Udmurt - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Udmurt Wikipedia data. We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

πŸ“‹ Repository Contents

Models & Assets

  • Tokenizers (8k, 16k, 32k, 64k)
  • N-gram models (2, 3, 4, 5-gram)
  • Markov chains (context of 1, 2, 3, 4 and 5)
  • Subword N-gram and Markov chains
  • Embeddings in various sizes and dimensions (aligned and unaligned)
  • Language Vocabulary
  • Language Statistics

Performance Dashboard

Analysis and Evaluation


1. Tokenizer Evaluation

Tokenizer Compression

Tokenizer Fertility

Tokenizer OOV

Total Tokens

Results

Vocab Size Compression Avg Token Len UNK Rate Total Tokens
8k 3.543x 3.55 0.1375% 258,898
16k 3.952x 3.96 0.1534% 232,054
32k 4.311x 4.32 0.1673% 212,774
64k 4.565x πŸ† 4.57 0.1772% 200,933

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: Π‘Π°ΠΉΡ€Π°Π½ΡˆΡƒΡ€ () β€” Π£Π΄ΠΌΡƒΡ€Ρ‚ΠΈΡ‹ΡΡŒ ΠΏΠΈΡ‡ΠΈ ΡˆΡƒΡ€. Π‘Ρ‹Π·Π΅ Π―Ρ€ ёрослэн ΠΌΡƒΠ·ΡŠΠ΅ΠΌΠ΅Ρ‚Σ₯Π· Π½ΠΎ усС Π’ΡƒΠΌ ΡˆΡƒΡ€Π΅. ...

Vocab Tokens Count
8k ▁бай Ρ€Π°Π½ ΡˆΡƒΡ€ ▁() ▁— β–ΡƒΠ΄ΠΌΡƒΡ€Ρ‚ΠΈΡ‹ΡΡŒ ▁пичи β–ΡˆΡƒΡ€ . ▁бызС ... (+23 more) 33
16k ▁бай Ρ€Π°Π½ ΡˆΡƒΡ€ ▁() ▁— β–ΡƒΠ΄ΠΌΡƒΡ€Ρ‚ΠΈΡ‹ΡΡŒ ▁пичи β–ΡˆΡƒΡ€ . ▁бызС ... (+22 more) 32
32k ▁байран ΡˆΡƒΡ€ ▁() ▁— β–ΡƒΠ΄ΠΌΡƒΡ€Ρ‚ΠΈΡ‹ΡΡŒ ▁пичи β–ΡˆΡƒΡ€ . ▁бызС ▁яр ... (+20 more) 30
64k β–Π±Π°ΠΉΡ€Π°Π½ΡˆΡƒΡ€ ▁() ▁— β–ΡƒΠ΄ΠΌΡƒΡ€Ρ‚ΠΈΡ‹ΡΡŒ ▁пичи β–ΡˆΡƒΡ€ . ▁бызС ▁яр ▁ёрослэн ... (+19 more) 29

Sample 2: ОлСся Π–ΡƒΡ€Π°ΠΊΠΈΠ²ΡΡŒΠΊΠ° (; КиСв, Π‘Π‘Π‘Π , β€” Π£ΠΊΡ€Π°ΠΈΠ½ актриса. Π€ΠΈΠ»ΡŒΠΌΡŠΡ‘Ρ ΠžΡΡ‚Ρ€ΠΎΠ² Донбас Π°Π»Ρ„Π°Π²ΠΈ...

Vocab Tokens Count
8k ▁ол Сс я ▁Т ΡƒΡ€ Π°ΠΊ ΠΈΠ² ська ▁(; ▁киСв ... (+13 more) 23
16k ▁ол Сс я ▁Т ΡƒΡ€ Π°ΠΊ ΠΈΠ² ська ▁(; ▁киСв ... (+12 more) 22
32k ▁ол Сся ▁Тур Π°ΠΊΠΈΠ² ська ▁(; ▁киСв , ▁ссср , ... (+9 more) 19
64k ▁ол Сся ▁Туракив ська ▁(; ▁киСв , ▁ссср , ▁— ... (+8 more) 18

