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Современные LLM2 / 20

Модуль 2. Токенизация и эмбеддинги

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Ноутбук 2. BBPE и эмбеддинги: от строки к вектору

Основной ноутбук модуля

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Ноутбук 2. BBPE и эмбеддинги: от строки к вектору

Модуль 2. Токенизация и эмбеддинги — практический ноутбук

Этот ноутбук содержит учебный код с инженерной дисциплиной, а не промышленный токенизатор. Мы сохраняем прозрачный алгоритм, но добавляем воспроизводимые данные, контракты функций, проверки эквивалентности, сериализацию, отрицательные случаи и локальное измерение скорости. Реальные токенизаторы дополнительно используют инкрементальные индексы пар, SIMD, Rust/C++, параллелизм и потоковые API.

Colab-контракт: после Runtime → Run all все обязательные ячейки выполняются в чистой Google Colab-сессии. Ноутбук не читает соседние файлы и использует внешний корпус PUD 2.15: замороженные корпуса M2 и эталонный 4096-merge артефакт встроены внутрь с SHA-256.

Маршрут:

  1. настройка окружения и самодостаточные данные;

  2. наивное учебное ядро;

  3. точная оптимизация через дедупликацию чанков;

  4. BBPETokenizer: encode/decode и сериализация;

  5. аудит Harmony и политики специальных токенов;

  6. тесты корректности и численные инварианты лекции;

  7. сверка с HuggingFace tokenizers;

  8. локальное измерение скорости и граница учебной реализации;

  9. эмбеддинги: lookup, логиты, softmax, память и один шаг обучения.

Первый проход: запустите всё сверху вниз и прочитайте §1, §3–4 и §10.1. Второй: разберите оптимизацию, проверки, метрики и обучение таблицы (§2, §6–7, §10.2–10.3). Справочный: протокол и сравнение библиотек (§5, §8–9). Сеть нужна только для установки отсутствующих зависимостей и явно включённой сверки tiktoken.

Python
# Устанавливаем только пакеты, которых нет в текущем runtime.
import importlib.util
import subprocess
import sys

required = {"regex": "regex==2026.7.19", "numpy": "numpy==2.3.5"}
missing = [pip_name for module, pip_name in required.items()
           if importlib.util.find_spec(module) is None]
if missing:
    subprocess.check_call([sys.executable, "-m", "pip", "install", "-q", *missing])

INSTALL_OPTIONAL = False  # Set True to install the tested optional comparison.
HAS_TOKENIZERS = importlib.util.find_spec("tokenizers") is not None
if INSTALL_OPTIONAL and not HAS_TOKENIZERS:
    try:
        subprocess.check_call(
            [sys.executable, "-m", "pip", "install", "tokenizers==0.23.1"]
        )
    except subprocess.CalledProcessError as exc:
        print("Не удалось установить необязательный tokenizers:", exc)
    HAS_TOKENIZERS = importlib.util.find_spec("tokenizers") is not None
import importlib.metadata
print("Версии:", {name: importlib.metadata.version(name)
                    for name in required})
if HAS_TOKENIZERS:
    print("tokenizers:", importlib.metadata.version("tokenizers"))
print('Окружение готово.', "tokenizers=", HAS_TOKENIZERS)

0. Замороженные данные M2

Численный эксперимент должен иметь стабильный вход. В модуле используется фиксированная выборка из корпуса PUD 2.15: 833 предложения RU для обучения и 167 параллельных RU/EN предложений для проверки. Документы между частями не пересекаются. Ниже данные распаковываются в память. Большая служебная ячейка свёрнута, но её можно открыть и проверить: для каждого встроенного блока данных сверяется SHA-256.

PUD 2.15 · CC BY-SA 3.0. Текст и переводы предоставлены участниками PUD, переводческими командами DFKI, Google и сообществом Universal Dependencies. Сведения об авторах и исходные уведомления: RU, EN. Полный текст лицензии встроен как corpus_license. Извлекаем предложения без изменений, соединяем LF и разделяем по исходным документам; нормализации Unicode нет. Это учебный опыт с токенизатором, а не официальный протокол синтаксического анализа UD. corpus_manifest хранит ревизии и хеши. Текст корпуса и выровненные извлечения сохраняют CC BY-SA 3.0.

Python
import base64
import hashlib
import json
import math
import time
import zlib
from collections import Counter
import regex as re

_PACKED_ASSETS = {
    "train": ("""
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}

def unpack_asset(name: str) -> bytes:
    """Распаковывает встроенные данные и проверяет их SHA-256."""
    payload, expected_sha256 = _PACKED_ASSETS[name]
    compact_payload = "".join(payload.split())
    raw = zlib.decompress(base64.b85decode(compact_payload.encode("ascii")))
    actual_sha256 = hashlib.sha256(raw).hexdigest()
    if actual_sha256 != expected_sha256:
        raise RuntimeError(
            f"Embedded asset {name!r} failed SHA-256 verification: "
            f"{actual_sha256} != {expected_sha256}"
        )
    return raw

corpus_ru = unpack_asset("train").decode("utf-8")
corpus_en = unpack_asset("eval").decode("utf-8")
corpus_eval_ru = unpack_asset("holdout_ru").decode("utf-8")
corpus_train_en = unpack_asset("train_en").decode("utf-8")
corpus_manifest = json.loads(unpack_asset("provenance"))
aligned = [json.loads(line) for line in unpack_asset("aligned").decode("utf-8").splitlines()]
corpus_license = unpack_asset("license").decode("utf-8")
train_docs = {r["document"] for r in aligned if r["split"] == "train"}
eval_docs = {r["document"] for r in aligned if r["split"] == "eval"}
assert train_docs.isdisjoint(eval_docs)
assert len(aligned) == len({r["id"] for r in aligned}) == 1000
for split, lang, text in [("train", "ru", corpus_ru), ("train", "en", corpus_train_en),
                         ("eval", "ru", corpus_eval_ru), ("eval", "en", corpus_en)]:
    expected_text = "\n".join(r[lang] for r in aligned if r["split"] == split) + "\n"
    assert text == expected_text
    expected_sha = corpus_manifest["files"][f"m2_{split}_{lang}.txt"]["sha256"]
    assert hashlib.sha256(text.encode("utf-8")).hexdigest() == expected_sha
frozen_model = json.loads(unpack_asset("model").decode("utf-8"))
reference = json.loads(unpack_asset("reference").decode("utf-8"))
snapshot = json.loads(unpack_asset("snapshot").decode("utf-8"))

assert len(corpus_ru.encode("utf-8")) == reference["corpus"]["train_bytes"]
assert len(corpus_en.encode("utf-8")) == reference["corpus"]["eval_bytes"]
assert len(corpus_eval_ru.encode("utf-8")) == reference["corpus"]["holdout_ru_bytes"]
assert len(frozen_model["merges"]) == reference["model"]["merges"] == 4096
print(
    'Данные M2 распакованы и проверены' + ": "
    f"train={len(corpus_ru.encode('utf-8')):,} B, "
    f"held-out={len(corpus_en.encode('utf-8')):,} B, "
    f"merges={len(frozen_model['merges'])}"
)

1. Прозрачное учебное ядро

Три операции задают спецификацию: посчитать соседние пары, слить выбранную пару и повторить жадный шаг. При равной частоте выигрывает пара, встреченная первой при обходе; это правило разрешения равенств влияет на весь словарь и потому проверяется тестами.

