---
language: bar
language_name: BAR
language_family: germanic_west_continental
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - monolingual
  - family-germanic_west_continental
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: 3.790
  - name: best_isotropy
    type: isotropy
    value: 0.8361
  - name: vocabulary_size
    type: vocab
    value: 225914
generated: 2025-12-28
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **BAR** 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** | 3.051x | 3.01 | 0.0348% | 1,184,756 |
| **16k** | 3.320x | 3.27 | 0.0378% | 1,088,767 |
| **32k** | 3.568x | 3.52 | 0.0407% | 1,013,044 |
| **64k** | 3.790x 🏆 | 3.74 | 0.0432% | 953,541 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Platte County is a County in Nebraska in da USA.

 Beleg 

 Im Netz 

Kategorie:...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁plat te ▁county ▁is ▁a ▁county ▁in ▁nebraska ▁in ▁da ... (+10 more)` | 20 |
| 16k | `▁plat te ▁county ▁is ▁a ▁county ▁in ▁nebraska ▁in ▁da ... (+10 more)` | 20 |
| 32k | `▁platte ▁county ▁is ▁a ▁county ▁in ▁nebraska ▁in ▁da ▁usa ... (+9 more)` | 19 |
| 64k | `▁platte ▁county ▁is ▁a ▁county ▁in ▁nebraska ▁in ▁da ▁usa ... (+9 more)` | 19 |

**Sample 2:** `Union County. Obgruafa am 22. Feba 2011 is a County in South Carolina in da USA....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁union ▁county . ▁obgruafa ▁am ▁ 2 2 . ▁feba ... (+24 more)` | 34 |
| 16k | `▁union ▁county . ▁obgruafa ▁am ▁ 2 2 . ▁feba ... (+24 more)` | 34 |
| 32k | `▁union ▁county . ▁obgruafa ▁am ▁ 2 2 . ▁feba ... (+24 more)` | 34 |
| 64k | `▁union ▁county . ▁obgruafa ▁am ▁ 2 2 . ▁feba ... (+24 more)` | 34 |

**Sample 3:** `Des is a Iwablick iwas Joar 1561.

 Im Netz`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁des ▁is ▁a ▁iwablick ▁iwas ▁joar ▁ 1 5 6 ... (+4 more)` | 14 |
| 16k | `▁des ▁is ▁a ▁iwablick ▁iwas ▁joar ▁ 1 5 6 ... (+4 more)` | 14 |
| 32k | `▁des ▁is ▁a ▁iwablick ▁iwas ▁joar ▁ 1 5 6 ... (+4 more)` | 14 |
| 64k | `▁des ▁is ▁a ▁iwablick ▁iwas ▁joar ▁ 1 5 6 ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 64k achieves 3.790x compression
- **Lowest UNK Rate:** 8k with 0.0348% 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** | 26,677 🏆 | 14.70 | 159,756 | 14.4% | 35.4% |
| **2-gram** | 438 🏆 | 8.77 | 9,188 | 56.6% | 97.2% |
| **3-gram** | 61,390 | 15.91 | 246,468 | 9.0% | 25.7% |
| **3-gram** | 4,733 | 12.21 | 83,186 | 18.8% | 56.7% |
| **4-gram** | 99,269 | 16.60 | 386,315 | 9.1% | 23.6% |
| **4-gram** | 33,953 | 15.05 | 473,217 | 8.7% | 26.5% |

### Top 5 N-grams by Size

**2-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kategorie :` | 38,959 |
| 2 | `vo da` | 26,615 |
| 3 | `is a` | 23,040 |
| 4 | `in da` | 22,485 |
| 5 | `. de` | 21,082 |

**3-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `beleg kategorie :` | 6,999 |
| 2 | `isbn 3 -` | 5,924 |
| 3 | `. im netz` | 5,460 |
| 4 | `kategorie : ort` | 5,121 |
| 5 | `| | |` | 4,937 |

**4-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `, isbn 3 -` | 4,499 |
| 2 | `| align = "` | 3,879 |
| 3 | `align = " center` | 3,590 |
| 4 | `= " center "` | 3,590 |
| 5 | `kategorie : ort im` | 3,505 |


