README.md

---
language: mzn
language_name: Mazanderani
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: 4.106
  - name: best_isotropy
    type: isotropy
    value: 0.8345
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Mazanderani** 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** | 3.411x | 3.42 | 0.3343% | 164,223 |
| **16k** | 3.703x | 3.71 | 0.3630% | 151,257 |
| **32k** | 3.941x | 3.95 | 0.3863% | 142,131 |
| **64k** | 4.106x 🏆 | 4.11 | 0.4024% | 136,417 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `۴ میلادی تقویم ره اتا سال هسته که قرن اول میلادی گِدر بی‌یه. دکته‌ئون بزائه‌ئون ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁۴ ▁میلادی ▁تقویم ▁ره ▁اتا ▁سال ▁هسته ▁که ▁قرن ▁اول ... (+13 more)` | 23 |
| 16k | `▁۴ ▁میلادی ▁تقویم ▁ره ▁اتا ▁سال ▁هسته ▁که ▁قرن ▁اول ... (+13 more)` | 23 |
| 32k | `▁۴ ▁میلادی ▁تقویم ▁ره ▁اتا ▁سال ▁هسته ▁که ▁قرن ▁اول ... (+13 more)` | 23 |
| 64k | `▁۴ ▁میلادی ▁تقویم ▁ره ▁اتا ▁سال ▁هسته ▁که ▁قرن ▁اول ... (+13 more)` | 23 |

**Sample 2:** `داوید لمایتر اتا خونش‌کر مردی هسته که بولیوی کشور شنه. دپیته چرخه‌تو اٮسپانیولی ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁دا وید ▁ل مای تر ▁اتا ▁خونش ▁کر ▁مردی ▁هسته ... (+14 more)` | 24 |
| 16k | `▁داوید ▁ل مای تر ▁اتا ▁خونش ▁کر ▁مردی ▁هسته ▁که ... (+13 more)` | 23 |
| 32k | `▁داوید ▁ل مای تر ▁اتا ▁خونش ▁کر ▁مردی ▁هسته ▁که ... (+13 more)` | 23 |
| 64k | `▁داوید ▁ل مای تر ▁اتا ▁خونش ▁کر ▁مردی ▁هسته ▁که ... (+13 more)` | 23 |

**Sample 3:** `غلیله اتا شهر نوم هسته که متحده عربی امارات کشور شنه و رأس‌الخیمه اوستان دله دره...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁غ لی له ▁اتا ▁شهر ▁نوم ▁هسته ▁که ▁متحده ▁عربی ... (+25 more)` | 35 |
| 16k | `▁غ لی له ▁اتا ▁شهر ▁نوم ▁هسته ▁که ▁متحده ▁عربی ... (+21 more)` | 31 |
| 32k | `▁غ لی له ▁اتا ▁شهر ▁نوم ▁هسته ▁که ▁متحده ▁عربی ... (+21 more)` | 31 |
| 64k | `▁غ لی له ▁اتا ▁شهر ▁نوم ▁هسته ▁که ▁متحده ▁عربی ... (+21 more)` | 31 |