В трассе ниже первое слияние собирает «и», но второе соединяет пробел с первым байтом буквы. Сопоставьте каждый шаг с частотой выбранной пары: алгоритм может строить целые символы и их части в любом порядке, разрешённом этими частотами.

Python
PATTERN = re.compile(
    r"""'(?i:[sdmt]|ll|ve|re)|[^\r\n\p{L}\p{N}]?+\p{L}+|\p{N}{1,3}| ?[^\s\p{L}\p{N}]++[\r\n]*|\s*[\r\n]|\s+(?!\S)|\s+"""
)
Pair = tuple[int, int]
MergeTable = dict[Pair, int]

def pair_counts(chunks: list[list[int]]) -> Counter[Pair]:
    """Считает соседние пары в порядке корпуса; порядок Counter задаёт tie-break."""
    counts: Counter[Pair] = Counter()
    for chunk in chunks:
        counts.update(zip(chunk[:-1], chunk[1:]))
    return counts

def merge_pair_in_chunk(ids: list[int], pair: Pair, new_id: int) -> list[int]:
    """Сливает все неперекрывающиеся вхождения pair внутри одного чанка."""
    out: list[int] = []
    i = 0
    while i < len(ids):
        if i + 1 < len(ids) and (ids[i], ids[i + 1]) == pair:
            out.append(new_id)
            i += 2
        else:
            out.append(ids[i])
            i += 1
    return out

def merge_pair_in_corpus(
    chunks: list[list[int]], pair: Pair, new_id: int
) -> list[list[int]]:
    """Выполняет одно неперекрывающееся слияние отдельно в каждом чанке."""
    return [merge_pair_in_chunk(chunk, pair, new_id) for chunk in chunks]

def train_naive(text: str, num_merges: int) -> MergeTable:
    """Наивный точный BBPE-тренер: один полный проход по корпусу на merge."""
    if type(num_merges) is not int or num_merges < 0:
        raise ValueError("num_merges должен быть целым неотрицательным числом")
    chunks = [list(chunk.encode("utf-8")) for chunk in PATTERN.findall(text)]
    merges: MergeTable = {}
    for merge_index in range(num_merges):
        counts = pair_counts(chunks)
        if not counts:
            break
        pair = max(counts, key=counts.get)
        new_id = 256 + merge_index
        chunks = merge_pair_in_corpus(chunks, pair, new_id)
        merges[pair] = new_id
    return merges

toy = "низко низко летали ласточки, ласточки летали низко"
toy_chunks = PATTERN.findall(toy)
assert len(toy_chunks) == 8
assert sum(len(chunk.encode("utf-8")) for chunk in toy_chunks) == 93
print('Игрушечный корпус: 8 чанков, 93 байта — OK')

2. Точный ускоренный тренер: дедупликация чанков

Наивный вариант заново сканирует все вхождения каждого чанка. Здесь одинаковые чанки хранятся один раз, а статистика пар умножается на кратность. Это всё ещё учебная реализация: она понятнее промышленных индексов пар, но сохраняет точно тот же результат, включая правило разрешения равных частот. Эквивалентность не предполагается — она проверяется.

Python
class BBPETrainer:
    """Точный учебный тренер, хранящий каждый повторяющийся чанк один раз."""

    def __init__(self, num_merges: int):
        """Задаёт целое неотрицательное число шагов слияния."""
        if type(num_merges) is not int or num_merges < 0:
            raise ValueError("num_merges должен быть целым неотрицательным числом")
        self.num_merges = num_merges
        self.merges: MergeTable = {}

    @staticmethod
    def _weighted_pair_counts(
        unique_chunks: dict[str, list[int]], frequencies: dict[str, int]
    ) -> Counter[Pair]:
        """Считает пары по уникальным чанкам с весом, равным их кратности."""
        counts: Counter[Pair] = Counter()
        for chunk_text, ids in unique_chunks.items():
            frequency = frequencies[chunk_text]
            for pair in zip(ids[:-1], ids[1:]):
                counts[pair] += frequency
        return counts

    def train(self, text: str) -> "BBPETrainer":
        """Обучает таблицу слияний; равные частоты разрешаются порядком обхода корпуса."""
        frequencies: dict[str, int] = {}
        for chunk in PATTERN.findall(text):
            frequencies[chunk] = frequencies.get(chunk, 0) + 1

        # dict сохраняет порядок первого появления, а значит, и выбор при равных частотах.
        unique_chunks = {
            chunk: list(chunk.encode("utf-8")) for chunk in frequencies
        }
        self.merges = {}
        for merge_index in range(self.num_merges):
            counts = self._weighted_pair_counts(unique_chunks, frequencies)
            if not counts:
                break
            pair = max(counts, key=counts.get)
            new_id = 256 + merge_index
            for chunk, ids in unique_chunks.items():
                if len(ids) > 1:
                    unique_chunks[chunk] = merge_pair_in_chunk(ids, pair, new_id)
            self.merges[pair] = new_id
        return self

    def vocab_bytes(self) -> dict[int, bytes]:
        """Восстанавливает байты токенов по таблице слияний."""
        vocab = {token_id: bytes([token_id]) for token_id in range(256)}
        for (left, right), new_id in self.merges.items():
            vocab[new_id] = vocab[left] + vocab[right]
        return vocab

checks = [
    ("toy", toy, 30),
    ("RU slice", corpus_ru[:6000], 128),
]
for name, text, merge_count in checks:
    expected = train_naive(text, merge_count)
    actual = BBPETrainer(merge_count).train(text).merges
    assert actual == expected, f"trainer mismatch on {name}"

sample = corpus_ru[:12000]
start = time.perf_counter()
naive = train_naive(sample, 200)
naive_seconds = time.perf_counter() - start
start = time.perf_counter()
deduplicated = BBPETrainer(200).train(sample).merges
deduplicated_seconds = time.perf_counter() - start
assert naive == deduplicated
print(
    'Наивный и дедуплицированный тренеры совпали' + ": "
    f"12k chars × 200 merges, {naive_seconds:.2f}s vs "
    f"{deduplicated_seconds:.2f}s"
)

3. BBPETokenizer: ранги, decode и сериализация

На инференсе частот уже нет. Из присутствующих пар выбирается та, чей ранг слияния минимален. Decode объединяет байты токенов; параметр errors явно задаёт поведение на невалидном UTF-8. Сериализация ниже учебная и JSON-совместимая, но не обещает бинарной совместимости с конкретным tokenizer.json внешней библиотеки.

