README.md

---
language: alt
language_name: Southern Altai
language_family: turkic_siberian
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-turkic_siberian
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: 3.686
  - name: best_isotropy
    type: isotropy
    value: 0.8419
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

# Southern Altai - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Southern Altai** 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** | 3.486x | 3.49 | 0.3992% | 972,913 |
| **16k** | 3.686x 🏆 | 3.69 | 0.4221% | 920,240 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Оҥныут кошуун () — ӧвӧр моҥолдыҥ кошуун. Этимологиязы Оҥныут — (калка моҥолдоп о...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁оҥныут ▁кошуун ▁() ▁— ▁ӧвӧр ▁моҥолдыҥ ▁кошуун . ▁этимологиязы ▁оҥныут ... (+27 more)` | 37 |
| 16k | `▁оҥныут ▁кошуун ▁() ▁— ▁ӧвӧр ▁моҥолдыҥ ▁кошуун . ▁этимологиязы ▁оