---
language: sd
language_name: Sindhi
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: 3.934
  - name: best_isotropy
    type: isotropy
    value: 0.8385
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sindhi** 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** | 3.296x | 3.30 | 0.0928% | 803,595 |
| **16k** | 3.589x | 3.59 | 0.1011% | 737,928 |
| **32k** | 3.802x | 3.80 | 0.1071% | 696,754 |
| **64k** | 3.934x 🏆 | 3.94 | 0.1108% | 673,371 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `مؤرخه جو لفظ ڪنهن بہ تاريخ کي حڪايت ڏيڻ يا حوالو ڏيڻ جي لاء استعمال هوندو آهي۔ ج...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁م ؤر خ ه ▁جو ▁لفظ ▁ڪنهن ▁بہ ▁تاريخ ▁کي ... (+30 more)` | 40 |
| 16k | `▁مؤرخ ه ▁جو ▁لفظ ▁ڪنهن ▁بہ ▁تاريخ ▁کي ▁ح ڪا ... (+26 more)` | 36 |
| 32k | `▁مؤرخ ه ▁جو ▁لفظ ▁ڪنهن ▁بہ ▁تاريخ ▁کي ▁حڪا يت ... (+23 more)` | 33 |
| 64k | `▁مؤرخ ه ▁جو ▁لفظ ▁ڪنهن ▁بہ ▁تاريخ ▁کي ▁حڪايت ▁ڏيڻ ... (+22 more)` | 32 |

**Sample 2:** `جنوري فيبروري مارچ اپريل مئي جون جولاءِ آگسٽ سيپٽمبر آڪٽوبر نومبر ڊسمبر صدي`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁جنوري ▁فيبروري ▁مارچ ▁اپريل ▁مئي ▁جون ▁جولاءِ ▁آگسٽ ▁سيپٽمبر ▁آڪٽوبر ... (+3 more)` | 13 |
| 16k | `▁جنوري ▁فيبروري ▁مارچ ▁اپريل ▁مئي ▁جون ▁جولاءِ ▁آگسٽ ▁سيپٽمبر ▁آڪٽوبر ... (+3 more)` | 13 |
| 32k | `▁جنوري ▁فيبروري ▁مارچ ▁اپريل ▁مئي ▁جون ▁جولاءِ ▁آگسٽ ▁سيپٽمبر ▁آڪٽوبر ... (+3 more)` | 13 |
| 64k | `▁جنوري ▁فيبروري ▁مارچ ▁اپريل ▁مئي ▁جون ▁جولاءِ ▁آگسٽ ▁سيپٽمبر ▁آڪٽوبر ... (+3 more)` | 13 |

**Sample 3:** `مويا (شھر) پاڪستان جي صوبي سنڌ جي ضلعي ٽنڊو محمد خان جي تعلقي ٽنڊو غلام حيدر جو ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁مو يا ▁( ش ھر ) ▁پاڪستان ▁جي ▁صوبي ▁سنڌ ... (+33 more)` | 43 |
| 16k | `▁مو يا ▁( شھر ) ▁پاڪستان ▁جي ▁صوبي ▁سنڌ ▁جي ... (+32 more)` | 42 |
| 32k | `▁مو يا ▁( شھر ) ▁پاڪستان ▁جي ▁صوبي ▁سنڌ ▁جي ... (+30 more)` | 40 |
| 64k | `▁مويا ▁( شھر ) ▁پاڪستان ▁جي ▁صوبي ▁سنڌ ▁جي ▁ضلعي ... (+29 more)` | 39 |