Python
class BBPETokenizer:
    """Прозрачный byte-level BPE encoder/decoder для обучения и тестов."""

    def __init__(self, merges: MergeTable):
        """Проверяет упорядоченную таблицу слияний и восстанавливает байтовый словарь."""
        if not isinstance(merges, dict):
            raise ValueError("merges must be an ordered dict")
        self.merges = dict(merges)
        self._vocab: dict[int, bytes] = {
            token_id: bytes([token_id]) for token_id in range(256)
        }
        for rank, (pair, new_id) in enumerate(self.merges.items()):
            if (not isinstance(pair, tuple) or len(pair) != 2
                    or any(type(x) is not int for x in (*pair, new_id))):
                raise ValueError("merge entries must contain integer IDs, not bools")
            left, right = pair
            if new_id != 256 + rank:
                raise ValueError("new IDs must be consecutive in merge order from 256")
            if left not in self._vocab or right not in self._vocab:
                raise ValueError(
                    f"merge {(left, right)} references an unknown earlier token"
                )
            if new_id in self._vocab:
                raise ValueError(f"duplicate token id: {new_id}")
            self._vocab[new_id] = self._vocab[left] + self._vocab[right]

    def __len__(self) -> int:
        """Возвращает размер словаря, включая 256 байтовых токенов."""
        return len(self._vocab)

    def vocab_bytes(self) -> dict[int, bytes]:
        """Возвращает копию словаря ID → байты, чтобы вызывающий код не менял оригинал."""
        return dict(self._vocab)

    def _encode_chunk(self, ids: list[int]) -> list[int]:
        """Кодирует один regex-чанк, каждый раз применяя минимальный доступный ранг."""
        while len(ids) > 1:
            best_pair: Pair | None = None
            best_rank: int | None = None
            for pair in zip(ids[:-1], ids[1:]):
                rank = self.merges.get(pair)
                if rank is not None and (best_rank is None or rank < best_rank):
                    best_pair = pair
                    best_rank = rank
            if best_pair is None or best_rank is None:
                break
            ids = merge_pair_in_chunk(ids, best_pair, best_rank)
        return ids

    def encode(self, text: str) -> list[int]:
        """Кодирует Unicode-текст по чанкам, выбирая наименьший ранг слияния."""
        out: list[int] = []
        for chunk in PATTERN.findall(text):
            out.extend(self._encode_chunk(list(chunk.encode("utf-8"))))
        return out

    def decode(self, ids: list[int], *, errors: str = "replace") -> str:
        """Объединяет байты токенов и декодирует UTF-8 с явной политикой ошибок."""
        if any(type(token_id) is not int for token_id in ids):
            raise ValueError("decode expects integer IDs, not bools or floats")
        try:
            raw = b"".join(self._vocab[token_id] for token_id in ids)
        except KeyError as exc:
            raise ValueError(f"unknown token id: {exc.args[0]}") from exc
        return raw.decode("utf-8", errors=errors)

    def to_dict(self) -> dict:
        """Представляет упорядоченную таблицу слияний в формате, совместимом с JSON."""
        return {
            "version": "bbpe-course-2",
            "merges": [
                [left, right, new_id]
                for (left, right), new_id in self.merges.items()
            ],
        }

    def to_json(self) -> str:
        """Сохраняет учебный токенизатор в детерминированный JSON."""
        return json.dumps(self.to_dict(), ensure_ascii=False)

    @classmethod
    def from_dict(cls, obj: dict) -> "BBPETokenizer":
        """Создаёт токенизатор из проверенной структуры данных JSON."""
        if not isinstance(obj, dict) or obj.get("version") not in (
            "bbpe-course-1", "bbpe-course-2"
        ):
            raise ValueError("unsupported serialized tokenizer version")
        rows = obj.get("merges")
        if not isinstance(rows, list):
            raise ValueError("serialized tokenizer has no merge list")
        merges = {}
        for row in rows:
            if (not isinstance(row, list) or len(row) != 3
                    or any(type(x) is not int for x in row)):
                raise ValueError("each merge must be a list of three integer IDs")
            left, right, new_id = row
            if (left, right) in merges:
                raise ValueError("duplicate merge pair")
            merges[left, right] = new_id
        return cls(merges)

    @classmethod
    def from_json(cls, payload: str) -> "BBPETokenizer":
        """Создаёт токенизатор из строки JSON."""
        return cls.from_dict(json.loads(payload))

4. Полный 4096-merge артефакт без тяжёлого Colab-прогона

Полное обучение прозрачным Python-тренером намеренно не входит в обязательный Run all: его асимптотика полезна для понимания, но не для ожидания в учебной сессии. Вместо этого ноутбук загружает замороженный артефакт, реконструирует словарь и свежим обучением проверяет первые 256 слияний. Так основной маршрут остаётся быстрым, а происхождение артефакта не принимается на веру.

Python
full_tokenizer = BBPETokenizer.from_dict(frozen_model)
assert len(full_tokenizer) == reference["model"]["vocab_size"] == 4352

# Восстанавливаем и сравниваем весь байтовый словарь сохранённого артефакта.
artifact_vocab = {
    int(token_id): base64.b64decode(encoded_bytes)
    for encoded_bytes, token_id in frozen_model["vocab"].items()
}
assert artifact_vocab == full_tokenizer.vocab_bytes()

# Проверяем происхождение: заново обучаем начальную часть правил на фиксированных данных.
fresh_prefix = BBPETrainer(256).train(corpus_ru).merges
frozen_prefix = dict(list(full_tokenizer.merges.items())[:256])
assert fresh_prefix == frozen_prefix
print('Артефакт с 4096 слияниями и его первые 256 правил проверены')

5. Протокольный слой: воспроизведение снимка o200k_harmony

Учебный BBPE выше отвечает за обычный текст. Реальный токенизатор содержит ещё и служебный диапазон, кодирующий структуру сообщения. В официальной реализации o200k_harmony наследует обычные токены и предварительное разбиение от o200k_base, а затем добавляет именованные специальные токены и большой резерв. Здесь мы воспроизводим арифметику идентификаторов без сетевого доступа и отдельно показываем алиас: два имени могут ссылаться на один и тот же идентификатор.

Политика обработки специальных строк является частью границы доверия. Обычный encode в tiktoken по умолчанию отклоняет зарегистрированное написание специального токена; приложение должно явно разрешить его как управляющий токен либо потребовать кодирования как обычного текста.

