---
language: dv
language_name: Divehi
language_family: indoaryan_insular
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_insular
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: 5.583
  - name: best_isotropy
    type: isotropy
    value: 0.8795
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Divehi** 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** | 4.195x | 4.20 | 0.4815% | 567,427 |
| **16k** | 4.753x | 4.76 | 0.5455% | 500,811 |
| **32k** | 5.229x | 5.24 | 0.6001% | 455,260 |
| **64k** | 5.583x 🏆 | 5.59 | 0.6407% | 426,395 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ޅ.އަތޮޅު ތަޢުލީމީ މަރުކަޒަކީ ޅ. ހިންނަވަރުގައި ހުންނަ މަދަރުސާ އެކެވެ. ސްކޫލުތައ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ޅ . އަތޮޅު ▁ތަޢުލީމީ ▁މަރުކަޒ ަކީ ▁ޅ . ▁ހިން ނ ... (+7 more)` | 17 |
| 16k | `▁ޅ . އަތޮޅު ▁ތަޢުލީމީ ▁މަރުކަޒަކީ ▁ޅ . ▁ހިން ނ ަވަރު ... (+6 more)` | 16 |
| 32k | `▁ޅ . އަތޮޅު ▁ތަޢުލީމީ ▁މަރުކަޒަކީ ▁ޅ . ▁ހިންނ ަވަރު ގައި ... (+5 more)` | 15 |
| 64k | `▁ޅ . އަތޮޅު ▁ތަޢުލީމީ ▁މަރުކަޒަކީ ▁ޅ . ▁ހިންނަވަރުގައި ▁ހުންނަ ▁މަދަރުސާ ... (+3 more)` | 13 |

**Sample 2:** `ނިކަކޯޅި ބަވާސީ އަކީ ނިކަކޯޅިއެއްގެ ސިފައިގައި ފުރަގަސް ފަރާތުން ނިކުންނަ ބައްޔެ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ނިކ ަކޯ ޅި ▁ބ ަވާ ސީ ▁އަކީ ▁ނިކ ަކޯ ޅ ... (+9 more)` | 19 |
| 16k | `▁ނިކ ަކޯޅި ▁ބ ަވާ ސީ ▁އަކީ ▁ނިކ ަކޯ ޅ ިއެއްގެ ... (+6 more)` | 16 |
| 32k | `▁ނިކ ަކޯޅި ▁ބަވާސީ ▁އަކީ ▁ނިކ ަކޯ ޅިއެއްގެ ▁ސިފައިގައި ▁ފުރަގަސް ▁ފަރާތުން ... (+3 more)` | 13 |
| 64k | `▁ނިކަކޯޅި ▁ބަވާސީ ▁އަކީ ▁ނިކަކޯޅިއެއްގެ ▁ސިފައިގައި ▁ފުރަގަސް ▁ފަރާތުން ▁ނިކުންނަ ▁ބައްޔެކެވެ .` | 10 |

**Sample 3:** `ފައިފެޅުން އަކީ ބައްޔެއްގެ ސަބަބުން ފައިގެ ހުދުހަން އެކި ދިމަދމާލުން ކެނޑުމެވެ.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ފައި ފ ެޅ ުން ▁އަކީ ▁ބައްޔެއްގެ ▁ސަބަބުން ▁ފައިގެ ▁ހުދ ުހ ... (+9 more)` | 19 |
| 16k | `▁ފައި ފ ެޅުން ▁އަކީ ▁ބައްޔެއްގެ ▁ސަބަބުން ▁ފައިގެ ▁ހުދ ުހ ަން ... (+8 more)` | 18 |
| 32k | `▁ފައިފ ެޅުން ▁އަކީ ▁ބައްޔެއްގެ ▁ސަބަބުން ▁ފައިގެ ▁ހުދުހ ަން ▁އެކި ▁ދިމަދ ... (+4 more)` | 14 |
| 64k | `▁ފައިފެޅުން ▁އަކީ ▁ބައްޔެއްގެ ▁ސަބަބުން ▁ފައިގެ ▁ހުދުހަން ▁އެކި ▁ދިމަދމާލުން ▁ކެނޑުމެވެ .` | 10 |


