README.md

---
language: ur
language_name: Urdu
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: 4.066
  - name: best_isotropy
    type: isotropy
    value: 0.7965
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Urdu** 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** | 3.434x | 3.44 | 0.1597% | 2,494,826 |
| **16k** | 3.731x | 3.74 | 0.1735% | 2,296,340 |
| **32k** | 3.936x | 3.95 | 0.1830% | 2,176,646 |
| **64k** | 4.066x 🏆 | 4.08 | 0.1891% | 2,107,362 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `لائژوو چین کا ایک کاؤنٹی سطح شہر جو ژانگجیانگ میں واقع ہے۔ مزید دیکھیے چین فہرست...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁لائ ژ وو ▁چین ▁کا ▁ایک ▁کاؤنٹی ▁سطح ▁شہر ▁جو ... (+21 more)` | 31 |
| 16k | `▁لائ ژوو ▁چین ▁کا ▁ایک ▁کاؤنٹی ▁سطح ▁شہر ▁جو ▁ژ ... (+19 more)` | 29 |
| 32k | `▁لائ ژوو ▁چین ▁کا ▁ایک ▁کاؤنٹی ▁سطح ▁شہر ▁جو ▁ژانگ ... (+18 more)` | 28 |
| 64k | `▁لائ ژوو ▁چین ▁کا ▁ایک ▁کاؤنٹی ▁سطح ▁شہر ▁جو ▁ژانگ ... (+18 more)` | 28 |

**Sample 2:** `ساروی پاکستان کا ایک آباد مقام جو ضلع لاہور میں واقع ہے۔ مزید دیکھیے پاکستان پاک...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁سار وی ▁پاکستان ▁کا ▁ایک ▁آباد ▁مقام ▁جو ▁ضلع ▁لاہور ... (+16 more)` | 26 |
| 16k | `▁سار وی ▁پاکستان ▁کا ▁ایک ▁آباد ▁مقام ▁جو ▁ضلع ▁لاہور ... (+16 more)` | 26 |
| 32k | `▁سار وی ▁پاکستان ▁کا ▁ایک ▁آباد ▁مقام ▁جو ▁ضلع ▁لاہور ... (+16 more)` | 26 |
| 64k | `▁سار وی ▁پاکستان ▁کا ▁ایک ▁آباد ▁مقام ▁جو ▁ضلع ▁لاہور ... (+16 more)` | 26 |

