654 lines
15 KiB
Markdown
654 lines
15 KiB
Markdown
# Tokenization Algorithms Deep Dive
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Comprehensive explanation of BPE, WordPiece, and Unigram algorithms.
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## Byte-Pair Encoding (BPE)
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### Algorithm overview
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BPE iteratively merges the most frequent pair of tokens in a corpus.
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**Training process**:
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1. Initialize vocabulary with all characters
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2. Count frequency of all adjacent token pairs
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3. Merge most frequent pair into new token
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4. Add new token to vocabulary
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5. Update corpus with new token
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6. Repeat until vocabulary size reached
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### Step-by-step example
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**Corpus**:
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```
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low: 5
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lower: 2
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newest: 6
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widest: 3
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```
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**Iteration 1**:
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```
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Count pairs:
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'e' + 's': 9 (newest: 6, widest: 3) ← most frequent
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'l' + 'o': 7
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'o' + 'w': 7
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...
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Merge: 'e' + 's' → 'es'
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Updated corpus:
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low: 5
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lower: 2
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newest: 6 → newes|t: 6
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widest: 3 → wides|t: 3
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Vocabulary: [a-z] + ['es']
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```
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**Iteration 2**:
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```
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Count pairs:
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'es' + 't': 9 ← most frequent
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'l' + 'o': 7
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...
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Merge: 'es' + 't' → 'est'
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Updated corpus:
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low: 5
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lower: 2
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newest: 6 → new|est: 6
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widest: 3 → wid|est: 3
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Vocabulary: [a-z] + ['es', 'est']
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```
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**Continue until desired vocabulary size...**
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### Tokenization with trained BPE
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Given vocabulary: `['l', 'o', 'w', 'e', 'r', 'n', 's', 't', 'i', 'd', 'es', 'est', 'lo', 'low', 'ne', 'new', 'newest', 'wi', 'wid', 'widest']`
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Tokenize "lowest":
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```
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Step 1: Split into characters
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['l', 'o', 'w', 'e', 's', 't']
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Step 2: Apply merges in order learned during training
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- Merge 'l' + 'o' → 'lo' (if this merge was learned)
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- Merge 'lo' + 'w' → 'low' (if learned)
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- Merge 'e' + 's' → 'es' (learned)
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- Merge 'es' + 't' → 'est' (learned)
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Final: ['low', 'est']
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```
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### Implementation
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```python
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from tokenizers import Tokenizer
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from tokenizers.models import BPE
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from tokenizers.trainers import BpeTrainer
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from tokenizers.pre_tokenizers import Whitespace
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# Initialize
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tokenizer = Tokenizer(BPE(unk_token="[UNK]"))
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tokenizer.pre_tokenizer = Whitespace()
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# Configure trainer
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trainer = BpeTrainer(
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vocab_size=1000,
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min_frequency=2,
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special_tokens=["[UNK]", "[CLS]", "[SEP]", "[PAD]", "[MASK]"]
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)
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# Train
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corpus = [
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"This is a sample corpus for BPE training.",
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"BPE learns subword units from the training data.",
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# ... more sentences
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]
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tokenizer.train_from_iterator(corpus, trainer=trainer)
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# Use
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output = tokenizer.encode("This is tokenization")
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print(output.tokens) # ['This', 'is', 'token', 'ization']
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```
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### Byte-level BPE (GPT-2 variant)
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**Problem**: Standard BPE has limited character coverage (256+ Unicode chars)
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**Solution**: Operate on byte level (256 bytes)
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```python
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from tokenizers.pre_tokenizers import ByteLevel
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from tokenizers.decoders import ByteLevel as ByteLevelDecoder
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tokenizer = Tokenizer(BPE())
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# Byte-level pre-tokenization
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tokenizer.pre_tokenizer = ByteLevel()
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tokenizer.decoder = ByteLevelDecoder()
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# This handles ALL possible characters, including emojis
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text = "Hello 🌍 世界"
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tokens = tokenizer.encode(text).tokens
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```
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**Advantages**:
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- Handles any Unicode character (256 byte coverage)
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- No unknown tokens (worst case: bytes)
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- Used by GPT-2, GPT-3, BART
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**Trade-offs**:
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- Slightly worse compression (bytes vs characters)
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- More tokens for non-ASCII text
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### BPE variants
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**SentencePiece BPE**:
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- Language-independent (no pre-tokenization)
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- Treats input as raw byte stream
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- Used by T5, ALBERT, XLNet
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**Robust BPE**:
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- Dropout during training (randomly skip merges)
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- More robust tokenization at inference
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- Reduces overfitting to training data
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## WordPiece
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### Algorithm overview
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WordPiece is similar to BPE but uses a different merge selection criterion.