Sample 3: ΠšΡ€ΠΈΠ²ΠΎΠΉ Π ΠΎΠ³ ΠΌΠ΅Ρ‚Ρ€ΠΎΡ‚Ρ€Π°ΠΌ ( ΡƒΠΊΡ€. ΠšΡ€ΠΈΠ²ΠΎΡ€Ρ–Π·ΡŒΠΊΠΈΠΉ ΡˆΠ²ΠΈΠ΄ΠΊΡ–ΡΠ½ΠΈΠΉ Ρ‚Ρ€Π°ΠΌΠ²Π°ΠΉ )

Vocab Tokens Count
8k ▁кр ΠΈΠ² ΠΎΠΉ ▁ро Π³ ▁мСтро Ρ‚ Ρ€Π°ΠΌ ▁( ▁ук ... (+17 more) 27
16k ▁крив ΠΎΠΉ ▁рог ▁мСтро Ρ‚ Ρ€Π°ΠΌ ▁( ▁ук Ρ€ . ... (+12 more) 22
32k ▁крив ΠΎΠΉ ▁рог ▁мСтро Ρ‚Ρ€Π°ΠΌ ▁( ▁укр . ▁крив ΠΎΡ€ ... (+10 more) 20
64k ▁кривой ▁рог ▁мСтротрам ▁( ▁укр . ▁крив ΠΎΡ€ Ρ– зь ... (+5 more) 15

Key Findings

  • Best Compression: 64k achieves 4.565x compression
  • Lowest UNK Rate: 8k with 0.1375% unknown tokens
  • Trade-off: Larger vocabularies improve compression but increase model size
  • Recommendation: 32k vocabulary provides optimal balance for production use

2. N-gram Model Evaluation

N-gram Perplexity

N-gram Unique

N-gram Coverage

Results

N-gram Variant Perplexity Entropy Unique N-grams Top-100 Coverage Top-1000 Coverage
2-gram Word 4,224 12.04 9,045 20.2% 51.2%
2-gram Subword 646 πŸ† 9.34 3,769 43.9% 95.6%
3-gram Word 4,567 12.16 10,317 20.4% 49.5%
3-gram Subword 5,398 12.40 30,259 15.9% 50.6%
4-gram Word 9,357 13.19 19,488 14.9% 37.3%
4-gram Subword 23,964 14.55 134,461 8.6% 28.8%
5-gram Word 7,868 12.94 14,631 14.0% 37.7%
5-gram Subword 56,525 15.79 261,817 5.4% 21.0%

Top 5 N-grams by Size

2-grams (Word):

Rank N-gram Count
1 j j 743
2 1 Ρ‚Σ₯ 662
3 synonym of 638
4 now synonym 606
5 rchb f 601

3-grams (Word):

Rank N-gram Count
1 now synonym of 604
2 j j sm 569
3 Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос 559
4 Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ 533
5 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ 490

4-grams (Word):

Rank N-gram Count
1 Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ 484
2 ΡƒΠ»Σ₯ΡΡŒΡ‘Ρ Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ 482
3 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ Π³ΡƒΡ€Ρ‚Ρ‹Π½ 478
4 Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ 414
5 ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ Π³ΡƒΡ€Ρ‚ΡŠΡ‘Ρ 414

5-grams (Word):

Rank N-gram Count
1 ΡƒΠ»Σ₯ΡΡŒΡ‘Ρ Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ 482
2 Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ Π³ΡƒΡ€Ρ‚Ρ‹Π½ 478
3 Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ Π³ΡƒΡ€Ρ‚ΡŠΡ‘Ρ 414
4 адями Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос 404
5 Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ 396

2-grams (Subword):

Rank N-gram Count
1 Π½ _ 53,739
2 . _ 52,122
3 с ь 44,748
4 _ ΠΊ 43,958
5 , _ 37,972

3-grams (Subword):

Rank N-gram Count
1 с ь _ 23,826
2 _ β€” _ 21,444
3 Ρ‹ с ь 19,313
4 ъ Ρ‘ с 19,179
5 Ρ‹ Π½ _ 19,081

4-grams (Subword):

Rank N-gram Count
1 Ρ‹ с ь _ 17,835
2 л э н _ 16,383
3 _ Π½ ΠΎ _ 10,521
4 . _ β€” _ 9,347
5 ъ Ρ‘ с _ 7,031

5-grams (Subword):

