---
language: ku
language_name: 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: 4.370
  - name: best_isotropy
    type: isotropy
    value: 0.7399
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **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** | 3.563x | 3.56 | 0.1949% | 746,991 |
| **16k** | 3.892x | 3.89 | 0.2129% | 683,996 |
| **32k** | 4.164x | 4.17 | 0.2278% | 639,238 |
| **64k** | 4.370x 🏆 | 4.37 | 0.2390% | 609,081 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Velenderan gundekî ser bi navenda bajarê Keleyber li Azerbaycana Rojhilat ya Îra...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁vel end eran ▁gundekî ▁ser ▁bi ▁navenda ▁bajarê ▁keleyber ▁li ... (+8 more)` | 18 |
| 16k | `▁vel end eran ▁gundekî ▁ser ▁bi ▁navenda ▁bajarê ▁keleyber ▁li ... (+8 more)` | 18 |
| 32k | `▁vel end eran ▁gundekî ▁ser ▁bi ▁navenda ▁bajarê ▁keleyber ▁li ... (+8 more)` | 18 |
| 64k | `▁vel enderan ▁gundekî ▁ser ▁bi ▁navenda ▁bajarê ▁keleyber ▁li ▁azerbaycana ... (+7 more)` | 17 |

**Sample 2:** `Geleban (bi tirkî: Şimşirpınar), gundekî bi ser navçeya Bongilana Çewligê ve ye....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gel eb an ▁( bi ▁tirkî : ▁ş im ş ... (+23 more)` | 33 |
| 16k | `▁gel eb an ▁( bi ▁tirkî : ▁şim ş ir ... (+15 more)` | 25 |
| 32k | `▁gel eban ▁( bi ▁tirkî : ▁şim şir pınar ), ... (+11 more)` | 21 |
| 64k | `▁gel eban ▁( bi ▁tirkî : ▁şim şir pınar ), ... (+11 more)` | 21 |

**Sample 3:** `Sûrgûçiyan, Sûrgûç ango Sûrgiç (), gundekî ser bi navçeya Pêrtaga Dêrsimê ve ye....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sûr g ûç iyan , ▁sûr g ûç ▁ango ▁sûr ... (+20 more)` | 30 |
| 16k | `▁sûr g ûç iyan , ▁sûr g ûç ▁ango ▁sûr ... (+16 more)` | 26 |
| 32k | `▁sûrg ûç iyan , ▁sûrg ûç ▁ango ▁sûr gi ç ... (+14 more)` | 24 |
| 64k | `▁sûrg ûç iyan , ▁sûrg ûç ▁ango ▁sûr gi ç ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 4.370x compression
- **Lowest UNK Rate:** 8k with 0.1949% 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 | 14,229 | 13.80 | 132,552 | 22.5% | 44.1% |
| **2-gram** | Subword | 320 🏆 | 8.32 | 8,148 | 64.3% | 98.6% |
| **3-gram** | Word | 18,304 | 14.16 | 187,835 | 20.6% | 42.7% |
| **3-gram** | Subword | 2,663 | 11.38 | 62,607 | 25.7% | 69.3% |
| **4-gram** | Word | 26,715 | 14.71 | 323,171 | 17.3% | 41.3% |
| **4-gram** | Subword | 14,144 | 13.79 | 346,121 | 14.6% | 41.9% |
| **5-gram** | Word | 17,888 | 14.13 | 229,794 | 16.4% | 44.3% |
| **5-gram** | Subword | 48,651 | 15.57 | 1,002,432 | 10.2% | 29.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `girêdanên derve` | 50,967 |
| 2 | `çavkanî girêdanên` | 47,989 |
| 3 | `li herêma` | 36,724 |
| 4 | `ye nifûs` | 36,700 |
| 5 | `ye ku` | 34,741 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `çavkanî girêdanên derve` | 47,975 |
| 2 | `fransayê ye nifûs` | 27,476 |
| 3 | `ye nifûs mijarên` | 22,039 |
| 4 | `nifûs mijarên têkildar` | 19,681 |
| 5 | `komuneke li departmena` | 17,684 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ye nifûs mijarên têkildar` | 19,267 |
| 2 | `çavkanî girêdanên derve departmena` | 15,149 |
| 3 | `fransayê ye nifûs mijarên` | 14,463 |
| 4 | `fransayê ye nifûs binêre` | 12,648 |
| 5 | `ye nifûs binêre komunên` | 12,134 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `fransayê ye nifûs binêre komunên` | 12,134 |
| 2 | `fransayê ye nifûs mijarên têkildar` | 11,691 |
| 3 | `ye nifûs mijarên têkildar komunên` | 11,691 |
| 4 | `nifûs mijarên têkildar komunên departmena` | 10,895 |
| 5 | `ye nifûs binêre komunên departmena` | 8,007 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 1,034,839 |
| 2 | `a n` | 889,783 |
| 3 | `n _` | 854,518 |
| 4 | `ê _` | 845,822 |
| 5 | `_ d` | 812,035 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ê n _` | 385,025 |
| 2 | `_ d e` | 381,399 |
| 3 | `_ d i` | 290,862 |
| 4 | `y a _` | 272,477 |
| 5 | `_ l i` | 234,359 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l i _` | 223,090 |
| 2 | `_ j i _` | 141,221 |
| 3 | `_ d i _` | 128,134 |
| 4 | `_ b i _` | 127,189 |
| 5 | `_ k u _` | 123,226 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ y e . _` | 82,895 |
| 2 | `ê n _ d e` | 81,966 |
| 3 | `n ê n _ d` | 77,356 |
| 4 | `a v k a n` | 76,409 |
| 5 | `ç a v k a` | 76,375 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 320
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.8217 | 1.768 | 6.00 | 438,410 | 17.8% |
| **1** | Subword | 1.0332 | 2.047 | 6.60 | 4,043 | 0.0% |
| **2** | Word | 0.2614 | 1.199 | 1.72 | 2,621,616 | 73.9% |
| **2** | Subword | 0.8013 | 1.743 | 5.14 | 26,679 | 19.9% |
| **3** | Word | 0.0967 | 1.069 | 1.18 | 4,482,033 | 90.3% |
| **3** | Subword | 0.7934 | 1.733 | 4.32 | 137,032 | 20.7% |
| **4** | Word | 0.0346 🏆 | 1.024 | 1.06 | 5,290,949 | 96.5% |
| **4** | Subword | 0.7104 | 1.636 | 3.23 | 591,413 | 29.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `li gorî daxuyaniya peywirê xwe şîrove ˈ derba şûrê wî yên dilxwaz bû ji ber sedemên`
2. `û erebistana siûdîê tîran yek ji aliyê farisan ên cîhanê iucn iucn red kir vê șiklê`
3. `de bi navçeyê bi giştî hatiye parçe aliyê dewleta tirk ji wan bi pîrozkirina rojbûyîna wî`

