---
language: be
language_name: Belarusian
language_family: slavic_east
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-slavic_east
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: 4.771
  - name: best_isotropy
    type: isotropy
    value: 0.6444
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-06
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Belarusian** 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** | 3.599x | 3.60 | 0.0489% | 286,335 |
| **16k** | 4.042x | 4.05 | 0.0549% | 254,965 |
| **32k** | 4.455x | 4.46 | 0.0605% | 231,292 |
| **64k** | 4.771x 🏆 | 4.78 | 0.0648% | 215,975 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ланавычы () — вёска ў Самбірскім раёне Львоўскай вобласці Украіны. Крыніцы пункт...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ла на вы чы ▁() ▁— ▁вёска ▁ў ▁сам бі ... (+12 more)` | 22 |
| 16k | `▁ла на вы чы ▁() ▁— ▁вёска ▁ў ▁сам бі ... (+12 more)` | 22 |
| 32k | `▁ла на вычы ▁() ▁— ▁вёска ▁ў ▁самбі рскім ▁раёне ... (+9 more)` | 19 |
| 64k | `▁лана вычы ▁() ▁— ▁вёска ▁ў ▁самбірскім ▁раёне ▁львоўскай ▁вобласці ... (+6 more)` | 16 |

**Sample 2:** `Марсо () — французскае прозвішча. Вядомыя носьбіты Марсель Марсо, французскі арт...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁мар со ▁() ▁— ▁француз скае ▁прозвішча . ▁вядомыя ▁носьбіты ... (+17 more)` | 27 |
| 16k | `▁мар со ▁() ▁— ▁француз скае ▁прозвішча . ▁вядомыя ▁носьбіты ... (+16 more)` | 26 |
| 32k | `▁мар со ▁() ▁— ▁француз скае ▁прозвішча . ▁вядомыя ▁носьбіты ... (+15 more)` | 25 |
| 64k | `▁мар со ▁() ▁— ▁французскае ▁прозвішча . ▁вядомыя ▁носьбіты ▁марсель ... (+14 more)` | 24 |

**Sample 3:** `Вораніў () — вёска ў Гарадэнкіўскім раёне Івана-Франкоўскай вобласці Украіны. Кр...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁вора ніў ▁() ▁— ▁вёска ▁ў ▁гарад эн кі ўскім ... (+21 more)` | 31 |
| 16k | `▁вора ніў ▁() ▁— ▁вёска ▁ў ▁гарад эн кіўскім ▁раёне ... (+18 more)` | 28 |
| 32k | `▁вора ніў ▁() ▁— ▁вёска ▁ў ▁гарад эн кіўскім ▁раёне ... (+17 more)` | 27 |
| 64k | `▁вора ніў ▁() ▁— ▁вёска ▁ў ▁гарад эн кіўскім ▁раёне ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 64k achieves 4.771x compression
- **Lowest UNK Rate:** 8k with 0.0489% 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 | 115,602 | 16.82 | 1,101,685 | 11.4% | 25.2% |
| **2-gram** | Subword | 453 🏆 | 8.82 | 15,623 | 55.9% | 96.8% |
| **3-gram** | Word | 178,210 | 17.44 | 1,692,602 | 11.7% | 25.1% |
| **3-gram** | Subword | 4,191 | 12.03 | 146,010 | 18.7% | 59.5% |
| **4-gram** | Word | 289,150 | 18.14 | 2,823,610 | 9.4% | 24.9% |
| **4-gram** | Subword | 25,327 | 14.63 | 932,448 | 8.0% | 29.4% |
| **5-gram** | Word | 212,986 | 17.70 | 2,118,708 | 8.7% | 25.2% |
| **5-gram** | Subword | 104,621 | 16.67 | 3,234,164 | 4.5% | 17.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `0 10` | 188,589 |
| 2 | `10 0` | 184,434 |
| 3 | `0 09` | 178,217 |
| 4 | `09 0` | 172,685 |
| 5 | `у годзе` | 141,829 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `0 10 0` | 183,055 |
| 2 | `0 09 0` | 171,685 |
| 3 | `0 11 0` | 133,047 |
| 4 | `0 08 0` | 125,665 |
| 5 | `0 07 0` | 84,761 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `0 44 0 10` | 28,229 |
| 2 | `44 0 10 0` | 27,892 |
| 3 | `0 47 0 10` | 27,125 |
| 4 | `47 0 10 0` | 26,709 |
| 5 | `0 50 0 10` | 26,628 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `0 44 0 10 0` | 27,892 |
| 2 | `0 47 0 10 0` | 26,707 |
| 3 | `0 50 0 10 0` | 26,249 |
| 4 | `0 45 0 10 0` | 25,524 |
| 5 | `0 49 0 10 0` | 24,716 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 7,411,164 |
| 2 | `н а` | 5,858,867 |
| 3 | `р а` | 5,764,007 |
| 4 | `к а` | 4,983,576 |
| 5 | `_ п` | 4,779,657 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ п а` | 2,113,963 |
| 2 | `_ 0 ,` | 1,872,411 |
| 3 | `_ н а` | 1,678,358 |
| 4 | `н а _` | 1,430,853 |
| 5 | `_ п р` | 1,351,115 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а г а _` | 985,197 |
| 2 | `_ п р а` | 752,091 |
| 3 | `_ г о д` | 714,067 |
| 4 | `_ н а _` | 694,537 |
| 5 | `к а й _` | 548,513 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `к а г а _` | 467,479 |
| 2 | `с к а й _` | 409,977 |
| 3 | `с к а г а` | 393,058 |
| 4 | `б е л а р` | 392,561 |
| 5 | `е л а р у` | 392,043 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 453
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~17% 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 | 0.9802 | 1.973 | 10.66 | 1,600,794 | 2.0% |
| **1** | Subword | 0.4743 | 1.389 | 3.96 | 16,475 | 52.6% |
| **2** | Word | 0.3132 | 1.242 | 1.95 | 17,028,048 | 68.7% |
| **2** | Subword | 0.6391 | 1.557 | 4.81 | 65,298 | 36.1% |
| **3** | Word | 0.1128 | 1.081 | 1.23 | 33,045,925 | 88.7% |
| **3** | Subword | 0.8191 | 1.764 | 4.91 | 313,830 | 18.1% |
| **4** | Word | 0.0455 🏆 | 1.032 | 1.08 | 40,473,004 | 95.4% |
| **4** | Subword | 0.7606 | 1.694 | 3.75 | 1,541,159 | 23.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `0 06 0 1 мінскай вобласці беларусі ў раёне віцебскай губерні земскага самакіравання якая выказалася ...`
2. `і дзіцячы сад каралевы якія выменьвалі ў эджбастане бірмінгем сіці манчэстэр юнайтэд дзе адносна нев...`
3. `у годзе стала ўскосным выглядзе шоу consecința istorică sibiu mitropolitul andrei yahorau alena маё ...`