### Key Findings

- **Best Compression:** 64k achieves 3.934x compression
- **Lowest UNK Rate:** 8k with 0.0928% 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 | 38,713 | 15.24 | 131,770 | 8.7% | 25.8% |
| **2-gram** | Subword | 528 🏆 | 9.05 | 10,636 | 53.0% | 94.3% |
| **3-gram** | Word | 67,235 | 16.04 | 173,925 | 8.2% | 20.0% |
| **3-gram** | Subword | 4,815 | 12.23 | 79,077 | 21.4% | 55.9% |
| **4-gram** | Word | 100,042 | 16.61 | 258,539 | 9.6% | 19.9% |
| **4-gram** | Subword | 27,421 | 14.74 | 394,134 | 10.1% | 30.4% |
| **5-gram** | Word | 50,768 | 15.63 | 161,354 | 13.9% | 27.3% |
| **5-gram** | Subword | 99,142 | 16.60 | 989,725 | 5.7% | 19.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `طور تي` | 6,904 |
| 2 | `ڪيو ويو` | 6,538 |
| 3 | `ان جي` | 6,124 |
| 4 | `سنڌ جي` | 5,981 |
| 5 | `کان پوءِ` | 5,924 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `سنڌي ادبي بورڊ` | 2,484 |
| 2 | `پاڪستان جون جنرل` | 2,294 |
| 3 | `آرٽيڪل پاڪستان جون` | 2,294 |
| 4 | `اصل آرٽيڪل پاڪستان` | 2,294 |
| 5 | `جون جنرل اليڪشن` | 2,294 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `اصل آرٽيڪل پاڪستان جون` | 2,294 |
| 2 | `پاڪستان جون جنرل اليڪشن` | 2,294 |
| 3 | `آرٽيڪل پاڪستان جون جنرل` | 2,294 |
| 4 | `جنرل اليڪشن اصل آرٽيڪل` | 2,292 |
| 5 | `اليڪشن اصل آرٽيڪل پاڪستان` | 2,292 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `آرٽيڪل پاڪستان جون جنرل اليڪشن` | 2,294 |
| 2 | `اصل آرٽيڪل پاڪستان جون جنرل` | 2,294 |
| 3 | `اليڪشن اصل آرٽيڪل پاڪستان جون` | 2,292 |
| 4 | `جنرل اليڪشن اصل آرٽيڪل پاڪستان` | 2,292 |
| 5 | `جنرل اليڪشن جنرل اليڪشن اصل` | 1,838 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ي _` | 1,114,749 |
| 2 | `ن _` | 753,311 |
| 3 | `_ ج` | 557,070 |
| 4 | `و _` | 411,945 |
| 5 | `ا ن` | 385,837 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ج ي` | 277,174 |
| 2 | `ج ي _` | 273,527 |
| 3 | `ا ن _` | 231,693 |
| 4 | `_ ۾ _` | 172,549 |
| 5 | `_ ۽ _` | 138,576 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ج ي _` | 239,630 |
| 2 | `_ ج و _` | 103,948 |
| 3 | `_ آ ه ي` | 88,375 |
| 4 | `ن _ ج ي` | 75,849 |
| 5 | `_ ک ي _` | 60,920 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ن _ ج ي _` | 72,823 |
| 2 | `_ آ ه ي .` | 45,747 |
| 3 | `_ ک ا ن _` | 45,181 |
| 4 | `آ ه ي . _` | 42,956 |
| 5 | `_ س ا ن _` | 37,158 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 528
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~19% 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 | 0.9555 | 1.939 | 9.12 | 226,862 | 4.4% |
| **1** | Subword | 0.9881 | 1.984 | 9.49 | 3,118 | 1.2% |
| **2** | Word | 0.3286 | 1.256 | 1.91 | 2,067,523 | 67.1% |
| **2** | Subword | 0.8362 | 1.785 | 5.73 | 29,575 | 16.4% |
| **3** | Word | 0.1126 | 1.081 | 1.21 | 3,948,825 | 88.7% |
| **3** | Subword | 0.7606 | 1.694 | 4.20 | 169,537 | 23.9% |
| **4** | Word | 0.0359 🏆 | 1.025 | 1.05 | 4,752,539 | 96.4% |
| **4** | Subword | 0.6343 | 1.552 | 2.94 | 712,269 | 36.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `جي ماءُ فلاد قيا قبيلي جا ضلعا شامل ٿي ويا آرامي قبيلو ٻين اڳواڻن به سنڌو`
2. `جو پڌرنامو asean بيمسٽيڪ جو اندازو ٿي ھي ھڪ نگران حڪومت سياست آيو هو هن تڪ`
3. `آهي ان فارسي شعر چيل ھجي جتي ايراني ٻولين جا وڏا ڪن ٿيون جون شاخون مشق`