**Context Size 2:**

1. `girêdanên derve departmena cherê çavkanî girêdanên derve departmena moselle a li herêma baden württe...`
2. `çavkanî girêdanên derve departmena gardê çavkanî girêdanên derve bajarên di ser ji nû ve derxist bi ...`
3. `li herêma nouvelle aquitaine e ku li gurcistanê girara wê pîlaw û herwiha çend xaç û nîşanên`

**Context Size 3:**

1. `çavkanî girêdanên derve departmena dardogne fransa`
2. `fransayê ye nifûs binêre komunê departmena bas rhinê çavkanî girêdanên derve alpes de haute provence...`
3. `ye nifûs mijarên têkildar komunên departmena maine et loire ya li herêma normandiyayê ye ku li bakur...`

**Context Size 4:**

1. `ye nifûs mijarên têkildar komunên departmena jurayê çavkanî girêdanên derve departmena doubsê`
2. `çavkanî girêdanên derve departmena meurthe et moselle a li herêma grand estê ye ku li bakurê fransay...`
3. `fransayê ye nifûs mijarên têkildar komunên departmena yonneyê çavkanî girêdanên derve departmena mos...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ştura_hedaji_d_`
2. `ana_kurî_a_divka`
3. `ett-sîserên_dîla`

**Context Size 2:**

1. `a_îrj_avkaritarie`
2. `anxaneyê_herlê_us`
3. `n_pêkiyerdogrus_k`

**Context Size 3:**

1. `ên_îtan;_li_hesirm`
2. `_dezgîn_mane_ye._b`
3. `_di_di_‘işq_=_gund`

**Context Size 4:**

1. `_li_başûrê_fransayê`
2. `_ji_hêlin,_jina_îra`
3. `_di_lîsteyê_çaresan`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (591,413 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 | 200,380 |
| Total Tokens | 7,401,900 |
| Mean Frequency | 36.94 |
| Median Frequency | 3 |
| Frequency Std Dev | 1157.52 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | li | 225,647 |
| 2 | û | 207,064 |
| 3 | de | 143,257 |
| 4 | ji | 143,016 |
| 5 | bi | 136,679 |
| 6 | ye | 133,928 |
| 7 | di | 129,729 |
| 8 | ku | 124,115 |
| 9 | ya | 79,962 |
| 10 | çavkanî | 74,871 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | hamiyeke | 2 |
| 2 | birew | 2 |
| 3 | parvakirî | 2 |
| 4 | 12în | 2 |
| 5 | gûzvanê | 2 |
| 6 | amîloplastan | 2 |
| 7 | salyangoz | 2 |
| 8 | polonyayeke | 2 |
| 9 | norrmalmê | 2 |
| 10 | dîlgirtiyan | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0781 |
| R² (Goodness of Fit) | 0.998680 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 42.5% |
| Top 1,000 | 64.4% |
| Top 5,000 | 78.6% |
| Top 10,000 | 83.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9987 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 42.5% of corpus
- **Long Tail:** 190,380 words needed for remaining 16.1% 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 | 0.7399 | 0.3712 | N/A | N/A |
| **mono_64d** | 64 | 0.7365 | 0.2705 | N/A | N/A |
| **mono_128d** | 128 | 0.7399 🏆 | 0.2084 | N/A | N/A |
| **aligned_32d** | 32 | 0.7399 | 0.3592 | 0.0860 | 0.4080 |
| **aligned_64d** | 64 | 0.7365 | 0.2802 | 0.1400 | 0.5160 |
| **aligned_128d** | 128 | 0.7399 | 0.2108 | 0.2180 | 0.5780 |