### Key Findings

- **Best Perplexity:** 2-gram with 438
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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** | 0.6074 | 1.523 | 4.85 | 638,594 | 39.3% |
| **1** | 1.0706 | 2.100 | 7.75 | 3,379 | 0.0% |
| **2** | 0.2487 | 1.188 | 1.74 | 3,093,978 | 75.1% |
| **2** | 0.9487 | 1.930 | 6.44 | 26,199 | 5.1% |
| **3** | 0.0996 | 1.071 | 1.21 | 5,375,695 | 90.0% |
| **3** | 0.9366 | 1.914 | 4.86 | 168,731 | 6.3% |
| **4** | 0.0401 🏆 | 1.028 | 1.07 | 6,470,090 | 96.0% |
| **4** | 0.7672 🏆 | 1.702 | 3.38 | 820,482 | 23.3% |

### Generated Text Samples

Below are text samples generated from each Markov chain model:

**Context Size 1:**

1. `. 524 angewachsen und die fläche vo dera zoagt , par les ' n ) u`
2. `, isbn 978 - mal 1920 bis auf des is kemnath ( " franz kafka .`
3. `- deitscha schauspuia und a zaumgroida schdrudl is ois broad bekaunnt hans ( 2016 saha air`

**Context Size 2:**

1. `kategorie : artikel auf niederösterreichisch kategorie : ortsteil von wieseth kategorie : geboren 18...`
2. `vo da mathematik , schau gorkhaland`
3. `is a bruck ' nschlåg ; da linné aun an rio xingu . as gericht håtn zu`

**Context Size 3:**

1. `beleg kategorie : johann nestroy ; stücke 21 . s . highway 84 mindt . uma 32 kilometa`
2. `isbn 3 - 417 - 20675 - 8 ( teubner - studienbücher der geographie ) . im joa`
3. `kategorie : ort auf den färöern kategorie : streymoy`

**Context Size 4:**

1. `, isbn 3 - 406 - 46224 - 3 birgit zotz : destination tibet . touristisches image zwischen politik`
2. `| align = " center " | | - | berleu | | | | | | | |`
3. `= " center " | | | align = " center " | | | fatututa | | align`


### Key Findings

- **Best Predictability:** Context-4 with 96.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (820,482 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 | 225,914 |
| Total Tokens | 5,874,699 |
| Mean Frequency | 26.00 |
| Median Frequency | 3 |
| Frequency Std Dev | 709.74 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 139,734 |
| 2 | da | 136,994 |
| 3 | und | 120,375 |
| 4 | in | 102,834 |
| 5 | a | 93,585 |
| 6 | vo | 92,275 |
| 7 | is | 88,045 |
| 8 | im | 71,546 |
| 9 | kategorie | 39,103 |
| 10 | des | 34,614 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mechanisches | 2 |
| 2 | stabilisierungssystem | 2 |
| 3 | voeffentlecht | 2 |
| 4 | innpuls | 2 |
| 5 | buagstej | 2 |
| 6 | nuwenburg | 2 |
| 7 | kulturweges | 2 |
| 8 | spessartprojektes | 2 |
| 9 | terrassnfermig | 2 |
| 10 | tuamhigi | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9896 |
| R² (Goodness of Fit) | 0.999155 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.7% |
| Top 1,000 | 54.6% |
| Top 5,000 | 70.2% |
| Top 10,000 | 76.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9992 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.7% of corpus
- **Long Tail:** 215,914 words needed for remaining 23.1% 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** | 92,573 | 32 | 3.954 | 1.316 | 0.8131 |
| **mono_64d** | 92,573 | 64 | 4.642 | 1.256 | 0.8361 🏆 |
| **mono_128d** | 92,573 | 128 | 5.543 | 1.143 | 0.8310 |
| **embeddings_enhanced** | 0 | 0 | 0.000 | 0.000 | 0.0000 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.8361 (more uniform distribution)
- **Dimension Trade-off:** Higher dimensions capture more semantics but reduce isotropy
- **Vocabulary Coverage:** All models cover 92,573 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 (3.79x) with low UNK rate |
| N-gram | **5-gram** | Lowest perplexity (438) |
| Markov | **Context-4** | Highest predictability (96.0%) |
| 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 00:09:41*