---
language: ky
language_name: Kyrgyz
language_family: turkic_kipchak
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-turkic_kipchak
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: 4.474
  - name: best_isotropy
    type: isotropy
    value: 0.7339
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kyrgyz** 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** | 3.463x | 3.46 | 0.2417% | 1,335,548 |
| **16k** | 3.859x | 3.86 | 0.2693% | 1,198,672 |
| **32k** | 4.202x | 4.20 | 0.2932% | 1,100,887 |
| **64k** | 4.474x 🏆 | 4.48 | 0.3122% | 1,033,903 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Валенсия - Испания лигасында ойноочу футболдук клуб. Валенсия (Испания). футбол ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁вал енс ия ▁- ▁испания ▁л иг асында ▁ойн оочу ... (+16 more)` | 26 |
| 16k | `▁вал енс ия ▁- ▁испания ▁лиг асында ▁ойн оочу ▁футбол ... (+13 more)` | 23 |
| 32k | `▁вал енс ия ▁- ▁испания ▁лигасында ▁ойноочу ▁футболдук ▁клуб . ... (+8 more)` | 18 |
| 64k | `▁валенсия ▁- ▁испания ▁лигасында ▁ойноочу ▁футболдук ▁клуб . ▁валенсия ▁( ... (+4 more)` | 14 |

**Sample 2:** `Акцентология ( — басым, — сөз, окутууКасевич В. Б. ) — басымды иликтөөчү тил или...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ак цент ология ▁( ▁— ▁басым , ▁— ▁сөз , ... (+25 more)` | 35 |
| 16k | `▁ак цент ология ▁( ▁— ▁басым , ▁— ▁сөз , ... (+25 more)` | 35 |
| 32k | `▁ак цент ология ▁( ▁— ▁басым , ▁— ▁сөз , ... (+24 more)` | 34 |
| 64k | `▁акцент ология ▁( ▁— ▁басым , ▁— ▁сөз , ▁окутуу ... (+21 more)` | 31 |

**Sample 3:** `Реал Овьедо - Испания лигасында ойноочу футболдук клуб.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ре ал ▁о в ь ед о ▁- ▁испания ▁л ... (+8 more)` | 18 |
| 16k | `▁реал ▁о в ь ед о ▁- ▁испания ▁лиг асында ... (+6 more)` | 16 |
| 32k | `▁реал ▁ов ь ед о ▁- ▁испания ▁лигасында ▁ойноочу ▁футболдук ... (+2 more)` | 12 |
| 64k | `▁реал ▁ов ь едо ▁- ▁испания ▁лигасында ▁ойноочу ▁футболдук ▁клуб ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 64k achieves 4.474x compression
- **Lowest UNK Rate:** 8k with 0.2417% 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 | 24,309 | 14.57 | 200,338 | 16.1% | 40.8% |
| **2-gram** | Subword | 401 🏆 | 8.65 | 8,096 | 57.2% | 97.9% |
| **3-gram** | Word | 13,976 | 13.77 | 213,447 | 20.6% | 52.0% |
| **3-gram** | Subword | 3,260 | 11.67 | 71,568 | 20.8% | 64.9% |
| **4-gram** | Word | 20,293 | 14.31 | 405,510 | 19.9% | 50.7% |
| **4-gram** | Subword | 15,504 | 13.92 | 405,921 | 10.3% | 37.2% |
| **5-gram** | Word | 14,656 | 13.84 | 318,532 | 21.1% | 54.0% |
| **5-gram** | Subword | 48,833 | 15.58 | 1,138,729 | 7.2% | 25.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `колдонулган адабияттар` | 36,384 |
| 2 | `тышкы шилтемелер` | 25,799 |
| 3 | `тил жана` | 21,797 |
| 4 | `мамлекеттик тил` | 21,512 |
| 5 | `энциклопедия борбору` | 21,464 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `тил жана энциклопедия` | 21,456 |
| 2 | `жана энциклопедия борбору` | 21,427 |
| 3 | `мамлекеттик тил жана` | 21,290 |
| 4 | `колдонулган адабияттар кыргызстан` | 12,535 |
| 5 | `адабияттар кыргызстан улуттук` | 12,428 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `тил жана энциклопедия борбору` | 21,427 |
| 2 | `мамлекеттик тил жана энциклопедия` | 21,245 |
| 3 | `колдонулган адабияттар кыргызстан улуттук` | 12,425 |
| 4 | `б мамлекеттик тил жана` | 11,940 |
| 5 | `редактору асанов ү а` | 8,515 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `мамлекеттик тил жана энциклопедия борбору` | 21,216 |
| 2 | `б мамлекеттик тил жана энциклопедия` | 11,940 |
| 3 | `башкы редактору асанов ү а` | 8,515 |
| 4 | `том башкы редактору асанов ү` | 8,513 |
| 5 | `асанов ү а к 97` | 8,455 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _` | 1,699,467 |
| 2 | `_ к` | 1,353,946 |
| 3 | `а р` | 1,289,718 |
| 4 | `а н` | 1,276,765 |
| 5 | `_ б` | 1,066,604 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы н _` | 496,520 |
| 2 | `_ ж а` | 451,616 |
| 3 | `а р ы` | 399,154 |
| 4 | `_ к а` | 338,781 |
| 5 | `а н _` | 333,734 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н ы н _` | 272,294 |
| 2 | `а н а _` | 216,178 |
| 3 | `_ ж а н` | 213,551 |
| 4 | `ж а н а` | 203,061 |
| 5 | `ы н ы н` | 161,279 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ж а н а` | 202,652 |
| 2 | `ж а н а _` | 201,239 |
| 3 | `ы н ы н _` | 157,972 |
| 4 | `к ы р г ы` | 103,941 |
| 5 | `ы р г ы з` | 103,500 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 401
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.9833 | 1.977 | 8.72 | 500,825 | 1.7% |
| **1** | Subword | 0.9785 | 1.970 | 7.80 | 2,769 | 2.1% |
| **2** | Word | 0.2540 | 1.192 | 1.59 | 4,365,265 | 74.6% |
| **2** | Subword | 0.9572 | 1.942 | 6.53 | 21,569 | 4.3% |
| **3** | Word | 0.0694 | 1.049 | 1.12 | 6,951,636 | 93.1% |
| **3** | Subword | 0.8644 | 1.821 | 4.81 | 140,847 | 13.6% |
| **4** | Word | 0.0237 🏆 | 1.017 | 1.04 | 7,750,147 | 97.6% |
| **4** | Subword | 0.7006 | 1.625 | 3.21 | 676,843 | 29.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `жана comptuex машыгуусуна аткарган милдеттерине төмөндөгүлөр баштапкы материалы первого выступления ...`
2. `менен нуска аталышы менен мамиленин биринчи планга койгон макулдашуулар байыркы индо европа өлкөлөрү...`
3. `б кризистик кубулуштардын жардамы менен шартталган айталык асан уулу аны эми санарипке тоскоолдук жа...`