**Context Size 2:**

1. `0 10 0 34 0 12 0 38 0 11 0 53 0 09 0 41 0`
2. `10 0 55 0 09 0 46 0 10 0 63 0 08 0 75 0 07`
3. `0 09 0 54 0 09 0 47 0 10 0 48 0 10 0 45 0`

**Context Size 3:**

1. `0 10 0 37 0 12 0 45 0 10 0 60 0 08 0 58 0 09`
2. `0 09 0 54 0 09 0 50 0 09 so a 0 67 0 08 0 79`
3. `0 11 0 47 0 10 0 54 0 09 0 48 0 10 0 43 0 11`

**Context Size 4:**

1. `0 44 0 10 0 40 0 11 0 54 0 32 0 45 0 32 0 56 0`
2. `44 0 10 0 47 0 10 0 48 0 10 0 48 0 10 0 57 0 06`
3. `0 47 0 10 0 54 0 09 0 87 0 06 sbbc 0 78 0 07 0 47`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_бек»_мано_szk._`
2. `аёрларныкльбеніц`
3. `нагркаў_вай_stol`

**Context Size 2:**

1. `а_вылкі_ў_парышша`
2. `на_апілік_вы,_які`
3. `раў_звагарскаў_вы`

**Context Size 3:**

1. `_памка:_ю._тайскаг`
2. `_0,53_0,42_0,43_0,`
3. `_насцю_і_тавіч_см.`

**Context Size 4:**

1. `ага_заняў_і_паведа,`
2. `_прасійскаў_супольс`
3. `_годзе_прыезда_філь`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,541,159 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 | 741,819 |
| Total Tokens | 55,243,342 |
| Mean Frequency | 74.47 |
| Median Frequency | 4 |
| Frequency Std Dev | 3873.91 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 0 | 1,944,910 |
| 2 | і | 1,331,350 |
| 3 | у | 1,238,468 |
| 4 | ў | 1,161,043 |
| 5 | з | 862,221 |
| 6 | на | 708,262 |
| 7 | года | 367,568 |
| 8 | да | 290,434 |
| 9 | годзе | 258,378 |
| 10 | 10 | 239,964 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | девятке | 2 |
| 2 | дэкунаў | 2 |
| 3 | iovine | 2 |
| 4 | іавін | 2 |
| 5 | аёвіну | 2 |
| 6 | джэніка | 2 |
| 7 | мэрылінам | 2 |
| 8 | сардэшная | 2 |
| 9 | івасю | 2 |
| 10 | стеценко | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9714 |
| R² (Goodness of Fit) | 0.997383 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 29.3% |
| Top 1,000 | 50.6% |
| Top 5,000 | 67.4% |
| Top 10,000 | 74.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9974 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 29.3% of corpus
- **Long Tail:** 731,819 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)


