README.md

---
language: rue
language_name: Rusyn
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: 4.411
  - name: best_isotropy
    type: isotropy
    value: 0.8842
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Rusyn** 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** | 3.290x | 3.29 | 0.1243% | 213,920 |
| **16k** | 3.670x | 3.68 | 0.1387% | 191,769 |
| **32k** | 4.068x | 4.07 | 0.1537% | 173,017 |
| **64k** | 4.411x 🏆 | 4.42 | 0.1667% | 159,569 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Мокре є село на юговыходї Польска, котре было до акції Вісла лемківске. См. тыж ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁мо кре ▁є ▁село ▁на ▁юговыходї ▁польска , ▁котре ▁было ... (+21 more)` | 31 |
| 16k | `▁мо кре ▁є ▁село ▁на ▁юговыходї ▁польска , ▁котре ▁было ... (+20 more)` | 30 |
| 32k | `▁мо кре ▁є ▁село ▁на ▁юговыходї ▁польска , ▁котре ▁было ... (+20 more)` | 30 |
| 64k | `▁мокре ▁є ▁село ▁на ▁юговыходї ▁польска , ▁котре ▁было ▁до ... (+16 more)` | 26 |

**Sample 2:** `Подїї Народили ся Вмерли 6. авґуст - Дієґо Веласкес - іспаньскый малярь.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁подїї ▁народили ▁ся ▁вмерли ▁ 6 . ▁авґуст ▁- ▁ді ... (+11 more)` | 21 |
| 16k | `▁подїї ▁народили ▁ся ▁вмерли ▁ 6 . ▁авґуст ▁- ▁діє ... (+8 more)` | 18 |
| 32k | `▁подїї ▁народили ▁ся ▁вмерли ▁ 6 . ▁авґуст ▁- ▁дієґо ... (+5 more)` | 15 |
| 64k | `▁подїї ▁народили ▁ся ▁вмерли ▁ 6 . ▁авґуст ▁- ▁дієґо ... (+5 more)` | 15 |

**Sample 3:** `Браззавіль є головне місто Републикы Конґо. Браззавіль ся находить на ріцї Конґо...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁б раз зав і ль ▁є ▁головне ▁місто ▁републикы ▁конґо ... (+27 more)` | 37 |
| 16k | `▁б раз зав і ль ▁є ▁головне ▁місто ▁републикы ▁конґо ... (+26 more)` | 36 |
| 32k | `▁б раз зав іль ▁є ▁головне ▁місто ▁републикы ▁конґо . ... (+24 more)` | 34 |
| 64k | `▁браззавіль ▁є ▁головне ▁місто ▁републикы ▁конґо . ▁браззавіль ▁ся ▁находить ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 4.411x compression
- **Lowest UNK Rate:** 8k with 0.1243% 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 | 10,614 | 13.37 | 24,546 | 14.0% | 37.4% |
| **2-gram** | Subword | 526 🏆 | 9.04 | 5,647 | 52.8% | 95.7% |
| **3-gram** | Word | 9,841 | 13.26 | 24,254 | 15.8% | 40.1% |
| **3-gram** | Subword | 5,156 | 12.33 | 46,194 | 16.8% | 54.5% |
| **4-gram** | Word | 18,385 | 14.17 | 43,665 | 13.0% | 32.7% |
| **4-gram** | Subword | 30,193 | 14.88 | 223,060 | 7.1% | 26.5% |
| **5-gram** | Word | 13,867 | 13.76 | 33,423 | 14.6% | 35.9% |
| **5-gram** | Subword | 99,655 | 16.60 | 512,347 | 4.3% | 16.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `в року` | 3,677 |
| 2 | `и одказы` | 2,110 |
| 3 | `жерела и` | 2,110 |
| 4 | `у році` | 1,334 |
| 5 | `од року` | 1,180 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `жерела и одказы` | 2,105 |
| 2 | `до н е` | 598 |
| 3 | `є село на` | 537 |
| 4 | `ся споминать у` | 452 |
| 5 | `суть часточно або` | 406 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `суть часточно або цалком` | 406 |
| 2 | `тоты даны суть часточно` | 404 |
| 3 | `часточно або цалком основаны` | 403 |
| 4 | `даны суть часточно або` | 403 |
| 5 | `або цалком основаны на` | 403 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `суть часточно або цалком основаны` | 403 |
| 2 | `даны суть часточно або цалком` | 403 |
| 3 | `тоты даны суть часточно або` | 403 |
| 4 | `часточно або цалком основаны на` | 403 |
| 5 | `удкликованя тоты даны суть часточно` | 396 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 131,617 |
| 2 | `. _` | 114,502 |
| 3 | `_ п` | 111,446 |
| 4 | `, _` | 110,758 |
| 5 | `_ с` | 110,650 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ н а` | 45,319 |
| 2 | `_ п о` | 39,401 |
| 3 | `н а _` | 39,260 |
| 4 | `_ в _` | 33,668 |
| 5 | `ы й _` | 33,585 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ н а _` | 20,657 |
| 2 | `о г о _` | 19,623 |
| 3 | `_ с я _` | 17,241 |
| 4 | `н ы й _` | 13,918 |
| 5 | `_ р о к` | 12,809 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ к о т р` | 8,347 |
| 2 | `_ р о к у` | 8,240 |
| 3 | `р о к у _` | 7,765 |
| 4 | `с к о й _` | 7,639 |
| 5 | `к о г о _` | 7,038 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 526
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~16% 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 | 0.7013 | 1.626 | 4.03 | 211,794 | 29.9% |
| **1** | Subword | 1.1266 | 2.183 | 9.87 | 1,290 | 0.0% |
| **2** | Word | 0.1616 | 1.119 | 1.32 | 851,130 | 83.8% |
| **2** | Subword | 1.1281 | 2.186 | 6.90 | 12,737 | 0.0% |
| **3** | Word | 0.0409 | 1.029 | 1.06 | 1,118,017 | 95.9% |
| **3** | Subword | 0.9033 | 1.870 | 4.38 | 87,816 | 9.7% |
| **4** | Word | 0.0154 🏆 | 1.011 | 1.02 | 1,183,695 | 98.5% |
| **4** | Subword | 0.6650 | 1.586 | 2.78 | 384,232 | 33.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `в 182 663 марк ґарно 11 км по серии далшых ілустровав і дуже посполито знать кым`
2. `и египтом котрый мать але дѣдо и его мати різны фреквенції коло радиусом што стояли за`
3. `на рокенроли хоснують назву рѣкы уг о селѣ жило людий из найвеце познатый организатор медицины споло...`