**Context Size 2:**

1. `колдонулган адабияттар каратаев о к фергана ёрёёнъндёгъ кыргыздардын этностук жакындыктарын чагылдыр...`
2. `тышкы шилтемелер акшнын бардык шаарларынын статистикалары жөнүндө u s census bureau штатынын шаарлар...`
3. `тил жана энциклопедия борбору физика энциклопедиялык окуу куралы мамлекеттик тил жана энциклопедия б...`

**Context Size 3:**

1. `тил жана энциклопедия борбору isbn 046 1 түшүнүктөрү`
2. `жана энциклопедия борбору б isbn районунун суулары суулар`
3. `мамлекеттик тил жана энциклопедия борбору 784 бет илл isbn 978 4 облусу районунда төрөлгөндөр мугали...`

**Context Size 4:**

1. `тил жана энциклопедия борбору 832 бет илл isbn 978 9 элдери элдери`
2. `мамлекеттик тил жана энциклопедия борбору 400 бет isbn кыргызстан улуттук энциклопедия 7 том башкы р...`
3. `колдонулган адабияттар кыргызстан улуттук энциклопедия 7 том башкы ред ү а асанов к 97 б кыргыз энци...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_st»_омисетарты_`
2. `арызгакм_гулу._с`
3. `нан_ка_bn_"мөнор`

