---
language: glk
language_name: Gilaki
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: 3.924
  - name: best_isotropy
    type: isotropy
    value: 0.7395
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-09
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Gilaki** 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** | 3.040x | 3.04 | 0.8455% | 224,022 |
| **16k** | 3.382x | 3.39 | 0.9407% | 201,331 |
| **32k** | 3.692x | 3.70 | 1.0270% | 184,426 |
| **64k** | 3.924x 🏆 | 3.93 | 1.0915% | 173,524 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `تولد من هست در جریان باشید😅 ایتفاقان تولدان مرگان توشکه رده : سیا ما روزان رده:ت...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁تول د ▁من ▁هست ▁در ▁ج ریان ▁باش ید 😅 ... (+16 more)` | 26 |
| 16k | `▁تولد ▁من ▁هست ▁در ▁ج ریان ▁باش ید 😅 ▁ایتفاقان ... (+15 more)` | 25 |
| 32k | `▁تولد ▁من ▁هست ▁در ▁جریان ▁باشید 😅 ▁ایتفاقان ▁تولدان ▁مرگان ... (+13 more)` | 23 |
| 64k | `▁تولد ▁من ▁هست ▁در ▁جریان ▁باشید 😅 ▁ایتفاقان ▁تولدان ▁مرگان ... (+13 more)` | 23 |

**Sample 2:** `کیاسرا ایسم ایته جی روستاهان لفمجان دهستان ، لاجان شهرستان مرکزی بخش ایسه اوستان...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁کی اسرا ▁ایسم ▁ایته ▁جی ▁روستاهان ▁لفمجان ▁دهستان ▁، ▁لاجان ... (+11 more)` | 21 |
| 16k | `▁کی اسرا ▁ایسم ▁ایته ▁جی ▁روستاهان ▁لفمجان ▁دهستان ▁، ▁لاجان ... (+11 more)` | 21 |
| 32k | `▁کی اسرا ▁ایسم ▁ایته ▁جی ▁روستاهان ▁لفمجان ▁دهستان ▁، ▁لاجان ... (+11 more)` | 21 |
| 64k | `▁کیاسرا ▁ایسم ▁ایته ▁جی ▁روستاهان ▁لفمجان ▁دهستان ▁، ▁لاجان ▁شهرستان ... (+10 more)` | 20 |