### Key Findings

- **Best Compression:** 64k achieves 5.583x compression
- **Lowest UNK Rate:** 8k with 0.4815% 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 | 10,033 | 13.29 | 18,085 | 11.2% | 34.3% |
| **2-gram** | Subword | 1,740 🏆 | 10.76 | 17,306 | 35.4% | 73.1% |
| **3-gram** | Word | 12,820 | 13.65 | 22,046 | 10.8% | 30.6% |
| **3-gram** | Subword | 11,965 | 13.55 | 83,683 | 14.8% | 40.7% |
| **4-gram** | Word | 44,408 | 15.44 | 64,258 | 6.5% | 16.2% |
| **4-gram** | Subword | 47,194 | 15.53 | 264,508 | 8.4% | 24.1% |
| **5-gram** | Word | 40,713 | 15.31 | 56,606 | 6.9% | 15.7% |
| **5-gram** | Subword | 104,406 | 16.67 | 409,837 | 5.5% | 16.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ވަނަ އަހަރު` | 1,832 |
| 2 | `ނުވަތަ އަކީ` | 707 |
| 3 | `ވަނަ އަހަރުގެ` | 673 |
| 4 | `ވަނަ ދުވަހެވެ` | 616 |
| 5 | `މީގެ އިތުރުން` | 596 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `އަކީ މީލާދީ ކަލަންޑަރުގެ` | 375 |
| 2 | `ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ` | 364 |
| 3 | `ބަންދު ދުވަސްތަކާއި ފާހަގަ` | 364 |
| 4 | `ފާހަގަ ކުރެވޭ ދުވަހެއްގެ` | 364 |
| 5 | `ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި` | 364 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ފާހަގަ ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި` | 364 |
| 2 | `ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ` | 364 |
| 3 | `ބަންދު ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ` | 364 |
| 4 | `އުފަންވި މީހުން މަރުވި މީހުން` | 349 |
| 5 | `މީހުން ބަންދު ދުވަސްތަކާއި ފާހަގަ` | 340 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ބަންދު ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ` | 364 |
| 2 | `ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި` | 364 |
| 3 | `މީހުން ބަންދު ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ` | 340 |
| 4 | `މަރުވި މީހުން ބަންދު ދުވަސްތަކާއި ފާހަގަ` | 339 |
| 5 | `މީހުން މަރުވި މީހުން ބަންދު ދުވަސްތަކާއި` | 329 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ން _` | 90,135 |
| 2 | `ގެ _` | 83,101 |
| 3 | `. _` | 66,551 |
| 4 | `ވެ .` | 64,305 |
| 5 | `އި _` | 60,871 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ވެ . _` | 61,497 |
| 2 | `އެ ވެ .` | 36,492 |
| 3 | `ގަ އި _` | 36,034 |
| 4 | `ތަ އް _` | 10,452 |
| 5 | `ކެ ވެ .` | 10,355 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `އެ ވެ . _` | 35,128 |
| 2 | `ކެ ވެ . _` | 9,815 |
| 3 | `_ އަ ދި _` | 9,086 |
| 4 | `ވެ . _ މި` | 8,503 |
| 5 | `ވެ . _ އެ` | 6,652 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ އެ ވެ . _` | 6,310 |
| 2 | `ވެ އެ ވެ . _` | 5,392 |
| 3 | `ގަ އެ ވެ . _` | 4,655 |
| 4 | `_ އެ ން މެ _` | 4,586 |
| 5 | `އެ ވެ . _ މި` | 4,463 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 1,740
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~17% 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 | 0.7502 | 1.682 | 4.34 | 120,955 | 25.0% |
| **1** | Subword | 1.3036 | 2.468 | 18.11 | 2,104 | 0.0% |
| **2** | Word | 0.1780 | 1.131 | 1.33 | 523,452 | 82.2% |
| **2** | Subword | 0.8357 | 1.785 | 4.91 | 38,101 | 16.4% |
| **3** | Word | 0.0519 | 1.037 | 1.08 | 692,308 | 94.8% |
| **3** | Subword | 0.5690 | 1.484 | 2.88 | 187,098 | 43.1% |
| **4** | Word | 0.0200 🏆 | 1.014 | 1.03 | 741,793 | 98.0% |
| **4** | Subword | 0.3828 | 1.304 | 1.92 | 538,145 | 61.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `އަދި ބެންގާޅީ ފިލްމްތަކުގައި އެބަޔަކާއެކު ނ އަތޮޅުގައި މީހުން މަރުވި މީހުން ވިހަނީ ފަންސަވީސް އަހަރާ...`
2. `އެވެ ސިސްޓެމިކް ލޫޕަސް އެރިތެމަޓޯސަސް ގެ ނަންދެވުނު މަޝްހޫރު ބުދު ހަރުކުރުމަށް ތައްޔާރު ކުރައްވައިގެ...`
3. `އަކީ ޢަރަބީންގެ ގާތުގައި މިއީ ދުނިޔޭގައި 58 ވަނަ އަހަރާ ހަމައަށް މަސައްކަތްކުރައްވައިފައި ވަނީ އަމުރ...`