Rank N-gram Count
1 Ρƒ Π΄ ΠΌ Ρƒ Ρ€ 5,330
2 Π΄ ΠΌ Ρƒ Ρ€ Ρ‚ 5,329
3 _ Ρƒ Π΄ ΠΌ Ρƒ 4,783
4 _ Ρ‘ Ρ€ ΠΎ с 4,592
5 ΠΈ Ρ‹ с ь _ 4,529

Key Findings

  • Best Perplexity: 2-gram (subword) with 646
  • Entropy Trend: Decreases with larger n-grams (more predictable)
  • Coverage: Top-1000 patterns cover ~21% of corpus
  • Recommendation: 4-gram or 5-gram for best predictive performance

3. Markov Chain Evaluation

Markov Entropy

Markov Contexts

Markov Branching

Results

Context Variant Avg Entropy Perplexity Branching Factor Unique Contexts Predictability
1 Word 0.6992 1.624 3.81 87,992 30.1%
1 Subword 0.9862 1.981 7.60 1,200 1.4%
2 Word 0.1500 1.110 1.29 333,544 85.0%
2 Subword 0.9701 1.959 6.05 9,108 3.0%
3 Word 0.0464 1.033 1.08 427,340 95.4%
3 Subword 0.8614 1.817 4.08 55,078 13.9%
4 Word 0.0213 πŸ† 1.015 1.04 457,825 97.9%
4 Subword 0.5986 1.514 2.45 224,742 40.1%

Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

Context Size 1:

  1. Π½ΠΎ ΡŽΡΠΊΠ°Ρ€Π΅ Π°Ρ‚Π°Π΅Π· агнСшка Π½ΠΎ Π΄ΡƒΠ½Π°ΠΉ ΠΌΠΌ ΠΏΠ°Π»Π° адями Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· ΠΏΡƒΡ€Π³Π° ёрослэн ΠΌΡƒΠ·ΡŠΠ΅ΠΌΠ΅Ρ‚Σ₯Π· ΡˆΡƒΠ½Π΄Ρ‹ пуксён ΠΏΠ°Π»Π»...
  2. Π°Ρ€Ρ‹Π½ 1 58 Π°Ρ€Ρ‹Π½ распрСдСлСниС Π±Π΅Ρ€Π΅ ΠΊΡƒΠ·ΠΎΠ½ Π½Π΅Ρ„Ρ‚Π΅Ρ€Π°Π·Π²Π΅Π΄ΠΊΠ° ΡƒΡ‡Π°ΡΡ‚ΠΎΠΊΡŠΡ‘Ρ сад ёросын ΠΊΠ°ΠΌΠ±Π°Ρ€ΠΊΠ° ΠΊΠ°Ρ€Ρ‹Π½ казахстан...
  3. Ρ‚Σ₯ ΠΌΠ°Π΅ ΠΏΠΈΡ‡ΠΈ ΠΏΡƒΡ€Π³Π°Ρ‹ΡΡŒ ΡΠ΅Π»ΡŒΠ»Π΅ΡΡ…ΠΎΠ· ΠΎΠ·ΡŒΡ‹ ΠΈΠΊ ΡΠ΅Π·ΡŒΡ‹ ΠΊΣ§ΠΆΡ‹ ӝук ΠΏΣ§Π·ΡŒΡ‚ΠΎ Π²Σ§ΡΡŒΡΡ‹ Π±Π΅Ρ€Π΅ Π±Π°ΡƒΡˆΠ΅Π² софин ΣŸΡƒΡ‡

Context Size 2:

  1. j j wood in j j sm ex koord schum galeola kuhlii rchb f hook f summerh
  2. 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ Π³ΡƒΡ€Ρ‚Ρ‹Π½ 77 адями Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ Π³ΡƒΡ€Ρ‚ΡŠΡ‘Ρ ΡƒΠ»ΠΎΠ½ интыоссы Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»...
  3. synonym of didactylus paradoxa luer dalstrΓΆm эквадор stelis nana lindl эквадор stelis pudens luer эк...