**Sample 3:** `بیلاژ محله ایسم ایته جی روستاهان آهندان دهستان ، لاجان شهرستان مرکزی بخش ایسه او...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁بی لا ژ ▁محله ▁ایسم ▁ایته ▁جی ▁روستاهان ▁آهندان ▁دهستان ... (+13 more)` | 23 |
| 16k | `▁بی لا ژ ▁محله ▁ایسم ▁ایته ▁جی ▁روستاهان ▁آهندان ▁دهستان ... (+13 more)` | 23 |
| 32k | `▁بیلا ژ ▁محله ▁ایسم ▁ایته ▁جی ▁روستاهان ▁آهندان ▁دهستان ▁، ... (+12 more)` | 22 |
| 64k | `▁بیلا ژ ▁محله ▁ایسم ▁ایته ▁جی ▁روستاهان ▁آهندان ▁دهستان ▁، ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 3.924x compression
- **Lowest UNK Rate:** 8k with 0.8455% 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 | 452 | 8.82 | 22,372 | 68.3% | 84.5% |
| **2-gram** | Subword | 289 🏆 | 8.17 | 5,138 | 70.6% | 97.4% |
| **3-gram** | Word | 859 | 9.75 | 38,047 | 59.7% | 79.2% |
| **3-gram** | Subword | 1,264 | 10.30 | 39,676 | 47.4% | 79.1% |
| **4-gram** | Word | 1,740 | 10.76 | 75,476 | 51.1% | 71.1% |
| **4-gram** | Subword | 3,145 | 11.62 | 166,775 | 39.8% | 68.3% |
| **5-gram** | Word | 2,593 | 11.34 | 80,402 | 46.0% | 65.5% |
| **5-gram** | Subword | 5,057 | 12.30 | 329,311 | 36.7% | 64.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ٚ مئن` | 95,400 |
| 2 | `أ شأر` | 62,694 |
| 3 | `ٚ شأرستان` | 56,570 |
| 4 | `شأرستان ٚ` | 49,032 |
| 5 | `ايسه گه` | 41,300 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ٚ مئن نهأ` | 40,846 |
| 2 | `شأرستان ٚ مئن` | 36,418 |
| 3 | `ايته جه آمريکا` | 34,104 |
| 4 | `ٚ شأرستان ٚ` | 33,251 |
| 5 | `شأران ايسه گه` | 31,561 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `شأرستان ٚ مئن نهأ` | 36,381 |
| 2 | `ٚ مئن نهأ ؤ` | 31,068 |
| 3 | `آمريکا آمار ٚ مرکز` | 31,056 |
| 4 | `ؤ آمريکا آمار ٚ` | 31,054 |
| 5 | `نفر اعلام بۊگۊده سربس` | 31,054 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ؤ آمريکا آمار ٚ مرکز` | 31,054 |
| 2 | `نهأ ؤ آمريکا آمار ٚ` | 31,053 |
| 3 | `ٚ مئن نهأ ؤ آمريکا` | 31,053 |
| 4 | `شأرستان ٚ مئن نهأ ؤ` | 31,051 |
| 5 | `مئن نهأ ؤ آمريکا آمار` | 31,051 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ا ن` | 344,074 |
| 2 | `_ٚ _` | 304,817 |
| 3 | `ه _` | 274,936 |
| 4 | `_ ش` | 270,095 |
| 5 | `_ ا` | 227,254 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ش أ` | 217,137 |
| 2 | `ش أ ر` | 216,916 |
| 3 | `س ت ا` | 152,303 |
| 4 | `_ٚ _ م` | 132,016 |
| 5 | `ت ا ن` | 125,309 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ش أ ر` | 216,867 |
| 2 | `س ت ا ن` | 123,160 |
| 3 | `ا ن _ٚ _` | 107,779 |
| 4 | `_ م ئ ن` | 103,927 |
| 5 | `_ٚ _ م ئ` | 95,459 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ٚ _ م ئ ن` | 95,452 |
| 2 | `ر س ت ا ن` | 92,229 |
| 3 | `ش أ ر س ت` | 87,042 |
| 4 | `أ ر س ت ا` | 87,041 |
| 5 | `_ ش أ ر س` | 87,035 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 289
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~65% 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 | 0.5992 | 1.515 | 3.83 | 109,448 | 40.1% |
| **1** | Subword | 1.2417 | 2.365 | 11.40 | 995 | 0.0% |
| **2** | Word | 0.1612 | 1.118 | 1.39 | 416,225 | 83.9% |
| **2** | Subword | 1.0373 | 2.052 | 6.72 | 11,334 | 0.0% |
| **3** | Word | 0.0547 | 1.039 | 1.14 | 571,714 | 94.5% |
| **3** | Subword | 0.7917 | 1.731 | 3.86 | 76,144 | 20.8% |
| **4** | Word | 0.0260 🏆 | 1.018 | 1.09 | 645,056 | 97.4% |
| **4** | Subword | 0.5603 | 1.475 | 2.44 | 293,705 | 44.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ٚ سر أ شأر دۊئل ٚ مرکز سال تومامه به اۊ زمت که گرم شاهندشت قلعه`
2. `أ ۱ ۲۳۶ نفر مردأکان ۰ خانوار ۶۰۵ نفر اعلام بۊگۊده سربس شأرستان ٚ جمعيت أ`
3. `مئن clark ايته جه ايصفهان ٚ اۊستان ٚ جمعيت أ شأر لاریمر ٚ مرکز آمار ٚ`

**Context Size 2:**

1. `ٚ مئن نهأ ؤ آمريکا آمار ٚ مرکز سال ٚ مئن farley ايته جه آمريکا شأران ايسه`
2. `أ شأر ٚ جمعيت ۸ ۷۱۰ نفر ۲ ۹۰۶ خانوار بۊ عنوان نتایج سرشماری عمومی نفوس و`
3. `ٚ شأرستان آیؤوا شأران en pena pobre puerto rico ايته جه آمريکا شأران ايسه گه نطنز ٚ`

**Context Size 3:**

1. `ٚ مئن نهأ ؤ آمريکا آمار ٚ مرکز أ شأر ٚ جمعيت أ ۳۵۲ نفر اعلام بۊگۊده سربس`
2. `شأرستان ٚ مئن نهأ ؤ آمريکا آمار ٚ مرکز أ شأر ٚ جمعيت أ نفر اعلام بۊگۊده سربس`
3. `ايته جه آمريکا شأرستانان ايسه گه اينديانا شينه أ شأر بیر ٚ شأرستان ٚ مئن نهأ ؤ آمريکا`

**Context Size 4:**

1. `شأرستان ٚ مئن نهأ ؤ آمريکا آمار ٚ مرکز أ شأر ٚ جمعيت أ ۷۹ نفر اعلام بۊگۊده سربس`
2. `ٚ مئن نهأ ؤ آمريکا آمار ٚ مرکز أ شأر ٚ جمعيت أ ۸۹ نفر اعلام بۊگۊده سربس ٚ`
3. `آمريکا آمار ٚ مرکز سال ٚ مئن أ شأر ٚ جمعيت أ نفر اعلام بۊگۊده سربس ٚ شأرستان اؤکلاهؤما`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ته_آم_گهر_ٚ_(معي`
2. `ایکز_بای_نه._(اد`
3. `ن_زوستؤر_زوامیتا`

