---
language: ckb
language_name: Central Kurdish
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: 4.804
  - name: best_isotropy
    type: isotropy
    value: 0.8085
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

# Central Kurdish - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Central Kurdish** 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** | 3.742x | 3.74 | 0.0597% | 899,331 |
| **16k** | 4.157x | 4.16 | 0.0663% | 809,551 |
| **32k** | 4.517x | 4.52 | 0.0721% | 745,101 |
| **64k** | 4.804x 🏆 | 4.80 | 0.0766% | 700,630 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `پیشوا () شارێکە لە پارێزگای تاران، ئێران. ئەمانەش ببینە پێڕستی شارەکانی ئێران پێ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁پیش وا ▁() ▁شارێکە ▁لە ▁پارێزگای ▁تاران ، ▁ئێران . ... (+12 more)` | 22 |
| 16k | `▁پیش وا ▁() ▁شارێکە ▁لە ▁پارێزگای ▁تاران ، ▁ئێران . ... (+12 more)` | 22 |
| 32k | `▁پیش وا ▁() ▁شارێکە ▁لە ▁پارێزگای ▁تاران ، ▁ئێران . ... (+12 more)` | 22 |
| 64k | `▁پیش وا ▁() ▁شارێکە ▁لە ▁پارێزگای ▁تاران ، ▁ئێران . ... (+12 more)` | 22 |

**Sample 2:** `پەنەما نەتەوەیەکی بەشداربووی ئۆڵۆمپیادی ھاوینەی بوو کە لە ١٧ی ئایار تا ١٢ی ئابی ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁پەن ەم ا ▁نەتەوەیەکی ▁بەشداربووی ▁ئۆڵۆمپیادی ▁ھاوینەی ▁بوو ▁کە ▁لە ... (+20 more)` | 30 |
| 16k | `▁پەنەما ▁نەتەوەیەکی ▁بەشداربووی ▁ئۆڵۆمپیادی ▁ھاوینەی ▁بوو ▁کە ▁لە ▁١٧ی ▁ئایار ... (+14 more)` | 24 |
| 32k | `▁پەنەما ▁نەتەوەیەکی ▁بەشداربووی ▁ئۆڵۆمپیادی ▁ھاوینەی ▁بوو ▁کە ▁لە ▁١٧ی ▁ئایار ... (+14 more)` | 24 |
| 64k | `▁پەنەما ▁نەتەوەیەکی ▁بەشداربووی ▁ئۆڵۆمپیادی ▁ھاوینەی ▁بوو ▁کە ▁لە ▁١٧ی ▁ئایار ... (+14 more)` | 24 |