### Key Findings

- **Best Compression:** 64k achieves 4.106x compression
- **Lowest UNK Rate:** 8k with 0.3343% 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 | 1,968 | 10.94 | 38,757 | 45.2% | 71.9% |
| **2-gram** | Subword | 298 🏆 | 8.22 | 7,046 | 69.1% | 97.1% |
| **3-gram** | Word | 2,369 | 11.21 | 52,894 | 41.8% | 71.1% |
| **3-gram** | Subword | 1,818 | 10.83 | 48,796 | 36.9% | 76.1% |
| **4-gram** | Word | 3,695 | 11.85 | 89,441 | 37.0% | 65.4% |
| **4-gram** | Subword | 6,187 | 12.60 | 209,004 | 25.9% | 58.2% |
| **5-gram** | Word | 4,502 | 12.14 | 83,447 | 33.5% | 61.7% |
| **5-gram** | Subword | 13,144 | 13.68 | 447,722 | 21.0% | 51.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `هسته که` | 52,733 |
| 2 | `دله دره` | 33,946 |
| 3 | `نوم هسته` | 28,820 |
| 4 | `و ونه` | 28,158 |
| 5 | `بی‌یه منابع` | 25,419 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `نوم هسته که` | 28,021 |
| 2 | `نفر بی‌یه منابع` | 22,845 |
| 3 | `آمریکای متحده ایالات` | 17,920 |
| 4 | `دله دره و` | 16,188 |
| 5 | `هسته که آمریکای` | 14,732 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `که آمریکای متحده ایالات` | 14,707 |
| 2 | `آمریکای متحده ایالات دله` | 14,703 |
| 3 | `هسته که آمریکای متحده` | 14,699 |
| 4 | `متحده ایالات دله دره` | 14,693 |
| 5 | `ایالات دله دره و` | 14,693 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `هسته که آمریکای متحده ایالات` | 14,699 |
| 2 | `که آمریکای متحده ایالات دله` | 14,695 |
| 3 | `متحده ایالات دله دره و` | 14,692 |
| 4 | `آمریکای متحده ایالات دله دره` | 14,692 |
| 5 | `که سرشماری گته ونه جمعیت` | 14,689 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ه _` | 698,566 |
| 2 | `_ ا` | 336,637 |
| 3 | `ن _` | 321,772 |
| 4 | `ی _` | 310,701 |
| 5 | `س ت` | 285,751 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ا ی` | 146,460 |
| 2 | `ه . _` | 142,947 |
| 3 | `ش ه ر` | 139,676 |
| 4 | `_ ش ه` | 138,829 |
| 5 | `_ و _` | 137,717 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ش ه ر` | 131,690 |
| 2 | `ه _ و _` | 104,983 |
| 3 | `_ د ل ه` | 104,893 |
| 4 | `_ ک ه _` | 101,332 |
| 5 | `_ ه س ت` | 98,369 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د ل ه _` | 96,373 |
| 2 | `_ ه س ت ه` | 95,332 |
| 3 | `ه س ت ه _` | 75,623 |
| 4 | `ه _ ک ه _` | 66,982 |
| 5 | `_ و ن ه _` | 65,930 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 298
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~51% 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 | 0.7718 | 1.707 | 5.36 | 136,033 | 22.8% |
| **1** | Subword | 1.0095 | 2.013 | 9.26 | 1,969 | 0.0% |
| **2** | Word | 0.2322 | 1.175 | 1.56 | 721,647 | 76.8% |
| **2** | Subword | 0.8667 | 1.823 | 5.64 | 18,228 | 13.3% |
| **3** | Word | 0.0688 | 1.049 | 1.15 | 1,114,822 | 93.1% |
| **3** | Subword | 0.7398 | 1.670 | 3.74 | 102,751 | 26.0% |
| **4** | Word | 0.0264 🏆 | 1.018 | 1.07 | 1,259,544 | 97.4% |
| **4** | Subword | 0.5692 | 1.484 | 2.56 | 383,834 | 43.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `و اینستاگرام درون واقع بَیی‌یه مرکز آمار پورتال منابع باغشاه محمد بن اسحاق نیوتن هسته و`
2. `دله دره جمعیت نفر هر اتا سیوا بیّن ایران آمارِ سرشماری گته ونه جمعیت اینتا دهستون`
3. `که سرشماری گته ونه جمیعت زیر سه خانوار بی‌یه منابع چشمه پچیک کوشکک هسته و دانشگائون`

**Context Size 2:**

1. `هسته که برونئی ِکشور بائه کارلا گیلبرتا برونی تدسکی به ایتالیایی firenze تلفظ فیرنتزه اتا از وشون`
2. `دله دره جمعیت اینتا روستا قشلاق شرقی دهستون شِنه و اینتی که سرشماری گته ونه جمعیت نفر`
3. `نوم هسته که مازرون اوستان میون جمِیهَت مردی نوم و نفر زنی نوم هستنه منابع مردی خونش‌کرون`