Python
mergeable_ids = 199_998
named_protocol_tokens = {
    "<|startoftext|>": 199_998,
    "<|endoftext|>": 199_999,
    "<|return|>": 200_002,
    "<|constrain|>": 200_003,
    "<|channel|>": 200_005,
    "<|start|>": 200_006,
    "<|end|>": 200_007,
    "<|message|>": 200_008,
    "<|call|>": 200_012,
    "<|endofprompt|>": 200_018,
}
reserved_tokens = {
    "<|reserved_200000|>": 200_000,
    "<|reserved_200001|>": 200_001,
    "<|reserved_200004|>": 200_004,
    "<|reserved_200009|>": 200_009,
    "<|reserved_200010|>": 200_010,
    "<|reserved_200011|>": 200_011,
} | {f"<|reserved_{i}|>": i for i in range(200_013, 201_088)}
# reserved_200018 и endofprompt ссылаются на один ID.
special_tokens = named_protocol_tokens | reserved_tokens

assert len(named_protocol_tokens) == 10
assert len([name for name in special_tokens if name.startswith("<|reserved_")]) == 1_081
assert len(special_tokens) == 1_091
assert len(set(special_tokens.values())) == 1_090
assert special_tokens["<|endofprompt|>"] == special_tokens["<|reserved_200018|>"]
assert mergeable_ids + len(set(special_tokens.values())) == 201_088
print('Harmony, снимок: 199 998 обычных ID + 1 090 уникальных специальных ID = 201 088 — OK')

Снимок и необязательная сверка библиотеки

Источник и SHA-256 сохранены во встроенном snapshot. Основная ячейка выше воспроизводит снимок от 11 октября 2026 года, а не читает установленную библиотеку. Следующая ячейка по умолчанию выключена: она требует tiktoken и может скачать его публичный словарь. Выводит версию; несовпадение с датированным снимком — явная ошибка.

Python
base_fact = snapshot["tokenizer_counts"]["o200k_base.tiktoken"]
qwen_fact = snapshot["tokenizer_counts"]["qwen3_tokenizer.json"]
qwen_config = snapshot["tokenizer_counts"]["qwen3_config.json"]
assert base_fact["actual_defined_ids"] == 200000
assert base_fact["max_id_plus_one"] - base_fact["actual_defined_ids"] == 19
assert qwen_config["config_vocab_size"] - qwen_fact["unique_defined_ids"] == 267
print("Дата снимка:", snapshot["observed_at"])
print("o200k_base: определённые ID / диапазон ID:", 200000, 200019)
print("Qwen3-8B: определённые ID / строки модели:", 151669, 151936)

RUN_LIVE_TIKTOKEN = False
if RUN_LIVE_TIKTOKEN:
    import tiktoken
    print("Версия tiktoken:", importlib.metadata.version("tiktoken"))
    real = tiktoken.get_encoding("o200k_harmony")
    # Здесь намеренно читаются внутренние поля; фиксируйте выведенную версию в отчёте.
    assert real._special_tokens == special_tokens
    assert len(real._mergeable_ranks) == mergeable_ids
    assert real.n_vocab == 201088
    try:
        real.encode("<|start|>")
    except ValueError:
        pass
    else:
        raise AssertionError("default special-token rejection expected")
    assert real.encode("<|start|>", allowed_special={"<|start|>"}) == [200006]
    ordinary = real.encode("<|start|>", disallowed_special=())
    assert 200006 not in ordinary
    assert real.decode(ordinary) == "<|start|>"

6. Корректность: round-trip, два encode и повреждённый UTF-8

Тестируем не только успешный сценарий. Строки включают эмодзи, смешанные письменности, комбинирующие знаки, табы и переводы строк. Жадный encode сравнивается с медленным последовательным применением merge-правил на коротких строках.

Python
def encode_sequential(text: str, merges: MergeTable) -> list[int]:
    """Медленный эталон: применяет все слияния по порядку обучения."""
    chunks = [list(chunk.encode("utf-8")) for chunk in PATTERN.findall(text)]
    for pair, new_id in merges.items():
        chunks = merge_pair_in_corpus(chunks, pair, new_id)
    return [token_id for chunk in chunks for token_id in chunk]

nasty = [
    "Привет, мир! 🚀🚀",
    "naïve café — déjà vu",
    "混合 scripts وعربى и русский",
    "e\u0301clair (комбинирующий акцент)",
    "табы и переводы строк:\tA\nB  ",
    "digits: 1234567890; date: 2026-07-17",
]
for text in nasty:
    encoded = full_tokenizer.encode(text)
    assert full_tokenizer.decode(encoded, errors="strict") == text
    assert encoded == encode_sequential(text, full_tokenizer.merges)

# Один начальный байт четырёхбайтовой последовательности намеренно нарушает UTF-8.
assert full_tokenizer.decode([0xF0]) == "�"
try:
    full_tokenizer.decode([999_999])
except ValueError:
    pass
else:
    raise AssertionError("unknown token ids must be rejected")

roundtrip = BBPETokenizer.from_json(full_tokenizer.to_json())
assert roundtrip.encode(nasty[0]) == full_tokenizer.encode(nasty[0])
assert roundtrip.decode(roundtrip.encode(nasty[0]), errors="strict") == nasty[0]
invalid_payloads = [
    {"version": "future", "merges": []},
    {"version": "bbpe-course-2", "merges": [[97, 98, -1]]},
    {"version": "bbpe-course-2", "merges": [[97, 98, 257]]},
    {"version": "bbpe-course-2", "merges": [[97, 98, 256], [97, 98, 257]]},
    {"version": "bbpe-course-2", "merges": [[97, 98, 256], [256, 99, 256]]},
    {"version": "bbpe-course-2", "merges": [[256, 98, 256]]},
    {"version": "bbpe-course-2", "merges": [[True, 98, 256]]},
    {"version": "bbpe-course-2", "merges": [[97.5, 98, 256]]},
    {"version": "bbpe-course-2", "merges": [["97", 98, 256]]},
    {"version": "bbpe-course-2", "merges": [[97, 98]]},
]
for payload in invalid_payloads:
    try:
        BBPETokenizer.from_dict(payload)
    except ValueError:
        pass
    else:
        raise AssertionError(f"invalid artifact accepted: {payload}")
assert BBPETokenizer.from_dict({"version": "bbpe-course-2", "merges": []}).encode("ab") == [97, 98]
assert full_tokenizer.encode("Привет") == reference["greeting_ids"] == [943, 370, 301]
assert PATTERN.findall("Hello world!") == ["Hello", " world", "!"]
assert PATTERN.findall("1234567") == ["123", "456", "7"]
# Нормализация меняет восстанавливаемый текст: пример NFKC.
import unicodedata
original = "A  e\u0301"
normalized = unicodedata.normalize("NFKC", original)
assert original != normalized
assert full_tokenizer.decode(full_tokenizer.encode(original), errors="strict") == original
assert full_tokenizer.decode(full_tokenizer.encode(normalized), errors="strict") == normalized
print('Round-trip, эквивалентность encode и сериализация — OK')

7. Числа лекции как исполняемые проверки

Эталонные значения принадлежат паре «замороженный корпус M2 × замороженный список слияний». Мы пересчитываем их в текущей сессии и сравниваем с встроенным reference_metrics.json.