**Context Size 2:**

1. `طور تي هڪ رسالو تحقيق الخلافة لکيو جو حيدرآباد بيورو جو چيئرمئن به ٿيو محمد شاھ جو`
2. `ڪيو ويو هو ان جو استحصال ڪندي احتياط سان ھلائڻو ھوندو آھي ٻيو تھھ پھرئين تھھ جي`
3. `ان جي ئي صحبت آسو صوفي بڻيو آسو رام جي قتل واري الزام تي گرفتار ڪيو ويو`

**Context Size 3:**

1. `سنڌي ادبي بورڊ حوالا جي تاريخ جي تاريخ جون ڳالهيون 180 سنڌ جي مختصر تاريخ ص84 85 سال`
2. `پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آرٽيڪل پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آرٽيڪل پاڪستا...`
3. `آرٽيڪل پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آرٽيڪل پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آرٽيڪل...`

**Context Size 4:**

1. `آرٽيڪل پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آرٽيڪل پاڪستان جون جنرل اليڪشن جنرل اليڪشن جنرل اليڪش...`
2. `اصل آرٽيڪل پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آرٽيڪل پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آر...`
3. `پاڪستان جون جنرل اليڪشن جنرل اليڪشن اصل آرٽيڪل پاڪستان جون جنرل اليڪشن پاڪستان جي قومي اسيمبلي جون ع...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_آهي_و_انن_ٻڌائي`
2. `يو_پري_سيوامحالي`
3. `اڌرنهد_ٽين_و_ويءَ`

**Context Size 2:**

1. `ي_وس،_سنڌ_۾_ڪله_ج`
2. `ن_ورتحري_قبضو_ٿين`
3. `_جو_واقرر_ڳاٽوزين`

**Context Size 3:**

1. `_جي_ذيلي_يا_مريڪٽر`
2. `جي_ويندو_هو._اسي_ڪ`
3. `ان_علائي،_وچ_۾_ٻٽي`

**Context Size 4:**

1. `_جي_حيثيت_۾،_شمشيرن`
2. `_جو_هڪ_هندستان_ھٿ_ڏ`
3. `_آهي.،_عضويات)_۾_ڪي`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (712,269 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 | 101,453 |
| Total Tokens | 5,390,213 |
| Mean Frequency | 53.13 |
| Median Frequency | 4 |
| Frequency Std Dev | 1038.92 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | جي | 240,979 |
| 2 | جو | 104,513 |
| 3 | آهي | 87,558 |
| 4 | کي | 61,555 |
| 5 | تي | 51,826 |
| 6 | کان | 45,610 |
| 7 | سان | 38,559 |
| 8 | جا | 33,418 |
| 9 | ان | 33,002 |
| 10 | the | 32,948 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | جوالامکي | 2 |
| 2 | باريري | 2 |
| 3 | آسامائي | 2 |
| 4 | بالمِڪي | 2 |
| 5 | شويتامبر | 2 |
| 6 | چوٽرا | 2 |
| 7 | هديارا | 2 |
| 8 | سُکوچڪ | 2 |
| 9 | ڪاٺواري | 2 |
| 10 | گرودوارا | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0832 |
| R² (Goodness of Fit) | 0.989336 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.9% |
| Top 1,000 | 60.7% |
| Top 5,000 | 80.7% |
| Top 10,000 | 87.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9893 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.9% of corpus
- **Long Tail:** 91,453 words needed for remaining 12.5% 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 | 0.8385 🏆 | 0.3803 | N/A | N/A |
| **mono_64d** | 64 | 0.8313 | 0.3087 | N/A | N/A |
| **mono_128d** | 128 | 0.8167 | 0.2309 | N/A | N/A |
| **aligned_32d** | 32 | 0.8385 | 0.3802 | 0.0300 | 0.2040 |
| **aligned_64d** | 64 | 0.8313 | 0.3038 | 0.0820 | 0.3320 |
| **aligned_128d** | 128 | 0.8167 | 0.2420 | 0.1040 | 0.3860 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8385 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3077. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.4% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.436** | 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 |
|--------|----------|
| `-ا` | اسڪيمون, اجهامي, انڊونيشا |
| `-م` | مبينہ, مسلمہ, مون |
| `-س` | سيليبس, ساون, ساهيڙين |
| `-ڪ` | ڪﺌﻲ, ڪلنگ, ڪئٽئلن |
| `-ال` | الدراسات, اللھ, المنورہ |
| `-ب` | بادشاهتي, بنتِ, باک |
| `-پ` | پرزور, پڙھي, پتن |
| `-و` | وهندي, واڊ, وسيامل |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ن` | اسڪيمون, ھڙتالن, دماغن |
| `-ي` | ڳائجي, وهندي, کي |
| `-s` | minorities, indies, endophytes |
| `-ا` | انڊونيشا, ڌاڍا, سنزا |
| `-e` | hoernle, dengue, deville |
| `-n` | marathon, ruskin, cern |
| `-و` | کیو, سھتو, ماپبو |
| `-ون` | اسڪيمون, مون, ساون |