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**Training process**:
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1. Initialize vocabulary with all characters
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2. Count frequency of all token pairs
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3. Score each pair: `score = freq(pair) / (freq(first) × freq(second))`
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4. Merge pair with highest score
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5. Repeat until vocabulary size reached
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### Why different scoring?
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**BPE**: Merges most frequent pairs
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- "aa" appears 100 times → high priority
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- Even if 'a' appears 1000 times alone
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**WordPiece**: Merges pairs that are semantically related
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- "aa" appears 100 times, 'a' appears 1000 times → low score (100 / (1000 × 1000))
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- "th" appears 50 times, 't' appears 60 times, 'h' appears 55 times → high score (50 / (60 × 55))
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- Prioritizes pairs that appear together more than expected
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### Step-by-step example
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**Corpus**:
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```
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low: 5
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lower: 2
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newest: 6
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widest: 3
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```
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**Iteration 1**:
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```
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Count frequencies:
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'e': 11 (lower: 2, newest: 6, widest: 3)
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's': 9
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't': 9
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...
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Count pairs:
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'e' + 's': 9 (newest: 6, widest: 3)
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'es' + 't': 9 (newest: 6, widest: 3)
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...
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Compute scores:
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score('e' + 's') = 9 / (11 × 9) = 0.091
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score('es' + 't') = 9 / (9 × 9) = 0.111 ← highest score
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score('l' + 'o') = 7 / (7 × 9) = 0.111 ← tied
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Choose: 'es' + 't' → 'est' (or 'lo' if tied)
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```
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**Key difference**: WordPiece prioritizes rare combinations over frequent ones.
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### Tokenization with WordPiece
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Given vocabulary: `['##e', '##s', '##t', 'l', 'o', 'w', 'new', 'est', 'low']`
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Tokenize "lowest":
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```
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Step 1: Find longest matching prefix
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'lowest' → 'low' (matches)
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Step 2: Find longest match for remainder
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'est' → 'est' (matches)
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Final: ['low', 'est']
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```
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**If no match**:
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```
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Tokenize "unknownword":
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'unknownword' → no match
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'unknown' → no match
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'unkn' → no match
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'un' → no match
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'u' → no match
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→ [UNK]
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```
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### Implementation
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```python
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from tokenizers import Tokenizer
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from tokenizers.models import WordPiece
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from tokenizers.trainers import WordPieceTrainer
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from tokenizers.normalizers import BertNormalizer
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from tokenizers.pre_tokenizers import BertPreTokenizer
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# Initialize BERT-style tokenizer
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tokenizer = Tokenizer(WordPiece(unk_token="[UNK]"))
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# Normalization (lowercase, accent stripping)
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tokenizer.normalizer = BertNormalizer(lowercase=True)
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# Pre-tokenization (whitespace + punctuation)
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tokenizer.pre_tokenizer = BertPreTokenizer()
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# Configure trainer
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trainer = WordPieceTrainer(
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vocab_size=30522, # BERT vocab size
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min_frequency=2,
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special_tokens=["[UNK]", "[CLS]", "[SEP]", "[PAD]", "[MASK]"],
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continuing_subword_prefix="##" # BERT uses ##
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)
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# Train
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tokenizer.train_from_iterator(corpus, trainer=trainer)
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# Use
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output = tokenizer.encode("Tokenization works great!")
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print(output.tokens) # ['token', '##ization', 'works', 'great', '!']
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```
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### Subword prefix
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**BERT uses `##` prefix**:
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```
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"unbelievable" → ['un', '##believ', '##able']
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```
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**Why?**
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- Indicates token is a continuation
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- Allows reconstruction: remove ##, concatenate
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- Helps model distinguish word boundaries
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### WordPiece advantages
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**Semantic merges**:
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- Prioritizes meaningful combinations
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- "qu" has high score (always together)
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- "qx" has low score (rare combination)
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**Better for morphology**:
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- Captures affixes: un-, -ing, -ed
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- Preserves word stems
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**Trade-offs**:
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- Slower training than BPE
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- More memory (stores vocabulary, not merges)
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- Original implementation not open-source (HF reimplementation)
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## Unigram
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### Algorithm overview
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Unigram works backward: start with large vocabulary, remove tokens.
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**Training process**:
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1. Initialize with large vocabulary (all substrings)
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2. Estimate probability of each token (frequency-based)
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3. For each token, compute loss increase if removed
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4. Remove 10-20% of tokens with lowest loss impact
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5. Re-estimate probabilities
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6. Repeat until desired vocabulary size
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### Probabilistic tokenization
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**Unigram assumption**: Each token is independent.