### 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 | 0.6096 | 0.3533 | N/A | N/A |
| **mono_64d** | 64 | 0.6408 | 0.2859 | N/A | N/A |
| **mono_128d** | 128 | 0.6444 | 0.2271 | N/A | N/A |
| **aligned_32d** | 32 | 0.6096 | 0.3568 | 0.0440 | 0.3040 |
| **aligned_64d** | 64 | 0.6408 | 0.2908 | 0.1380 | 0.5080 |
| **aligned_128d** | 128 | 0.6444 🏆 | 0.2362 | 0.2300 | 0.6220 |

### Key Findings

- **Best Isotropy:** aligned_128d with 0.6444 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2917. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 23.0% 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 | **0.467** | 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 |
|--------|----------|
| `-па` | параллельной, падаплёка, падкіданні |
| `-ка` | канавалава, кафедрамі, калеснікава |
| `-пр` | прышчэпаўшчына, прыпяцкі, прапіткі |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | гароха, прышчэпаўшчына, падаплёка |
| `-га` | паўднёвага, іпацеўскага, міжазёрнага |
| `-кі` | леанінскі, прыпяцкі, прапіткі |
| `-ай` | кіянкай, ольстэрскай, найноўшай |
| `-ага` | паўднёвага, іпацеўскага, міжазёрнага |
| `-ая` | рудэральная, прымененая, свальбардская |
| `-аў` | шакіраваў, вігаў, шукальнікаў |
| `-на` | прышчэпаўшчына, непэсрэдна, скампанавана |

### 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 |
|------|----------|------------------|----------|
| `анск` | 1.51x | 1027 contexts | ганск, данск, канск |
| `нска` | 1.55x | 503 contexts | унска, янска, інская |
| `насц` | 1.79x | 190 contexts | насце, насця, насцю |
| `асел` | 2.08x | 87 contexts | асель, аселі, расел |
| `елар` | 2.39x | 47 contexts | белар, селар, гелар |
| `ўска` | 1.58x | 236 contexts | еўска, іўска, ёўскае |
| `аецц` | 2.20x | 48 contexts | маецца, каецца, лаецца |
| `тычн` | 1.49x | 233 contexts | этычны, стычня, этычна |
| `нскі` | 1.34x | 416 contexts | енскі, янскі, інскі |
| `ельн` | 1.32x | 342 contexts | ельню, ельна, ельні |
| `ходз` | 1.47x | 182 contexts | ходзі, ходза, ходзь |
| `ання` | 1.47x | 174 contexts | рання, вання, арання |

### 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 |
|--------|--------|-----------|----------|
| `-па` | `-а` | 57 words | падлічваюцца, павета |
| `-ка` | `-а` | 51 words | карахана, каралькова |
| `-пр` | `-а` | 33 words | прынцэса, працягваюцца |
| `-па` | `-ыя` | 14 words | падпружныя, пасярэбраныя |
| `-па` | `-ай` | 14 words | паўлавіцкай, пагібельнай |
| `-ка` | `-ая` | 14 words | карнуая, карэспандэнцкая |
| `-ка` | `-на` | 13 words | карахана, кадрына |
| `-ка` | `-га` | 13 words | калевальскага, каларадскага |
| `-па` | `-кі` | 13 words | пакупкі, палачанкі |
| `-па` | `-га` | 13 words | папаленага, палаткавага |

### 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 |
|------|-----------------|------------|------|
| галіцынаўка | **`галіцын-аў-ка`** | 6.0 | `галіцын` |
| перакладчыкаў | **`перакладчык-аў`** | 4.5 | `перакладчык` |
| зікуратаў | **`зікурат-аў`** | 4.5 | `зікурат` |
| астраблемай | **`астраблем-ай`** | 4.5 | `астраблем` |
| авіяатрадаў | **`авіяатрад-аў`** | 4.5 | `авіяатрад` |
| гукарадаў | **`гукарад-аў`** | 4.5 | `гукарад` |
| цырульнікаў | **`цырульнік-аў`** | 4.5 | `цырульнік` |
| адпраўшчыкаў | **`адпраўшчык-аў`** | 4.5 | `адпраўшчык` |
| рэдэмптарыстаў | **`рэдэмптарыст-аў`** | 4.5 | `рэдэмптарыст` |
| кулінараў | **`кулінар-аў`** | 4.5 | `кулінар` |
| іньігесаў | **`іньігес-аў`** | 4.5 | `іньігес` |
| гэлтахтаў | **`гэлтахт-аў`** | 4.5 | `гэлтахт` |
| рэгістрацыйна | **`рэгістрацый-на`** | 4.5 | `рэгістрацый` |
| чапаеўскага | **`чапаеўск-ага`** | 4.5 | `чапаеўск` |
| грунтоўка | **`грунтоў-ка`** | 4.5 | `грунтоў` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Belarusian 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 (4.77x) |
| N-gram | **2-gram** | Lowest perplexity (453) |
| Markov | **Context-4** | Highest predictability (95.4%) |
| 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},
  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: 2026-01-06 15:57:39*