Batak Toba - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Batak Toba 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 3.300x 3.30 0.2266% 1,666,856
16k 3.529x 3.53 0.2423% 1,558,753
32k 3.662x πŸ† 3.66 0.2515% 1,502,009

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: Janji i ma sada huta (desa) na adong di Kecamatan Siempat Nempu Hilir, Kabupaten...

Vocab Tokens Count
8k ▁janji ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+16 more) 26
16k ▁janji ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+16 more) 26
32k ▁janji ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+16 more) 26

Sample 2: Siboras i ma sada huta (desa) na adong di Kecamatan Silima Pungga Pungga, Kabupa...

Vocab Tokens Count
8k ▁sib oras ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ... (+16 more) 26
16k ▁siboras ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+15 more) 25
32k ▁siboras ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+15 more) 25

Sample 3: Sukorejo i ma sada huta na adong di Kecamatan Ulujami, Kabupaten Pemalang, Propi...

Vocab Tokens Count
8k ▁suk orejo ▁i ▁ma ▁sada ▁huta ▁na ▁adong ▁di ▁kecamatan ... (+11 more) 21
16k ▁sukorejo ▁i ▁ma ▁sada ▁huta ▁na ▁adong ▁di ▁kecamatan ▁ulujami ... (+10 more) 20
32k ▁sukorejo ▁i ▁ma ▁sada ▁huta ▁na ▁adong ▁di ▁kecamatan ▁ulujami ... (+10 more) 20

Key Findings

  • Best Compression: 32k achieves 3.662x compression
  • Lowest UNK Rate: 8k with 0.2266% 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 8,503 13.05 26,404 17.5% 42.9%
2-gram Subword 185 πŸ† 7.53 3,447 77.7% 99.2%
3-gram Word 22,449 14.45 43,137 8.4% 25.3%
3-gram Subword 1,216 10.25 18,046 38.1% 83.2%
4-gram Word 44,360 15.44 67,584 5.9% 16.2%
4-gram Subword 5,587 12.45 70,061 19.7% 54.7%
5-gram Word 29,774 14.86 42,910 7.1% 18.6%
5-gram Subword 17,403 14.09 153,430 12.1% 36.7%

Top 5 N-grams by Size

2-grams (Word):

Rank N-gram Count
1 angka na 4,424
2 dung i 4,327
3 ni si 4,060
4 i ma 3,682
5 ni jahowa 2,892

3-grams (Word):

Rank N-gram Count
1 anak ni si 1,613
2 i ma sada 784
3 na adong di 741
4 dung i ninna 735
5 hata ni jahowa 703

4-grams (Word):

Rank N-gram Count
1 on do hata ni 423
2 i ma sada huta 417
3 songon on do hata 408
4 na adong di kecamatan 353
5 angka anak ni si 336

5-grams (Word):

Rank N-gram Count
1 songon on do hata ni 406
2 on do hata ni jahowa 250
3 i ma sada huta na 215
4 desa na adong di kecamatan 191
5 km jala godang ni ruasna 175

2-grams (Subword):

Rank N-gram Count
1 a _ 206,965
2 a n 205,323
3 n g 154,062
4 i _ 142,882
5 n a 122,548

3-grams (Subword):

Rank N-gram Count
1 a n g 81,918
2 _ m a 76,355
3 n a _ 58,981
4 _ n a 53,557
5 a n _ 51,287

4-grams (Subword):

Rank N-gram Count
1 _ n i _ 34,904
2 _ n a _ 33,621
3 _ d i _ 25,919
4 a n g k 24,948
5 _ m a _ 23,827

5-grams (Subword):

Rank N-gram Count
1 a n g k a 19,235
2 _ a n g k 17,946
3 n g k a _ 17,765
4 _ j a l a 14,671
5 j a l a _ 14,594

