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README.md

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+---
+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*

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