---
language: hi
language_name: Hindi
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: 4.250
  - name: best_isotropy
    type: isotropy
    value: 0.8141
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Hindi - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Hindi** 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** | 3.436x | 3.44 | 0.0604% | 2,277,747 |
| **16k** | 3.796x | 3.80 | 0.0667% | 2,061,793 |
| **32k** | 4.066x | 4.07 | 0.0715% | 1,924,898 |
| **64k** | 4.250x 🏆 | 4.25 | 0.0747% | 1,841,478 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `जेरोम इसाक फ्रीडमन अमेरिका के प्रसिद्द वैज्ञानिक हैं। में इन्हें भौतिक विज्ञान म...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ज ेर ोम ▁इस ाक ▁फ्री ड मन ▁अमेरिका ▁के ... (+19 more)` | 29 |
| 16k | `▁जेर ोम ▁इस ाक ▁फ्री ड मन ▁अमेरिका ▁के ▁प्रसि ... (+17 more)` | 27 |
| 32k | `▁जेर ोम ▁इस ाक ▁फ्री ड मन ▁अमेरिका ▁के ▁प्रसिद्द ... (+16 more)` | 26 |
| 64k | `▁जेरोम ▁इसाक ▁फ्री ड मन ▁अमेरिका ▁के ▁प्रसिद्द ▁वैज्ञानिक ▁हैं ... (+14 more)` | 24 |

**Sample 2:** `मवैया हंडिया, इलाहाबाद, उत्तर प्रदेश स्थित एक गाँव है। भूगोल जनसांख्यिकी यातायात...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁म वै या ▁हंडिया , ▁इलाहाबाद , ▁उत्तर ▁प्रदेश ▁स्थित ... (+16 more)` | 26 |
| 16k | `▁म वै या ▁हंडिया , ▁इलाहाबाद , ▁उत्तर ▁प्रदेश ▁स्थित ... (+16 more)` | 26 |
| 32k | `▁म वैया ▁हंडिया , ▁इलाहाबाद , ▁उत्तर ▁प्रदेश ▁स्थित ▁एक ... (+15 more)` | 25 |
| 64k | `▁म वैया ▁हंडिया , ▁इलाहाबाद , ▁उत्तर ▁प्रदेश ▁स्थित ▁एक ... (+15 more)` | 25 |

