---
language: kk
language_name: Kazakh
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: 4.977
  - name: best_isotropy
    type: isotropy
    value: 0.7010
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kazakh** 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** | 3.772x | 3.77 | 0.3045% | 1,829,937 |
| **16k** | 4.241x | 4.24 | 0.3424% | 1,627,264 |
| **32k** | 4.650x | 4.65 | 0.3754% | 1,484,160 |
| **64k** | 4.977x 🏆 | 4.98 | 0.4018% | 1,386,763 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Оқиғалар Туғандар Тағы қара: : жылы туғандар Қайтыс болғандар Тағы қара: : жылы ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁жылы ▁туғандар ▁қайтыс ▁болғандар ... (+11 more)` | 21 |
| 16k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁жылы ▁туғандар ▁қайтыс ▁болғандар ... (+11 more)` | 21 |
| 32k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁жылы ▁туғандар ▁қайтыс ▁болғандар ... (+11 more)` | 21 |
| 64k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁жылы ▁туғандар ▁қайтыс ▁болғандар ... (+11 more)` | 21 |

**Sample 2:** `Оқиғалар Туғандар Тағы қара: : з. д. 849 жылы туғандар Қайтыс болғандар Тағы қар...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁з . ▁д . ... (+27 more)` | 37 |
| 16k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁з . ▁д . ... (+27 more)` | 37 |
| 32k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁з . ▁д . ... (+27 more)` | 37 |
| 64k | `▁оқиғалар ▁туғандар ▁тағы ▁қара : ▁: ▁з . ▁д . ... (+27 more)` | 37 |

**Sample 3:** `Денвер () — Колорадо штатының Денвер округіне жататын АҚШ қаласы.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ден вер ▁() ▁— ▁кол ор адо ▁штатының ▁ден вер ... (+5 more)` | 15 |
| 16k | `▁ден вер ▁() ▁— ▁колорадо ▁штатының ▁ден вер ▁округіне ▁жататын ... (+3 more)` | 13 |
| 32k | `▁ден вер ▁() ▁— ▁колорадо ▁штатының ▁ден вер ▁округіне ▁жататын ... (+3 more)` | 13 |
| 64k | `▁ден вер ▁() ▁— ▁колорадо ▁штатының ▁ден вер ▁округіне ▁жататын ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 4.977x compression
- **Lowest UNK Rate:** 8k with 0.3045% 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 | 50,781 | 15.63 | 635,206 | 13.5% | 36.3% |
| **2-gram** | Subword | 408 🏆 | 8.67 | 14,531 | 58.9% | 97.3% |
| **3-gram** | Word | 31,735 | 14.95 | 735,424 | 16.7% | 45.1% |
| **3-gram** | Subword | 3,241 | 11.66 | 127,100 | 21.8% | 66.2% |
| **4-gram** | Word | 42,856 | 15.39 | 1,354,792 | 17.2% | 44.2% |
| **4-gram** | Subword | 16,071 | 13.97 | 781,025 | 10.8% | 38.2% |
| **5-gram** | Word | 32,278 | 14.98 | 1,073,181 | 18.4% | 45.9% |
| **5-gram** | Subword | 53,942 | 15.72 | 2,515,495 | 6.8% | 25.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `сыртқы сілтемелер` | 94,884 |
| 2 | `тұрғындарының саны` | 63,172 |
| 3 | `жер аумағы` | 60,266 |
| 4 | `дереккөздер сыртқы` | 59,467 |
| 5 | `алып жатқан` | 58,019 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `алып жатқан жер` | 57,518 |
| 2 | `жатқан жер аумағы` | 57,501 |
| 3 | `дереккөздер сыртқы сілтемелер` | 53,338 |
| 4 | `жылғы мәліметтер бойынша` | 37,228 |
| 5 | `бойынша тұрғындарының саны` | 37,149 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `алып жатқан жер аумағы` | 57,501 |
| 2 | `мәліметтер бойынша тұрғындарының саны` | 37,144 |
| 3 | `жылғы мәліметтер бойынша тұрғындарының` | 37,139 |
| 4 | `жер аумақтарынан ағып өтеді` | 22,912 |
| 5 | `су алабы өңіріне жатады` | 22,794 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `жылғы мәліметтер бойынша тұрғындарының саны` | 37,139 |
| 2 | `су алабы өңіріне жатады өзеннің` | 22,791 |
| 3 | `федерациясы табиғи ресурстар және экология` | 22,789 |
| 4 | `сыртқы сілтемелер ресей федерациясы табиғи` | 22,789 |
| 5 | `сілтемелер ресей федерациясы табиғи ресурстар` | 22,789 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы _` | 4,184,362 |
| 2 | `а р` | 3,959,987 |
| 3 | `н _` | 3,570,515 |
| 4 | `а н` | 3,529,083 |
| 5 | `а л` | 3,338,151 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы ң _` | 1,429,377 |
| 2 | `_ қ а` | 1,294,982 |
| 3 | `н д а` | 1,265,853 |
| 4 | `а н _` | 1,237,704 |
| 5 | `е н _` | 1,131,817 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н ы ң _` | 994,945 |
| 2 | `ы н д а` | 897,950 |
| 3 | `ы н ы ң` | 649,967 |
| 4 | `д ы . _` | 602,358 |
| 5 | `л ы қ _` | 590,402 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы н ы ң _` | 640,895 |
| 2 | `ж ә н е _` | 461,132 |
| 3 | `_ ж ә н е` | 461,108 |
| 4 | `і н і ң _` | 415,949 |
| 5 | `ы н д а _` | 372,714 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 408
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.9389 | 1.917 | 10.11 | 1,229,299 | 6.1% |
| **1** | Subword | 1.0239 | 2.033 | 7.20 | 7,217 | 0.0% |
| **2** | Word | 0.2789 | 1.213 | 1.72 | 12,407,759 | 72.1% |
| **2** | Subword | 0.7626 | 1.697 | 5.39 | 51,715 | 23.7% |
| **3** | Word | 0.0788 | 1.056 | 1.14 | 21,365,193 | 92.1% |
| **3** | Subword | 0.8061 | 1.748 | 4.76 | 278,483 | 19.4% |
| **4** | Word | 0.0283 🏆 | 1.020 | 1.05 | 24,363,984 | 97.2% |
| **4** | Subword | 0.7342 | 1.664 | 3.54 | 1,325,004 | 26.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `және идеялас тұрғанын естиміз қалыпты жағдайда ғана шығатын кезден бастап бесінші айла басшысын ауыс...`
2. `бойынша тұрғындарының саны 4 вильнюс баку ауданында комарка орналасқан шаңды дауылдарға байланысты б...`
3. `су торабына дейін өзен сағасы тиксна өзенінің құйылысына дейінгі аралықта дәстүргүлдер ашық хоккей с...`