**Sample 3:** `انڈونیشیا کی ثقافت سے مراد انڈونیشیا کا ثقافتی ورثہ ہے۔ حوالہ جات ثقافت مشرقی ای...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁انڈونیشیا ▁کی ▁ثقافت ▁سے ▁مراد ▁انڈونیشیا ▁کا ▁ثقافتی ▁ورثہ ▁ہے۔ ... (+6 more)` | 16 |
| 16k | `▁انڈونیشیا ▁کی ▁ثقافت ▁سے ▁مراد ▁انڈونیشیا ▁کا ▁ثقافتی ▁ورثہ ▁ہے۔ ... (+6 more)` | 16 |
| 32k | `▁انڈونیشیا ▁کی ▁ثقافت ▁سے ▁مراد ▁انڈونیشیا ▁کا ▁ثقافتی ▁ورثہ ▁ہے۔ ... (+6 more)` | 16 |
| 64k | `▁انڈونیشیا ▁کی ▁ثقافت ▁سے ▁مراد ▁انڈونیشیا ▁کا ▁ثقافتی ▁ورثہ ▁ہے۔ ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 64k achieves 4.066x compression
- **Lowest UNK Rate:** 8k with 0.1597% 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 | 71,880 | 16.13 | 920,952 | 12.1% | 28.0% |
| **2-gram** | Subword | 407 🏆 | 8.67 | 31,986 | 59.9% | 96.3% |
| **3-gram** | Word | 315,178 | 18.27 | 2,297,981 | 8.3% | 17.4% |
| **3-gram** | Subword | 3,547 | 11.79 | 203,673 | 25.5% | 63.2% |
| **4-gram** | Word | 765,780 | 19.55 | 4,319,755 | 7.4% | 14.2% |
| **4-gram** | Subword | 19,593 | 14.26 | 1,069,845 | 12.6% | 37.0% |
| **5-gram** | Word | 617,009 | 19.23 | 3,316,122 | 7.9% | 15.7% |
| **5-gram** | Subword | 75,628 | 16.21 | 3,267,447 | 7.4% | 25.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `کے لیے` | 246,197 |
| 2 | `حوالہ جات` | 212,286 |
| 3 | `واقع ہے` | 138,739 |
| 4 | `مزید دیکھیے` | 134,662 |
| 5 | `ہے اور` | 134,251 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `میں واقع ہے` | 98,697 |
| 2 | `ہے مزید دیکھیے` | 91,225 |
| 3 | `ریاستہائے متحدہ امریکا` | 75,905 |
| 4 | `شہر حوالہ جات` | 70,046 |
| 5 | `کے شہر حوالہ` | 69,949 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `کے شہر حوالہ جات` | 69,947 |
| 2 | `ڈیٹا سے مختلف مختصر` | 60,477 |
| 3 | `سے مختلف مختصر وضاحت` | 60,477 |
| 4 | `میں واقع ہے تفصیلات` | 57,274 |
| 5 | `واقع ہے مزید دیکھیے` | 56,176 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ڈیٹا سے مختلف مختصر وضاحت` | 60,477 |
| 2 | `مطابقت رکھنے والی مختصر تفصیل` | 36,597 |
| 3 | `ڈیٹا سے مطابقت رکھنے والی` | 36,597 |
| 4 | `سے مطابقت رکھنے والی مختصر` | 36,597 |
| 5 | `ریاستہائے متحدہ امریکا کا ایک` | 32,162 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ک` | 8,939,155 |
| 2 | `ے _` | 7,506,929 |
| 3 | `ی _` | 7,229,403 |
| 4 | `_ ا` | 6,895,736 |
| 5 | `_ م` | 5,580,612 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ی ں _` | 2,526,926 |
| 2 | `ک ے _` | 2,439,009 |
| 3 | `_ ک ے` | 2,399,929 |
| 4 | `_ ک ی` | 2,309,611 |
| 5 | `_ م ی` | 2,222,538 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ک ے _` | 2,395,195 |
| 2 | `م ی ں _` | 1,913,836 |
| 3 | `_ م ی ں` | 1,894,953 |
| 4 | `_ ک ی _` | 1,654,644 |
| 5 | `_ ا و ر` | 1,206,959 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ م ی ں _` | 1,841,071 |
| 2 | `_ ا و ر _` | 1,180,320 |
| 3 | `_ ا ی ک _` | 540,019 |
| 4 | `_ ہ ے ۔ _` | 533,595 |
| 5 | `ن _ ک ے _` | 281,812 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 407
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.7878 | 1.726 | 10.02 | 931,321 | 21.2% |
| **1** | Subword | 1.0778 | 2.111 | 8.71 | 12,123 | 0.0% |
| **2** | Word | 0.4142 | 1.333 | 2.63 | 9,325,685 | 58.6% |
| **2** | Subword | 0.7107 | 1.637 | 4.70 | 105,552 | 28.9% |
| **3** | Word | 0.2036 | 1.152 | 1.51 | 24,486,673 | 79.6% |
| **3** | Subword | 0.6567 | 1.576 | 3.92 | 496,416 | 34.3% |
| **4** | Word | 0.0977 🏆 | 1.070 | 1.19 | 36,918,721 | 90.2% |
| **4** | Subword | 0.6391 | 1.557 | 3.25 | 1,947,168 | 36.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `کے خلاف شمالی افریقی ارکان پارلیمنٹ جان جیکب آباد مقامات ڈیٹا سے قبل مسیح rishi 24`
2. `میں اس پر پہچان ایک وسیع تحقیق کی جاتی ہے اور دیگر نے بنا مزید دیکھیے`
3. `کی سپریم کورٹ سی پی سی اے حسینہ اور 626 0 126 نے مسترد کرتے ہوئے`

**Context Size 2:**

1. `کے لیے دو فرسٹ کلاس کرکٹ میں ان کی نمائندگی کرتے ہیں اور طنز کرتے اور حقانیت`
2. `حوالہ جات بیرونی روابط طرطلیان کا معما بنی ہوئی ایک ترقی یافتہ ڈویژن فور کے لیے حملہ`
3. `واقع ہے مزید دیکھیے لتھووینیا فہرست لتھووینیا کے نامکمل مضامین ڈیٹا سے مختلف مختصر وضاحت کی پیدائشیں`