Python
def tokenizer_prefix(merge_count: int) -> BBPETokenizer:
    """Строит токенизатор по первым merge_count сохранённым правилам."""
    if not 0 <= merge_count <= len(full_tokenizer.merges):
        raise ValueError("merge_count is outside the frozen artifact")
    return BBPETokenizer(dict(list(full_tokenizer.merges.items())[:merge_count]))

def bytes_per_token(tokenizer: BBPETokenizer, text: str) -> float:
    """Делит число байтов UTF-8 на число токенов; результат кодирования должен быть непустым."""
    token_count = len(tokenizer.encode(text))
    if token_count == 0:
        raise ValueError("bytes/token is undefined for empty output")
    return len(text.encode("utf-8")) / token_count

print('merges | RU train | RU eval | EN eval | RU-фраза | EN-фраза')
for merge_text, expected in reference["curve"].items():
    merge_count = int(merge_text)
    tokenizer = tokenizer_prefix(merge_count)
    actual = [
        round(bytes_per_token(tokenizer, corpus_ru), 3),
        round(bytes_per_token(tokenizer, corpus_en), 3),
        len(tokenizer.encode(reference["samples"]["ru"])),
        len(tokenizer.encode(reference["samples"]["en"])),
    ]
    assert actual == expected, (merge_count, actual, expected)
    ru_eval = round(bytes_per_token(tokenizer, corpus_eval_ru), 3)
    assert ru_eval == reference["holdout_ru_curve"][merge_text]
    for name, text in [("ru_train", corpus_ru), ("ru_eval", corpus_eval_ru), ("en_eval", corpus_en)]:
        assert len(tokenizer.encode(text)) == reference["corpus_token_counts"][merge_text][name]
    print(
        f"{merge_count:6d} | {actual[0]:8.3f} | {ru_eval:7.3f} | {actual[1]:11.3f} | "
        f"{actual[2]:9d} | {actual[3]:9d}"
    )

fertility_texts = {
    "RU проза": "Языковые модели предсказывают следующий токен по контексту.",
    "EN prose": "Language models predict the next token from context.",
    "Python": "def encode(text):\n    return [merges.get(p, p) for p in pairs(text)]",
    "Числа": "1234 + 5678 = 6912; 2026-07-04",
}
fertility_labels = {'RU проза': 'RU проза', 'EN prose': 'EN prose', 'Python': 'Python', 'Числа': 'Числа'}
print("\n" + 'Домен      | токены | слова | fertility | bytes/token')
for name, text in fertility_texts.items():
    token_count = len(full_tokenizer.encode(text))
    word_count = len(re.findall(r"\p{L}+|\p{N}+", text))
    assert word_count > 0  # These four fixed examples all contain letter/digit runs.
    actual = [
        token_count,
        word_count,
        round(token_count / word_count, 2),
        round(len(text.encode("utf-8")) / token_count, 2),
    ]
    assert actual == reference["fertility"][name], (name, actual)
    label = fertility_labels[name]
    print(
        f"{label:10s} | {actual[0]:6d} | {actual[1]:5d} | "
        f"{actual[2]:9.2f} | {actual[3]:11.2f}"
    )
print('Все численные инварианты лекции воспроизведены')

Контроль по выровненным предложениям

Bytes/token зависит от кодировки. Для одинакового содержания сравним число токенов на 167 параллельных предложениях, без добавленных переводов строк. Это результат одного RU-обученного словаря, а не универсальное отношение стоимости языков. В необязательном опыте обучите такой же BBPE на corpus_train_en и повторите обе оценки.

Python
evaluation = [row for row in aligned if row["split"] == "eval"]
assert len(evaluation) == 167
for lang in ("ru", "en"):
    counts = [len(full_tokenizer.encode(row[lang])) for row in evaluation]
    assert sum(counts) == reference["aligned_eval_token_counts"][lang]
    print(lang, "токенов:", sum(counts), "токенов/предложение:", sum(counts) / len(counts))
RUN_REVERSE_TRAINING = False
if RUN_REVERSE_TRAINING:
    en_tokenizer = BBPETokenizer(BBPETrainer(4096).train(corpus_train_en).merges)
    for lang in ("ru", "en"):
        total = sum(len(en_tokenizer.encode(row[lang])) for row in evaluation)
        print("Обучен на EN", lang, "токенов/предложение:", total / len(evaluation))

8. Сверка с HuggingFace tokenizers

Rust-реализация обучается на том же RU-корпусе и с тем же размером словаря. Побитового совпадения не ждём: ByteLevel pre-tokenizer и tie-break отличаются. Проверяем более ограниченный эмпирический результат — близкий масштаб сжатия на этих двух корпусах. Для проверки на новых данных того же языка используйте также corpus_eval_ru. Установка необязательного пакета включается флагом INSTALL_OPTIONAL; проверена версия 0.23.1.

Python
if HAS_TOKENIZERS:
    from tokenizers import Tokenizer, decoders, models, pre_tokenizers, trainers

    hf_tokenizer = Tokenizer(models.BPE())
    hf_tokenizer.pre_tokenizer = pre_tokenizers.ByteLevel(add_prefix_space=False)
    hf_tokenizer.decoder = decoders.ByteLevel()
    hf_trainer = trainers.BpeTrainer(
        vocab_size=reference["model"]["vocab_size"],
        show_progress=False,
        initial_alphabet=pre_tokenizers.ByteLevel.alphabet(),
    )
    start = time.perf_counter()
    hf_tokenizer.train_from_iterator([corpus_ru], trainer=hf_trainer)
    hf_train_seconds = time.perf_counter() - start

    def hf_bytes_per_token(text: str) -> float:
        """Вычисляет байты UTF-8 на токен для сопоставляемой модели HuggingFace."""
        return len(text.encode("utf-8")) / len(hf_tokenizer.encode(text).ids)

    rows = [
        ("bytes/token RU (train)", bytes_per_token(full_tokenizer, corpus_ru),
         hf_bytes_per_token(corpus_ru)),
        ("bytes/token EN (held-out)", bytes_per_token(full_tokenizer, corpus_en),
         hf_bytes_per_token(corpus_en)),
    ]
    print('метрика                      наш BBPE   HF tokenizers')
    for name, ours, theirs in rows:
        print(f"{name:28s} {ours:10.3f} {theirs:15.3f}")
        assert abs(ours - theirs) / theirs < 0.12

    sample_text = reference["samples"]["ru"]
    assert hf_tokenizer.decode(hf_tokenizer.encode(sample_text).ids) == sample_text
    assert rows[0][1] > rows[1][1] and rows[0][2] > rows[1][2]
    print(f"{'HF round-trip и проверка масштаба компрессии — OK'}; обучение={hf_train_seconds:.2f}s")
else:
    hf_tokenizer = None
    print('Опциональная сверка с HuggingFace пропущена: пакет tokenizers недоступен')