**Context Size 3:**

1. `نوم هسته که فرانسهِ آلپ ماریتیم دله دره اینتا شهر فروانیه استان دله هسته و این روز دله`
2. `نفر بی‌یه منابع شهرستان نیویورک شهر و روستائون en new york city متحده ایالات آمریکا دله اولین‌بار سه`
3. `آمریکای متحده ایالات دله دره و آیووا ایالت شنه این شهر ماریون شهرستان دله کـَته و سال میلادی`

**Context Size 4:**

1. `که آمریکای متحده ایالات دله دره و کلرادو ایالت شنه این شهر اوکلاند شهرستان دله کـَته و سال میلادی`
2. `آمریکای متحده ایالات دله دره و نیویورک ایالت شنه این شهر جانسون شهرستان دله کـَته و سال میلادی اینتی`
3. `هسته که آمریکای متحده ایالات دله دره و مونتانا ایالت شنه این شهر بنتون شهرستان دله کـَته و ونه`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_مالهستی_ین_سر_ش`
2. `اهسابخوانه،_بع_ب`
3. `ه_ش_ت_برس_مل_دلا`

**Context Size 2:**

1. `ه_و_اینه_سبکوم_هسّ`
2. `_ایالاد_ره_سر،_وش`
3. `ن_که_آمالت_ایر_گز`

**Context Size 3:**

1. `_این_زوون_موسیقی_ا`
2. `ه._اینتی_۲۳٫۸_کیلو`
3. `شهرون_روستان_ملی_ز`

**Context Size 4:**

1. `_شهرستان_دله_دنیا،_`
2. `ه_و_ونه_اتا_آمریکای`
3. `_دله_باتنه_کشورون_ف`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (383,834 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 | 62,931 |
| Total Tokens | 3,102,430 |
| Mean Frequency | 49.30 |
| Median Frequency | 3 |
| Frequency Std Dev | 1191.35 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | و | 138,138 |
| 2 | دله | 104,875 |
| 3 | که | 101,499 |
| 4 | هسته | 95,318 |
| 5 | ونه | 66,160 |
| 6 | اتا | 64,796 |
| 7 | منابع | 55,354 |
| 8 | شهرستان | 53,609 |
| 9 | ره | 47,333 |
| 10 | سال | 45,951 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | produced | 2 |
| 2 | crop | 2 |
| 3 | brandy | 2 |
| 4 | additive | 2 |
| 5 | planted | 2 |
| 6 | fuel | 2 |
| 7 | stem | 2 |
| 8 | blight | 2 |
| 9 | helianthi | 2 |
| 10 | alternaria | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1390 |
| R² (Goodness of Fit) | 0.998996 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 58.1% |
| Top 1,000 | 78.3% |
| Top 5,000 | 89.1% |
| Top 10,000 | 93.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9990 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 58.1% of corpus
- **Long Tail:** 52,931 words needed for remaining 7.0% 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 | 0.8345 🏆 | 0.3161 | N/A | N/A |
| **mono_64d** | 64 | 0.7563 | 0.2719 | N/A | N/A |
| **mono_128d** | 128 | 0.5078 | 0.2460 | N/A | N/A |
| **aligned_32d** | 32 | 0.8345 | 0.3171 | 0.0080 | 0.0520 |
| **aligned_64d** | 64 | 0.7563 | 0.2751 | 0.0140 | 0.1060 |
| **aligned_128d** | 128 | 0.5078 | 0.2372 | 0.0480 | 0.1780 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8345 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2772. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.8% 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 | **0.207** | 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` | ایازکندی, اسطوره‌شناسی, اینرهودن |
| `-م` | مملکتون, منچسترر, مونتنگرو |
| `-ب` | بقدرت, بدبده, بی‌بون |
| `-ک` | کوریبه, کومِک, کانده |
| `-س` | سیدروپولیس, سلستین, سِیمین |
| `-د` | دپوشیئن, دزاکور, دِرِس‌هاکردن |
| `-ت` | توله, توربین, تنگدشت |
| `-ن` | نوازنده, نهجیر, نِوشتنه |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ن` | دپوشیئن, صحرااسفنداران, ِنارنجستان |
| `-ی` | وشون‌های, ایازکندی, اسطوره‌شناسی |
| `-ا` | آلپرکاتا, چیپوا, قارن‌سرا |
| `-ون` | مملکتون, کنتون, بی‌بون |
| `-ه` | توله, نوازنده, کوریبه |
| `-ر` | دزاکور, نهجیر, منچسترر |
| `-و` | نووارو, مونتنگرو, مارلبورو |
| `-ان` | صحرااسفنداران, ِنارنجستان, روستاییان |

