Eastern Mari - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

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

📋 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 3.658x 3.66 0.0886% 476,276
16k 3.968x 3.97 0.0961% 439,027
32k 4.189x 4.19 0.1015% 415,901
64k 4.335x 🏆 4.34 0.1050% 401,897

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: Ворзель () — Украиныште Киев велыште Буча кундемыштыже верланыше посёлко. Калыкч...

Vocab Tokens Count
8k ▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more) 26
16k ▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more) 26
32k ▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more) 26
64k ▁ворзель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ▁верланыше ▁посёлко ... (+14 more) 24

Sample 2: Пункт () — дюймын 1/72 наре ужашыже лийше кӱшычын ӱлык шрифтын висымкугытшо.

Vocab Tokens Count
8k ▁пункт ▁() ▁— ▁д юй мын ▁ 1 / 7 ... (+17 more) 27
16k ▁пункт ▁() ▁— ▁дюй мын ▁ 1 / 7 2 ... (+15 more) 25
32k ▁пункт ▁() ▁— ▁дюй мын ▁ 1 / 7 2 ... (+10 more) 20
64k ▁пункт ▁() ▁— ▁дюймын ▁ 1 / 7 2 ▁наре ... (+8 more) 18

Sample 3: 238 ий — III курымын ийже. Мо лийын Кӧ шочын Кӧ колен курым

Vocab Tokens Count
8k ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) 17
16k ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) 17
32k ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) 17
64k ▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more) 17

Key Findings

  • Best Compression: 64k achieves 4.335x compression
  • Lowest UNK Rate: 8k with 0.0886% 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 3,582 11.81 26,265 34.2% 60.8%
2-gram Subword 439 🏆 8.78 3,878 54.6% 97.4%
3-gram Word 4,130 12.01 36,566 34.5% 60.2%
3-gram Subword 3,337 11.70 33,949 19.6% 64.9%
4-gram Word 7,186 12.81 70,518 30.8% 54.1%
4-gram Subword 13,025 13.67 159,935 11.7% 42.2%
5-gram Word 6,518 12.67 62,229 31.1% 55.2%
5-gram Subword 29,667 14.86 355,981 9.8% 34.7%

Top 5 N-grams by Size

2-grams (Word):

Rank N-gram Count
1 марий эл 13,258
2 йошкар ола 10,954
3 республики марий 9,354
4 великой отечественной 6,261
5 отечественной войне 6,227

3-grams (Word):

Rank N-gram Count
1 республики марий эл 9,353
2 великой отечественной войне 6,227
3 в великой отечественной 6,214
4 народа в великой 6,200
5 подвиг народа в 6,199

4-grams (Word):

Rank N-gram Count
1 в великой отечественной войне 6,214
2 народа в великой отечественной 6,200
3 документов подвиг народа в 6,199
4 подвиг народа в великой 6,199
5 банк документов подвиг народа 6,196

5-grams (Word):

Rank N-gram Count
1 народа в великой отечественной войне 6,200
2 документов подвиг народа в великой 6,199
3 подвиг народа в великой отечественной 6,199
4 банк документов подвиг народа в 6,196
5 в великой отечественной войне гг 6,196

2-grams (Subword):

Rank N-gram Count
1 . _ 184,996
2 е _ 147,576
3 л а 134,439
4 _ к 133,534
5 а р 121,950

3-grams (Subword):

Rank N-gram Count
1 и й _ 64,060
2 ы н _ 57,801
3 _ м а 49,403
4 м а р 48,489
5 р и й 42,988

4-grams (Subword):

Rank N-gram Count
1 м а р и 41,511
2 _ м а р 41,069
3 а р и й 40,250
4 в л а к 32,702
5 р и й _ 32,360

5-grams (Subword):

Rank N-gram Count
1 м а р и й 39,931
2 _ м а р и 36,163
3 - в л а к 32,274
4 а р и й _ 30,689
5 в л а к _ 23,835