**Context Size 2:**

1. `в року завойована наполеоном и перестала фунґовати ґеоґрафія село біляковка є на берегови жовтого мо...`
2. `жерела и одказы dukla ottův slovník naučný сонѣчный день звѣздный або сидеричный цивилный деньинтерв...`
3. `и одказы сахаров н а римского корсакова ксения борис годунов м п бажана к том 1 трёшников`

**Context Size 3:**

1. `жерела и одказы christopher mick lemberg lwow and lviv violence and ethnicity in a contested city pu...`
2. `до н е кетувім межи тым не быв зафіксованый у каноні до 2 стороча н е приблизноє число`
3. `є село на словеньску в окресї спіська нова вес кошіцькый край спіська нова вес обывательство зложіня...`

**Context Size 4:**

1. `суть часточно або цалком основаны на перекладі статі фонтиняси на украйиньскӯв вікіпедії чісло ревіз...`
2. `тоты даны суть часточно або цалком основаны на перекладї статї љубаништа на сирбськӯв вікіпедії чісл...`
3. `або цалком основаны на перекладі статі вулиця колекторна на украйиньскӯв вікіпедії чісло ревізії не ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_паламу_вщивѣген`
2. `овѣтукомаїй_матї`
3. `адака_біквій_рго`

**Context Size 2:**

1. `а_слїше,_ка,_—_ма`
2. `._30._фері_цесир_`
3. `_передалничналны.`

**Context Size 3:**

1. `_напад_фактерітова`
2. `_по_чика_етного_ві`
3. `на_рез_котры_суть:`

**Context Size 4:**

1. `_на_перемѣнчив_ся_к`
2. `ого_походять_в_часѣ`
3. `_ся_и_одказы_мадярс`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (384,232 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 | 84,558 |
| Total Tokens | 1,223,713 |
| Mean Frequency | 14.47 |
| Median Frequency | 3 |
| Frequency Std Dev | 217.87 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | в | 36,163 |
| 2 | и | 27,056 |
| 3 | на | 20,924 |
| 4 | ся | 17,775 |
| 5 | у | 13,552 |
| 6 | з | 11,579 |
| 7 | і | 11,179 |
| 8 | до | 8,169 |
| 9 | року | 8,165 |
| 10 | а | 7,713 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | материалознавства | 2 |
| 2 | функционалной | 2 |
| 3 | кришталох | 2 |
| 4 | горбаля | 2 |
| 5 | державотворчих | 2 |
| 6 | стремлѣнях | 2 |
| 7 | римьска | 2 |
| 8 | корно | 2 |
| 9 | везувий | 2 |
| 10 | апеннинах | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9166 |
| R² (Goodness of Fit) | 0.999279 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 27.8% |
| Top 1,000 | 49.1% |
| Top 5,000 | 66.9% |
| Top 10,000 | 75.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9993 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 27.8% of corpus
- **Long Tail:** 74,558 words needed for remaining 24.9% 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 | 0.8842 | 0.2989 | N/A | N/A |
| **mono_64d** | 64 | 0.8306 | 0.2451 | N/A | N/A |
| **mono_128d** | 128 | 0.4664 | 0.2104 | N/A | N/A |
| **aligned_32d** | 32 | 0.8842 🏆 | 0.3014 | 0.0240 | 0.1280 |
| **aligned_64d** | 64 | 0.8306 | 0.2433 | 0.0420 | 0.1980 |
| **aligned_128d** | 128 | 0.4664 | 0.2111 | 0.0580 | 0.2400 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8842 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2517. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.8% 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 | **1.231** | 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 |
|--------|----------|
| `-с` | статуса, снагов, сентиментализма |