**Context Size 2:**

1. `ان_(ايسه_ده._سربس`
2. `_ٚ_مار_ٚ_مئن_گه_گه_`
3. `ه_کي_شأر_هم_بۊ_ۊ_`

**Context Size 3:**

1. `_شأرستان_ٚ_مرکز،_سا`
2. `شأرستان_ايته_جه_آم`
3. `ستان_ٚ_مئن_نهأ_ؤ_آم`

**Context Size 4:**

1. `_شأر_ايشماردن_جه_آم`
2. `ستان_ٚ_مئن_نهأ_ؤ_آمر`
3. `ان_ٚ_مئن_نهأ_ؤ_آمريک`


### 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 (293,705 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 | 46,285 |
| Total Tokens | 2,415,643 |
| Mean Frequency | 52.19 |
| Median Frequency | 3 |
| Frequency Std Dev | 1903.39 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ٚ | 304,843 |
| 2 | أ | 119,882 |
| 3 | مئن | 103,681 |
| 4 | شأرستان | 80,615 |
| 5 | شأر | 66,303 |
| 6 | آمريکا | 65,573 |
| 7 | شأران | 63,407 |
| 8 | ايسه | 56,161 |
| 9 | جه | 56,023 |
| 10 | ؤ | 55,643 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | سبزان | 2 |
| 2 | بۊلغاران | 2 |
| 3 | استعمارکۊنان | 2 |
| 4 | بامؤييد | 2 |
| 5 | آلفؤنسؤ | 2 |
| 6 | ميناب | 2 |
| 7 | بحرين | 2 |
| 8 | قطيف | 2 |
| 9 | واسکؤ | 2 |
| 10 | گاما | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0546 |
| R² (Goodness of Fit) | 0.992625 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 74.1% |
| Top 1,000 | 84.7% |
| Top 5,000 | 91.8% |
| Top 10,000 | 94.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9926 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 74.1% of corpus
- **Long Tail:** 36,285 words needed for remaining 5.2% 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 | 0.7395 | 0.3894 | N/A | N/A |
| **mono_64d** | 64 | 0.5770 | 0.3519 | N/A | N/A |
| **mono_128d** | 128 | 0.2174 | 0.3507 | N/A | N/A |
| **aligned_32d** | 32 | 0.7395 🏆 | 0.3921 | 0.0080 | 0.0960 |
| **aligned_64d** | 64 | 0.5770 | 0.3499 | 0.0280 | 0.2120 |
| **aligned_128d** | 128 | 0.2174 | 0.3609 | 0.0600 | 0.2880 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7395 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3658. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 6.0% 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 | **0.010** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ان` | أتابکيان, کوهبنان, دوشمنان |

### 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 |
|------|----------|------------------|----------|
| `ستان` | 1.38x | 183 contexts | آستان, دستان, استان |
| `یران` | 1.53x | 48 contexts | هیران, میران, ایران |
| `وستا` | 1.47x | 46 contexts | کوستا, اوستا, روستا |
| `رستا` | 1.36x | 61 contexts | رستاق, پرستان, رستاقˇ |
| `انان` | 1.58x | 29 contexts | سانان, بانان, خانان |
| `روست` | 1.53x | 17 contexts | مروست, روستا, بروستر |
| `اوست` | 1.66x | 13 contexts | اوستا, اوستاد, اوستان |
| `ۊستا` | 1.35x | 23 contexts | اۊستا, رۊستا, گۊستاو |
| `انوا` | 1.63x | 12 contexts | انواع, انوارˇ, خانوار |
| `ايال` | 1.64x | 8 contexts | ايالت, ايالات, ايالته |
| `رۊست` | 1.54x | 9 contexts | رۊستا, رۊستم, برۊستن |
| `يالت` | 1.69x | 7 contexts | ايالت, ايالته, ايالتˇ |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| وایکینگان | **`وایکینگ-ان`** | 4.5 | `وایکینگ` |
| بازيکؤنان | **`بازيکؤن-ان`** | 4.5 | `بازيکؤن` |
| هخامنشيان | **`هخامنشي-ان`** | 4.5 | `هخامنشي` |
| ویراستاران | **`ویراستار-ان`** | 4.5 | `ویراستار` |
| استانداردان | **`استاندارد-ان`** | 4.5 | `استاندارد` |
| کیشاورزان | **`کیشاورز-ان`** | 4.5 | `کیشاورز` |
| انقلابیان | **`انقلابی-ان`** | 4.5 | `انقلابی` |
| خاندنکسان | **`خاندنکس-ان`** | 4.5 | `خاندنکس` |
| دموکراتان | **`دموکرات-ان`** | 4.5 | `دموکرات` |
| دانشجویان | **`دانشجوی-ان`** | 4.5 | `دانشجوی` |
| اؤتريشيان | **`اؤتريشي-ان`** | 4.5 | `اؤتريشي` |
| هونرمندان | **`هونرمند-ان`** | 4.5 | `هونرمند` |
| کامپیوتران | **`کامپیوتر-ان`** | 4.5 | `کامپیوتر` |
| موهاجرتان | **`موهاجرت-ان`** | 4.5 | `موهاجرت` |
| بیمارستانان | **`بیمارست-ان-ان`** | 3.0 | `بیمارست` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Gilaki 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 (3.92x) |
| N-gram | **2-gram** | Lowest perplexity (289) |
| 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: 2026-01-09 23:47:34*