Context Size 3:

  1. now synonym of crocodeilanthe cauliflora lindl luer pleurothallis pilostoma коста Ρ€ΠΈΠΊΠ° now synonym o...
  2. j j sm liparis cyperifolia ridl liparis dalessandroi dodson liparis dalzellii hook f liparis xanthin...
  3. Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ Π³ΡƒΡ€Ρ‚Ρ‹Π½ 378 адями Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ Π³ΡƒΡ€Ρ‚ΡŠΡ‘Ρ ΡƒΠ»ΠΎΠ½ интыоссы

Context Size 4:

  1. Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ Π³ΡƒΡ€Ρ‚Ρ‹Π½ 1 адями Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· ΠΏΡƒΡ€Π³Π° Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос ΠΏΡƒΡ€Π³Π° Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ Π³ΡƒΡ€Ρ‚ΡŠΡ‘Ρ ΡƒΠ»ΠΎΠ½ ΠΈΠ½Ρ‚...
  2. ΡƒΠ»Σ₯ΡΡŒΡ‘Ρ Π°Ρ€Ρ‹Π½ 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ Π³ΡƒΡ€Ρ‚Ρ‹Π½ 82 адями Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ Π³ΡƒΡ€Ρ‚ΡŠΡ‘Ρ ΡƒΠ»ΠΎΠ½ интыос...
  3. 1 Ρ‚Σ₯ Ρ‚ΠΎΠ»ΡˆΠΎΡ€Π΅ Π³ΡƒΡ€Ρ‚Ρ‹Π½ 43 адями Π»Ρ‹Π΄ΡŠΡΡΡŒΠΊΠΈΠ· Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ ΡƒΠ»ΠΎΠ½ интыос Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ Π³ΡƒΡ€Ρ‚ΡŠΡ‘Ρ ΡƒΠ»ΠΎΠ½ интыоссы

Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

Context Size 1:

  1. _кСныст_Ρ‡Ρ‹Π½ΠΈ_._Π΄
  2. Π°ΠΉ,_ктСрспёсканы
  3. сь._taccyncrs_ва

Context Size 2:

  1. Π½_1-Ρ‚Σ₯сь_болос._e
  2. ._β€”_вылэсовитич_(
  3. сь._β€”_aglowiedipt

Context Size 3:

  1. сь_Π²Ρ‹Π»ΡŒ_Π²Π΅Π½Π³Ρ€Π°Π²_ΠΌΠΎ
  2. _β€”_ΠΊΠΎΡΡ‚ΡŒ_садово_ΠΏΡ€
  3. Ρ‹ΡΡŒ_Π΅Π²Ρ€ΠΎΠΊ_(hoehne_

Context Size 4:

  1. Ρ‹ΡΡŒ_улос,_ΠΊΡƒΠ±ΠΈΠΊΠ΅Ρ‚_с
  2. лэн_Π±Ρ‹Π΄ΣŸΠ°Π»Π°Π·_Π΄Σ₯сько
  3. _Π½ΠΎ_ΠΏΠΈΡ‡ΠΈ_луыса._Π°._

Key Findings

  • Best Predictability: Context-4 (word) with 97.9% predictability
  • Branching Factor: Decreases with context size (more deterministic)
  • Memory Trade-off: Larger contexts require more storage (224,742 contexts)
  • Recommendation: Context-3 or Context-4 for text generation

4. Vocabulary Analysis

Zipf's Law

Top Words

Coverage Curve

Statistics

Metric Value
Vocabulary Size 35,258
Total Tokens 485,306
Mean Frequency 13.76
Median Frequency 3
Frequency Std Dev 88.68

Most Common Words

Rank Word Frequency
1 Π½ΠΎ 10,962
2 Π°Ρ€Ρ‹Π½ 3,468
3 Ρ‚Σ₯ 2,839
4 ΡƒΠ΄ΠΌΡƒΡ€Ρ‚ 2,798
5 luer 2,289
6 Π³ΡƒΡ€Ρ‚ 2,284
7 Ρ‘Ρ€ΠΎΡΡ‹ΡΡŒ 2,189
8 1 2,085
9 со 1,987
10 j 1,734

Least Common Words (from vocabulary)