**Context Size 3:**

1. `میں واقع ہے تفصیلات ییپچس ضلع کا رقبہ 53 944 مربع کلومیٹر ہے اس کی مجموعی آبادی 6`
2. `ہے مزید دیکھیے جرمنی کی ریاستیں 16 بھارت کی ریاستیں بلحاظ آبادی حوالہ جات میں قائم ہونے والے`
3. `ریاستہائے متحدہ امریکا ریاستہائے متحدہ امریکا کا ایک ٹاؤن شپ جو کلنٹن کاؤنٹی اوہائیو اوہائیو 61 310 ...`

**Context Size 4:**

1. `کے شہر حوالہ جات میں آباد ہونے والے مقامات ڈیٹا سے مختلف مختصر وضاحت کے آباد مقامات میں مرگ`
2. `ڈیٹا سے مختلف مختصر وضاحت مزاحیہ ڈراما فلمیں فلمیں متحدہ میں زنا کے بارے میں فلمیں فلمیں سے تخلیق`
3. `میں واقع ہے تفصیلات لا شاپیل این والگوڈیمار کا رقبہ 108 02 مربع کلومیٹر ہے اور اس کی مجموعی`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_16_دیکاس_مد_کے_`
2. `ا_اتھروساہے_لے۔_`
3. `یں_tad_ا_نیا_205`

**Context Size 2:**

1. `_کی_پان_ال_ہور_بر`
2. `ے_ان_میں_معا_مغرب`
3. `ی_ول_گار_پیدارکھی`

**Context Size 3:**

1. `یں_کا_کورپینیجرینڈ`
2. `کے_بلندیر_بِکری_علی`
3. `_کے_تھے۔_ابھ_انھوں`

**Context Size 4:**

1. `_کے_نتیجے_میں_واقع_`
2. `میں_جہاں_i_tehsil_w`
3. `_میں_وشون-شوگر_پار،`


### Key Findings

- **Best Predictability:** Context-4 (word) with 90.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,947,168 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 | 395,742 |
| Total Tokens | 58,544,950 |
| Mean Frequency | 147.94 |
| Median Frequency | 4 |
| Frequency Std Dev | 7177.12 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | کے | 2,399,956 |
| 2 | میں | 1,897,386 |
| 3 | کی | 1,727,992 |
| 4 | اور | 1,185,297 |
| 5 | ہے | 1,085,895 |
| 6 | سے | 991,149 |
| 7 | کا | 802,866 |
| 8 | نے | 660,570 |
| 9 | اس | 581,153 |
| 10 | پر | 570,105 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | yarns | 2 |
| 2 | anika | 2 |
| 3 | dailystar | 2 |
| 4 | دامنیوں | 2 |
| 5 | دریاچۂ | 2 |
| 6 | murgap | 2 |
| 7 | دیمقراطیت | 2 |
| 8 | الممتنعة | 2 |
| 9 | کرداراے | 2 |
| 10 | قیطابای | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1596 |
| R² (Goodness of Fit) | 0.989996 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 40.8% |
| Top 1,000 | 67.7% |
| Top 5,000 | 84.7% |
| Top 10,000 | 89.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9900 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 40.8% of corpus
- **Long Tail:** 385,742 words needed for remaining 10.1% 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 | 0.7965 🏆 | 0.3746 | N/A | N/A |
| **mono_64d** | 64 | 0.7804 | 0.3072 | N/A | N/A |
| **mono_128d** | 128 | 0.7411 | 0.2584 | N/A | N/A |
| **aligned_32d** | 32 | 0.7965 | 0.3667 | 0.0900 | 0.3980 |
| **aligned_64d** | 64 | 0.7804 | 0.3243 | 0.1900 | 0.5220 |
| **aligned_128d** | 128 | 0.7411 | 0.2599 | 0.2640 | 0.6360 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7965 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3152. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 26.4% 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 | **-0.387** | 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 |
|--------|----------|
| `-ال` | الازہار, الحسينی, الكرخی |
| `-ا` | الازہار, اعادی, اسکن |
| `-م` | موزولینی, مشہورہ, میلوم |
| `-ب` | بیٹاہے, بمبی, بدیشگرام |
| `-س` | سکھانے, سگاچے, سووموٹو |
| `-ک` | کورینتینے, کتابتِ, کٹمور |
| `-و` | وملل, وففینگے, وولڈز |
| `-ت` | تبصروں, تحس, ترسیلات |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ی` | نمامی, اعادی, بمبی |
| `-ا` | آئیڈیلا, چھیڈا, سنگڑا |
| `-ن` | اسکن, ڑککن, لعبدالرحمن |
| `-s` | anthonys, carpets, condoles |
| `-n` | usenon, areairon, bannerman |
| `-e` | linkage, lafitte, ampère |
| `-ں` | پنجابیوں, بیروتژاں, تبصروں |
| `-ر` | الازہار, کٹمور, خائر |