Key Findings

  • Best Perplexity: 2-gram (subword) with 439
  • Entropy Trend: Decreases with larger n-grams (more predictable)
  • Coverage: Top-1000 patterns cover ~35% 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 0.8000 1.741 5.03 109,319 20.0%
1 Subword 1.2025 2.301 10.94 715 0.0%
2 Word 0.2053 1.153 1.44 547,819 79.5%
2 Subword 1.1275 2.185 7.46 7,818 0.0%
3 Word 0.0723 1.051 1.14 786,559 92.8%
3 Subword 0.9049 1.872 4.46 58,298 9.5%
4 Word 0.0392 🏆 1.028 1.08 893,046 96.1%
4 Subword 0.6302 1.548 2.69 260,070 37.0%

Generated Text Samples (Word-based)

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

Context Size 1:

  1. марий эл юринский район 304 с 123 лашт тыгак ончо тылзын коло ияш туныктен тӱвырам кучылтмаш
  2. влак историк влак посёлок боровской российыште вологда вел виче да калабрий регионын рӱдолаже сарман...
  3. с 35 ч 1 еҥ ий численность населения городских населенных пунктов звениговский муниципальный район с...

Context Size 2:

  1. марий эл по делам архивов государственный архив республики марий эл республикын йӱдвел кипр турций р...
  2. йошкар ола с 125 158 15 ключева м а чап тамга орденын кавалерж кылвер влак хутор балезина
  3. республики марий эл по делам архивов государственный архив республики марий эл администрация муницип...

Context Size 3:

  1. республики марий эл оршанский район сборник документальных очерков йошкар ола комитет республики мар...
  2. великой отечественной войне гг кузнецов михаил сарманаевич i степенян ачамланде сар орден да йошкар ...
  3. в великой отечественной войне гг аралымылан степенян чап орден влакын кавалерже ийласе кугу ачамланд...

Context Size 4:

  1. в великой отечественной войне гг заровняев василий фёдорович ийласе кугу ачамланде сарын участникше ...
  2. народа в великой отечественной войне гг 11px i степенян ачамланде сар орденын кавалерже ийласе кугу ...
  3. документов подвиг народа в великой отечественной войне гг суаплан медальэлектронный банк документов ...

Generated Text Samples (Subword-based)

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

Context Size 1:

  1. _165_ушктренынап
  2. аск_-штлик_je_йс
  3. еше_«стэл:_ичий)

Context Size 2:

  1. ._*_matheleptedia
  2. е_ке,_эҥеш_марсти
  3. _кӧ_кумарий)_jah_

Context Size 3:

  1. ий_элын,_марий_йӱл
  2. ын_моча_куснен_кун
  3. _мари-кушто_дене_в

Context Size 4:

  1. марий-влак_кундемыш
  2. _марий_эл,_админист
  3. арий_эл_по_делам_ар

Key Findings

  • Best Predictability: Context-4 (word) with 96.1% predictability
  • Branching Factor: Decreases with context size (more deterministic)
  • Memory Trade-off: Larger contexts require more storage (260,070 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 48,490
Total Tokens 1,425,889
Mean Frequency 29.41
Median Frequency 4
Frequency Std Dev 331.81

Most Common Words

Rank Word Frequency
1 марий 30,639
2 влак 26,643
3 с 22,173
4 в 15,995
5 эл 13,818
6 йошкар 13,689
7 ола 13,467
8 ий 11,834
9 ял 11,645
10 и 11,569

Least Common Words (from vocabulary)

Rank Word Frequency
1 слегка 2
2 расстроены 2
3 покачав 2
4 брать 2
5 поглаживая 2
6 настраивать 2
7 взял 2
8 взмахнул 2
9 поплыла 2
10 комнате 2

Zipf's Law Analysis

Metric Value
Zipf Coefficient 1.1394
R² (Goodness of Fit) 0.995171
Adherence Quality excellent

Coverage Analysis

Top N Words Coverage
Top 100 36.4%
Top 1,000 67.2%
Top 5,000 84.2%
Top 10,000 90.0%