Rank Word Frequency
1 Ρ‚Π΅Π»Π΅Π³Ρ€Π°ΠΌ 2
2 Ρ„Π΅ΠΌΠΈΠ½ΠΈΠ·ΠΌΠ»Ρ‹ 2
3 Π²ΠΎΡ‚Ρ‡ΠΈΠ½Π° 2
4 Ρ„Π΅ΠΌΠΈΠ½ΠΈΠ·ΠΌ 2
5 Π³Π»ΠΎΠ±Π°Π»ΠΈΡΡ‚ΡŠΡ‘ΡΠ»ΡΠ½ 2
6 пСльмСнь 2
7 сСкта 2
8 вСрсиозы 2
9 Π²Π΅Ρ€Π°ΡΡŒΠΊΠ΅Ρ‚ 2
10 эрис 2

Zipf's Law Analysis

Metric Value
Zipf Coefficient 1.0076
RΒ² (Goodness of Fit) 0.990825
Adherence Quality excellent

Coverage Analysis

Top N Words Coverage
Top 100 22.1%
Top 1,000 54.2%
Top 5,000 76.3%
Top 10,000 85.1%

Key Findings

  • Zipf Compliance: RΒ²=0.9908 indicates excellent adherence to Zipf's law
  • High Frequency Dominance: Top 100 words cover 22.1% of corpus
  • Long Tail: 25,258 words needed for remaining 14.9% coverage

5. Word Embeddings Evaluation

Embedding Isotropy

Similarity Matrix

t-SNE Words

t-SNE Sentences

5.1 Cross-Lingual Alignment

Alignment Quality

Multilingual t-SNE

5.2 Model Comparison

Model Dimension Isotropy Semantic Density Alignment R@1 Alignment R@10
mono_32d 32 0.6980 0.3482 N/A N/A
mono_64d 64 0.4125 0.3188 N/A N/A
mono_128d 128 0.0749 0.3189 N/A N/A
aligned_32d 32 0.6980 πŸ† 0.3505 0.0080 0.1280
aligned_64d 64 0.4125 0.3252 0.0260 0.1660
aligned_128d 128 0.0749 0.3271 0.0420 0.1880

Key Findings

  • Best Isotropy: aligned_32d with 0.6980 (more uniform distribution)
  • Semantic Density: Average pairwise similarity of 0.3314. Lower values indicate better semantic separation.
  • Alignment Quality: Aligned models achieve up to 4.2% R@1 in cross-lingual retrieval.
  • Recommendation: 128d aligned for best cross-lingual performance

6. Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

6.1 Productivity & Complexity

Metric Value Interpretation Recommendation
Productivity Index 5.000 High morphological productivity Reliable analysis
Idiomaticity Gap 0.793 High formulaic/idiomatic content -

6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

Productive Prefixes

Prefix Examples
-ΠΊ ΠΊΠΈΡ‚, ΠΊΡƒΠ±ΠΎΠΊΠ°Π·, космСтичСской
-с списокСзлэн, сСрСм, ΡΡŽΡ€Ρ€Π΅Π°Π»ΠΈΠ·ΠΌ
-ΠΏ ΠΏΠ΅Ρ‚Ρ€Π°, ΠΏΡ€ΠΎΠΊΡƒΡ€ΠΎΡ€Π΅Π·, ΠΏΣ§ΠΉΡˆΡƒΡ€Π°Π»ΠΎ
-Π² Π²Ρ‹ΠΆΠΎΠ½Π½ΠΈ, Π²Ρ‹ΠΆΡ‹Ρ‹ΡΡŒΡ‚Ρ‹Π·Ρ‹, Π²Π°Π»Π°Π·
-Π± бСрлинэ, Π±Π°Π²Π°Ρ€ΠΈΡ‹ΡΡŒ, Π±ΠΎΡ€ΠΎΠΊ
-Π° алТирлэн, австрия, алСксандрович
-ΠΌ мазунинской, ΠΌΠ΅Ρ…Π°Π½ΠΈΠΊ, ΠΌΠΎΠ·ΠΌΡ‹Ρ‚Σ₯сь
-Ρ‚ Ρ‚Π΅Π°Ρ‚Ρ€Π°Π»ΡŒΠ½Π°Ρ, Ρ‚Π΅ΠΎΡ€ΠΈΠ΅Π½, Ρ‚Π°Π»ΠΈΠ±ΡŠΡ‘ΡΠ»Ρ‹