**Sample 3:** `माधवी हिन्दी फिल्मों की एक प्रसिद्ध अभिनेत्री हैं। व्यक्तिगत जीवन फिल्मी सफर प्र...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁माध वी ▁हिन्दी ▁फिल्मों ▁की ▁एक ▁प्रसिद्ध ▁अभिनेत्री ▁हैं । ... (+14 more)` | 24 |
| 16k | `▁माध वी ▁हिन्दी ▁फिल्मों ▁की ▁एक ▁प्रसिद्ध ▁अभिनेत्री ▁हैं । ... (+12 more)` | 22 |
| 32k | `▁माधवी ▁हिन्दी ▁फिल्मों ▁की ▁एक ▁प्रसिद्ध ▁अभिनेत्री ▁हैं । ▁व्यक्तिगत ... (+11 more)` | 21 |
| 64k | `▁माधवी ▁हिन्दी ▁फिल्मों ▁की ▁एक ▁प्रसिद्ध ▁अभिनेत्री ▁हैं । ▁व्यक्तिगत ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.250x compression
- **Lowest UNK Rate:** 8k with 0.0604% 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 | 99,591 | 16.60 | 936,439 | 10.1% | 23.9% |
| **2-gram** | Subword | 2,241 🏆 | 11.13 | 158,282 | 38.5% | 70.6% |
| **3-gram** | Word | 399,267 | 18.61 | 1,969,797 | 5.9% | 14.2% |
| **3-gram** | Subword | 22,500 | 14.46 | 933,655 | 15.0% | 35.5% |
| **4-gram** | Word | 884,119 | 19.75 | 3,325,655 | 5.2% | 12.2% |
| **4-gram** | Subword | 140,402 | 17.10 | 4,229,461 | 7.4% | 21.2% |
| **5-gram** | Word | 517,438 | 18.98 | 2,208,715 | 8.0% | 17.2% |
| **5-gram** | Subword | 516,632 | 18.98 | 8,451,936 | 4.4% | 13.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `के लिए` | 298,043 |
| 2 | `जाता है` | 144,432 |
| 3 | `रूप में` | 130,790 |
| 4 | `के रूप` | 124,867 |
| 5 | `के साथ` | 119,967 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `के रूप में` | 123,170 |
| 2 | `इन्हें भी देखें` | 48,061 |
| 3 | `करने के लिए` | 45,421 |
| 4 | `किया जाता है` | 36,326 |
| 5 | `किया गया था` | 35,930 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `का एक गाँव है` | 19,177 |
| 2 | `है इन्हें भी देखें` | 16,636 |
| 3 | `जिले का एक गाँव` | 14,515 |
| 4 | `सरकार का आधिकारिक जालपृष्ठ` | 12,365 |
| 5 | `भारत सरकार के आधिकारिक` | 12,363 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `जिले का एक गाँव है` | 14,430 |
| 2 | `सरकार के आधिकारिक पोर्टल पर` | 12,360 |
| 3 | `भारत सरकार के आधिकारिक पोर्टल` | 12,359 |
| 4 | `उत्तराखण्ड सरकार का आधिकारिक जालपृष्ठ` | 10,606 |
| 5 | `में विस्तृत एवं प्रामाणिक जानकारी` | 10,604 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `र _` | 3,514,012 |
| 2 | `के _` | 2,568,356 |
| 3 | `_ के` | 2,390,034 |
| 4 | `, _` | 1,985,295 |
| 5 | `न _` | 1,962,003 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ के _` | 2,311,181 |
| 2 | `_ में _` | 1,613,203 |
| 3 | `_ की _` | 1,000,357 |
| 4 | `औ र _` | 977,524 |
| 5 | `_ औ र` | 976,951 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ औ र _` | 973,900 |
| 2 | `_ है । _` | 728,766 |
| 3 | `_ ए क _` | 550,979 |
| 4 | `_ प र _` | 374,271 |
| 5 | `_ के _ लि` | 322,541 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ के _ लि ए` | 298,051 |
| 2 | `के _ लि ए _` | 290,034 |
| 3 | `ता _ है । _` | 229,566 |
| 4 | `_ क र ने _` | 156,232 |
| 5 | `_ जा ता _ है` | 144,571 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 2,241
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~13% 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 | 0.7477 | 1.679 | 9.12 | 1,271,248 | 25.2% |
| **1** | Subword | 0.8713 | 1.829 | 13.88 | 36,229 | 12.9% |
| **2** | Word | 0.3806 | 1.302 | 2.43 | 11,582,358 | 61.9% |
| **2** | Subword | 0.6086 | 1.525 | 5.14 | 502,605 | 39.1% |
| **3** | Word | 0.1696 | 1.125 | 1.40 | 28,143,624 | 83.0% |
| **3** | Subword | 0.5073 | 1.421 | 3.65 | 2,584,793 | 49.3% |
| **4** | Word | 0.0689 🏆 | 1.049 | 1.13 | 39,392,974 | 93.1% |
| **4** | Subword | 0.4131 | 1.331 | 2.43 | 9,433,636 | 58.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `के प्रयासों के बाद गैन्डैल्फ़ के साथ स्थगित कर सभिको अचंभे में तर्क के नए स्थापित`
2. `में जीप वैन ज़ांड्ट एंड फ़्रैंसिस न्यूयॉर्क टाइम्स 10 से समझना लोगों को पुलिस ने सक्रिय`
3. `है लेनार्ट के साथ जारी की खेती श्रम बाजार में जेमस्टोन्स ब्रुन्सविक शामिल हो जाता है`

**Context Size 2:**

1. `के लिए वात्स्यायन ने कविता और नई विश्व व्यवस्था बनाने की सख्त जरूरत थी 24 फरवरी हिन्दी`
2. `जाता है कारण यह था कि जिन तस्वीरों में मंदिर के बगल में देखे बिना इस घोषणा`
3. `रूप में जिन में पाइथागोरस पहला व्यक्ति है जो वास्तविकता पर कम से कम कमाने वाले सदस्यों`