Key Findings

  • Best Perplexity: 2-gram (subword) with 185
  • Entropy Trend: Decreases with larger n-grams (more predictable)
  • Coverage: Top-1000 patterns cover ~37% 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 0.9199 1.892 6.44 50,491 8.0%
1 Subword 0.9288 1.904 7.09 1,431 7.1%
2 Word 0.3746 1.296 2.02 324,952 62.5%
2 Subword 0.7034 1.628 4.04 10,144 29.7%
3 Word 0.1537 1.112 1.28 656,964 84.6%
3 Subword 0.6472 1.566 3.17 40,950 35.3%
4 Word 0.0591 πŸ† 1.042 1.09 838,369 94.1%
4 Subword 0.5206 1.435 2.40 129,601 47.9%

Generated Text Samples (Word-based)

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

Context Size 1:

  1. ni tano naung leleng on marupaya maningkathon kesadaran masarakat na pauli pintu ni si hannas dohot
  2. na talup do angka naposongku alai anggo raoanna nang jahudi tubu ni halak batak di tongatongamu
  3. i si arni anak ni harangan na mengatur istimewa dok gumodang sian saluhut na nidabuna i

Context Size 2:

  1. angka na di ginjang ni angka ompunami umbahen manjadi angka i tu ahu do jahowa molo ahu
  2. dung i ro di salelenglelengna psalmen 94 94 1 ale anaha sai parateatehon hamu panariason ni bibirhon
  3. ni si jakkob anak ni si rehabeam di jerusalem 7 17 dua lombu lima birubiru tunggal sada

Context Size 3:

  1. anak ni si aron hahanasida i marhalado di joro ni jahowa tungkan jolo ni rimberimbe i 40 27
  2. i ma sada nagara na maringanan di lobu panjang
  3. na adong di halak batak toba tombur tarbahen sian sibuk ni manuk na dibumbui

Context Size 4:

  1. on do hata ni tuhan jahowa nunga pola hupatoltol tanganku maruari ingkon lehononku do i tu ompumuna ...
  2. i ma sada huta na adong di kecamatan silima pungga pungga kabupaten dairi propinsi sumatera utara in...
  3. songon on do hata ni tuhan jahowa hape so tutu jahowa mandok 22 29 ia situan na torop isi

Generated Text Samples (Subword-based)

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

Context Size 1:

  1. _man_i_sa_nina_s
  2. amai_palalaseu_n
  3. ndi_α―”_no_pa_de_d

Context Size 2:

  1. a_lamar_na._jalut
  2. ani_ni_ahit_bando
  3. ng_dongkop_hot_ad

Context Size 3:

  1. angitlawa_rajai,_d
  2. _marhalahite_hite_
  3. na_sapangku_imbolo

Context Size 4:

  1. _ni_jahowa_hamu_ang
  2. _na_marsaro_mameuth
  3. _di_jeremia_7_novem

Key Findings

  • Best Predictability: Context-4 (word) with 94.1% predictability
  • Branching Factor: Decreases with context size (more deterministic)
  • Memory Trade-off: Larger contexts require more storage (129,601 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 24,923
Total Tokens 971,594
Mean Frequency 38.98
Median Frequency 4
Frequency Std Dev 557.86

Most Common Words

Rank Word Frequency
1 ni 34,971
2 na 33,958
3 i 32,913
4 ma 26,658
5 di 25,940
6 tu 20,429
7 do 19,116
8 angka 17,411
9 jala 14,584
10 dohot 13,515

Least Common Words (from vocabulary)

Rank Word Frequency
1 α―‡α―”α―’α―ͺα―‰α―²α―– 2
2 kayo 2
3 uttar 2
4 ltr 2
5 font 2
6 ebrima 2
7 border 2
8 cellpadding 2
9 td 2
10 align 2

Zipf's Law Analysis

Metric Value
Zipf Coefficient 1.1806
RΒ² (Goodness of Fit) 0.997033
Adherence Quality excellent

Coverage Analysis

Top N Words Coverage
Top 100 53.7%
Top 1,000 78.5%
Top 5,000 91.4%
Top 10,000 95.7%