Productive Suffixes

Suffix Examples
-Π½ алТирлэн, гвинСяын, Π½Π°Π±Π΅Ρ€Π΅ΠΆΠ½ΠΎΠΉΡ‹Π½
-эн алТирлэн, цСхСзлэн, Π΅Π»ΡŒΡ†ΠΈΠ½Π»ΡΠ½
-a parvula, michelia, glaucophylla
-Π· Π²Π°Π»Π°Π·, ΠΊΡƒΠ±ΠΎΠΊΠ°Π·, ΠΏΡ€ΠΎΠΊΡƒΡ€ΠΎΡ€Π΅Π·
-сь Π±Π°Π²Π°Ρ€ΠΈΡ‹ΡΡŒ, ΠΌΠΎΠ·ΠΌΡ‹Ρ‚Σ₯сь, Π΄ΡΡ€Π΅ΠΌΠ»ΡΡΡŒ
-ь Π±Π°Π²Π°Ρ€ΠΈΡ‹ΡΡŒ, ΠΌΠΎΠ·ΠΌΡ‹Ρ‚Σ₯сь, Π΄ΡΡ€Π΅ΠΌΠ»ΡΡΡŒ
-Ρ‹Π½ гвинСяын, Π½Π°Π±Π΅Ρ€Π΅ΠΆΠ½ΠΎΠΉΡ‹Π½, Π΅Π²Ρ€ΠΎΠΏΠ°Ρ‹Π½
-Ρ‹ Π²Ρ‹ΠΆΡ‹Ρ‹ΡΡŒΡ‚Ρ‹Π·Ρ‹, ӝутΣ₯ΡΡŒΠΊΠΈΠ·Ρ‹, ΡˆΡƒΠ΄Σ₯ΡΡŒΠ»Ρ‹

6.3 Bound Stems (Lexical Roots)

Bound stems are high-frequency subword units that are semantically cohesive but rarely appear as standalone words. These often correspond to the 'core' of a word that requires inflection or derivation to be valid.

Stem Cohesion Substitutability Examples
иськ 1.61x 95 contexts иськСм, миськон, иськСмС
anth 2.47x 18 contexts euanthe, panther, anthrax
Ρ‚ΡŠΡ‘Ρ 1.67x 59 contexts ΡŽΡ€Ρ‚ΡŠΡ‘Ρ, ΠΊΡƒΡ‚ΡŠΡ‘Ρ, ΠΊΠ°Ρ‚ΡŠΡ‘Ρ
тэмы 2.15x 22 contexts итэмын, актэмыр, ватэмын
Ρ€ΡŠΡ‘Ρ 1.52x 81 contexts Σ§Ρ€ΡŠΡ‘Ρ, Π°Ρ€ΡŠΡ‘Ρ, ΡˆΡƒΡ€ΡŠΡ‘Ρ
Ρ‚Σ₯сь 1.61x 61 contexts ΠΊΡƒΡ‚Σ₯сь, Ρ‡ΡƒΡ‚Σ₯сь, ΠΏΠΎΡ‚Σ₯сь
эмын 2.07x 23 contexts улэмын, алэмын, луэмын
ΡŠΡ‘ΡΡ‹ 1.46x 83 contexts ΠΎΠΆΡŠΡ‘ΡΡ‹, Π°Ρ€ΡŠΡ‘ΡΡ‹, ΡƒΠΆΡŠΡ‘ΡΡ‹Π·
ской 2.07x 20 contexts чудской, риТской, вотской
Π½ΡŠΡ‘Ρ 1.70x 39 contexts Π΄ΡƒΠ½ΡŠΡ‘Ρ, Π²Ρ‹Π½ΡŠΡ‘Ρ, ΡΠΈΠ½ΡŠΡ‘Ρ
яськ 1.57x 28 contexts сяська, сяськаС, сяськая
Π΅ΠΌΡ‹Π½ 1.71x 18 contexts Π²Π°Π΅ΠΌΡ‹Π½, ΠΎΡˆΠ΅ΠΌΡ‹Π½, ΡƒΡ‚Π΅ΠΌΡ‹Π½