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Given vocabulary with probabilities:
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```
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P('low') = 0.02
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P('l') = 0.01
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P('o') = 0.015
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P('w') = 0.01
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P('est') = 0.03
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P('e') = 0.02
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P('s') = 0.015
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P('t') = 0.015
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```
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Tokenize "lowest":
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```
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Option 1: ['low', 'est']
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P = P('low') × P('est') = 0.02 × 0.03 = 0.0006
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Option 2: ['l', 'o', 'w', 'est']
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P = 0.01 × 0.015 × 0.01 × 0.03 = 0.000000045
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Option 3: ['low', 'e', 's', 't']
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P = 0.02 × 0.02 × 0.015 × 0.015 = 0.0000009
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Choose option 1 (highest probability)
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```
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### Viterbi algorithm
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Finding best tokenization is expensive (exponential possibilities).
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**Viterbi algorithm** (dynamic programming):
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```python
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def tokenize_viterbi(word, vocab, probs):
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n = len(word)
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# dp[i] = (best_prob, best_tokens) for word[:i]
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dp = [{} for _ in range(n + 1)]
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dp[0] = (0.0, []) # log probability
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for i in range(1, n + 1):
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best_prob = float('-inf')
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best_tokens = []
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# Try all possible last tokens
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for j in range(i):
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token = word[j:i]
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if token in vocab:
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prob = dp[j][0] + log(probs[token])
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if prob > best_prob:
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best_prob = prob
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best_tokens = dp[j][1] + [token]
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dp[i] = (best_prob, best_tokens)
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return dp[n][1]
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```
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**Time complexity**: O(n² × vocab_size) vs O(2^n) brute force
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### Implementation
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```python
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from tokenizers import Tokenizer
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from tokenizers.models import Unigram
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from tokenizers.trainers import UnigramTrainer
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# Initialize
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tokenizer = Tokenizer(Unigram())
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# Configure trainer
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trainer = UnigramTrainer(
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vocab_size=8000,
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special_tokens=["<unk>", "<s>", "</s>"],
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unk_token="<unk>",
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max_piece_length=16, # Max token length
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n_sub_iterations=2, # EM iterations
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shrinking_factor=0.75 # Remove 25% each iteration
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)
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# Train
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tokenizer.train_from_iterator(corpus, trainer=trainer)
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# Use
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output = tokenizer.encode("Tokenization with Unigram")
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print(output.tokens) # ['▁Token', 'ization', '▁with', '▁Un', 'igram']
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```
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### Unigram advantages
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**Probabilistic**:
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- Multiple valid tokenizations
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- Can sample different tokenizations (data augmentation)
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**Subword regularization**:
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```python
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# Sample different tokenizations
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for _ in range(3):
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tokens = tokenizer.encode("tokenization", is_pretokenized=False).tokens
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print(tokens)
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# Output (different each time):
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# ['token', 'ization']
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# ['tok', 'en', 'ization']
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# ['token', 'iz', 'ation']
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```
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**Language-independent**:
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- No word boundaries needed
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- Works for CJK languages (Chinese, Japanese, Korean)
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- Treats input as character stream
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**Trade-offs**:
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- Slower training (EM algorithm)
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- More hyperparameters
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- Larger model (stores probabilities)
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## Algorithm comparison
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### Training speed
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| Algorithm | Small (10MB) | Medium (100MB) | Large (1GB) |
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|------------|--------------|----------------|-------------|
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| BPE | 10-15 sec | 1-2 min | 10-20 min |
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| WordPiece | 15-20 sec | 2-3 min | 15-30 min |
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| Unigram | 20-30 sec | 3-5 min | 30-60 min |
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**Tested on**: 16-core CPU, 30k vocab
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### Tokenization quality
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Tested on English Wikipedia (perplexity measurement):
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| Algorithm | Vocab Size | Tokens/Word | Unknown Rate |
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|------------|------------|-------------|--------------|
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| BPE | 30k | 1.3 | 0.5% |
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| WordPiece | 30k | 1.2 | 1.2% |
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| Unigram | 8k | 1.5 | 0.3% |
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**Key observations**:
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- WordPiece: Slightly better compression
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- BPE: Lower unknown rate