Key Findings

  • Zipf Compliance: RΒ²=0.9970 indicates excellent adherence to Zipf's law
  • High Frequency Dominance: Top 100 words cover 53.7% of corpus
  • Long Tail: 14,923 words needed for remaining 4.3% 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 0.8133 0.3464 N/A N/A
mono_64d 64 0.7715 0.2725 N/A N/A
mono_128d 128 0.4709 0.2523 N/A N/A
aligned_32d 32 0.8133 πŸ† 0.3386 0.0140 0.1240
aligned_64d 64 0.7715 0.2780 0.0560 0.2460
aligned_128d 128 0.4709 0.2525 0.1340 0.3160

Key Findings

  • Best Isotropy: aligned_32d with 0.8133 (more uniform distribution)
  • Semantic Density: Average pairwise similarity of 0.2900. Lower values indicate better semantic separation.
  • Alignment Quality: Aligned models achieve up to 13.4% 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 -0.493 Low formulaic 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
-ma mangain, manuhati, mamingkiri
-pa pangir, pahosing, parsonduk
-di disiorhon, didege, diri
-man mangain, manuhati, mangkasiholi
-mar marilah, marhabanhaban, marnioli
-ha hapistaranmuna, harajaon, hanna
-par parsonduk, partalianta, parnidaan
-si sitorus, sitalutuk, sinimpan

Productive Suffixes

Suffix Examples
-n disiorhon, mangain, getasan
-a acara, opatsa, hapistaranmuna
-on disiorhon, harajaon, mandaon
-an getasan, nangkohan, bulanan
-na hapistaranmuna, etonganna, utamana
-hon disiorhon, hinungkuphon, ditoishon
-ng humosing, pahosing, taretong
-nna etonganna, hanna, salpuanna

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
anga 1.61x 127 contexts angan, langa, sanga
angk 1.53x 157 contexts angka, bangko, angkal
ngka 1.56x 89 contexts angka, bungka, engkau
mang 1.64x 61 contexts amang, mangan, memang
ngko 1.70x 42 contexts bangko, ingkon, angkot
bang 1.45x 72 contexts bange, abang, bangis
ingk 1.48x 60 contexts lingka, ingkau, ingkon
onga 1.68x 36 contexts tonga, longa, bongal
bahe 1.79x 26 contexts bahen, dibahe, ibahen
ngan 1.40x 65 contexts angan, ingan, mangan
ongo 1.62x 36 contexts longo, kongo, rongom
angg 1.31x 78 contexts anggi, anggo, angguk

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
-pa -n 358 words parsapataan, partingkian
-ma -n 206 words marpadanpadan, marharajaon
-pa -on 200 words patoltolhon, paimbarhon
-pa -a 184 words pallawa, pasalihonsa
-pa -an 157 words parsapataan, partingkian
-di -n 156 words disiaphon, dilembagahon
-di -on 134 words disiaphon, dilembagahon
-ha -n 128 words hasundatan, hasusaan
-pa -na 119 words parsuhatonmuna, pabalionna
-ma -on 116 words marharajaon, mangaluhon

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
pabotohononku pa-boto-hon-on-ku 9.0 boto
paradiananku par-adian-an-ku 7.5 adian
sipasahaton si-pa-sahat-on 7.5 sahat
marparmangsian mar-par-mang-sian 7.5 sian
panailingku pan-aili-ng-ku 7.5 aili
pardonganan par-dong-an-an 7.5 dong
marhamuliaon mar-ha-mulia-on 7.5 mulia
diparsiajari di-par-si-ajari 7.5 ajari
sipaingotna si-pa-ingot-na 7.5 ingot
sipatudoson si-pa-tudos-on 7.5 tudos
dipangasahon di-pan-gasa-hon 7.5 gasa
situtungon si-tutu-ng-on 7.5 tutu
pasahaton pa-sahat-on 6.0 sahat
parbungkason par-bungkas-on 6.0 bungkas
dipajomba di-pa-jomba 6.0 jomba

6.6 Linguistic Interpretation

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


7. Summary & Recommendations

Performance Dashboard

Production Recommendations

Component Recommended Rationale
Tokenizer 32k BPE Best compression (3.66x)
N-gram 2-gram Lowest perplexity (185)
Markov Context-4 Highest predictability (94.1%)
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) 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: 2026-01-03 18:37:11

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