---
language: fa
language_name: Persian
language_family: iranian_western
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-iranian_western
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: 4.243
  - name: best_isotropy
    type: isotropy
    value: 0.8001
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-12
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Persian** 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** | 3.527x | 3.53 | 0.1283% | 3,130,017 |
| **16k** | 3.861x | 3.86 | 0.1405% | 2,859,317 |
| **32k** | 4.095x | 4.10 | 0.1490% | 2,696,153 |
| **64k** | 4.243x 🏆 | 4.24 | 0.1543% | 2,602,283 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ماتشووتسی یک منطقهٔ مسکونی در بلغارستان است که در تریاونا واقع شده‌است. جستارهای...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁مات شو وت سی ▁یک ▁منطقهٔ ▁مسکونی ▁در ▁بلغارستان ▁است ... (+23 more)` | 33 |
| 16k | `▁مات شو وت سی ▁یک ▁منطقهٔ ▁مسکونی ▁در ▁بلغارستان ▁است ... (+23 more)` | 33 |
| 32k | `▁مات شو وتسی ▁یک ▁منطقهٔ ▁مسکونی ▁در ▁بلغارستان ▁است ▁که ... (+21 more)` | 31 |
| 64k | `▁مات شو وتسی ▁یک ▁منطقهٔ ▁مسکونی ▁در ▁بلغارستان ▁است ▁که ... (+18 more)` | 28 |

**Sample 2:** `بیرم از شهرهای شهرستان لارستان در استان فارس ایران است. بیرم از روستاهای بخش خلی...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁بیرم ▁از ▁شهرهای ▁شهرستان ▁لارستان ▁در ▁استان ▁فارس ▁ایران ▁است ... (+24 more)` | 34 |
| 16k | `▁بیرم ▁از ▁شهرهای ▁شهرستان ▁لارستان ▁در ▁استان ▁فارس ▁ایران ▁است ... (+23 more)` | 33 |
| 32k | `▁بیرم ▁از ▁شهرهای ▁شهرستان ▁لارستان ▁در ▁استان ▁فارس ▁ایران ▁است ... (+22 more)` | 32 |
| 64k | `▁بیرم ▁از ▁شهرهای ▁شهرستان ▁لارستان ▁در ▁استان ▁فارس ▁ایران ▁است ... (+20 more)` | 30 |