### 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 |
|------|----------|------------------|----------|
| `رستا` | 1.66x | 62 contexts | رستاق, هرستا, پرستار |
| `یران` | 1.55x | 72 contexts | هیران, حیران, میران |
| `ارنه` | 2.10x | 17 contexts | یارنه, نارنه, خارنه |
| `ینتا` | 1.77x | 29 contexts | یینتا, سینتا, هینتا |
| `روست` | 1.81x | 25 contexts | پروست, اروست, مروست |
| `اوست` | 1.80x | 20 contexts | اوستن, اوستش, اوستا |
| `ایال` | 1.88x | 16 contexts | ایالت, پایال, ایالات |
| `ومتر` | 2.05x | 10 contexts | سومتر, کلومتر, كیلومتر |
| `یالت` | 2.03x | 9 contexts | ایالت, یالتا, ِایالت |
| `اتنه` | 1.96x | 9 contexts | گاتنه, باتنه, ناتنه |
| `هستو` | 1.74x | 12 contexts | هستون, لهستون, بهستون |
| `لومت` | 2.01x | 8 contexts | کالومت, کلومتر, كیلومتر |

### 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` | 83 words | اینگلیسی, استارکی |
| `-ب` | `-ه` | 61 words | بمونه, بديه |
| `-ا` | `-ن` | 59 words | الدن, اسکشن |
| `-ب` | `-ن` | 50 words | بشناسن, بونان |
| `-م` | `-ی` | 50 words | ماهی, مهرابی |
| `-م` | `-ن` | 49 words | مزن, مالئون |
| `-ا` | `-ا` | 46 words | امانقلوا, اونیدا |
| `-ب` | `-ی` | 44 words | بازخوانی, بی‌طرفی |
| `-د` | `-ن` | 44 words | دیتن, دویین |
| `-ک` | `-ا` | 40 words | کلائودیا, کوروما |

### 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 |
|------|-----------------|------------|------|
| فیلسوف‌هایی | **`فیلسوف‌ه-ای-ی`** | 7.5 | `ای` |
| شهرکجفرسون | **`شهرکجفر-س-ون`** | 7.5 | `س` |
| زوون‌شناس | **`زوون‌ش-ن-اس`** | 7.5 | `ن` |
| اٮسپانیایی | **`اٮسپانیا-ی-ی`** | 7.5 | `ی` |
| کانزاس‌سیتی | **`کانزاس‌س-ی-تی`** | 7.5 | `ی` |
| پورفئیریو | **`پورفئیر-ی-و`** | 7.5 | `ی` |
| دانشجویان | **`دانشجو-ی-ان`** | 7.5 | `ی` |
| سرخپوستونی | **`سرخپوست-ون-ی`** | 6.0 | `سرخپوست` |
| ماکاپارانا | **`ما-کا-پارانا`** | 6.0 | `پارانا` |
| دوخانواری | **`دو-خانوار-ی`** | 6.0 | `خانوار` |
| هاکِردِنه | **`هاکِردِن-ه`** | 4.5 | `هاکِردِن` |
| والنزوئلا | **`و-ال-نزوئلا`** | 4.5 | `نزوئلا` |
| شانزدهمین | **`شانزدهم-ین`** | 4.5 | `شانزدهم` |
| جنوب‌وَری | **`جنوب‌وَر-ی`** | 4.5 | `جنوب‌وَر` |
| رییس‌جمهوری | **`رییس‌جمهور-ی`** | 4.5 | `رییس‌جمهور` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Mazanderani 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 (4.11x) |
| N-gram | **2-gram** | Lowest perplexity (298) |
| Markov | **Context-4** | Highest predictability (97.4%) |
| 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 14:36:37*