---
language: az
language_name: AZ
language_family: turkic_oghuz
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - monolingual
  - family-turkic_oghuz
license: mit
library_name: wikilangs
pipeline_tag: feature-extraction
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: 4.560
  - name: best_isotropy
    type: isotropy
    value: 0.8153
  - name: vocabulary_size
    type: vocab
    value: 807823
generated: 2025-12-27
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **AZ** 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-gram)
- Markov chains (context of 1, 2, 3 and 4)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions
- 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. Summary & Recommendations](#6-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 3.637x | 3.59 | 0.0980% | 1,442,215 |
| **16k** | 4.016x | 3.97 | 0.1082% | 1,305,814 |
| **32k** | 4.326x | 4.27 | 0.1165% | 1,212,431 |
| **64k** | 4.560x 🏆 | 4.50 | 0.1229% | 1,150,092 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Hadisələr 

 Doğumlar 

 Vəfatlar 
 Soqdian — e.ə. 424–423-cü illərdə hakimiyyət...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁hadisələr ▁doğumlar ▁vəfatlar ▁s oq di an ▁— ▁e . ... (+21 more)` | 31 |
| 16k | `▁hadisələr ▁doğumlar ▁vəfatlar ▁s oq dian ▁— ▁e . ə ... (+19 more)` | 29 |
| 32k | `▁hadisələr ▁doğumlar ▁vəfatlar ▁s oq dian ▁— ▁e . ə ... (+18 more)` | 28 |
| 64k | `▁hadisələr ▁doğumlar ▁vəfatlar ▁soq dian ▁— ▁e . ə . ... (+17 more)` | 27 |

**Sample 2:** `() —  aləminin  dəstəsinin  fəsiləsinin  cinsinə aid bitki növü.

 İstinadlar 

...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |
| 16k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |
| 32k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |
| 64k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |

**Sample 3:** `() —  aləminin  dəstəsinin  fəsiləsinin  cinsinə aid bitki növü.

 İstinadlar 

...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |
| 16k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |
| 32k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |
| 64k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 4.560x compression
- **Lowest UNK Rate:** 8k with 0.0980% 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 Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | 116,331 🏆 | 16.83 | 1,418,191 | 12.2% | 25.0% |
| **2-gram** | 463 🏆 | 8.85 | 22,197 | 55.1% | 96.6% |
| **3-gram** | 409,514 | 18.64 | 2,779,660 | 7.3% | 16.3% |
| **3-gram** | 4,354 | 12.09 | 215,243 | 19.6% | 58.8% |
| **4-gram** | 1,285,123 | 20.29 | 5,336,948 | 4.2% | 9.8% |
| **4-gram** | 24,655 | 14.59 | 1,308,669 | 10.0% | 31.8% |

### Top 5 N-grams by Size

**2-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i ̇` | 824,078 |
| 2 | `- ci` | 452,530 |
| 3 | `kateqoriya :` | 365,784 |
| 4 | `. i` | 236,809 |
| 5 | `ci ildə` | 221,298 |

**3-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. i ̇` | 227,697 |
| 2 | `- ci ildə` | 220,310 |
| 3 | `i ̇ stinadlar` | 171,011 |
| 4 | `- cü ildə` | 76,499 |
| 5 | `( ) —` | 70,885 |

**4-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. i ̇ stinadlar` | 103,078 |
| 2 | `i ̇ stinadlar kateqoriya` | 65,368 |
| 3 | `̇ stinadlar kateqoriya :` | 65,368 |
| 4 | `i ̇ stinadlar xarici` | 45,918 |
| 5 | `̇ stinadlar xarici keçidlər` | 45,490 |


### Key Findings

- **Best Perplexity:** 2-gram with 463
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~32% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | 0.7520 | 1.684 | 8.95 | 1,994,233 | 24.8% |
| **1** | 1.3997 | 2.638 | 10.24 | 7,113 | 0.0% |
| **2** | 0.3489 | 1.274 | 2.24 | 17,848,485 | 65.1% |
| **2** | 0.8515 | 1.804 | 6.20 | 72,786 | 14.8% |
| **3** | 0.1419 | 1.103 | 1.34 | 39,971,548 | 85.8% |
| **3** | 0.8951 | 1.860 | 5.05 | 451,475 | 10.5% |
| **4** | 0.0656 🏆 | 1.046 | 1.14 | 53,703,949 | 93.4% |
| **4** | 0.7324 🏆 | 1.661 | 3.53 | 2,281,437 | 26.8% |