Key Findings

  • Zipf Compliance: R²=0.9952 indicates excellent adherence to Zipf's law
  • High Frequency Dominance: Top 100 words cover 36.4% of corpus
  • Long Tail: 38,490 words needed for remaining 10.0% 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 0.8198 🏆 0.3483 N/A N/A
mono_64d 64 0.7400 0.2927 N/A N/A
mono_128d 128 0.3509 0.2627 N/A N/A
aligned_32d 32 0.8198 0.3439 0.0120 0.1120
aligned_64d 64 0.7400 0.2932 0.0280 0.1860
aligned_128d 128 0.3509 0.2652 0.0520 0.2340

Key Findings

  • Best Isotropy: mono_32d with 0.8198 (more uniform distribution)
  • Semantic Density: Average pairwise similarity of 0.3010. Lower values indicate better semantic separation.
  • Alignment Quality: Aligned models achieve up to 5.2% 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 0.590 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
кертшылан, кравцов, капитон
-п пургыж, пайгусово, пырысым
саксофон, составитель, садретдинов
такая, таҥаса, тимофеевский
-ко командирын, кокыте, колмо
мурымыж, марийкалыкым, модшын
автора, аквалангым, акр
вашталтыш, ведра, веткино

Productive Suffixes

Suffix Examples
культовые, литературйылме, руэмское
кертшылан, капитон, чурийвылышан
хайруллина, дата, таҥаса
флоренций, тимофеевский, заведующий
яким, редакцийжым, марийкалыкым
пайгусово, общественно, качейкино
-ым редакцийжым, марийкалыкым, иктешлымашым
-ий флоренций, тимофеевский, заведующий

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
ндем 2.44x 22 contexts киндем, шындем, тандем
ланд 2.03x 35 contexts ландау, юланда, мланде
рлан 1.84x 37 contexts арлан, ерлан, хорлан
айон 2.14x 19 contexts район, района, районе
демы 2.09x 20 contexts айдемын, айдемыш, айдемым
райо 2.14x 16 contexts район, района, районе
унде 2.45x 10 contexts кундем, кундемна, кундемже
альн 1.70x 25 contexts дальний, дальние, вокально
енно 1.95x 16 contexts фенно, именно, военно
кунд 2.26x 9 contexts кунда, кундем, секунд
лект 1.38x 36 contexts лекте, лектыш, лектыт
верл 2.01x 8 contexts верла, верлам, уверла

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
122 words комнате, каҥашыме
-п 121 words правление, периодике
109 words клапан, катян
90 words савырнымыже, следовательже
-п 71 words пӧлкажын, пуртыман
69 words скревын, савырашлан
69 words колжо, кузьменко
65 words тиде, тюркское
63 words куклина, коведяева
60 words мардежан, музыкан

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
автономный автоном-н-ый 7.5 н
диалектный диалект-н-ый 7.5 н
отвлеченный отвлечен-н-ый 7.5 н
министертвын министерт-в-ын 7.5 в
всемарийском в-се-марийском 7.5 марийском
материалах материал-а-х 7.5 а
фильмыште фильм-ыш-те 6.0 фильм
биологийын биолог-ий-ын 6.0 биолог
тунемыныт тунем-ын-ыт 6.0 тунем
комплексыште комплекс-ыш-те 6.0 комплекс
абхазийын абхаз-ий-ын 6.0 абхаз
каҥашымаш каҥаш-ым-аш 6.0 каҥаш
шотландийын шотланд-ий-ын 6.0 шотланд
философийже философ-ий-же 6.0 философ
вашталтымаш вашталт-ым-аш 6.0 вашталт

6.6 Linguistic Interpretation

Automated Insight: The language Eastern Mari 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 (4.34x)
N-gram 2-gram Lowest perplexity (439)
Markov Context-4 Highest predictability (96.1%)
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) × 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.

R² (Coefficient of Determination)

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

Intuition: R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.

What to seek: R² > 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: 2026-01-10 11:49:08

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Dataset used to train wikilangs/mhr