---
language: av
language_name: AV
language_family: caucasian_northeast
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - monolingual
  - family-caucasian_northeast
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: 4.583
  - name: best_isotropy
    type: isotropy
    value: 0.8716
  - name: vocabulary_size
    type: vocab
    value: 38576
generated: 2025-12-27
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **AV** 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** | 3.534x | 3.49 | 0.0801% | 219,599 |
| **16k** | 3.897x | 3.84 | 0.0884% | 199,103 |
| **32k** | 4.254x | 4.20 | 0.0965% | 182,410 |
| **64k** | 4.583x 🏆 | 4.52 | 0.1039% | 169,325 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Кванирукъ (латиназул мацӀалда ventriculus) — гӀадамасул лага-черх. 

Категория:Г...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁кван ир укъ ▁( латиназул ▁мацӏалда ▁v ent ric ul ... (+14 more)` | 24 |
| 16k | `▁кван ир укъ ▁( латиназул ▁мацӏалда ▁v ent ric ulus ... (+13 more)` | 23 |
| 32k | `▁кванирукъ ▁( латиназул ▁мацӏалда ▁v ent ric ulus ) ▁— ... (+11 more)` | 21 |
| 64k | `▁кванирукъ ▁( латиназул ▁мацӏалда ▁vent ric ulus ) ▁— ▁гӏадамасул ... (+10 more)` | 20 |

**Sample 2:** `Гудермес ( ) — Россиялъул Буртиялъ жумхӀурияталда бугеб шагьар.
Сунж-хъалаялдаса...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁г уд ер мес ▁( ▁) ▁— ▁россиялъул ▁бурт иялъ ... (+36 more)` | 46 |
| 16k | `▁гуд ер мес ▁( ▁) ▁— ▁россиялъул ▁бурт иялъ ▁жум ... (+33 more)` | 43 |
| 32k | `▁гудермес ▁( ▁) ▁— ▁россиялъул ▁буртиялъ ▁жумхӏ урият алда ▁бугеб ... (+25 more)` | 35 |
| 64k | `▁гудермес ▁( ▁) ▁— ▁россиялъул ▁буртиялъ ▁жумхӏурият алда ▁бугеб ▁шагьар ... (+22 more)` | 32 |

**Sample 3:** `Лъугьа-бахъинал 

 Гьаруна 

 Хвана 


Категория:1927`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁лъугьа - бахъинал ▁гьаруна ▁хвана ▁категория : 1 9 2 ... (+1 more)` | 11 |
| 16k | `▁лъугьа - бахъинал ▁гьаруна ▁хвана ▁категория : 1 9 2 ... (+1 more)` | 11 |
| 32k | `▁лъугьа - бахъинал ▁гьаруна ▁хвана ▁категория : 1 9 2 ... (+1 more)` | 11 |
| 64k | `▁лъугьа - бахъинал ▁гьаруна ▁хвана ▁категория : 1 9 2 ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 64k achieves 4.583x compression
- **Lowest UNK Rate:** 8k with 0.0801% 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** | 5,221 🏆 | 12.35 | 14,725 | 20.8% | 49.4% |
| **2-gram** | 502 🏆 | 8.97 | 5,314 | 55.0% | 94.9% |
| **3-gram** | 8,074 | 12.98 | 19,718 | 16.9% | 42.5% |
| **3-gram** | 4,078 | 11.99 | 36,896 | 22.5% | 60.1% |
| **4-gram** | 18,096 | 14.14 | 39,973 | 12.6% | 31.2% |
| **4-gram** | 18,482 | 14.17 | 151,649 | 12.4% | 35.7% |

### Top 5 N-grams by Size

**2-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `категория :` | 6,060 |
| 2 | `) .` | 2,431 |
| 3 | `) ,` | 2,098 |
| 4 | `) —` | 1,555 |
| 5 | `. —` | 1,376 |

**3-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. география росу` | 645 |
| 2 | `география росу буго` | 645 |
| 3 | `. категория :` | 622 |
| 4 | `мугъчӏваял категория :` | 614 |
| 5 | `лъугьа - бахъинал` | 597 |

**4-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. география росу буго` | 630 |
| 2 | `география росу буго мухъалъул` | 513 |
| 3 | `. мугъчӏваял категория :` | 483 |
| 4 | `лъугьа - бахъинал гьаруна` | 471 |
| 5 | `- бахъинал гьаруна хвана` | 461 |