**Sample 3:** `بێثێل () شارێکە دەکەوێتە ویلایەتی ئالاسکا، ئەمریکا. ژمارەی دانیشتووانی بەپێی سەر...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁بێ ث ێل ▁() ▁شارێکە ▁دەکەوێتە ▁ویلایەتی ▁ئالاسکا ، ▁ئەمریکا ... (+18 more)` | 28 |
| 16k | `▁بێ ث ێل ▁() ▁شارێکە ▁دەکەوێتە ▁ویلایەتی ▁ئالاسکا ، ▁ئەمریکا ... (+18 more)` | 28 |
| 32k | `▁بێ ث ێل ▁() ▁شارێکە ▁دەکەوێتە ▁ویلایەتی ▁ئالاسکا ، ▁ئەمریکا ... (+18 more)` | 28 |
| 64k | `▁بێ ث ێل ▁() ▁شارێکە ▁دەکەوێتە ▁ویلایەتی ▁ئالاسکا ، ▁ئەمریکا ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 4.804x compression
- **Lowest UNK Rate:** 8k with 0.0597% 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 | 43,391 | 15.41 | 224,985 | 11.6% | 28.8% |
| **2-gram** | Subword | 307 🏆 | 8.26 | 12,264 | 66.4% | 97.8% |
| **3-gram** | Word | 66,250 | 16.02 | 298,666 | 10.5% | 25.9% |
| **3-gram** | Subword | 2,476 | 11.27 | 92,875 | 29.2% | 70.6% |
| **4-gram** | Word | 100,774 | 16.62 | 472,614 | 10.7% | 24.7% |
| **4-gram** | Subword | 13,099 | 13.68 | 482,188 | 14.0% | 42.0% |
| **5-gram** | Word | 72,668 | 16.15 | 353,585 | 11.8% | 27.3% |
| **5-gram** | Subword | 47,108 | 15.52 | 1,228,808 | 7.9% | 26.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `لە ساڵی` | 47,065 |
| 2 | `کە لە` | 28,992 |
| 3 | `و لە` | 26,652 |
| 4 | `بەستەرە دەرەکییەکان` | 19,291 |
| 5 | `سەرچاوەکان بەستەرە` | 17,555 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `سەرچاوەکان بەستەرە دەرەکییەکان` | 17,516 |
| 2 | `دەستی بە چالاکی` | 7,882 |
| 3 | `لە دەستی بە` | 7,873 |
| 4 | `بە چالاکی کردووە` | 7,857 |
| 5 | `ئەمریکییەکانی سەدەی ٢٠ەم` | 7,760 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `دەستی بە چالاکی کردووە` | 7,857 |
| 2 | `لە دەستی بە چالاکی` | 7,838 |
| 3 | `کردووە سەرچاوەکان بەستەرە دەرەکییەکان` | 6,699 |
| 4 | `پیاوە ئەمریکییەکانی سەدەی ٢٠ەم` | 6,045 |
| 5 | `ئەمریکییە لە دەستی بە` | 5,227 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `لە دەستی بە چالاکی کردووە` | 7,827 |
| 2 | `ئەمریکییە لە دەستی بە چالاکی` | 5,227 |
| 3 | `ئەکتەرێکی ئەمریکییە لە دەستی بە` | 5,224 |
| 4 | `چالاکی کردووە سەرچاوەکان بەستەرە دەرەکییەکان` | 4,624 |
| 5 | `دەستی بە چالاکی کردووە سەرچاوەکان` | 4,624 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ی _` | 3,411,049 |
| 2 | `ە _` | 1,937,601 |
| 3 | `ا ن` | 1,774,322 |
| 4 | `_ ب` | 1,264,353 |
| 5 | `ە ک` | 1,085,531 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ل ە` | 875,397 |
| 2 | `ن ی _` | 698,413 |
| 3 | `ل ە _` | 639,579 |
| 4 | `ا ن ی` | 592,978 |
| 5 | `_ ب ە` | 565,735 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ل ە _` | 625,605 |
| 2 | `ە ک ا ن` | 467,335 |
| 3 | `ا ن ی _` | 454,442 |
| 4 | `ک ا ن _` | 226,640 |
| 5 | `ک ا ن ی` | 214,980 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ە ک ا ن _` | 217,466 |
| 2 | `ک ا ن ی _` | 198,040 |
| 3 | `ە ک ا ن ی` | 193,300 |
| 4 | `ی ە ک ا ن` | 146,991 |
| 5 | `ی ی ە ک ا` | 135,823 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 307
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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 | 0.8150 | 1.759 | 7.19 | 625,283 | 18.5% |
| **1** | Subword | 1.1771 | 2.261 | 7.84 | 5,867 | 0.0% |
| **2** | Word | 0.2642 | 1.201 | 1.74 | 4,486,871 | 73.6% |
| **2** | Subword | 0.7063 | 1.632 | 4.63 | 46,011 | 29.4% |
| **3** | Word | 0.0868 | 1.062 | 1.16 | 7,800,583 | 91.3% |
| **3** | Subword | 0.7560 | 1.689 | 4.12 | 212,847 | 24.4% |
| **4** | Word | 0.0293 🏆 | 1.021 | 1.05 | 9,049,668 | 97.1% |
| **4** | Subword | 0.6434 | 1.562 | 2.94 | 877,504 | 35.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `لە ئۆڵۆمپیادی زستانەی پێکھاتووە لە ساڵی لەلایەن ھێربێرت بێرگ لە ڕۆژھەڵاتی ویلایەتە یەکگرتووەکان کە پ...`
2. `و تا ٤ی حوزەیرانی لە ١٩ی ئەیلوولی لە بەردەم ماڵەکەی دەسووتێ و بەم شێوەیەن و بنچینەکانی`
3. `بە ڕەچەڵەک هەنگاری یانۆس پرۆھاسکا ١٠ی ئەیلوولی بەنەخۆشی لە سەر ڕێڕەوەکە لە ڕێشە وشەی بە زمانی`

**Context Size 2:**

1. `لە ساڵی مەحموود پاشا ناردی بۆ لای خوا ڕاکێشێت پیاوێک ھەبوو کە لە ئەڵمانیا دانراون فیلمانەی لە`
2. `کە لە ئاشەکاندا بۆ ھاڕینەوەی گەنم بە کار دەھێنن ئەمەش سوود لە باروودۆخی کوژرانی خۆپیشاندەرانی کورد ک...`
3. `و لە ساڵی دروستکراوە و کارەکتەری ھونەریەکەی بە جەنەڕاڵی شانۆی کوردی سقز یەکێک لە خودایانی ھیندووەکان...`