6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

Prefix Suffix Frequency Examples
-ΠΊ -Π½ 157 words ΠΊΡƒΠ±Π΅Ρ€Ρ‚Π΅Π½, ΠΊΡƒΠ΄Ρ‹ΠΌΠΊΠ°Ρ€Ρ‹Π½
-Ρ‚ -Π½ 71 words Ρ‚Ρ€ΠΎΠΏΠΈΠ½ΠΈΠ½, трактэн
-ΠΏ -Π½ 70 words пСтровичлэн, ΠΏΠ»Π°Π½
-ΠΊ -Π· 70 words катэныз, ΠΊΠΎΠ»Π»Π΅Π³ΠΈΠ΅Π·
-ΠΊ -Ρ‹ 64 words ΠΊΠΈΠ²Π°Π»Ρ‚Σ₯сСзлы, ΠΊΡƒΠ·ΡŒΡ‹ΠΌΠ»Ρ‹
-ΠΏ -Π· 64 words пыронэз, палозяз
-ΠΊ -эн 64 words кивалтэтэзлэн, ΠΊΠ°Π»Ρ‹ΠΊΡŠΡ‘ΡΠ»ΡΠ½
-с -Π½ 63 words суданлэн, спринтын
-Π² -Π½ 61 words Π²Π°Π»Π°ΠΌΠΎΠ½, Π²Π°Π»Ρ‚Σ₯ΡΡŒΡ‘ΡΡ‹Π·Π»ΡΠ½
-Π³ -Π½ 53 words гСроСзлэн, гСрбСзлэн

6.5 Recursive Morpheme Segmentation

Using Recursive Hierarchical Substitutability, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., prefix-prefix-root-suffix).

Word Suggested Split Confidence Stem
комитСтсы ΠΊΠΎΠΌΠΈΡ‚Π΅Ρ‚-с-Ρ‹ 7.5 с
Ρ„Π°ΠΊΡƒΠ»ΡŒΡ‚Π΅Ρ‚ΡΡ Ρ„Π°ΠΊΡƒΠ»ΡŒΡ‚Π΅Ρ‚-с-э 7.5 с
ΠΏΡ€ΠΎΡ†Π΅Π½Ρ‚Ρ‹ΡΡŒ ΠΏΡ€ΠΎΡ†Π΅Π½Ρ‚-Ρ‹-сь 6.0 ΠΏΡ€ΠΎΡ†Π΅Π½Ρ‚
ΡΡΡ‹Π»ΠΊΠ°Ρ‹ΡΡŒ ссылка-Ρ‹-сь 6.0 ссылка
ΡˆΠΎΡ€ΠΌΡƒΣ΅Ρ‹ΡΡŒ ΡˆΠΎΡ€ΠΌΡƒΣ΅-Ρ‹-сь 6.0 ΡˆΠΎΡ€ΠΌΡƒΣ΅
ΡˆΠΊΠΎΠ»Π°ΠΎΡΠ»Ρ‹ школа-ос-Π»Ρ‹ 6.0 школа
группаослы Π³Ρ€ΡƒΠΏΠΏΠ°-ос-Π»Ρ‹ 6.0 Π³Ρ€ΡƒΠΏΠΏΠ°
ΠΈΡΡ‚ΠΎΡ€ΠΈΡ‹ΡΡŒ истори-Ρ‹-сь 6.0 истори
ΠΎΠΊΡ€ΡƒΠ³ΡŠΡ‘ΡΡ‹ ΠΎΠΊΡ€ΡƒΠ³ΡŠΡ‘Ρ-Ρ‹ 4.5 ΠΎΠΊΡ€ΡƒΠ³ΡŠΡ‘Ρ
планСтаос ΠΏΠ»Π°Π½Π΅Ρ‚Π°-ос 4.5 ΠΏΠ»Π°Π½Π΅Ρ‚Π°
Турналистикая Турналистика-я 4.5 Турналистика
систСмаын систСма-Ρ‹Π½ 4.5 систСма
куартолэзСн куартолэзС-Π½ 4.5 куартолэзС
Π²ΠΎΠ·ΡŒΠΌΠ°Ρ‚ΠΎΠ½ Π²ΠΎΠ·ΡŒΠΌΠ°Ρ‚ΠΎ-Π½ 4.5 Π²ΠΎΠ·ΡŒΠΌΠ°Ρ‚ΠΎ
Ρ€Π°Π·Π΄Π΅Π»ΡŠΡ‘ΡΡ‹Π· Ρ€Π°Π·Π΄Π΅Π»ΡŠΡ‘Ρ-Ρ‹Π· 4.5 Ρ€Π°Π·Π΄Π΅Π»ΡŠΡ‘Ρ

6.6 Linguistic Interpretation

Automated Insight: The language Udmurt shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

Note on Idiomaticity: The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.