9. Измерение скорости и граница применимости

Измерение ниже зависит от CPU и версии библиотек; оно не является опубликованным результатом производительности. Его задача — показать порядок разрыва между прозрачным Python-кодом и Rust-ядром. Скорость не входит в проверку корректности.

Python
def benchmark_bytes_per_second(fn, text: str, repeat: int = 3) -> float:
    """Возвращает лучшую скорость кодирования из повторов, в байтах UTF-8 в секунду."""
    if repeat <= 0:
        raise ValueError("repeat must be positive")
    best_seconds = math.inf
    for _ in range(repeat):
        start = time.perf_counter()
        fn(text)
        best_seconds = min(best_seconds, time.perf_counter() - start)
    return len(text.encode("utf-8")) / best_seconds

benchmark_text = corpus_ru + corpus_en
ours_bps = benchmark_bytes_per_second(full_tokenizer.encode, benchmark_text)
if hf_tokenizer is not None:
    hf_bps = benchmark_bytes_per_second(
        lambda text: hf_tokenizer.encode(text).ids, benchmark_text
    )
    print(
        f"скорость кодирования: учебный Python={ours_bps / 1e6:.2f} MB/s | "
        f"HF Rust={hf_bps / 1e6:.2f} MB/s | отношение={hf_bps / ours_bps:.1f}x"
    )
else:
    print(f"скорость кодирования: учебный Python={ours_bps / 1e6:.2f} MB/s | HF пропущен")

10. Эмбеддинги: выбор строки, обучение и память

10.1. От ID к векторам и обратно к оценкам ID

Начните с таблицы E размера 3×2. E[ids] выбирает строки; h @ U вычисляет логиты — оценки следующего ID. Сравните связанные веса U = E.T с независимой U. Устойчивый softmax превращает оценки в вероятности. Здесь h задан вручную; получение состояния из последовательности разберём в М3. Эти векторы показывают операции, но не изображают выученную семантику.

До запуска: предскажите форму X и ID с наибольшей вероятностью. Совпадёт ли он с ID 0, если h равен строке E[0]? Проверьте ответ и объясните роль скалярных произведений.

Python
"""Небольшая практика по эмбеддингам на NumPy; код встроен в оба учебных ноутбука.

Пример показывает операции с заданными весами; языковая модель здесь не обучена.
Для выполнения не нужны файлы, загрузки, GPU или импорты из репозитория.
"""
import numpy as np


def softmax(logits):
    """Нормирует по последней оси; вычитание максимума обеспечивает численную устойчивость."""
    values = np.asarray(logits, dtype=np.float64)
    exp_values = np.exp(values - values.max(axis=-1, keepdims=True))
    return exp_values / exp_values.sum(axis=-1, keepdims=True)


def embedding_budget(vocab_size, dim, *, tied, bytes_per_parameter=2):
    """Считает уникальные веса и их байты, без смещения и состояний обучения."""
    if any(type(x) is not int or x <= 0 for x in (vocab_size, dim, bytes_per_parameter)):
        raise ValueError("размеры и bytes_per_parameter должны быть положительными целыми числами")
    if type(tied) is not bool:
        raise ValueError("tied должен быть логическим значением")
    parameters = vocab_size * dim * (1 if tied else 2)
    payload = parameters * bytes_per_parameter
    return {"parameters": parameters, "bytes": payload, "GiB": payload / 2**30}


E = np.array([[1., 0.], [2., 0.], [0., 1.]])
ids = np.array([0, 2, 0])
X = E[ids]
assert X.shape == (3, 2)
np.testing.assert_array_equal(X, [[1, 0], [0, 1], [1, 0]])

h = np.array([1., 0.])  # Состояние задано вручную; Transformer его не вычислял.
U_untied = np.array([[0., 1., -1.], [2., 0., 1.]])
z_tied = h @ E.T
z_untied = h @ U_untied
p_tied = softmax(z_tied)
np.testing.assert_array_equal(z_tied, [1, 2, 0])
np.testing.assert_array_equal(z_untied, [0, 1, -1])
np.testing.assert_allclose(p_tied, [0.24472847105479764, 0.6652409557748218, 0.09003057317038046])
assert int(p_tied.argmax()) == 1  # Проекция со связанными весами не обращает выбор строки.
np.testing.assert_allclose(softmax(z_tied + 10_000), p_tied)
assert np.isclose(softmax(z_untied).sum(), 1.)
print("выбранные строки:", X.tolist())
print("логиты: связанные / независимые веса:", z_tied.tolist(), z_untied.tolist())
print("вероятности при связанных весах:", p_tied.round(6).tolist())

10.2. Почему повторяющиеся ID накапливают градиент

Теперь обучим саму таблицу на простой задаче: приблизим выбранные строки к нулевым целевым векторам. Для этого уменьшаем квадратичную потерю L=12∑t∥E[it]−Yt∥2L=\tfrac12\sum_t\|E[i_t]-Y_t\|^2. Производная одного слагаемого по выбранной строке равна E[it]−YtE[i_t]-Y_t. Градиент собирает такие производные для всех элементов таблицы; он показывает, как меняется потеря при небольшом изменении весов. При ID [0,2,0] строка 0 участвует дважды: её вклады складываются. Строка 1 вообще не используется.

np.add.at суммирует оба вклада. Для сравнения посмотрите на wrong_grad: запись grad[ids] += ... использует временный массив и теряет повторный вклад. Независимая проверка конечными разностями чуть увеличивает и уменьшает один вес, затем делит разность потерь на расстояние между этими двумя значениями.

До запуска: найдите градиент строки 0 вручную. Затем проверьте шаг Enew=E−0.1∇ELE_{\mathrm{new}}=E-0.1\nabla_E L: потеря должна уменьшиться с 1.5 до 1.045. В этой задаче нет выходной проекции; при обучении языковой модели связанные веса получают градиент также через выход. Здесь мы изолируем обучение операции выбора строк.