**Sample 3:** `+اچ‌ام‌اس سوخه سوخه یک کشتی بود. منابع پادشاهی متحده در جنگ نیروی دریایی پادشاهی...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁+ اچ ▁ام ▁اس ▁سو خه ▁سو خه ▁یک ▁کشتی ... (+14 more)` | 24 |
| 16k | `▁+ اچ ▁ام ▁اس ▁سو خه ▁سو خه ▁یک ▁کشتی ... (+14 more)` | 24 |
| 32k | `▁+ اچ ▁ام ▁اس ▁سو خه ▁سو خه ▁یک ▁کشتی ... (+14 more)` | 24 |
| 64k | `▁+ اچ ▁ام ▁اس ▁سو خه ▁سو خه ▁یک ▁کشتی ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 4.243x compression
- **Lowest UNK Rate:** 8k with 0.1283% 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 | 183,630 | 17.49 | 3,336,831 | 10.3% | 24.0% |
| **2-gram** | Subword | 379 🏆 | 8.57 | 47,558 | 62.6% | 96.5% |
| **3-gram** | Word | 832,344 | 19.67 | 7,731,216 | 6.6% | 15.3% |
| **3-gram** | Subword | 3,487 | 11.77 | 356,084 | 24.3% | 63.9% |
| **4-gram** | Word | 1,844,924 | 20.82 | 13,689,983 | 5.8% | 13.6% |
| **4-gram** | Subword | 20,559 | 14.33 | 2,014,430 | 11.9% | 35.4% |
| **5-gram** | Word | 1,346,906 | 20.36 | 10,076,229 | 6.1% | 15.2% |
| **5-gram** | Subword | 88,433 | 16.43 | 6,647,245 | 7.0% | 22.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `که در` | 744,271 |
| 2 | `است که` | 697,906 |
| 3 | `در سال` | 661,273 |
| 4 | `ایالات متحده` | 589,928 |
| 5 | `متحده آمریکا` | 513,365 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ایالات متحده آمریکا` | 512,065 |
| 2 | `پیوند به بیرون` | 415,452 |
| 3 | `منابع پیوند به` | 379,528 |
| 4 | `است که در` | 319,325 |
| 5 | `اهل ایالات متحده` | 267,325 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `منابع پیوند به بیرون` | 379,441 |
| 2 | `اهل ایالات متحده آمریکا` | 266,562 |
| 3 | `جستارهای وابسته فهرست شهرهای` | 174,335 |
| 4 | `واقع شده‌است جستارهای وابسته` | 97,965 |
| 5 | `شده‌است جستارهای وابسته فهرست` | 92,488 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `واقع شده‌است جستارهای وابسته فهرست` | 91,004 |
| 2 | `شده‌است جستارهای وابسته فهرست شهرهای` | 90,657 |
| 3 | `منابع پیوند به بیرون گمر` | 86,274 |
| 4 | `پیوند به بیرون گمر شهرهای` | 85,065 |
| 5 | `فوتبال مرد دور از وطن` | 72,579 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ی _` | 28,243,898 |
| 2 | `_ ا` | 26,288,926 |
| 3 | `ه _` | 24,954,894 |
| 4 | `_ ب` | 20,887,663 |
| 5 | `ر _` | 20,421,774 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د ر` | 10,106,333 |
| 2 | `د ر _` | 9,224,307 |
| 3 | `ا ن _` | 8,509,406 |
| 4 | `ا ی _` | 7,222,284 |
| 5 | `_ و _` | 7,113,673 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د ر _` | 8,890,815 |
| 2 | `_ ب ه _` | 5,096,564 |
| 3 | `_ ا ز _` | 4,585,049 |
| 4 | `ه ا ی _` | 4,091,676 |
| 5 | `_ ا س ت` | 3,806,104 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ا ی ن _` | 2,178,073 |
| 2 | `ا س ت . _` | 1,832,058 |
| 3 | `س ت ا ن _` | 1,682,900 |
| 4 | `ه _ د ر _` | 1,583,560 |
| 5 | `ی _ د ر _` | 1,470,602 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 379
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.8548 | 1.809 | 13.21 | 2,678,882 | 14.5% |
| **1** | Subword | 1.3337 | 2.520 | 11.38 | 15,482 | 0.0% |
| **2** | Word | 0.4362 | 1.353 | 2.75 | 35,320,736 | 56.4% |
| **2** | Subword | 0.7134 | 1.640 | 4.92 | 176,248 | 28.7% |
| **3** | Word | 0.1895 | 1.140 | 1.46 | 96,895,216 | 81.1% |
| **3** | Subword | 0.6916 | 1.615 | 4.21 | 866,499 | 30.8% |
| **4** | Word | 0.0781 🏆 | 1.056 | 1.15 | 141,487,399 | 92.2% |
| **4** | Subword | 0.6685 | 1.589 | 3.49 | 3,645,685 | 33.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `در ایالات متحده آمریکا و کانادای ژاپنی‌تبار را بر پایه سرشماری مرکز ملی حزب جمهوری خلق`
2. `و شهرک‌ها در مورد حقد و در سال ادوارد آزبورن افشا می‌کند در مهد کلیسای سنت`
3. `به بیرون وب‌گاه الهام از مفاهیم کلی به یاد می‌شود در بمبئی وجود دارد که خطر`

**Context Size 2:**

1. `که در حوزه قضایی آن را به اجرا پرداخت جایی که پیام معاد خود را با گفتن`
2. `است که در آتش انداخته بود که روز فرا می‌رسد مردمانی که احتمالاً بیشترین اطلاعات را از`
3. `در سال خورشیدی در یازده سینما در فیلیسن در سلام سینما پایان مراحل به آموزش را نیز`

**Context Size 3:**

1. `ایالات متحده آمریکا بازی کرده‌است منابع پیوند به بیرون دانشگاه ملی تایوان جمهوری چین بر تایوان میلاد...`
2. `پیوند به بیرون درخت تجزیه منابع ویکی انگلیسی حشرات شیمیایی پیاده‌گردی شیمیایی خانگی آفت`
3. `منابع پیوند به بیرون خرد سنجاب جوندگان`

