wikilangs/bh

Bihari languages - Wikilangs Models

Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on Bihari languages 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

Analysis and Evaluation

• 1. Tokenizer Evaluation
• 2. N-gram Model Evaluation
• 3. Markov Chain Evaluation
• 4. Vocabulary Analysis
• 5. Word Embeddings Evaluation
• 6. Morphological Analysis (Experimental)
• 7. Summary & Recommendations
• Metrics Glossary
• Visualizations Index

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1. Tokenizer Evaluation

Results

Vocab Size	Compression	Avg Token Len	UNK Rate	Total Tokens
8k	3.440x	3.44	0.1739%	367,965
16k	3.744x	3.75	0.1893%	338,089
32k	3.961x	3.96	0.2003%	319,582
64k	4.105x 🏆	4.11	0.2075%	308,421

Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

Sample 1: नेल्सन मंडेला दक्खिन अफिरका के पहिला करिया राष्ट्रपति आ पहिला चुनल गइल राष्ट्रपत...

Vocab	Tokens	Count
8k	▁ने ल् सन ▁मंड ेला ▁दक्खिन ▁अफिरका ▁के ▁पहिला ▁करिया ... (+9 more)	19
16k	▁ने ल्सन ▁मंड ेला ▁दक्खिन ▁अफिरका ▁के ▁पहिला ▁करिया ▁राष्ट्रपति ... (+8 more)	18
32k	▁नेल्सन ▁मंड ेला ▁दक्खिन ▁अफिरका ▁के ▁पहिला ▁करिया ▁राष्ट्रपति ▁आ ... (+7 more)	17
64k	▁नेल्सन ▁मंड ेला ▁दक्खिन ▁अफिरका ▁के ▁पहिला ▁करिया ▁राष्ट्रपति ▁आ ... (+7 more)	17

Sample 2: बबुआ कलां भारत के झारखंड राज्य में एक ठो कसबा बाटे। के शहर‏‎ आ कस्बा

Vocab	Tokens	Count
8k	▁ब ब ुआ ▁कला ं ▁भारत ▁के ▁झारखंड ▁राज्य ▁में ... (+9 more)	19
16k	▁ब बुआ ▁कला ं ▁भारत ▁के ▁झारखंड ▁राज्य ▁में ▁एक ... (+8 more)	18
32k	▁ब बुआ ▁कलां ▁भारत ▁के ▁झारखंड ▁राज्य ▁में ▁एक ▁ठो ... (+7 more)	17
64k	▁बबुआ ▁कलां ▁भारत ▁के ▁झारखंड ▁राज्य ▁में ▁एक ▁ठो ▁कसबा ... (+6 more)	16

Sample 3: घटना जनम - मन्मथनाथ गुप्त - भारतीय स्वतन्त्रता संग्राम क एगो प्रमुख क्रान्तिकारी...

Vocab	Tokens	Count
8k	▁घटना ▁जनम ▁- ▁म न् म थ नाथ ▁गुप्त ▁- ... (+28 more)	38
16k	▁घटना ▁जनम ▁- ▁म न् मथ नाथ ▁गुप्त ▁- ▁भारतीय ... (+26 more)	36
32k	▁घटना ▁जनम ▁- ▁मन् मथ नाथ ▁गुप्त ▁- ▁भारतीय ▁स्वतन्त्रता ... (+21 more)	31
64k	▁घटना ▁जनम ▁- ▁मन्मथनाथ ▁गुप्त ▁- ▁भारतीय ▁स्वतन्त्रता ▁संग्राम ▁क ... (+17 more)	27

Key Findings

• Best Compression: 64k achieves 4.105x compression
• Lowest UNK Rate: 8k with 0.1739% unknown tokens
• Trade-off: Larger vocabularies improve compression but increase model size
• Recommendation: 32k vocabulary provides optimal balance for production use

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2. N-gram Model Evaluation

Results

N-gram	Variant	Perplexity	Entropy	Unique N-grams	Top-100 Coverage	Top-1000 Coverage
2-gram	Word	9,136	13.16	29,778	16.5%	43.4%
2-gram	Subword	1,496 🏆	10.55	21,749	39.6%	76.5%
3-gram	Word	13,783	13.75	38,633	15.8%	36.1%
3-gram	Subword	11,127	13.44	93,435	16.7%	42.3%
4-gram	Word	17,572	14.10	53,047	17.6%	35.4%
4-gram	Subword	44,731	15.45	294,486	9.1%	27.8%
5-gram	Word	8,139	12.99	30,163	24.3%	46.7%
5-gram	Subword	95,769	16.55	421,404	6.3%	19.7%

Top 5 N-grams by Size

2-grams (Word):

Rank	N-gram	Count
1	सभ के	4,152
2	भारत के	3,812
3	रूप में	3,160
4	के रूप	2,936
5	देखल जाय	2,147

3-grams (Word):