**Context Size 3:**

1. `के रूप में हॉलीवुड के पेशेवर लोगों के लिए उचित वक्त का इंतजार करने लगे उसे मारने के`
2. `इन्हें भी देखें उत्तराखण्ड के जिले उत्तराखण्ड के नगर कुमाऊँ मण्डल गढ़वाल मण्डल बाहरी कड़ियाँ उत्तराख...`
3. `करने के लिए सरकार द्वारा कोई वित्तीय सहायता प्राप्त हुई थी उन्होंने 14 फरवरी को विजय हजारे ट्रॉफी`

**Context Size 4:**

1. `का एक गाँव है बाहरी कड़ियाँ छत्तीसगढ़ सांस्कृतिक छत्तीसगढ जनजातियां कला खेल गोठ सतनाम पंथ छत्तीसगढ़ ...`
2. `है इन्हें भी देखें उत्तराखण्ड के जिले उत्तराखण्ड के नगर कुमाऊँ मण्डल गढ़वाल मण्डल बाहरी कड़ियाँ उत्त...`
3. `जिले का एक गाँव है बाहरी कड़ियाँ छत्तीसगढ़ सांस्कृतिक छत्तीसगढ जनजातियां कला खेल गोठ सतनाम पंथ छत्ती...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_के_का_इन्हें_की_दिरों_दमाने`
2. `र_अवल_विधानी_वर्ष_विश्लेष`
3. `क_आंकलालका_उगाव_नेगिस्तानी`

**Context Size 2:**

1. `र_ने_के_मंदिर_महाविद्यालय_`
2. `के_लिखने_में_इसे_कि_फ़िल्म_है`
3. `_के_पौड़ी_का_कुओमिक_रहने_`

**Context Size 3:**

1. `_के_बाद_वीकेंड_इंडोनेशिया_कोर`
2. `_में_52_नवंबर_दिए_गए।_`
3. `_की_मांग_की_कुछ_देशों_में_शामि`

**Context Size 4:**

1. `_और_युग_के_उत्तराखण्ड_राज्य_उ`
2. `_है।_कायाको_का_परित्याग_करती_`
3. `_एक_गाँव_है।_सूत्र_नहीं_देता_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (9,433,636 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 | 503,387 |
| Total Tokens | 51,225,358 |
| Mean Frequency | 101.76 |
| Median Frequency | 4 |
| Frequency Std Dev | 5660.20 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | के | 2,319,434 |
| 2 | में | 1,706,170 |
| 3 | है | 1,377,542 |
| 4 | की | 1,046,592 |
| 5 | और | 978,950 |
| 6 | से | 789,677 |
| 7 | का | 776,115 |
| 8 | को | 650,931 |
| 9 | एक | 563,314 |
| 10 | हैं | 479,404 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | तरॉरी | 2 |
| 2 | ग़ौरीद | 2 |
| 3 | ओकहर्स्ट | 2 |
| 4 | ओवरडेवलपमेंट | 2 |
| 5 | मिस्कैवेज | 2 |
| 6 | ज़ाल्स्की | 2 |
| 7 | aita | 2 |
| 8 | सूरजनसिंह | 2 |
| 9 | दीवानबगी | 2 |
| 10 | आशेक | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0969 |
| R² (Goodness of Fit) | 0.991607 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.0% |
| Top 1,000 | 63.2% |
| Top 5,000 | 80.3% |
| Top 10,000 | 86.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9916 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.0% of corpus
- **Long Tail:** 493,387 words needed for remaining 13.9% 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 | 0.8141 | 0.3993 | N/A | N/A |
| **mono_64d** | 64 | 0.7949 | 0.3123 | N/A | N/A |
| **mono_128d** | 128 | 0.7461 | 0.2670 | N/A | N/A |
| **aligned_32d** | 32 | 0.8141 🏆 | 0.3944 | 0.0840 | 0.4400 |
| **aligned_64d** | 64 | 0.7949 | 0.3145 | 0.2320 | 0.5660 |
| **aligned_128d** | 128 | 0.7461 | 0.2559 | 0.2760 | 0.6860 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8141 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3239. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 27.6% 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 | **0.307** | 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 |
|--------|----------|
| `-स` | सुना, सिस्सु, स्नेहभरे |
| `-क` | करतारी, कोबिता, क्लिफफोर्ड |
| `-म` | माबैन, मखीजा, महाराना |
| `-ब` | बाइटों, ब्रेवहार्ट्स, ब्लूहोल |
| `-प` | पांडिकाट्ट, पर्यवेक्षणीय, प्रसन्नतापूवर्क |
| `-अ` | अहमदगर, अर्गला, अंजुल |
| `-र` | रगति, राठौरों, रतनगड |
| `-ज` | जीप्स, जच्चन्धवग्गो, जवहार |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-न` | गेलसान, माबैन, गमभन |
| `-र` | डाइबर, नयानगर, दखर |
| `-स` | जीप्स, ब्रेवहार्ट्स, नॉमिनेशंस |
| `-s` | siblings, sheriffs, hieroglyphics |
| `-क` | नखचंद्रक, प्रसन्नतापूवर्क, बाहुबंधक |
| `-ल` | नौटियाल, ब्लूहोल, आवर्तकाल |
| `-त` | द्विपरत, कुत, ऑस्ट्रेलियाभारत |
| `-ट` | पांडिकाट्ट, एग्रीमेंट, यूरोसेंट |

