---
language: bh
language_name: Bihari languages
language_family: indoaryan_central
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-indoaryan_central
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 4.105
  - name: best_isotropy
    type: isotropy
    value: 0.8673
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

# 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

![Performance Dashboard](visualizations/performance_dashboard.png)

### Analysis and Evaluation

- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
- [4. Vocabulary Analysis](#4-vocabulary-analysis)
- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
- [7. Summary & Recommendations](#7-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

![Tokenizer Fertility](visualizations/tokenizer_fertility.png)

![Tokenizer OOV](visualizations/tokenizer_oov.png)

![Total Tokens](visualizations/tokenizer_total_tokens.png)

### 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

---
## 2. N-gram Model Evaluation

![N-gram Perplexity](visualizations/ngram_perplexity.png)

![N-gram Unique](visualizations/ngram_unique.png)

![N-gram Coverage](visualizations/ngram_coverage.png)

### 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

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### 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

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/zipf_law.png)

![Top Words](visualizations/top20_words.png)

![Coverage Curve](visualizations/vocab_coverage.png)

### 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

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 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

---
## 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.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### 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 |


---
## 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](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

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

```bibtex
@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](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

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