| `-п` | писомны, пухов, половці |
| `-по` | половці, подкарпатске, події |
| `-в` | вырїшив, возродный, вызнаменаня |
| `-к` | контраст, калция, капитола |
| `-д` | дробных, довгы, достойне |
| `-м` | мучили, министерия, майдана |
| `-б` | бӯлш, братьска, будоватися |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | статуса, зараза, збірника |
| `-й` | фактичный, оперный, нижной |
| `-ый` | фактичный, оперный, возродный |
| `-и` | глядати, мучили, ледови |
| `-о` | судного, лондонского, стилізовано |
| `-ы` | писомны, шпеціалны, довгы |
| `-х` | дробных, формах, термінах |
| `-м` | джорджом, завершінём, урядном |

### 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 |
|------|----------|------------------|----------|
| `пере` | 2.10x | 80 contexts | перем, перес, переш |
| `ньск` | 1.98x | 75 contexts | коньска, даньска, бряньск |
| `ност` | 1.91x | 79 contexts | иностр, ностер, юность |
| `котр` | 2.08x | 43 contexts | котре, котрї, котря |
| `блас` | 2.53x | 21 contexts | область, обласна, областї |
| `ован` | 1.56x | 132 contexts | јован, йована, слован |
| `усин` | 2.20x | 31 contexts | кусин, русин, русинъ |
| `арпа` | 2.50x | 18 contexts | арпада, карпат, карпаты |
| `ласт` | 1.78x | 58 contexts | пласт, власті, класти |
| `карп` | 2.45x | 18 contexts | карпов, карпат, карпаты |
| `ател` | 1.77x | 45 contexts | сателит, нательо, нушател |
| `обла` | 2.41x | 15 contexts | облак, облапя, облакы |

### 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 |
|--------|--------|-----------|----------|
| `-п` | `-а` | 118 words | печатна, пострадала |
| `-п` | `-и` | 106 words | пристройили, підсумками |
| `-п` | `-й` | 87 words | передчасной, працовной |
| `-с` | `-а` | 67 words | справована, суверенітета |
| `-к` | `-а` | 64 words | кіла, костянтинівка |
| `-с` | `-й` | 62 words | ставровский, судовый |
| `-п` | `-я` | 61 words | переименованя, плачіня |
| `-к` | `-й` | 60 words | класічной, кашырьскый |
| `-п` | `-ы` | 57 words | полемикы, польовы |
| `-п` | `-м` | 56 words | позорованём, педаґоґічнім |

### 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 |
|------|-----------------|------------|------|
| прибивать | **`прибив-а-ть`** | 7.5 | `а` |
| финанчного | **`финанчн-о-го`** | 7.5 | `о` |
| признаками | **`призна-ка-ми`** | 7.5 | `ка` |
| жетысуская | **`жетысус-ка-я`** | 7.5 | `ка` |
| вопросами | **`вопрос-а-ми`** | 7.5 | `а` |
| крестного | **`крест-но-го`** | 6.0 | `крест` |
| заселеный | **`за-селен-ый`** | 6.0 | `селен` |
| старовікыма | **`старовік-ым-а`** | 6.0 | `старовік` |
| лингвистох | **`лингвист-ох`** | 4.5 | `лингвист` |
| шпециалного | **`шпециално-го`** | 4.5 | `шпециално` |
| традициях | **`традиция-х`** | 4.5 | `традиция` |
| аристотела | **`аристотел-а`** | 4.5 | `аристотел` |
| прінціпів | **`прінціпі-в`** | 4.5 | `прінціпі` |
| генерална | **`генерал-на`** | 4.5 | `генерал` |
| организмох | **`организм-ох`** | 4.5 | `организм` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Rusyn 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 (4.41x) |
| N-gram | **2-gram** | Lowest perplexity (526) |
| Markov | **Context-4** | Highest predictability (98.5%) |
| 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},
  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: 2026-01-10 19:06:10*