Python
# Шаг обучения с квадратичной потерей; это не кросс-энтропия следующего токена.
targets = np.zeros_like(X)


def lookup_loss(table):
    return 0.5 * np.sum((table[ids] - targets) ** 2)


grad = np.zeros_like(E)
np.add.at(grad, ids, X - targets)  # Два вхождения ID 0 должны дать два вклада.
np.testing.assert_array_equal(grad, [[2, 0], [0, 0], [0, 1]])

# Расширенная индексация создаёт временный массив; повторы ID не суммируются.
wrong_grad = np.zeros_like(E)
wrong_grad[ids] += X - targets
np.testing.assert_array_equal(wrong_grad, [[1, 0], [0, 0], [0, 1]])
assert not np.array_equal(wrong_grad, grad)

# Независимая проверка конечными разностями обнаруживает ошибку при повторении индексов.
epsilon = 1e-6
numeric_grad = np.zeros_like(E)
for index in np.ndindex(E.shape):
    plus, minus = E.copy(), E.copy()
    plus[index] += epsilon
    minus[index] -= epsilon
    numeric_grad[index] = (lookup_loss(plus) - lookup_loss(minus)) / (2 * epsilon)
np.testing.assert_allclose(grad, numeric_grad, atol=1e-9)
updated_E = E - 0.1 * grad
np.testing.assert_allclose(updated_E, [[0.8, 0], [2, 0], [0, 0.9]])
assert np.isclose(lookup_loss(E), 1.5)
assert np.isclose(lookup_loss(updated_E), 1.045)
assert lookup_loss(updated_E) < lookup_loss(E)
print("градиент:", grad.tolist())
print("потеря до / после:", lookup_loss(E), lookup_loss(updated_E))

10.3. Сколько памяти занимают таблицы

Для словаря из V строк ширины d одна таблица содержит Vd весов. При независимой выходной матрице уникальных весов вдвое больше. BF16 требует два байта на вес; состояния оптимизатора, градиенты и промежуточные активации в эту оценку не входят. Сначала оцените память для V = 16384 и d = 512, затем сравните с результатом. Меняйте vocab_size, dim и tied в начале ячейки и проследите, какая часть памяти растёт. Проверка 16 MiB относится к исходным размерам; остальные строки таблицы сохраняют собственные фиксированные входы.

Python
# Меняйте эти входы для своего опыта; ниже остаются фиксированные примеры моделей.
vocab_size, dim, tied = 16384, 512, True
budgets = {
    "gpt-oss-120b": embedding_budget(201088, 2880, tied=False),
    "Llama-3.1-8B": embedding_budget(128256, 4096, tied=False),
    "expansion 100000 to 262000": embedding_budget(262000-100000, 4096, tied=False),
    "ваша конфигурация": embedding_budget(vocab_size, dim, tied=tied),
}
assert budgets["gpt-oss-120b"]["parameters"] == 1_158_266_880
assert budgets["Llama-3.1-8B"]["bytes"] == 2_101_346_304
assert budgets["expansion 100000 to 262000"]["parameters"] == 1_327_104_000
if (vocab_size, dim, tied) == (16384, 512, True):
    assert budgets["ваша конфигурация"]["bytes"] == 16 * 2**20
for name, budget in budgets.items():
    print(name, budget)

Упражнения

  1. [самостоятельно] Добавьте специальные токены так, чтобы обычный encode никогда не создавал их из пользовательского текста, а отдельный метод вставлял только явные маркеры.

  2. [самостоятельно] Реализуйте инкрементальный UTF-8 decoder, который буферизует неполную последовательность между вызовами feed(token_id).

  3. [проект] Добавьте LRU-кэш на уровне pre-tokenization чанков и сравните повторяющийся и почти уникальный корпус.

  4. [проект] Замените полный пересчёт пар инкрементальным индексом. Отдельно докажите тестом, что правило разрешения равных частот и список слияний не изменились.


Все обязательные ячейки рассчитаны на чистый Colab/CPU. Замороженные данные M2 не связаны с изменяемым содержимым других модулей.

Демо проектных упражнений модуля 2 — Метрики сегментации и снимок специальных ID

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Демо проектных упражнений модуля 2 — Метрики сегментации и снимок специальных ID

Демо-реализация, не готовое решение полномасштабного проекта. Два примера на язык иллюстрируют агрегацию и опасность неверного знаменателя. wordrun_proxy считает серии букв/цифр и знаки, а не выполняет WordPiece; пробелы он отбрасывает. Китайская строка даёт одну серию букв, не одно лингвистическое слово. Это учебные сегментаторы, не рейтинг токенизаторов. Второе демо воспроизводит датированный снимок Harmony, не проверяя установленную библиотеку. Все входы малы, детерминированы и работают без сети на CPU. Цель — проверить интерфейсы, метрики, инварианты и структуру отчёта до расходования GPU/API-бюджета.

Python
from __future__ import annotations
import importlib.util, subprocess, sys
for package in ("numpy", "matplotlib"):
    if importlib.util.find_spec(package) is None:
        subprocess.check_call([sys.executable, "-m", "pip", "install", "-q", package])


import math
import random
import time
from collections import Counter, defaultdict

import matplotlib.pyplot as plt
import numpy as np

SEED = 20260801
random.seed(SEED)
np.random.seed(SEED)
print(f"воспроизводимый тестовый запуск; seed={SEED}")
DEMO_LANGUAGE = 'ru'

1. Что именно стоит в знаменателе?

Сегментируем две короткие фразы на каждом из четырёх языков тремя способами. Байтовый сегментатор выдаёт UTF-8-байты, символьный — кодовые точки, третий — серии букв/цифр и отдельные знаки препинания. Последний отбрасывает пробелы, поэтому его нельзя считать обратимым токенизатором. Сначала делим общее число единиц на общее число серий букв/цифр, затем — на число выровненных предложений.

Перед запуском подумайте, почему китайская строка даёт одну серию и как это изменит левую панель. Сравнивайте числа вместе с определением знаменателя: одинаковый цвет на разных панелях не означает одинаковое значение. Две фразы показывают механику метрики, но не позволяют судить об эффективности токенизации языка.