**Context Size 2:**

1. `ވަނަ އަހަރު ފެކަލްޓީ އޮފް އިންޖިނިއަރިންގ އެންޑް ޓެކްނޮލޮޖީ އާރްޔޫއީޓީ ސައިޚް މުޖީބުރު ރަޙްމާން ބަން...`
2. `ނުވަތަ އަކީ މިޔަރުގެ ވައްތަރެކެވެ މިއީ އަތޮޅުން ބޭރުގައި ކުރާ ލޭނުގެ މަސްވެރިކަމުގައެވެ މިމަސް އެންމ...`
3. `ވަނަ އަހަރުގެ ބޯހިމެނުމުގެ ނަތީޖާތައް ދައްކާގޮތުން މާޅޮސްމަޑުލު އުތުރުބުރީގެ އާބާދީ އިތުރުވަމުން ދިއ...`

**Context Size 3:**

1. `އަކީ މީލާދީ ކަލަންޑަރުގެ 146 ވަނަ ދުވަހެވެ ޙާދިސާތައް އުފަންވި މީހުން މަރުވި މީހުން ބަންދު ދުވަސްތަކ...`
2. `ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި ދިވެހިރާއްޖެ މަސްވެރިންގެ ދުވަސް`
3. `ބަންދު ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި ނޯވޭ ޔުނިއަން ޑިސޮލިއުޝަން ޑޭ ޖޫން 18 ސެސެލް ޤ...`

**Context Size 4:**

1. `ބަންދު ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި ދިވެހިރާއްޖެ ޖުމުހޫރީ ދުވަސް`
2. `ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި ޖުލައި 4 އެމެރިކާގެ މިނިވަން ދުވަސް ޖުލައި 4 ފިލިޕީނޯ...`
3. `އުފަންވި މީހުން މަރުވި މީހުން ބަންދު ދުވަސްތަކާއި ފާހަގަ ކުރެވޭ ދުވަހެއްގެ ގޮތުގައި ކުޑަކުދިންގެ ދުވ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ދެފައިން_އަދ._އަލް_ފައި_`
2. `ން_ޒުވާ_ފައެވެ._މަރުނުވާ_e`
3. `އި_ބޭބޭހެއުފެށިމަދުވަޑަކަލާގެ_`

**Context Size 2:**

1. `ން_•_pectight:_މިސްކި`
2. `ގެ_ކުރައްވަމުން_ރުސް_ގޮމާ_ދިރު`
3. `._މިން_ކަރައާއި_އޮތް_އިންޑަރު`

**Context Size 3:**

1. `ވެ._ކޯފުއްޕި_ޖެހުމުން_ބޭރުގައްޔާ`
2. `ގައި_ޚިދުމަތްކުރައްވާފައެވެ._ވަނަ`
3. `އެވެ._މިއީ_ފަރި_ރީކޯ_މޫސަބޭގެ_`