### Key Findings

- **Best Perplexity:** 2-gram with 502
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~36% 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** | 0.5741 | 1.489 | 3.65 | 105,500 | 42.6% |
| **1** | 1.3715 | 2.587 | 12.28 | 1,091 | 0.0% |
| **2** | 0.1898 | 1.141 | 1.41 | 384,678 | 81.0% |
| **2** | 1.0636 | 2.090 | 6.00 | 13,391 | 0.0% |
| **3** | 0.0614 | 1.043 | 1.11 | 542,652 | 93.9% |
| **3** | 0.8006 | 1.742 | 3.64 | 80,309 | 19.9% |
| **4** | 0.0249 🏆 | 1.017 | 1.04 | 599,240 | 97.5% |
| **4** | 0.5368 🏆 | 1.451 | 2.24 | 292,181 | 46.3% |

### Generated Text Samples

Below are text samples generated from each Markov chain model:

**Context Size 1:**

1. `. хундерилифастандартгьо ̄ ⲛ ̄ л . costumes caucasus circassians caucasus . — anatidae хъизан патагӏ...`
2. `, къагiидаби . амма руго . байрамал лъугьа - бакъбаккул кавказияб календар категория : гардарики ,`
3. `- абилеб ) мугъчӏваял категория : « вечера на хадидже категория : пко « моноклеr »`

**Context Size 2:**

1. `категория : гӏанди - гӏорул жанилъуда , ралъдал гьумералдаса 1869 метраялъ тіадегіан . хіоралъул тіа...`
2. `) . эратосфениде ( iii гӏ . байбихьи ) букіана патрикиясул титул , гьелдаса хадуб дагъистаналде .`
3. `) , лачен ( falco peregrinus ) , продолжительность 2 ч . ii – i гіасрабазул гіорхъода`

**Context Size 3:**

1. `география росу буго мухъалъул центер уркарахъалдаса 50 км - лъ жанубияб бакътӏерхьудехун . демографи...`
2. `. география росу буго ралъдал гьурматӏама 606 метралъ борхалъуда , мухъалъул центер хунзахъа шималия...`
3. `. категория : ираналъул останал * категория : азиялъул исламиял хіаракатчагіи категория : тіалибан`

**Context Size 4:**

1. `. география росу буго мухъалъул марказ лъаратӏаса 11 км - алъ шималалдехун . демография ккола моноэт...`
2. `география росу буго мухъалъул центер дешлахӏаралдаса 13 км - лъ рикӏкӏад . история 1886 соналъул бая...`
3. `. мугъчӏваял категория : гӏандалазул бол чагӏи категория : кавказалъул имамзаби`


### Key Findings

- **Best Predictability:** Context-4 with 97.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (292,181 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 | 38,576 |
| Total Tokens | 474,364 |
| Mean Frequency | 12.30 |
| Median Frequency | 3 |
| Frequency Std Dev | 81.10 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ва | 7,190 |
| 2 | категория | 6,086 |
| 3 | буго | 5,703 |
| 4 | бугеб | 2,911 |
| 5 | ккола | 2,903 |
| 6 | росу | 2,847 |
| 7 | мухъалъул | 2,671 |
| 8 | гьеб | 2,187 |
| 9 | дагъистаналъул | 1,923 |
| 10 | росдал | 1,903 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | уркутамахьи | 2 |
| 2 | континуумалде | 2 |
| 3 | къулецӏмаги | 2 |
| 4 | гьаркӏасуниб | 2 |
| 5 | махӏарги | 2 |
| 6 | пилибхиталъул | 2 |
| 7 | заповедникалда | 2 |
| 8 | пилибхит | 2 |
| 9 | лъалъадул | 2 |
| 10 | хӏанчӏи | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9487 |
| R² (Goodness of Fit) | 0.992879 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.2% |
| Top 1,000 | 49.8% |
| Top 5,000 | 72.6% |
| Top 10,000 | 82.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9929 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.2% of corpus
- **Long Tail:** 28,576 words needed for remaining 17.8% 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** | 12,900 | 32 | 4.114 | 0.854 | 0.8716 🏆 |
| **mono_64d** | 12,900 | 64 | 4.625 | 0.771 | 0.7752 |
| **mono_128d** | 12,900 | 128 | 4.775 | 0.759 | 0.3123 |
| **embeddings_enhanced** | 0 | 0 | 0.000 | 0.000 | 0.0000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8716 (more uniform distribution)
- **Dimension Trade-off:** Higher dimensions capture more semantics but reduce isotropy
- **Vocabulary Coverage:** All models cover 12,900 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 (4.58x) with low UNK rate |
| N-gram | **5-gram** | Lowest perplexity (502) |
| Markov | **Context-4** | Highest predictability (97.5%) |
| 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},
  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 20:39:38*