**Context Size 2:**

1. `н_андүгү,_7_банан`
2. `_көпчүлгөө_нуу_бү`
3. `аратын_үзүндары_р`

**Context Size 3:**

1. `ын_кээ_(ги)_(режес`
2. `_жана_ишет._к_978_`
3. `арын_ийин_көкөтөрү`

**Context Size 4:**

1. `нын_оң_жээктегереги`
2. `ана_айдын_макалат._`
3. `_жаныбар_азайгашкар`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (676,843 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 | 227,514 |
| Total Tokens | 10,409,036 |
| Mean Frequency | 45.75 |
| Median Frequency | 4 |
| Frequency Std Dev | 744.95 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | жана | 201,356 |
| 2 | менен | 102,056 |
| 3 | б | 73,049 |
| 4 | боюнча | 55,620 |
| 5 | кыргыз | 49,452 |
| 6 | суу | 49,420 |
| 7 | мамлекеттик | 44,758 |
| 8 | бир | 44,485 |
| 9 | а | 43,591 |
| 10 | колдонулган | 39,748 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | никосиянын | 2 |
| 2 | кипра | 2 |
| 3 | акротиринин | 2 |
| 4 | темуриддер | 2 |
| 5 | phere | 2 |
| 6 | нарсингхани | 2 |
| 7 | binibining | 2 |
| 8 | айтжан | 2 |
| 9 | колода | 2 |
| 10 | раскол | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0382 |
| R² (Goodness of Fit) | 0.992694 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 23.4% |
| Top 1,000 | 52.7% |
| Top 5,000 | 72.0% |
| Top 10,000 | 79.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9927 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 23.4% of corpus
- **Long Tail:** 217,514 words needed for remaining 20.6% 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 | 0.7339 🏆 | 0.3620 | N/A | N/A |
| **mono_64d** | 64 | 0.7191 | 0.2908 | N/A | N/A |
| **mono_128d** | 128 | 0.7165 | 0.2106 | N/A | N/A |
| **aligned_32d** | 32 | 0.7339 | 0.3558 | 0.0320 | 0.1660 |
| **aligned_64d** | 64 | 0.7191 | 0.2842 | 0.0600 | 0.2540 |
| **aligned_128d** | 128 | 0.7165 | 0.2104 | 0.0720 | 0.2880 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7339 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2856. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 7.2% 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 | **1.151** | 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 |
|--------|----------|
| `-к` | көргөндө, калача, карбиддер |
| `-а` | акылынын, азербайджанда, адамынын |
| `-ка` | калача, карбиддер, карпас |
| `-с` | сезгенүүлөрүндө, сүйлөдү, суахили |
| `-т` | төмөндөшү, тогол, тооруганда |
| `-б` | брайли, бронхиалдык, болгодуктан |
| `-ма` | мартьяновго, магнат, мамлекетпн |
| `-м` | миллиметрдик, мартьяновго, магнат |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | акылынын, шейбанилердин, адамынын |
| `-а` | өзалдынча, жазгандарга, калача |
| `-ын` | акылынын, адамынын, барын |
| `-ы` | звёзды, вазийпасы, юаны |
| `-ин` | шейбанилердин, шалтаевдин, илинин |
| `-ан` | болгодуктан, жасалмалуулуктан, алған |
| `-р` | карбиддер, гребнер, багбандар |
| `-к` | миллиметрдик, бронхиалдык, акшыйрак |

### 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 |
|------|----------|------------------|----------|
| `арды` | 1.76x | 180 contexts | зарды, барды, дарды |
| `ргыз` | 2.39x | 35 contexts | ыргыз, хыргыз, кыргыз |
| `ктар` | 1.47x | 245 contexts | ыктар, уктар, актар |
| `асын` | 1.44x | 274 contexts | гасын, тасын, жасын |
| `лган` | 1.49x | 192 contexts | ылган, алган, қилган |
| `арын` | 1.38x | 241 contexts | барын, жарын, шарын |
| `леке` | 2.29x | 26 contexts | келеке, белеке, телеке |
| `улга` | 1.48x | 136 contexts | кулга, уулга, тулга |
| `рдын` | 1.86x | 46 contexts | ырдын, крдын, тардын |
| `екет` | 2.07x | 28 contexts | зекет, секет, рекет |
| `ыргы` | 1.61x | 64 contexts | ыргып, кыргы, ыргыз |
| `етти` | 1.46x | 69 contexts | шетти, четти, бетти |

### 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 |
|--------|--------|-----------|----------|
| `-к` | `-н` | 294 words | кенжекаранын, кылжейрен |
| `-а` | `-н` | 198 words | агарткан, акимдерин |
| `-т` | `-н` | 185 words | телефондоштуруунун, таралуунун |
| `-б` | `-н` | 154 words | буковинанын, боткодон |
| `-к` | `-а` | 138 words | каарданса, курмана |
| `-с` | `-н` | 137 words | системасынын, сапарларынын |
| `-а` | `-а` | 92 words | арина, алматыга |
| `-м` | `-н` | 86 words | макрофагдын, мамтелерадиосунун |
| `-к` | `-ы` | 85 words | коллекцияларды, колдонулгандыгы |
| `-к` | `-ын` | 81 words | кенжекаранын, кыяктын |

### 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 |
|------|-----------------|------------|------|
| референдумдан | **`референдум-да-н`** | 7.5 | `да` |
| калининская | **`калининск-а-я`** | 7.5 | `а` |
| өнөктөштөрүнө | **`өнөктөштөрү-н-ө`** | 7.5 | `н` |
| табакчалардан | **`табакчалар-да-н`** | 7.5 | `да` |
| шарпылдак | **`шарпыл-да-к`** | 7.5 | `да` |
| коомдоштуруунун | **`коомдоштуруу-н-ун`** | 7.5 | `н` |
| топтолушунун | **`топтолушу-н-ун`** | 7.5 | `н` |
| облустардан | **`облустар-да-н`** | 7.5 | `да` |
| үйрөтүүнү | **`үйрөтүү-н-ү`** | 7.5 | `н` |
| конуштардагы | **`конуштар-да-гы`** | 7.5 | `да` |
| келишкени | **`келишке-н-и`** | 7.5 | `н` |
| сактандыруунун | **`сактандыруу-н-ун`** | 7.5 | `н` |
| стадионунда | **`стадиону-н-да`** | 7.5 | `н` |
| секрециянын | **`секреция-н-ын`** | 7.5 | `н` |
| пёшинская | **`пёшинс-ка-я`** | 7.5 | `ка` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kyrgyz 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 (4.47x) |
| N-gram | **2-gram** | Lowest perplexity (401) |
| Markov | **Context-4** | Highest predictability (97.6%) |
| 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 10:13:59*