**Context Size 2:**

1. `сыртқы сілтемелер ресми сайты саксония елді мекендері ауыл аты киіз үй тәрізді түрғын үйі кіреді жақ...`
2. `тұрғындарының саны 174 адамды құрайды алып жатқан жер аумағы 20 км жерде таулы теңіз деңгейінен 176 ...`
3. `жер аумағы 17 6 54 55 1 24 25 км дей жерде үлкен сарышығанақ қолтығында шөл белдемінде`

**Context Size 3:**

1. `алып жатқан жер аумағы 3 5 км шамасында fips коды сыртқы ақш тың барлық қалалары жайында статистикал...`
2. `жатқан жер аумағы 9 23 км шамасында коммунаның insee коды пошта индексі демографиясы жылғы мәліметте...`
3. `дереккөздер сыртқы сілтемелер ресми сайты францияның ұлттық статистика және экономикалық зерттеулер ...`

**Context Size 4:**

1. `алып жатқан жер аумағы 33 56 км шамасында елді мекеннің автомобиль коды fb ресми идентификациялық ко...`
2. `мәліметтер бойынша тұрғындарының саны 41 адамды құрайды алып жатқан жер аумағы 711 649 км шамасында ...`
3. `жылғы мәліметтер бойынша тұрғындарының саны 650 адамды құрайды 31 желтоқсан жыл алып жатқан жер аума...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_бі._патық,_мтіл`
2. `апең_бері_қ_қ_жа`
3. `ыле_ұзамдардынды`