### Generated Text Samples

Below are text samples generated from each Markov chain model:

**Context Size 1:**

1. `. şerlər əsasən observantlar monastırlarının bəzilərinin əvvəllər per teodor hertslin başlatdığı işğ...`
2. `, buenos - dən az saylı xəstəxanada həkim , 316 kvadrat metrdən çox öz qoşunu təbrizi`
3. `- ci ildə yarananlar kateqoriya : 46 - ci ildə baş verən əsas götürərək . orta`

**Context Size 2:**

1. `i ̇ stinadlar xarici keçidlər бухарский трактат о каллиграфах и художниках трактат о каллиграфах и х...`
2. `- ci ildə i ̇ raqa , hindistana və hətta oğlundan dörd il sonra " psm3 "`
3. `kateqoriya : şuşanın görməli yerləri kateqoriya : sionistlər kateqoriya : germi şəhristanının kəndlə...`

**Context Size 3:**

1. `. i ̇ ki cilddə . i cild . bakı : nafta - press , 2013 ) (`
2. `- ci ildə yarananlar kateqoriya : 8 iyunda yarananlar kateqoriya : universitas 21 kateqoriya : azərb...`
3. `i ̇ stinadlar xarici keçidlər həmçinin bax kateqoriya : yaponiya hüquqşünasları kateqoriya : azərbay...`

**Context Size 4:**

1. `. i ̇ stinadlar mənbə " treska " kateqoriya : avropa dağ sistemləri kateqoriya : gürcüstan relyefi k...`
2. `̇ stinadlar kateqoriya : traktorçular kateqoriya : azərbaycan pambıqçıları kateqoriya : azərbaycan s...`
3. `i ̇ stinadlar kateqoriya : xorvatiyanın olimpiya həndbolçuları kateqoriya : 2016 yay olimpiya oyunla...`


### Key Findings

- **Best Predictability:** Context-4 with 93.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,281,437 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 | 807,823 |
| Total Tokens | 58,755,251 |
| Mean Frequency | 72.73 |
| Median Frequency | 4 |
| Frequency Std Dev | 2550.61 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | və | 1,490,176 |
| 2 | i | 892,240 |
| 3 | ci | 455,280 |
| 4 | ildə | 414,485 |
| 5 | ilə | 413,230 |
| 6 | kateqoriya | 366,496 |
| 7 | bir | 366,287 |
| 8 | bu | 362,130 |
| 9 | azərbaycan | 248,838 |
| 10 | də | 234,167 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | cërrik | 2 |
| 2 | liamın | 2 |
| 3 | liamla | 2 |
| 4 | backstab | 2 |
| 5 | antonioi | 2 |
| 6 | nipissinq | 2 |
| 7 | votivkirche | 2 |
| 8 | pirtle | 2 |
| 9 | takaxasinin | 2 |
| 10 | caporael | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9771 |
| R² (Goodness of Fit) | 0.992093 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.3% |
| Top 1,000 | 46.6% |
| Top 5,000 | 66.6% |
| Top 10,000 | 74.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9921 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.3% of corpus
- **Long Tail:** 797,823 words needed for remaining 25.5% 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)

### Model Comparison

| Model | Vocab Size | Dimension | Avg Norm | Std Norm | Isotropy |
|-------|------------|-----------|----------|----------|----------|
| **mono_32d** | 509,900 | 32 | 3.229 | 0.928 | 0.8153 🏆 |
| **mono_64d** | 509,900 | 64 | 3.675 | 0.940 | 0.8024 |
| **mono_128d** | 509,900 | 128 | 4.156 | 0.943 | 0.7626 |
| **embeddings_enhanced** | 0 | 0 | 0.000 | 0.000 | 0.0000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8153 (more uniform distribution)
- **Dimension Trade-off:** Higher dimensions capture more semantics but reduce isotropy
- **Vocabulary Coverage:** All models cover 509,900 words
- **Recommendation:** 100d for balanced semantic capture and efficiency

---
## 6. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **32k BPE** | Best compression (4.56x) with low UNK rate |
| N-gram | **5-gram** | Lowest perplexity (463) |
| Markov | **Context-4** | Highest predictability (93.4%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |

---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  publisher = {HuggingFace},
  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)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2025-12-27 22:29:22*