**Context Size 4:**

1. `منابع پیوند به بیرون گمر شهرهای ایتالیا و شهرک‌ها در ونتو استان پادوا گوتیک در ونتو`
2. `اهل ایالات متحده آمریکا زن فیلم صامت اهل ارمنستان زن فیلم اهل ارمنستان انستیتو دولتی هنری و نمایشی ا...`
3. `جستارهای وابسته فهرست شهرهای پرو منابع پیوند به بیرون سیارک در دادگان اجرام کوچک ناسا آسمانی کشف‌شده...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_راشدین_انهر_قا_`
2. `ار_کر_دروده_ستاب`
3. `ی_جه_ماز_–_جملوُر`

**Context Size 2:**

1. `ی_که_زنده_اقتل‌عا_`
2. `_اویه_همهٔ_ازده_ار`
3. `ه_داده_کمی_مان_گر`

**Context Size 3:**

1. `_در_ایتکامنی_ککوال`
2. `در_با_بر_ورزش_زوده`
3. `ان_محسوب_می‌کند._بس`

**Context Size 4:**

1. `_در_سوالاچیق،_ماه_م`
2. `_به_شهرستان_اضافه_ش`
3. `_از_سال_و_میدان_مسئ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (3,645,685 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 | 1,135,755 |
| Total Tokens | 210,116,418 |
| Mean Frequency | 185.00 |
| Median Frequency | 4 |
| Frequency Std Dev | 14539.94 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | در | 8,951,565 |
| 2 | و | 7,141,934 |
| 3 | به | 5,299,752 |
| 4 | از | 4,633,530 |
| 5 | که | 3,237,693 |
| 6 | است | 2,577,235 |
| 7 | را | 2,215,110 |
| 8 | این | 2,214,119 |
| 9 | با | 1,931,901 |
| 10 | یک | 1,432,476 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ناصربک | 2 |
| 2 | نساف | 2 |
| 3 | پاردائف | 2 |
| 4 | araviiskaia | 2 |
| 5 | berardesca | 2 |
| 6 | ویمشورست | 2 |
| 7 | نوک‌الکترودها | 2 |
| 8 | آلچیاتی | 2 |
| 9 | امبلماتا | 2 |
| 10 | دیلماما | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0967 |
| R² (Goodness of Fit) | 0.988576 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.5% |
| Top 1,000 | 61.6% |
| Top 5,000 | 80.0% |
| Top 10,000 | 86.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9886 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.5% of corpus
- **Long Tail:** 1,125,755 words needed for remaining 14.0% 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 | 0.8001 🏆 | 0.4045 | N/A | N/A |
| **mono_64d** | 64 | 0.7876 | 0.3078 | N/A | N/A |
| **mono_128d** | 128 | 0.7520 | 0.2408 | N/A | N/A |
| **aligned_32d** | 32 | 0.8001 | 0.4053 | 0.1940 | 0.6040 |
| **aligned_64d** | 64 | 0.7876 | 0.3077 | 0.3400 | 0.7420 |
| **aligned_128d** | 128 | 0.7520 | 0.2452 | 0.4980 | 0.8600 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8001 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3186. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 49.8% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.338** | 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 |
|--------|----------|
| `-ا` | استنزبری, ایواشوف, الفهری |
| `-م` | ملاکین, مينرالي, مهدیست‌ها |
| `-ال` | الفهری, السِّنینَ, القیود |
| `-ب` | بلوتوس, بوفالوشهر, برخی‌تبار |
| `-ت` | تویت, تعطيلات, تی‌تی‌پی |
| `-با` | باشگاهش, باغکاری, بادالگاچی |
| `-ک` | کاسانی, کرایچگو, کوسونوکی |
| `-س` | سکایی, سنگ‌دژ, سدۀ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ی` | استنزبری, کاسانی, پورتیشی |
| `-ن` | نداپلاتین, ملاکین, پاستوریزه‌کردن |
| `-ا` | قدیموا, آنامادووا, هاسلاوا |
| `-ای` | فون‌های, غزل‌های, جوشانده‌ای |
| `-ان` | پلاتهکونمبولقهرمان, گل‌سان, دنیاداران |
| `-ه` | دیوسه, ورازده, استودله |
| `-ها` | مهدیست‌ها, شکنجه‌گرها, دوده‌ها |
| `-ر` | بوفالوشهر, شغار, ۴۴۰هزار |