**Context Size 3:**

1. `سەرچاوەکان بەستەرە دەرەکییەکان فیلمە پیاوە ئەمریکییەکان تەلەڤیزیۆنی پیاوی ئەمریکی نێرەکانی کۆلۆرادۆ ...`
2. `دەستی بە چالاکی کردووە بەشداریی لە فیلمی ٣٠ ڕۆژ لە شەو و ڕۆژێکدا تەنھا ٢ کاتژمێر خەوتووە زۆرینەی`
3. `لە دەستی بە چالاکی کردووە بەشداریی لە زنجیرەی ھاوسدا کردووە سەرچاوەکان بەستەرە دەرەکییەکان پیاوە ئەم...`

**Context Size 4:**

1. `دەستی بە چالاکی کردووە سەرچاوەکان بەستەرە دەرەکییەکان پیاوە ئەمریکییەکانی سەدەی ٢٠ەم فیلمە پیاوە ئەم...`
2. `لە دەستی بە چالاکی کردووە و تا بەردەوام بووە سەرچاوەکان بەستەرە دەرەکییەکان پیاوە ئەمریکییەکانی سەدە...`
3. `کردووە سەرچاوەکان بەستەرە دەرەکییەکان پیاوە ئەمریکییەکانی سەدەی ٢٠ەم مافەکانی کۆمەڵگەی پەلکەزێڕینە ل...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_خصعە_ڕشدەکدیلە_`
2. `ەوەری_بانگەتی_بی`
3. `ی_تری_خانۆ_باموی`

**Context Size 2:**

1. `ی_جیادارەندادەی_ب`
2. `ە_پێ_کانە_ئامەزەک`
3. `انی_پەی_بۆ_گەکانی`

**Context Size 3:**

1. `_لە_بڕیاری_موونی_ئ`
2. `نی_ژمار_ناو_ھەبوو.`
3. `لە_ھاوی_و_لەسەنگی_`

**Context Size 4:**

1. `_لە_بەکار_و_دانوستا`
2. `انی_جینگ،_مایکل_٣_ئ`
3. `ەکان_بۆ_نیشتووان_ئە`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (877,504 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 | 254,727 |
| Total Tokens | 10,896,559 |
| Mean Frequency | 42.78 |
| Median Frequency | 4 |
| Frequency Std Dev | 1719.93 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | لە | 632,400 |
| 2 | و | 442,707 |
| 3 | بە | 216,191 |
| 4 | کە | 179,841 |
| 5 | بۆ | 132,098 |
| 6 | ساڵی | 84,358 |
| 7 | سەرچاوەکان | 63,400 |
| 8 | بوو | 61,016 |
| 9 | لەگەڵ | 54,346 |
| 10 | ئەم | 49,216 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | microarchitecture | 2 |
| 2 | gigabit | 2 |
| 3 | ethernet | 2 |
| 4 | سوپەرکۆمپیوتەرەکە | 2 |
| 5 | تایوانیا | 2 |
| 6 | بایۆمۆلیکولەر | 2 |
| 7 | principatele | 2 |
| 8 | دۆمنیتۆر | 2 |
| 9 | باربو | 2 |
| 10 | کاتارجیو | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0274 |
| R² (Goodness of Fit) | 0.992430 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 31.2% |
| Top 1,000 | 55.6% |
| Top 5,000 | 73.7% |
| Top 10,000 | 80.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9924 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 31.2% of corpus
- **Long Tail:** 244,727 words needed for remaining 19.5% 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 | 0.8085 | 0.3591 | N/A | N/A |
| **mono_64d** | 64 | 0.8061 | 0.2799 | N/A | N/A |
| **mono_128d** | 128 | 0.7738 | 0.2134 | N/A | N/A |
| **aligned_32d** | 32 | 0.8085 🏆 | 0.3647 | 0.0280 | 0.1960 |
| **aligned_64d** | 64 | 0.8061 | 0.2755 | 0.0680 | 0.3020 |
| **aligned_128d** | 128 | 0.7738 | 0.2095 | 0.0960 | 0.3920 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8085 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2837. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 9.6% 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 | **0.020** | 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 |
|--------|----------|
| `-ئە` | ئەرمەنستانەوە, ئەرزەروم, ئەمبڕێلاوە |
| `-بە` | بەڕوودا, بەیاوبەس, بەلتیک |
| `-دە` | دەدایە, دەشتانە, دەیبرد |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ی` | ویکیپدیای, نەوەکەی, جاگتای |
| `-ە` | ئینگلستانەوە, چۆنە, ناوەکیە |
| `-ن` | ئامانجەکان, کارلێککارەکان, ھەمەدانیان |
| `-ان` | ئامانجەکان, کارلێککارەکان, ھەمەدانیان |
| `-نی` | بووەکانی, مەجنونی, کۆمیکسەکانی |
| `-وە` | ئینگلستانەوە, تریەوە, ئەرمەنستانەوە |
| `-ەوە` | ئینگلستانەوە, تریەوە, ئەرمەنستانەوە |
| `-ەی` | نەوەکەی, وەزیفەی, حەوانەوەی |