### 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 |
|------|----------|------------------|----------|
| `nter` | 3.13x | 80 contexts | inter, enter, unter |
| `atio` | 3.06x | 61 contexts | patio, ation, ratio |
| `tion` | 2.97x | 67 contexts | tiong, ation, nation |
| `ctio` | 3.12x | 40 contexts | action, actions, section |
| `iona` | 3.07x | 26 contexts | ciona, fiona, acciona |
| `ubli` | 2.96x | 23 contexts | hubli, publié, public |
| `rpor` | 3.33x | 11 contexts | corpore, corpora, airport |
| `onal` | 3.05x | 11 contexts | tonal, monal, zonal |
| `guid` | 3.19x | 9 contexts | guide, guido, eguide |

### 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 |
|--------|--------|-----------|----------|
| `-क` | `-र` | 33 words | कुक्कुटेश्वर, कंपोज़र |
| `-स` | `-स` | 33 words | सोफ्रोनियस, सत्यदास |
| `-प` | `-स` | 30 words | प्रोड्क्शन्स, पैवोनिस |
| `-म` | `-र` | 28 words | माष्टर, मऊरानीपुर |
| `-स` | `-न` | 27 words | सेक्‍शन, सीस्तान |
| `-स` | `-र` | 24 words | साहेर, सूर्यवीर |
| `-प` | `-न` | 24 words | पराधीन, पिकायून |
| `-प` | `-त` | 23 words | पिएत, प्रोग्रामित |
| `-स` | `-क` | 23 words | सौंदर्यबोधक, सफलतार्पूक |
| `-व` | `-र` | 22 words | वुर, विज्कगवर्नर |

### 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 |
|------|-----------------|------------|------|
| संगीतनाटक | **`संगीतना-ट-क`** | 7.5 | `ट` |
| साहित्यकर | **`साहित्य-क-र`** | 7.5 | `क` |
| sanderson | **`sanders-on`** | 4.5 | `sanders` |
| hornbills | **`hornbill-s`** | 4.5 | `hornbill` |
| मैगाट्रॉनस | **`मैगाट्रॉन-स`** | 4.5 | `मैगाट्रॉन` |
| जनसांख्यकीय | **`जनसांख्यकी-य`** | 4.5 | `जनसांख्यकी` |
| इन्फ्लुएंसस | **`इन्फ्लुएंस-स`** | 4.5 | `इन्फ्लुएंस` |
| österreichs | **`österreich-s`** | 4.5 | `österreich` |
| दक्षिणमध्य | **`द-क-्षिणमध्य`** | 4.5 | `्षिणमध्य` |
| अर्धसूत्र | **`अ-र-्धसूत्र`** | 4.5 | `्धसूत्र` |
| anatolian | **`anatoli-an`** | 4.5 | `anatoli` |
| responded | **`respond-ed`** | 4.5 | `respond` |
| paralympics | **`paralympic-s`** | 4.5 | `paralympic` |
| उष्मागतिक | **`उष्मागति-क`** | 4.5 | `उष्मागति` |
| एजेंसियाँ | **`ए-ज-ेंसियाँ`** | 4.5 | `ेंसियाँ` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Hindi 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 (4.25x) |
| N-gram | **2-gram** | Lowest perplexity (2,241) |
| Markov | **Context-4** | Highest predictability (93.1%) |
| 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](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: 2026-01-10 08:17:37*