**Context Size 4:**

1. `އެވެ._ނާސްޕަތީ_ގައި_އަޅުގަނޑުމެން`
2. `ކެވެ._އެއީ_ރޭގަނޑު_ގިރާކުރި_ތަޖް`
3. `_އަދި_ހޯދިފައެއް_ނުލިބި_އެވެ._އު`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (538,145 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 | 51,567 |
| Total Tokens | 801,622 |
| Mean Frequency | 15.55 |
| Median Frequency | 3 |
| Frequency Std Dev | 104.10 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | އަދި | 9,274 |
| 2 | އެވެ | 6,692 |
| 3 | އަކީ | 5,688 |
| 4 | ވަނަ | 5,329 |
| 5 | ނުވަތަ | 4,623 |
| 6 | ވެސް | 4,608 |
| 7 | އެންމެ | 4,606 |
| 8 | ގެ | 3,870 |
| 9 | މި | 3,411 |
| 10 | އާއި | 3,404 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ޤާނޫނެއްގައި | 2 |
| 2 | ކަނޑައަޅައިފައިވާ | 2 |
| 3 | އިސްތިއުނާފަށް | 2 |
| 4 | ތަޢާރުޟުވާކަމަށް | 2 |
| 5 | ޓްރައިބިއުނަލަކުން | 2 |
| 6 | އެންޓަޓެއިންމަންޓުން | 2 |
| 7 | costus | 2 |
| 8 | ހުއިސުނަކީ | 2 |
| 9 | fatah | 2 |
| 10 | ސަބްސްކްރައިބް | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9604 |
| R² (Goodness of Fit) | 0.990212 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.5% |
| Top 1,000 | 48.5% |
| Top 5,000 | 71.9% |
| Top 10,000 | 81.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9902 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.5% of corpus
- **Long Tail:** 41,567 words needed for remaining 18.7% 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 | 0.8795 | 0.3207 | N/A | N/A |
| **mono_64d** | 64 | 0.8617 | 0.2441 | N/A | N/A |
| **mono_128d** | 128 | 0.6946 | 0.1877 | N/A | N/A |
| **aligned_32d** | 32 | 0.8795 🏆 | 0.3125 | 0.0040 | 0.0580 |
| **aligned_64d** | 64 | 0.8617 | 0.2426 | 0.0300 | 0.1720 |
| **aligned_128d** | 128 | 0.6946 | 0.1963 | 0.0620 | 0.2160 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8795 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2507. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 6.2% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.063** | 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 |
|--------|----------|
| `-އެ` | އެންވައިރޮމަންޓަލް, އެތިސްޓުންނެވެ, އެދެބޭކަލުންގެ |
| `-އަ` | އަމަލުތައް, އަބްދުއްރަހުމާނު, އަހައްމާއިދީ |
| `-މަ` | މައްޗައް, މަދަވީ, މަސައްކަތްޕުޅާއި |
| `-އި` | އިއްވި, އިނާމެކެވެ, އިނބަރަސްކަލާނގެ |
| `-ބަ` | ބައްޕާފުޅެވެ, ބަށީގެ, ބަނޑުހައިވުން |
| `-މި` | މިޔަރުތައް, މިޑުލާ, މިޗިގަންގެ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ް` | ރަނގަޅުކޮށް, ތައިރޮޑް, ރަދީފް |
| `-ެ` | ބައްޕާފުޅެވެ, ޞޫފީންގެ, މުޅިރާއްޖޭގެ |
| `-ި` | ގުޅިފައި, ކުރީކޮޅުގަޔާއި, ކާއިނާތުގައި |
| `-ން` | ބަނޑުހައިވުން, ފޮނުވާލުމުން, ދޭކަން |
| `-ގެ` | ޞޫފީންގެ, މުޅިރާއްޖޭގެ, ބަށީގެ |
| `-އި` | ގުޅިފައި, ކުރީކޮޅުގަޔާއި, ކާއިނާތުގައި |
| `-ވެ` | ބައްޕާފުޅެވެ, އުފަންކޮށްފައެވެ, ތިއޭޓަރެވެ |
| `-ެވެ` | ބައްޕާފުޅެވެ, އުފަންކޮށްފައެވެ, ތިއޭޓަރެވެ |