### 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 |
|------|----------|------------------|----------|
| `اشگا` | 2.96x | 41 contexts | اشگاه, باشگا, باشگال |
| `باشگ` | 2.67x | 48 contexts | باشگه, باشگل, باشگا |
| `تحده` | 2.61x | 43 contexts | متحده, متحدهٔ, متحدهچ |
| `انشگ` | 2.62x | 38 contexts | انشگاه, دانشگا, رانشگر |
| `مپیک` | 2.77x | 30 contexts | امپیک, تمپیکو, المپیک |
| `نشگا` | 2.75x | 30 contexts | انشگاه, تنشگاه, دانشگا |
| `یلاد` | 2.19x | 70 contexts | گیلاد, ایلاد, نیلاد |
| `شهرس` | 2.26x | 58 contexts | شهرسپ, شهرست, شهرسب |
| `تفاد` | 2.66x | 29 contexts | انتفاد, ستفاده, استفاد |
| `یتال` | 1.72x | 168 contexts | ایتال, خیتال, آیتال |
| `فاده` | 2.56x | 30 contexts | افاده, اسفاده, ستفاده |
| `تلوی` | 2.22x | 35 contexts | تلوین, اتلوی, تلوید |

### 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` | `-ی` | 117 words | الجزیره‌ای, استیشنی |
| `-م` | `-ی` | 95 words | مانچویی, مغالطه‌ی |
| `-ا` | `-ا` | 74 words | ازینوا, اوریساهارا |
| `-ا` | `-ن` | 69 words | اوتیچیان, ازروحانیون |
| `-ب` | `-ی` | 68 words | ب‍ال‍ی‍ن‍ی, بیخبری |
| `-ت` | `-ی` | 63 words | ترویانی, توپ‌بازی |
| `-ک` | `-ی` | 61 words | کژکارکردی, کاردستی |
| `-م` | `-ن` | 60 words | مالک‌شدن, مورمحمدخان |
| `-م` | `-ا` | 58 words | موتسا, میتکیانا |
| `-ک` | `-ا` | 57 words | کولاگینا, کورولوندیا |

### 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 |
|------|-----------------|------------|------|
| جواهرکلام | **`جواهرکل-ا-م`** | 7.5 | `ا` |
| دسانگتوایس | **`دسانگتو-ای-س`** | 7.5 | `ای` |
| درپیرعباس | **`درپیرعب-ا-س`** | 7.5 | `ا` |
| امان‌بایف | **`امان‌ب-ای-ف`** | 7.5 | `ای` |
| فایده‌گرایی | **`فایده‌گر-ای-ی`** | 7.5 | `ای` |
| دروه‌هایی | **`دروه‌ه-ای-ی`** | 7.5 | `ای` |
| کلاسیک‌گرا | **`کلاسیک‌گ-ر-ا`** | 7.5 | `ر` |
| فاحشه‌هایی | **`فاحشه‌ه-ای-ی`** | 7.5 | `ای` |
| ماردریایی | **`ماردری-ای-ی`** | 7.5 | `ای` |
| همرقص‌هایت | **`همرقص‌ه-ای-ت`** | 7.5 | `ای` |
| بازنگری‌هایی | **`بازنگری‌ه-ای-ی`** | 7.5 | `ای` |
| فراکسیون‌هایی | **`فراکسیون‌ه-ای-ی`** | 7.5 | `ای` |
| سودرکولای | **`سودرکو-ل-ای`** | 7.5 | `ل` |
| دیتمارهامان | **`دیتمارها-م-ان`** | 7.5 | `م` |
| واختنهایم | **`واختنه-ای-م`** | 7.5 | `ای` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Persian 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 (4.24x) |
| N-gram | **2-gram** | Lowest perplexity (379) |
| Markov | **Context-4** | Highest predictability (92.2%) |
| 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: 2026-01-12 22:54:37*