7. Summary & Recommendations

Performance Dashboard

Production Recommendations

Component Recommended Rationale
Tokenizer 64k BPE Best compression (4.56x)
N-gram 2-gram Lowest perplexity (646)
Markov Context-4 Highest predictability (97.9%)
Embeddings 100d Balanced semantic capture and isotropy

Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

Tokenizer Metrics

Compression Ratio

Definition: The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.

Intuition: Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.

What to seek: Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

Average Token Length (Fertility)

Definition: Mean number of characters per token produced by the tokenizer.

Intuition: Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.

What to seek: Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

Unknown Token Rate (OOV Rate)

Definition: Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.

Intuition: Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.

What to seek: Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

N-gram Model Metrics

Perplexity

Definition: Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.

Intuition: If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.

What to seek: Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

Entropy

Definition: Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.

Intuition: High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.

What to seek: Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

Coverage (Top-K)

Definition: Percentage of corpus occurrences explained by the top K most frequent n-grams.

Intuition: High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.

What to seek: Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

Markov Chain Metrics

Average Entropy

Definition: Mean entropy across all contexts, measuring average uncertainty in next-word prediction.

Intuition: Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).

What to seek: Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

Branching Factor

Definition: Average number of unique next tokens observed for each context.

Intuition: High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).

What to seek: Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

Predictability

Definition: Derived metric: (1 - normalized_entropy) Γ— 100%. Indicates how deterministic the model's predictions are.

Intuition: 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.

What to seek: Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

Vocabulary & Zipf's Law Metrics

Zipf's Coefficient

Definition: The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.

Intuition: A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.

What to seek: Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

RΒ² (Coefficient of Determination)

Definition: Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.

Intuition: RΒ² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.

What to seek: RΒ² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

Vocabulary Coverage

Definition: Cumulative percentage of corpus tokens accounted for by the top N words.

Intuition: Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.

What to seek: Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

Word Embedding Metrics

Isotropy

Definition: Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.

Intuition: High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.

What to seek: Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

Average Norm

Definition: Mean magnitude (L2 norm) of word vectors in the embedding space.

Intuition: Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.

What to seek: Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

Cosine Similarity

Definition: Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).

Intuition: Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.

What to seek: Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

t-SNE Visualization

Definition: t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.

Intuition: Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.

What to seek: Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

General Interpretation Guidelines

  1. Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
  2. Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
  3. Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
  4. Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
  5. Language-specific patterns: Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.

Visualizations Index

Visualization Description
Tokenizer Compression Compression ratios by vocabulary size
Tokenizer Fertility Average token length by vocabulary
Tokenizer OOV Unknown token rates
Tokenizer Total Tokens Total tokens by vocabulary
N-gram Perplexity Perplexity by n-gram size
N-gram Entropy Entropy by n-gram size
N-gram Coverage Top pattern coverage
N-gram Unique Unique n-gram counts
Markov Entropy Entropy by context size
Markov Branching Branching factor by context
Markov Contexts Unique context counts
Zipf's Law Frequency-rank distribution with fit
Vocab Frequency Word frequency distribution
Top 20 Words Most frequent words
Vocab Coverage Cumulative coverage curve
Embedding Isotropy Vector space uniformity
Embedding Norms Vector magnitude distribution
Embedding Similarity Word similarity heatmap
Nearest Neighbors Similar words for key terms
t-SNE Words 2D word embedding visualization
t-SNE Sentences 2D sentence embedding visualization
Position Encoding Encoding method comparison
Model Sizes Storage requirements
Performance Dashboard Comprehensive performance overview

About This Project

Data Source

Models trained on wikipedia-monthly - a monthly snapshot of Wikipedia articles across 300+ languages.

Project

A project by Wikilangs - Open-source NLP models for every Wikipedia language.

Maintainer

Omar Kamali - Omneity Labs

Citation

If you use these models in your research, please cite:

@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}

License

MIT License - Free for academic and commercial use.

Links


Generated by Wikilangs Models Pipeline

Report Date: 2026-01-11 02:18:53

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Dataset used to train wikilangs/udm