---
language: ce
language_name: CE
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: 3.716
  - name: best_isotropy
    type: isotropy
    value: 0.8750
  - name: vocabulary_size
    type: vocab
    value: 267119
generated: 2025-12-28
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **CE** 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** | 2.743x | 2.70 | 1.0676% | 595,703 |
| **16k** | 3.096x | 3.04 | 1.2050% | 527,806 |
| **32k** | 3.417x | 3.36 | 1.3298% | 478,250 |
| **64k** | 3.716x 🏆 | 3.65 | 1.4461% | 439,790 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ДагӀйурд () — Азербайджанан Ходжалин кӀоштара эвла.

 Бахархой 

 Билгалдахарш 
...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁да гӏ й ур д ▁() ▁— ▁азербайджанан ▁х од ... (+17 more)` | 27 |
| 16k | `▁дагӏ йур д ▁() ▁— ▁азербайджанан ▁ход ж алин ▁кӏоштара ... (+13 more)` | 23 |
| 32k | `▁дагӏ йур д ▁() ▁— ▁азербайджанан ▁ходжалин ▁кӏоштара ▁эвла . ... (+9 more)` | 19 |
| 64k | `▁дагӏ йур д ▁() ▁— ▁азербайджанан ▁ходжалин ▁кӏоштара ▁эвла . ... (+9 more)` | 19 |

**Sample 2:** `Перселл (Миссури)
 Перселл (Оклахома)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁пер сел л ▁( миссури ) ▁пер сел л ▁( ... (+2 more)` | 12 |
| 16k | `▁пер сел л ▁( миссури ) ▁пер сел л ▁( ... (+2 more)` | 12 |
| 32k | `▁пер сел л ▁( миссури ) ▁пер сел л ▁( ... (+2 more)` | 12 |
| 64k | `▁пер селл ▁( миссури ) ▁пер селл ▁( оклахома )` | 10 |

**Sample 3:** `Эль Баро (Мочитлан)
 Эль Баро (Сан Мигел Тотолапан)
 Эль Баро (Хенерал Элиодоро ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁эль ▁баро ▁( м оч ит лан ) ▁эль ▁баро ... (+21 more)` | 31 |
| 16k | `▁эль ▁баро ▁( м оч итлан ) ▁эль ▁баро ▁( ... (+18 more)` | 28 |
| 32k | `▁эль ▁баро ▁( м оч итлан ) ▁эль ▁баро ▁( ... (+11 more)` | 21 |
| 64k | `▁эль ▁баро ▁( моч итлан ) ▁эль ▁баро ▁( сан ... (+10 more)` | 20 |


### Key Findings

- **Best Compression:** 64k achieves 3.716x compression
- **Lowest UNK Rate:** 8k with 1.0676% 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** | 3,434 🏆 | 11.75 | 180,710 | 25.5% | 63.0% |
| **2-gram** | 484 🏆 | 8.92 | 7,755 | 52.4% | 97.1% |
| **3-gram** | 5,932 | 12.53 | 322,719 | 16.0% | 53.7% |
| **3-gram** | 2,779 | 11.44 | 72,318 | 22.8% | 66.2% |
| **4-gram** | 7,779 | 12.93 | 709,202 | 12.7% | 49.4% |
| **4-gram** | 7,269 | 12.83 | 422,662 | 15.4% | 47.3% |

### Top 5 N-grams by Size

**2-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. —` | 1,635,703 |
| 2 | `категори :` | 1,346,163 |
| 3 | `нах беха` | 1,039,301 |
| 4 | `беха меттигаш` | 953,016 |
| 5 | `м .` | 797,532 |

**3-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `нах беха меттигаш` | 952,979 |
| 2 | `( ) —` | 477,700 |
| 3 | `меттигаш категори :` | 455,946 |
| 4 | `беха меттигаш категори` | 448,323 |
| 5 | `. а .` | 416,844 |

**4-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `беха меттигаш категори :` | 448,323 |
| 2 | `нах беха меттигаш категори` | 448,323 |
| 3 | `. — м .` | 345,745 |
| 4 | `— м . :` | 345,423 |
| 5 | `кӏоштан нах беха меттигаш` | 256,924 |