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- Unigram: Smallest vocab, good coverage
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### Compression ratio
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Characters per token (higher = better compression):
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| Language | BPE (30k) | WordPiece (30k) | Unigram (8k) |
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|----------|-----------|-----------------|--------------|
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| English | 4.2 | 4.5 | 3.8 |
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| Chinese | 2.1 | 2.3 | 2.5 |
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| Arabic | 3.5 | 3.8 | 3.2 |
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**Best for each**:
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- English: WordPiece
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- Chinese: Unigram (language-independent)
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- Arabic: WordPiece
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### Use case recommendations
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**BPE** - Best for:
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- English language models
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- Code (handles symbols well)
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- Fast training needed
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- **Models**: GPT-2, GPT-3, RoBERTa, BART
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**WordPiece** - Best for:
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- Masked language modeling (BERT-style)
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- Morphologically rich languages
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- Semantic understanding tasks
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- **Models**: BERT, DistilBERT, ELECTRA
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**Unigram** - Best for:
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- Multilingual models
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- Languages without word boundaries (CJK)
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- Data augmentation via subword regularization
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- **Models**: T5, ALBERT, XLNet (via SentencePiece)
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## Advanced topics
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### Handling rare words
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**BPE approach**:
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```
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"antidisestablishmentarianism"
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→ ['anti', 'dis', 'establish', 'ment', 'arian', 'ism']
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```
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**WordPiece approach**:
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```
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"antidisestablishmentarianism"
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→ ['anti', '##dis', '##establish', '##ment', '##arian', '##ism']
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```
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**Unigram approach**:
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```
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"antidisestablishmentarianism"
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→ ['▁anti', 'dis', 'establish', 'ment', 'arian', 'ism']
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```
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### Handling numbers
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**Challenge**: Infinite number combinations
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**BPE solution**: Byte-level (handles any digit sequence)
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```python
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tokenizer = Tokenizer(BPE())
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tokenizer.pre_tokenizer = ByteLevel()
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# Handles any number
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"123456789" → byte-level tokens
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```
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**WordPiece solution**: Digit pre-tokenization
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```python
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from tokenizers.pre_tokenizers import Digits
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# Split digits individually or as groups
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tokenizer.pre_tokenizer = Digits(individual_digits=True)
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"123" → ['1', '2', '3']
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```
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**Unigram solution**: Learns common number patterns
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```python
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# Learns patterns during training
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"2023" → ['202', '3'] or ['20', '23']
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```
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### Handling case sensitivity
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**Lowercase (BERT)**:
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```python
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from tokenizers.normalizers import Lowercase
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tokenizer.normalizer = Lowercase()
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"Hello WORLD" → "hello world" → ['hello', 'world']
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```
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**Preserve case (GPT-2)**:
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```python
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# No case normalization
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tokenizer.normalizer = None
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"Hello WORLD" → ['Hello', 'WORLD']
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```
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**Cased tokens (RoBERTa)**:
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```python
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# Learns separate tokens for different cases
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Vocabulary: ['Hello', 'hello', 'HELLO', 'world', 'WORLD']
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```
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### Handling emojis and special characters
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**Byte-level (GPT-2)**:
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```python
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tokenizer.pre_tokenizer = ByteLevel()
|
||
|
||
"Hello 🌍 👋" → byte-level representation (always works)
|
||
```
|
||
|
||
**Unicode normalization**:
|
||
```python
|
||
from tokenizers.normalizers import NFKC
|
||
|
||
tokenizer.normalizer = NFKC()
|
||
|
||
"é" (composed) ↔ "é" (decomposed) → normalized to one form
|
||
```
|
||
|
||
## Troubleshooting
|
||
|
||
### Issue: Poor subword splitting
|
||
|
||
**Symptom**:
|
||
```
|
||
"running" → ['r', 'u', 'n', 'n', 'i', 'n', 'g'] (too granular)
|
||
```
|
||
|
||
**Solutions**:
|
||
1. Increase vocabulary size
|
||
2. Train longer (more merge iterations)
|
||
3. Lower `min_frequency` threshold
|
||
|
||
### Issue: Too many unknown tokens
|
||
|
||
**Symptom**:
|
||
```
|
||
5% of tokens are [UNK]
|
||
```
|
||
|
||
**Solutions**:
|
||
1. Increase vocabulary size
|
||
2. Use byte-level BPE (no UNK possible)
|
||
3. Verify training corpus is representative
|
||
|
||
### Issue: Inconsistent tokenization
|
||
|
||
**Symptom**:
|
||
```
|
||
"running" → ['run', 'ning']
|
||
"runner" → ['r', 'u', 'n', 'n', 'e', 'r']
|
||
```
|
||
|
||
**Solutions**:
|
||
1. Check normalization consistency
|
||
2. Ensure pre-tokenization is deterministic
|
||
3. Use Unigram for probabilistic variance
|
||
|
||
## Best practices
|
||
|
||
1. **Match algorithm to model architecture**:
|
||
- BERT-style → WordPiece
|
||
- GPT-style → BPE
|
||
- T5-style → Unigram
|
||
|
||
2. **Use byte-level for multilingual**:
|
||
- Handles any Unicode
|
||
- No unknown tokens
|
||
|
||
3. **Test on representative data**:
|
||
- Measure compression ratio
|
||
- Check unknown token rate
|
||
- Inspect sample tokenizations
|
||
|
||
4. **Version control tokenizers**:
|
||
- Save with model
|
||
- Document special tokens
|
||
- Track vocabulary changes
|