### 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 |
|------|----------|------------------|----------|
| `انیا` | 1.88x | 226 contexts | کانیا, خانیا, شانیا |
| `ییەک` | 1.50x | 396 contexts | چییەک, دییەک, دییەکی |
| `ەمری` | 2.19x | 44 contexts | دەمری, عەمری, کەمری |
| `مریک` | 2.13x | 48 contexts | ئێمریک, ئیمریک, ئەمریک |
| `اوەک` | 1.50x | 247 contexts | تاوەک, ماوەک, ڕاوەکە |
| `وەکا` | 1.61x | 150 contexts | وەکار, بوەکان, وەکاری |
| `ەڵات` | 1.71x | 100 contexts | هەڵات, سەڵات, خەڵات |
| `ەسەر` | 1.59x | 133 contexts | بەسەر, ئەسەر, کەسەر |
| `رەکا` | 1.38x | 274 contexts | ترەکان, چرەکان, مۆرەکان |
| `ەرچا` | 2.05x | 42 contexts | سەرچاو, بەرچاو, بەرچاون |
| `رچاو` | 1.84x | 60 contexts | قرچاو, رچاوه, سەرچاو |
| `ردنی` | 1.72x | 80 contexts | كردنی, مردنی, بردنی |

### 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 |
|--------|--------|-----------|----------|
| `-بە` | `-ی` | 83 words | بەرەوپێشبردنی, بەتانی |
| `-بە` | `-ە` | 50 words | بەدواوەیە, بەدواداچوونەکە |
| `-ئە` | `-ە` | 49 words | ئەفسانەییە, ئەستێرەیەکەوە |
| `-دە` | `-ە` | 45 words | دەروونییەکانییەوە, دەرئەنجامەکە |
| `-ئە` | `-ی` | 44 words | ئەهێنی, ئەوێی |
| `-بە` | `-ن` | 38 words | بەرپرسەکەیان, بەرنامەکان |
| `-دە` | `-ن` | 34 words | دەخرێن, دەکران |
| `-دە` | `-ی` | 32 words | دەپەیوەندی, دەبیری |
| `-بە` | `-نی` | 31 words | بەرەوپێشبردنی, بەتانی |
| `-دە` | `-وە` | 26 words | دەروونییەکانییەوە, دەگوازیتەوە |

### 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 |
|------|-----------------|------------|------|
| خراپەکارانەی | **`خراپەکار-ان-ەی`** | 6.0 | `خراپەکار` |
| گیاندارانەی | **`گیاندار-ان-ەی`** | 6.0 | `گیاندار` |
| کارانەیان | **`کاران-ەی-ان`** | 6.0 | `کاران` |
| ئۆرانیەوە | **`ئۆرا-نی-ەوە`** | 6.0 | `ئۆرا` |
| پسپۆڕانەوە | **`پسپۆڕ-ان-ەوە`** | 6.0 | `پسپۆڕ` |
| مێیەکانیان | **`مێیەک-انی-ان`** | 6.0 | `مێیەک` |
| ھاوسەرگیرییاندا | **`ھاوسەرگیریی-ان-دا`** | 6.0 | `ھاوسەرگیریی` |
| پێشەنگانەی | **`پێشەنگ-ان-ەی`** | 6.0 | `پێشەنگ` |
| ئابوورییەکانەوە | **`ئابوورییەک-ان-ەوە`** | 6.0 | `ئابوورییەک` |
| وەرزشکارانەی | **`وەرزشکار-ان-ەی`** | 6.0 | `وەرزشکار` |
| گۆرانییەکاندا | **`گۆرانییەک-ان-دا`** | 6.0 | `گۆرانییەک` |
| ئەمیرەکان | **`ئە-میرەک-ان`** | 6.0 | `میرەک` |
| ڕەبیعەیان | **`ڕەبیع-ەی-ان`** | 6.0 | `ڕەبیع` |
| بەھاندانی | **`بە-ھاند-انی`** | 6.0 | `ھاند` |
| ناوخۆییانەی | **`ناوخۆیی-ان-ەی`** | 6.0 | `ناوخۆیی` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Central Kurdish 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 (4.80x) |
| N-gram | **2-gram** | Lowest perplexity (307) |
| Markov | **Context-4** | Highest predictability (97.1%) |
| 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: 2026-01-04 00:20:16*