Python
INK = '#2E3440'
MUTED = '#4C566A'
BORDER = '#D8DEE9'
def plot_style():
    import matplotlib.pyplot as plt
    plt.rcParams.update({
        "font.family": "DejaVu Sans", "font.size": 12,
        "text.color": INK, "axes.labelcolor": INK, "axes.titlecolor": INK,
        "axes.titlesize": 17, "axes.titleweight": "bold", "axes.titlelocation": "left",
        "axes.labelsize": 13, "xtick.labelsize": 11, "ytick.labelsize": 11,
        "xtick.color": MUTED, "ytick.color": MUTED,
        "axes.edgecolor": BORDER, "axes.linewidth": .7,
        "axes.facecolor": "white", "figure.facecolor": "white", "savefig.facecolor": "white",
        "grid.color": BORDER, "grid.linewidth": .7, "axes.axisbelow": True,
        "legend.fontsize": 11, "legend.frameon": False, "savefig.dpi": 150,
        "xtick.major.size": 0, "ytick.major.size": 0,
    })

plot_style()

import re

corpus = {
    "en": ["models learn from tokens", "a short test"],
    "ru": ["модели учатся на токенах", "короткий тест"],
    "es": ["modelos aprenden de tokens", "una prueba corta"],
    "zh": ["模型从词元学习", "简短测试"],
}

def word_runs(text):
    return re.findall(r"[^\W_]+", text, flags=re.UNICODE)

tokenizers = {
    "byte": lambda s: list(s.encode("utf-8")),
    "char": list,
    "wordrun_proxy": lambda s: re.findall(r"[^\W_]+|[^\w\s]", s, flags=re.UNICODE),
}

# Одинаковый учебный смысл; корпус не является репрезентативным бенчмарком.
fertility = np.zeros((len(corpus), len(tokenizers)))
units_per_sentence = np.zeros_like(fertility)
denominators = {}
for i, (lang, lines) in enumerate(corpus.items()):
    n_runs = sum(len(word_runs(line)) for line in lines)
    denominators[lang] = n_runs
    n_bytes = sum(len(line.encode("utf-8")) for line in lines)
    print(lang, "предложений / серий букв и цифр / байтов:", len(lines), n_runs, n_bytes)
    for j, (name, encode) in enumerate(tokenizers.items()):
        n_units = sum(len(encode(line)) for line in lines)
        fertility[i, j] = n_units / n_runs
        units_per_sentence[i, j] = n_units / len(lines)
        print("  ", name, "единиц:", n_units, "единиц/предложение:", units_per_sentence[i, j])

tr = lambda ru, en: ru if DEMO_LANGUAGE == 'ru' else en
fig, axes = plt.subplots(1, 2, figsize=(11, 6), layout='constrained')
titles = [tr('Единиц на серию букв/цифр', 'Units per letter/digit run'),
          tr('Единиц на предложение', 'Units per aligned sentence')]
labels = [tr('Байты', 'Bytes'), tr('Кодовые\nточки', 'Code\npoints'),
          tr('Серии и\nзнаки', 'Runs and\npunctuation')]
for ax, values, title in zip(axes, [fertility, units_per_sentence], titles):
    im = ax.imshow(values, cmap='Blues', vmin=0, vmax=values.max(), aspect='auto')
    ax.set(xticks=range(len(tokenizers)), xticklabels=labels,
           yticks=range(len(corpus)), yticklabels=list(corpus))
    ax.grid(False)
    for i in range(values.shape[0]):
        for j in range(values.shape[1]):
            ax.text(j, i, f'{values[i, j]:.1f}', ha='center', va='center',
                    color='white' if values[i, j] > values.max() * .65 else INK)
    ax.set_title(title, fontsize=14, pad=14)
    fig.colorbar(im, ax=ax, location='bottom', shrink=.9,
                 label=tr('Единиц; своя шкала у каждой панели', 'Units; each panel has its own scale'))
fig.suptitle(tr('Выбор знаменателя меняет сравнение', 'The denominator changes the comparison'),
             fontsize=17, fontweight='bold', color=INK)
plt.show()
assert denominators["zh"] == 2  # Две целые строки, а не два лингвистических слова.
assert np.isfinite(fertility).all()
assert units_per_sentence.shape == (4, 3)
assert [len(word_runs(line)) for line in corpus["zh"]] == [1, 1]

2. Почему число имён не равно числу ID?

Ниже восстановим карту специальных имён из закреплённого исходного кода tiktoken от 11 октября 2026 года. Два имени могут ссылаться на один ID: словарь Python считает имена, а set(special_to_id.values()) — уникальные значения. Перед запуском сопоставьте диапазон резервных ID с endofprompt; после запуска объясните разницу между 1091 именем и 1090 ID. Обычные токены занимают отдельный диапазон, поэтому к числу уникальных специальных ID можно прибавить 199998.

Python
# Снимок: 2026-10-11. Источник: openai/tiktoken revision 4e71bbe0c078468e00fefbf94b39849389f346e5.
# Сверка установленной библиотеки включается отдельно в основном ноутбуке М2.
mergeable_ids = 199_998
protocol_to_id = {
    "<|startoftext|>": 199_998,
    "<|endoftext|>": 199_999,
    "<|return|>": 200_002,
    "<|constrain|>": 200_003,
    "<|channel|>": 200_005,
    "<|start|>": 200_006,
    "<|end|>": 200_007,
    "<|message|>": 200_008,
    "<|call|>": 200_012,
    "<|endofprompt|>": 200_018,
}
reserved_to_id = {
    "<|reserved_200000|>": 200_000,
    "<|reserved_200001|>": 200_001,
    "<|reserved_200004|>": 200_004,
    "<|reserved_200009|>": 200_009,
    "<|reserved_200010|>": 200_010,
    "<|reserved_200011|>": 200_011,
    **{f"<|reserved_{i}|>": i for i in range(200_013, 201_088)},
}
special_to_id = protocol_to_id | reserved_to_id
special_ids = set(special_to_id.values())
aliases = {}
for name, token_id in special_to_id.items():
    aliases.setdefault(token_id, []).append(name)
aliases = {token_id: names for token_id, names in aliases.items() if len(names) > 1}

print("ID обычных токенов:", mergeable_ids)
print("специальные имена / уникальные ID:", len(special_to_id), len(special_ids))
print("имена одного ID:", aliases)
print("всего уникальных ID:", mergeable_ids + len(special_ids))
assert len(protocol_to_id) == 10
assert len(reserved_to_id) == 1_081
assert len(special_to_id) == 1_091
assert len(special_ids) == 1_090
assert aliases == {200_018: ["<|endofprompt|>", "<|reserved_200018|>"]}
assert mergeable_ids + len(special_ids) == 201_088

Переход к полному проекту

Замените учебный корпус на одинаковые строки FLORES для десяти языков, а упрощённые токенизаторы — на закреплённые версии реальных. Сохраняйте число токенов на выровненное предложение, число байтов и ревизию каждого артефакта. Для fertility задайте отдельные правила лингвистической сегментации языков; не выдавайте regex-серии за китайские слова.

Минимальный отчёт

  1. Версии данных, модели, кода и seed.

  2. Основная метрика, а также качество, стоимость, задержка и память там, где это применимо.

  3. Базовая линия, одинаковый бюджет и хотя бы один отрицательный контроль.

  4. Неудачные прогоны и границы обоснованных выводов.