### 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 |
|------|----------|------------------|----------|
| `ھارت` | 2.29x | 63 contexts | ہھارت, پھارت, دھارت |
| `مریک` | 2.26x | 41 contexts | امریک, مریکی, مریکہ |
| `اؤنٹ` | 2.16x | 43 contexts | ماؤنٹ, گاؤنٹ, کاؤنٹ |
| `کاؤن` | 2.21x | 39 contexts | کاؤنا, کاؤنی, کاؤنٹ |
| `اریخ` | 1.86x | 54 contexts | فاریخ, تاریخ, تاریخٰ |
| `لاقو` | 2.48x | 18 contexts | علاقو, الاقو, لاقوۃ |
| `ھلاڑ` | 2.91x | 11 contexts | ڈھلاڑ, کھلاڑ, لھلاڑی |
| `اقوا` | 2.16x | 27 contexts | اقوام, جاقوا, اقوال |
| `ختلف` | 2.31x | 20 contexts | اختلف, يختلف, مختلف |
| `ختصر` | 2.07x | 23 contexts | اختصر, مختصر, مختصرا |
| `الاق` | 1.77x | 39 contexts | الاقو, الاقصي, الاقصى |
| `تحدہ` | 2.47x | 11 contexts | متحدہ, 1متحدہ, المتحدہ |

### 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 |
|--------|--------|-----------|----------|
| `-ال` | `-ی` | 59 words | النفیسی, الأولی |
| `-ا` | `-ا` | 45 words | اورلینزلوویزیانا, اماٹیلا |
| `-ا` | `-ی` | 43 words | انڈیانامیامی, النفیسی |
| `-س` | `-ی` | 35 words | سریمورالی, سیارچوی |
| `-ک` | `-ی` | 32 words | کندی, کولاتیری |
| `-ال` | `-ن` | 31 words | الوالدين, الیکزاندرپشکن |
| `-ال` | `-ہ` | 28 words | العربیہ, السیارہ |
| `-م` | `-ی` | 26 words | مہرؤلی, مورنسی |
| `-ب` | `-ی` | 24 words | بحیری, بریطانی |
| `-ا` | `-ن` | 23 words | ابوالرین, انبان |

### 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 |
|------|-----------------|------------|------|
| ایکسیلنسی | **`ایکسیلن-س-ی`** | 7.5 | `س` |
| ریٹروگریڈ | **`ریٹروگر-ی-ڈ`** | 7.5 | `ی` |
| گراؤنڈبیونس | **`گراؤنڈبیو-ن-س`** | 7.5 | `ن` |
| کوستنجویکانہ | **`کوستنجویک-ان-ہ`** | 7.5 | `ان` |
| اورتعلیمی | **`اور-تعلیم-ی`** | 6.0 | `تعلیم` |
| مالمزبیری | **`م-الم-زبیری`** | 6.0 | `زبیری` |
| composers | **`composer-s`** | 4.5 | `composer` |
| نصیرآبادی | **`نصیرآباد-ی`** | 4.5 | `نصیرآباد` |
| تھیوبالڈس | **`تھیوبالڈ-س`** | 4.5 | `تھیوبالڈ` |
| ہائیڈریٹس | **`ہائیڈریٹ-س`** | 4.5 | `ہائیڈریٹ` |
| پیرالمپکس | **`پیرالمپک-س`** | 4.5 | `پیرالمپک` |
| dwellings | **`dwelling-s`** | 4.5 | `dwelling` |
| violations | **`violation-s`** | 4.5 | `violation` |
| positional | **`position-al`** | 4.5 | `position` |
| oscillators | **`oscillator-s`** | 4.5 | `oscillator` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Urdu 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 (4.07x) |
| N-gram | **2-gram** | Lowest perplexity (407) |
| Markov | **Context-4** | Highest predictability (90.2%) |
| 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: 2026-01-11 06:46:29*