### 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 |
|------|----------|------------------|----------|
| `tion` | 3.01x | 49 contexts | notion, nation, cation |
| `ريون` | 2.35x | 135 contexts | ڪريون, فريون, دريون |
| `يندا` | 2.25x | 112 contexts | نيندا, ويندا, ڏيندا |
| `atio` | 3.03x | 30 contexts | natio, ratio, nation |
| `يندي` | 1.83x | 114 contexts | ڪيندي, ٿيندي, ميندي |
| `يائي` | 1.69x | 117 contexts | بيائي, پيائي, ديائي |
| `يندڙ` | 1.79x | 89 contexts | ڏيندڙ, ايندڙ, ويندڙ |
| `ائون` | 1.53x | 148 contexts | مائون, ٹائون, لائون |
| `نهنج` | 2.12x | 34 contexts | تنهنجي, تنهنجو, پنهنجي |
| `اريخ` | 2.19x | 18 contexts | تاريخ, ٿاريخ, پاريخ |
| `علائ` | 2.47x | 10 contexts | علائق, علائي, علائقي |
| `ڪستا` | 2.24x | 11 contexts | سڪستان, پاڪستان, ترڪستان |

### 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 |
|--------|--------|-----------|----------|
| `-ا` | `-ن` | 55 words | اُنھَن, افشاريان |
| `-م` | `-ي` | 35 words | مائوزي, مھاڏي |
| `-ا` | `-ي` | 30 words | السنوسي, ائڪمي |
| `-پ` | `-ن` | 29 words | پبليڪشن, پپن |
| `-ڪ` | `-ن` | 29 words | ڪارواين, ڪنٽينرن |
| `-م` | `-ن` | 26 words | مارلن, ملهايون |
| `-ا` | `-ا` | 25 words | اورا, الما |
| `-ب` | `-ن` | 23 words | بوسٽن, بُڪين |
| `-س` | `-ن` | 23 words | سرنامن, سون |
| `-ا` | `-و` | 22 words | ايلنبرو, اجھو |

### 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 |
|------|-----------------|------------|------|
| انڊيپينڊنس | **`انڊيپينڊ-ن-س`** | 7.5 | `ن` |
| وڪيذريعات | **`وڪيذريع-ا-ت`** | 7.5 | `ا` |
| برهمپوترا | **`برهمپوت-ر-ا`** | 7.5 | `ر` |
| اصطلاحيات | **`اصطلاح-يا-ت`** | 6.0 | `اصطلاح` |
| interests | **`inter-es-ts`** | 6.0 | `inter` |
| المهاجرين | **`ال-مهاجرين`** | 4.5 | `مهاجرين` |
| periodical | **`periodic-al`** | 4.5 | `periodic` |
| ڊيموگرافيا | **`ڊيموگرافي-ا`** | 4.5 | `ڊيموگرافي` |
| interactions | **`interaction-s`** | 4.5 | `interaction` |
| anglicans | **`anglican-s`** | 4.5 | `anglican` |
| lansdowne | **`lansdown-e`** | 4.5 | `lansdown` |
| شاهواڻيءَ | **`ش-ا-هواڻيءَ`** | 4.5 | `هواڻيءَ` |
| presidente | **`president-e`** | 4.5 | `president` |
| orientales | **`oriental-es`** | 4.5 | `oriental` |
| شاگردياڻيون | **`شاگردياڻي-ون`** | 4.5 | `شاگردياڻي` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Sindhi 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 (3.93x) |
| N-gram | **2-gram** | Lowest perplexity (528) |
| Markov | **Context-4** | Highest predictability (96.4%) |
| 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 20:08:57*