### 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.

*No significant bound stems detected.*


### 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 |
|--------|--------|-----------|----------|
| `-އެ` | `-ް` | 155 words | އެއަކުން, އެކަކަށް |
| `-މަ` | `-ް` | 107 words | މަސްތަކެއް, މަރާގުޅޭގޮތުން |
| `-އަ` | `-ް` | 104 words | އަހަރުތަކަކަށް, އަލްއުސްތާޒް |
| `-އަ` | `-ެ` | 102 words | އަންތަނަނާރިވޯއެވެ, އަކަށެވެ |
| `-އި` | `-ް` | 91 words | އިތުރުވާން, އިއްޒަތްތެރިކަން |
| `-އެ` | `-ެ` | 87 words | އެމެރިކާގައެވެ, އެއްޗެވެ |
| `-މި` | `-ް` | 74 words | މިޞްރުން, މިޞްރަށް |
| `-މަ` | `-ެ` | 71 words | މަދޫގެ, މަރުހަލާއެކެވެ |
| `-ބަ` | `-ް` | 69 words | ބަހާއެއް, ބަދަލުކޮށްގެން |
| `-ބަ` | `-ެ` | 61 words | ބަނޑޭރިގެއިންނެވެ, ބަދަރުންނެވެ |

### 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 |
|------|-----------------|------------|------|
| ދިމާވެގެން | **`ދިމާ-ވެ-ގެ-ން`** | 7.5 | `ދިމާ` |
| ބުރައިގެން | **`ބުރަ-އި-ގެ-ން`** | 7.5 | `ބުރަ` |
| މީހުންނާއިގެން | **`މީހުންނާ-އި-ގެ-ން`** | 7.5 | `މީހުންނާ` |
| ބައްދަލުވެގެން | **`ބަ-އްދަލު-ވެ-ގެ-ން`** | 6.0 | `އްދަލު` |
| އެއްކޮށްގެން | **`އެ-އްކޮ-ށް-ގެ-ން`** | 6.0 | `އްކޮ` |
| އަނބުރައިގެން | **`އަ-ނބުރ-ައި-ގެ-ން`** | 6.0 | `ނބުރ` |
| ގެއްލިގެން | **`ގެއްލި-ގެ-ން`** | 6.0 | `ގެއްލި` |
| އެދަރިފުޅު | **`އެ-ދަރިފުޅު`** | 4.5 | `ދަރިފުޅު` |
| ބްލޮކޭޑްގެ | **`ބްލޮކޭޑް-ގެ`** | 4.5 | `ބްލޮކޭޑް` |
| ޤުރްއާނާއި | **`ޤުރްއާނާ-އި`** | 4.5 | `ޤުރްއާނާ` |
| ޚިތާނުކޮށްގެން | **`ޚިތާނުކޮ-ށް-ގެ-ން`** | 4.5 | `ޚިތާނުކޮ` |
| ވިސްނައިގެން | **`ވިސްނ-ައި-ގެ-ން`** | 4.5 | `ވިސްނ` |
| މަޚްލޫޤުންގެ | **`މަ-ޚްލޫޤު-ން-ގެ`** | 4.5 | `ޚްލޫޤު` |
| ކޮލަންބިޔާގެ | **`ކޮލަންބިޔާ-ގެ`** | 4.5 | `ކޮލަންބިޔާ` |
| މައިގަނޑަކަށް | **`މަ-އި-ގަނޑަކަ-ށް`** | 4.5 | `ގަނޑަކަ` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Divehi 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](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (5.58x) |
| N-gram | **2-gram** | Lowest perplexity (1,740) |
| Markov | **Context-4** | Highest predictability (98.0%) |
| 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: 2026-01-04 02:56:36*