Rank	N-gram	Count
1	के रूप में	2,742
2	इहो देखल जाय	2,001
3	के हिसाब से	1,425
4	संदर्भ बाहरी कड़ी	1,391
5	शहर आ कस्बा	1,209

4-grams (Word):

Rank	N-gram	Count
1	के शहर आ कस्बा	1,206
2	बाटे इहो देखल जाय	781
3	राज्य में एक ठो	666
4	के हिसाब से ई	539
5	में एगो जिला बाटे	536

5-grams (Word):

Rank	N-gram	Count
1	संदर्भ के शहर आ कस्बा	496
2	के जनगणना के हिसाब से	496
3	में एगो जिला बाटे एकर	465
4	जनसंख्या साल के जनगणना के	449
5	साल के जनगणना के हिसाब	448

2-grams (Subword):

Rank	N-gram	Count
1	के _	114,017
2	_ के	110,574
3	र _	75,090
4	ल _	68,378
5	न _	54,576

3-grams (Subword):

Rank	N-gram	Count
1	_ के _	108,779
2	_ में _	44,499
3	_ आ _	30,014
4	_ से _	20,994
5	ल _ जा	13,915

4-grams (Subword):

Rank	N-gram	Count
1	न _ के _	9,485
2	_ स भ _	8,539
3	_ ए गो _	8,025
4	र _ के _	7,333
5	ल _ जा ला	7,264

5-grams (Subword):

Rank	N-gram	Count
1	_ बा टे । _	5,947
2	_ भा र त _	5,876
3	_ सं द र्भ _	5,473
4	_ t h e _	4,933
5	ल _ ग इ ल	4,916

Key Findings

• Best Perplexity: 2-gram (subword) with 1,496
• Entropy Trend: Decreases with larger n-grams (more predictable)
• Coverage: Top-1000 patterns cover ~20% of corpus
• Recommendation: 4-gram or 5-gram for best predictive performance

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3. Markov Chain Evaluation

Results

Context	Variant	Avg Entropy	Perplexity	Branching Factor	Unique Contexts	Predictability
1	Word	0.8731	1.832	6.14	84,373	12.7%
1	Subword	0.9992	1.999	12.29	4,950	0.1%
2	Word	0.2948	1.227	1.78	516,874	70.5%
2	Subword	0.5582	1.472	4.02	60,819	44.2%
3	Word	0.1070	1.077	1.19	914,610	89.3%
3	Subword	0.5218	1.436	2.94	244,457	47.8%
4	Word	0.0352 🏆	1.025	1.05	1,084,862	96.5%
4	Subword	0.3349	1.261	1.87	719,467	66.5%

Generated Text Samples (Word-based)

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

Context Size 1:

1. के काम कइल जाला के जिला भारत के संतान लक्ष्मीदास जे पर्यावरणी आ मेडिकल कॉलेज दारोगा
2. में भगवान शिव के होखे ला दुनों जाना जाता था जो में जमल पानी प्रदूषण कहल
3. आ निर्वासित दुनों ओर ना कौनों सामान सभ के नाट्यमण्डली के संभाव्यता अध्‍ययन राइट्स ऑफ हिज

Context Size 2:

1. सभ के समर्थन वाली मीरा कुमार रहली ई कहल गइल आ सन ई में बेंजामिन फ्रैंकलिन के
2. भारत के 27वाँ शहर बाटे जनगणना आँकड़ा के मोताबिक राजा पृथु के नाँव सैयद शफ़ीक़ हुसैन रहल
3. रूप में रखल जाला 23 मार्च locks down over 100 and 1 450 m oromediterranean zone nemoral

Context Size 3:

1. के रूप में भी देखल जाला आ पोसल जाला इन्हन क कई गो अवतार कमल क फूल अतिरिक्त
2. इहो देखल जाय नारियल पानी नारियल गरी संदर्भ पानी
3. के हिसाब से ई भारत के 476वाँ शहर बाटे जनगणना आँकड़ा के मोताबिक एह शहर में लिंगानुपात 934

Context Size 4:

1. बाटे इहो देखल जाय भारत के शहर संदर्भ के शहर आ कस्बा के शहर आ कस्बा प्रदेश के शहर
2. राज्य में एक ठो कसबा बाटे इहो देखल जाय गुजरात के जिला संदर्भ बाहरी कड़ी ऑफिशियल वेबसाइट के जिला
3. के हिसाब से ई भारत के 204वाँ शहर बाटे जनगणना आँकड़ा के मोताबिक एह शहर में लिंगानुपात 883 आ

Generated Text Samples (Subword-based)

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

Context Size 1:

1. _शार_खाई_ऋ_भूगो_स्थापत्र_
2. र_के_बत_oudeasuña
3. के_में_का_djoriid_नित

Context Size 2:

1. के_युवल_जाति_बा_जे_दुनों_ची
2. _के_तुलसीदास_लोगन-पूर्व_में
3. र_द्वारा_पूरा_लोग_के_रूप_में

Context Size 3:

1. _के_पुरान_खान,_तसही_संभव
2. _में_तीन_गो_देस_बनल_ईस्ट_
3. _आ_सन्देश_पर_करा_जरूरत_

Context Size 4:

1. न_के_सीखल_आ_एह_मंदिर,_मा
2. _सभ_के_बिसेसता_के_कारण_मूल्य
3. _एगो_नागरिक_उत्पादन_के_प्रति_

Key Findings

• Best Predictability: Context-4 (word) with 96.5% predictability
• Branching Factor: Decreases with context size (more deterministic)
• Memory Trade-off: Larger contexts require more storage (719,467 contexts)
• Recommendation: Context-3 or Context-4 for text generation

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4. Vocabulary Analysis

Statistics

Metric	Value
Vocabulary Size	38,630
Total Tokens	1,241,622
Mean Frequency	32.14
Median Frequency	4
Frequency Std Dev	666.83

Most Common Words

Rank	Word	Frequency
1	के	109,386
2	में	46,201
3	आ	30,101
4	से	21,341
5	बा	11,787
6	ई	10,672
7	सभ	8,798
8	बाटे	8,511
9	जाला	8,084
10	एगो	8,063

Least Common Words (from vocabulary)

Rank	Word	Frequency
1	बंटवारे	2
2	सीटेंराष्ट्रीय	2
3	पासवानभाकपा	2
4	शेयरमतदान	2
5	तिथिबहुमतराष्ट्रीय	2
6	गठबंधनमहागठबंधन	2
7	मैट्रिज़सितंबर	2
8	बोनो	2
9	नगद	2
10	रचनन	2

Zipf's Law Analysis

Metric	Value
Zipf Coefficient	1.1214
R² (Goodness of Fit)	0.994355
Adherence Quality	excellent

Coverage Analysis

Top N Words	Coverage
Top 100	43.1%
Top 1,000	69.6%
Top 5,000	86.1%
Top 10,000	91.7%

Key Findings

• Zipf Compliance: R²=0.9944 indicates excellent adherence to Zipf's law
• High Frequency Dominance: Top 100 words cover 43.1% of corpus
• Long Tail: 28,630 words needed for remaining 8.3% coverage

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5. Word Embeddings Evaluation

5.1 Cross-Lingual Alignment

5.2 Model Comparison

Model	Dimension	Isotropy	Semantic Density	Alignment R@1	Alignment R@10
mono_32d	32	0.8673	0.3719	N/A	N/A
mono_64d	64	0.8240	0.2806	N/A	N/A
mono_128d	128	0.6337	0.2390	N/A	N/A
aligned_32d	32	0.8673 🏆	0.3586	0.0220	0.1540
aligned_64d	64	0.8240	0.2867	0.0220	0.2300
aligned_128d	128	0.6337	0.2384	0.0780	0.2560

Key Findings

• Best Isotropy: aligned_32d with 0.8673 (more uniform distribution)
• Semantic Density: Average pairwise similarity of 0.2959. Lower values indicate better semantic separation.
• Alignment Quality: Aligned models achieve up to 7.8% R@1 in cross-lingual retrieval.
• Recommendation: 128d aligned for best cross-lingual performance

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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	1.367	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.

No productive affixes detected.

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
ther	2.76x	26 contexts	there, other, mother
tion	2.68x	19 contexts	motion, action, nation
ount	2.74x	15 contexts	mount, count, counts
atio	2.66x	15 contexts	ratio, nation, nations
ctio	2.70x	14 contexts	action, section, actions
ater	2.74x	11 contexts	later, eater, water
stat	2.72x	10 contexts	stato, stats, state
vers	2.62x	11 contexts	verse, covers, rivers
rati	2.70x	9 contexts	ratio, rating, bharati
ment	2.55x	9 contexts	cement, ferment, element
ical	2.65x	8 contexts	typical, medical, optical
ated	2.73x	7 contexts	dated, stated, related

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.

No significant affix co-occurrences detected.

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).

Insufficient data for recursive segmentation.

6.6 Linguistic Interpretation

Automated Insight: The language Bihari languages 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.

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7. Summary & Recommendations

Production Recommendations

Component	Recommended	Rationale
Tokenizer	64k BPE	Best compression (4.10x)
N-gram	2-gram	Lowest perplexity (1,496)
Markov	Context-4	Highest predictability (96.5%)
Embeddings	100d	Balanced semantic capture and isotropy

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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

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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

• 🌐 Website: wikilangs.org
• 🤗 Models: huggingface.co/wikilangs
• 📊 Data: wikipedia-monthly
• 👤 Author: Omar Kamali
• 🤝 Sponsor: Featherless AI

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Generated by Wikilangs Models Pipeline

Report Date: 2026-01-03 18:51:04