### Key Findings

- **Best Isotropy:** mono_128d with 0.7399 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2834. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 21.8% 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 | **0.513** | 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 |
|--------|----------|
| `-s` | sharjah, seyemî, schelklingen |
| `-a` | adds, ardeuil, autrêches |
| `-b` | bermayiyek, berhevdanên, berdibin |
| `-m` | mabukê, malikek, mergey |
| `-d` | dayînan, dilsoj, dosches |
| `-k` | kyle, korpeleyê, komunîstî |
| `-p` | petran, porchères, projekte |
| `-t` | tometa, tak, turku |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | qeletiyan, dayînan, encûran |
| `-a` | yuksekkaya, tometa, nîveşkêla |
| `-e` | stryfe, sülze, xebitîne |
| `-ê` | mabukê, oxotskê, korpeleyê |
| `-s` | adds, autrêches, dosches |
| `-an` | qeletiyan, dayînan, encûran |
| `-î` | seyemî, mîlletî, komunîstî |
| `-ên` | berhevdanên, loviyên, xwîndevanên |

### 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 |
|------|----------|------------------|----------|
| `ista` | 1.64x | 194 contexts | mista, lista, rista |
| `ajar` | 2.40x | 35 contexts | hajar, bajar, qajar |
| `irêd` | 2.58x | 26 contexts | mirêd, girêda, girêde |
| `arêz` | 2.19x | 47 contexts | parêz, karêz, karêzî |
| `iyên` | 1.71x | 134 contexts | biyên, jiyên, siyên |
| `arên` | 1.82x | 89 contexts | karên, barên, parên |
| `ariy` | 1.63x | 142 contexts | ariya, ariyê, bariye |
| `edar` | 1.90x | 67 contexts | edara, xedar, edarî |
| `derv` | 2.72x | 18 contexts | derve, dervê, dervî |
| `erêm` | 2.52x | 23 contexts | herêm, kerêm, herêmê |
| `artm` | 2.82x | 14 contexts | qartmîn, hartmut, hartman |
| `vkan` | 2.68x | 14 contexts | kevkan, zêvkan, çavkan |

### 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 |
|--------|--------|-----------|----------|
| `-b` | `-n` | 109 words | bodelshausen, burggen |
| `-d` | `-n` | 95 words | diwemîn, dahatin |
| `-m` | `-n` | 87 words | moan, mgran |
| `-s` | `-a` | 77 words | shea, sîtokîneza |
| `-k` | `-n` | 75 words | konsertên, kalkên |
| `-s` | `-n` | 72 words | seban, singleên |
| `-b` | `-a` | 72 words | bihorîna, brega |
| `-b` | `-e` | 71 words | bergonce, bixemilîne |
| `-p` | `-n` | 68 words | polîmeran, pyrenean |
| `-p` | `-a` | 67 words | philharmoniya, plotnikova |

### 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 |
|------|-----------------|------------|------|
| hemandemî | **`hemande-m-î`** | 7.5 | `m` |
| dihatibûne | **`dihatibû-n-e`** | 7.5 | `n` |
| afirandîne | **`afirandî-n-e`** | 7.5 | `n` |
| bourlhonne | **`bourlhon-n-e`** | 7.5 | `n` |
| lêkonînên | **`lêkonî-n-ên`** | 7.5 | `n` |
| hildijart | **`hildij-a-rt`** | 7.5 | `a` |
| pressagny | **`pressag-n-y`** | 7.5 | `n` |
| zaravayeke | **`zaravay-e-ke`** | 7.5 | `e` |
| bandoreke | **`bandor-e-ke`** | 7.5 | `e` |
| pêşînsala | **`pêşîns-al-a`** | 7.5 | `al` |
| tenikbayê | **`tenikb-a-yê`** | 7.5 | `a` |
| xiangyang | **`xiang-ya-ng`** | 6.0 | `xiang` |
| villerest | **`viller-es-t`** | 6.0 | `viller` |
| vezîkulên | **`vezîkul-ên`** | 4.5 | `vezîkul` |
| okinawayê | **`okinawa-yê`** | 4.5 | `okinawa` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kurdish shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.37x) |
| N-gram | **2-gram** | Lowest perplexity (320) |
| Markov | **Context-4** | Highest predictability (96.5%) |
| 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 09:22:24*