### Key Findings

- **Best Perplexity:** 2-gram with 484
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~47% 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** | 0.4898 | 1.404 | 3.61 | 596,401 | 51.0% |
| **1** | 1.0551 | 2.078 | 11.42 | 1,510 | 0.0% |
| **2** | 0.2471 | 1.187 | 1.75 | 2,141,469 | 75.3% |
| **2** | 1.0286 | 2.040 | 7.78 | 17,227 | 0.0% |
| **3** | 0.1096 | 1.079 | 1.30 | 3,726,034 | 89.0% |
| **3** | 0.8548 | 1.809 | 4.95 | 133,970 | 14.5% |
| **4** | 0.0635 🏆 | 1.045 | 1.17 | 4,825,259 | 93.6% |
| **4** | 0.7262 🏆 | 1.654 | 3.28 | 662,768 | 27.4% |

### Generated Text Samples

Below are text samples generated from each Markov chain model:

**Context Size 1:**

1. `. геогр . — м . а беттанашкахь , цуьнан гуш болу седин атмосфера конвекцина дикка`
2. `, йуккъера барам 2000 . изд . catherine b . surface properties of chicle extraction in`
3. `— июль ( по зарубежным странам ) кӏеззиг къилбаседехьа хокана мотт буьйцуш долу ӏаьнцаклимат калужск...`

**Context Size 2:**

1. `. — екатеринбург : у - фактория , 2006 . альперович м . родригеса , м .`
2. `категори : сербин нах беха меттигаш категори : мексикин нах беха меттигаш категори : витебскан облас...`
3. `нах беха меттигаш категори : мексикин нах беха меттиг . географи . бахархойн дукхалла бахархойн дукх...`

**Context Size 3:**

1. `( ) — российн федерацин вологдин областан междуреченскан кӏоштара дӏатесна эвла . бахархойн дукхалла...`
2. `нах беха меттигаш категори : молдавин нах беха меттигаш категори : ацш гуонаш ru : калмен ( округ`
3. `меттигаш категори : идальго штатан нах беха меттигаш категори : белхан категори категори : новосибир...`

**Context Size 4:**

1. `беха меттигаш категори : подлясьен воеводаллин нах беха меттигаш категори : абатца нисйина нах беха ...`
2. `нах беха меттигаш категори : лаха калифорни штатан нах беха меттигаш категори : вилча жудецан коммун...`
3. `. — м . : высшая школа , 2005 . — 463 с . — isbn 5060045196 . новая`


### Key Findings

- **Best Predictability:** Context-4 with 93.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (662,768 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 | 267,119 |
| Total Tokens | 73,448,738 |
| Mean Frequency | 274.97 |
| Median Frequency | 3 |
| Frequency Std Dev | 8220.95 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | а | 1,816,439 |
| 2 | категори | 1,354,932 |
| 3 | нах | 1,049,211 |
| 4 | беха | 1,039,698 |
| 5 | меттигаш | 968,759 |
| 6 | йу | 814,168 |
| 7 | м | 798,682 |
| 8 | климат | 741,279 |
| 9 | в | 737,093 |
| 10 | билгалдахарш | 631,115 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | эмпачадо | 2 |
| 2 | энано | 2 |
| 3 | эскопетал | 2 |
| 4 | эскриторио | 2 |
| 5 | макариос | 2 |
| 6 | эроика | 2 |
| 7 | скирринг | 2 |
| 8 | зигуинчор | 2 |
| 9 | зигуиншор | 2 |
| 10 | люксембургхо | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.8071 |
| R² (Goodness of Fit) | 0.946340 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 40.3% |
| Top 1,000 | 81.6% |
| Top 5,000 | 96.4% |
| Top 10,000 | 97.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9463 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 40.3% of corpus
- **Long Tail:** 257,119 words needed for remaining 2.4% 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** | 105,624 | 32 | 6.269 | 1.405 | 0.8750 🏆 |
| **mono_64d** | 105,624 | 64 | 6.426 | 0.986 | 0.8540 |
| **mono_128d** | 105,624 | 128 | 6.612 | 0.771 | 0.7972 |
| **embeddings_enhanced** | 0 | 0 | 0.000 | 0.000 | 0.0000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8750 (more uniform distribution)
- **Dimension Trade-off:** Higher dimensions capture more semantics but reduce isotropy
- **Vocabulary Coverage:** All models cover 105,624 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 (3.72x) with low UNK rate |
| N-gram | **5-gram** | Lowest perplexity (484) |
| Markov | **Context-4** | Highest predictability (93.6%) |
| 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},
  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: 2025-12-28 17:05:28*