**Context Size 2:**

1. `ы_қары_еуі_жаңа_-`
2. `аратаралдің_се_от`
3. `н_көп_б.)._жылдың`

**Context Size 3:**

1. `ың_құмдары_бұжымда`
2. `_қалы_тегіш_соң_жа`
3. `ндағы_1_17_59_кере`

**Context Size 4:**

1. `ның_ақысымен_қуатын`
2. `ындары_теңіздер_жақ`
3. `ының_құрылғанындағы`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,325,004 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 | 538,078 |
| Total Tokens | 35,515,416 |
| Mean Frequency | 66.00 |
| Median Frequency | 4 |
| Frequency Std Dev | 1426.50 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | және | 461,374 |
| 2 | бойынша | 214,790 |
| 3 | су | 213,722 |
| 4 | жылы | 206,615 |
| 5 | мен | 203,657 |
| 6 | км | 180,670 |
| 7 | дереккөздер | 166,770 |
| 8 | 1 | 129,114 |
| 9 | өзен | 122,193 |
| 10 | коды | 120,681 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | изомеризациясы | 2 |
| 2 | шолқара | 2 |
| 3 | uruperbat | 2 |
| 4 | сунж | 2 |
| 5 | тайдуланың | 2 |
| 6 | гидразинді | 2 |
| 7 | монопропеллент | 2 |
| 8 | оксазиридин | 2 |
| 9 | гидразон | 2 |
| 10 | расшиг | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0557 |
| R² (Goodness of Fit) | 0.990942 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.8% |
| Top 1,000 | 51.8% |
| Top 5,000 | 71.0% |
| Top 10,000 | 78.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9909 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.8% of corpus
- **Long Tail:** 528,078 words needed for remaining 21.9% 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 | 0.7010 🏆 | 0.3649 | N/A | N/A |
| **mono_64d** | 64 | 0.6917 | 0.2922 | N/A | N/A |
| **mono_128d** | 128 | 0.6268 | 0.2367 | N/A | N/A |
| **aligned_32d** | 32 | 0.7010 | 0.3419 | 0.0560 | 0.2380 |
| **aligned_64d** | 64 | 0.6917 | 0.3003 | 0.0880 | 0.3400 |
| **aligned_128d** | 128 | 0.6268 | 0.2449 | 0.1360 | 0.4220 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7010 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2968. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 13.6% 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 | **0.788** | 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` | капитолийге, күнделекті, кердер |
| `-а` | анжервиль, айлазан, айвазовскийдің |
| `-с` | саттарұлы, сыйларға, суасты |
| `-т` | тұншықтырғыш, тоғысып, түйеқус |
| `-б` | бапанға, бәсекеде, бүркітбайқызы |
| `-ма` | маңыздылығының, массей, макияж |
| `-м` | мустафи, маңыздылығының, миклошич |
| `-ба` | бапанға, байқапады, бағамдауға |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | десверн, ландшафтардан, жасақпен |
| `-ң` | фараонның, маңыздылығының, рецепторлардың |
| `-ың` | фараонның, маңыздылығының, рецепторлардың |
| `-а` | бапанға, диадема, сыйларға |
| `-ы` | бүркітбайқызы, саттарұлы, байқапады |
| `-ен` | жасақпен, цилиндрлермен, виннинген |
| `-ің` | кезеіңнің, сөздернің, айвазовскийдің |
| `-р` | кердер, селолар, бундшылар |

### 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 |
|------|----------|------------------|----------|
| `ықта` | 1.51x | 733 contexts | иықта, тықта, лықта |
| `рыны` | 2.01x | 96 contexts | арыны, орыны, рының |
| `ндер` | 1.52x | 395 contexts | үндер, өндер, әндер |
| `імет` | 2.09x | 59 contexts | окімет, ұкімет, үкімет |
| `сынд` | 1.64x | 169 contexts | сында, сынды, ұсында |
| `здер` | 1.57x | 168 contexts | іздер, өздер, ездер |
| `ндағ` | 1.71x | 110 contexts | ндағы, андағы, ындағы |
| `метт` | 1.65x | 109 contexts | метте, аметт, шометт |
| `йынш` | 2.32x | 25 contexts | йынша, ойыншы, ойынша |
| `рнал` | 1.66x | 88 contexts | арнал, арналы, журнал |
| `ұрғы` | 1.83x | 56 contexts | ұрғыр, тұрғы, бұрғы |
| `рекк` | 2.39x | 21 contexts | рекко, рекки, трекке |

### 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 |
|--------|--------|-----------|----------|
| `-т` | `-н` | 114 words | температурадан, табумен |
| `-с` | `-н` | 106 words | станциясымен, сутектермен |
| `-а` | `-ы` | 97 words | айтқалиұлы, автомобилды |
| `-к` | `-н` | 96 words | көміртектен, киімінеарналған |
| `-б` | `-н` | 92 words | билерден, боксшысымен |
| `-а` | `-н` | 89 words | алуандығымен, албин |
| `-а` | `-а` | 82 words | ангкорға, атерома |
| `-с` | `-а` | 81 words | снежана, сангина |
| `-т` | `-а` | 78 words | транскрипциясына, тактикаға |
| `-к` | `-а` | 75 words | канайма, колхозшыларда |

### 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 |
|------|-----------------|------------|------|
| дастаннан | **`дастан-н-ан`** | 7.5 | `н` |
| миллиарда | **`милли-ар-да`** | 7.5 | `ар` |
| хайпудырская | **`хайпудырск-а-я`** | 7.5 | `а` |
| сағынтаев | **`сағынта-е-в`** | 7.5 | `е` |
| ақсүңқарға | **`ақсүңқ-ар-ға`** | 7.5 | `ар` |
| жанрларын | **`жанрл-ар-ын`** | 7.5 | `ар` |
| тураланады | **`турала-на-ды`** | 7.5 | `на` |
| сарыжомарт | **`сарыжом-ар-т`** | 7.5 | `ар` |
| кодексінде | **`кодексі-н-де`** | 7.5 | `н` |
| экономикамен | **`экономика-м-ен`** | 7.5 | `м` |
| вулверхэмптонға | **`вулверхэмпто-н-ға`** | 7.5 | `н` |
| империума | **`империу-м-а`** | 7.5 | `м` |
| гидротехниканың | **`гидротехник-ан-ың`** | 6.0 | `гидротехник` |
| капитанға | **`капит-ан-ға`** | 6.0 | `капит` |
| алматыдан | **`алматы-да-н`** | 6.0 | `алматы` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kazakh 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 (4.98x) |
| N-gram | **2-gram** | Lowest perplexity (408) |
| Markov | **Context-4** | Highest predictability (97.2%) |
| 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 11:23:46*