff]);

unigram::mint(4);                     // 32 fresh bits from the OS CSPRNG, 4 tokens
unigram::matches(issued, presented);  // comparison that forgives a round trip

decode is liberal in what it accepts: any run of characters that is not an ASCII letter separates words, and case is ignored — so a value that came back hyphenated, re-wrapped across lines, comma-joined, quoted, or shouted still decodes to the bytes that were sent. It is exact in what it returns, though: an unknown word is refused and named, never skipped or guessed at.

matches compares decoded bytes when both sides are encoded values, and normalized strings otherwise — so values issued in some older format keep matching themselves without a migration.

What it costs

One word is one byte, and one word is one token, so an encoded value costs one token per byte — the same for every value. Against hex of the same payload, under Claude:

Roughly a quarter cheaper on average — but the flat cost matters more than the mean. Hex swings with the value, so a token budget built on it has to assume the worst case. This one is known before the value is minted.

The margin narrows under the GPT-4 vocabularies, where 32 bytes of hex average 37.1, and widens sharply under Llama's SentencePiece, where the same payload averages 58.2 against the same flat 32.

Choosing a length

Length is the entropy budget and the token budget at once — the two cannot drift apart, which is most of why this is easier to size than hex.

The right column is the birthday bound, k ≈ √(2·N·p), and it is the column to size against: collisions arrive at the square root of the space, not at the space. Sixteen words is a UUID's width, thirty-two a SHA-256's.

Two questions hide in that table and it answers only one. Collision is the right column — how many values may be outstanding before two coincide. Guessing is separate: mint draws from the OS CSPRNG, so every bit is unpredictable, but four words is 4.3 billion candidates, which is an afternoon for anything that can ask freely. Four words suits a value that is scoped, short-lived, and rate-limited — an acknowledgement nonce, a correlation id. A value a stranger can grind at wants eight or more, and at equal entropy the words are still the cheaper carrier.

The join is a space, deliberately

Tokenizer vocabularies hold their canonical word entries space-prefixed, so the space between two words is absorbed into the word that follows it and costs nothing. No other separator is free. Measured across all five families, an eight-byte value:

The join would cost almost as much as the payload. Encoded values travel inside quoted strings in practice, where embedded spaces are free — and decode accepts every one of those separators anyway, so a value that comes back joined differently is not a value that is lost.

The alphabet

256 entries of lowercase ASCII English, 4 to 11 characters, chosen under four constraints:

• One token under Claude, GPT-2/3 (r50k, p50k), GPT-3.5/4 (cl100k), GPT-4o (o200k), and Llama's SentencePiece — spanning both the BPE and SentencePiece families.
• No two entries within one character edit of each other. This is what puts a slipped character outside the alphabet instead of on a different valid word, and it is the property hex cannot have at any length.
• Nothing charged — no death, violence, race, gender, religion, or politics. These strings surface unbidden in transcripts, logs, and user-facing errors.
• No entry is an inflection of another, so a dropped plural cannot silently decode to a different byte.

The table is indexed by the byte each word encodes, so it is appended to, never rearranged: reordering an entry changes what every previously issued value decodes to.

Verifying it

The crate depends on nothing but the OS CSPRNG, at runtime or under test, and never tokenizes. cargo test covers the codec and the table's structure; it says nothing about cost.

Every number on this page is printed by verify-alphabet.py, which reads the alphabet straight out of src/lib.rs and re-measures it against all five families:

uv run verify-alphabet.py

Run it after any edit to the table. A green test suite alone establishes none of what this crate is named for.

License

MIT.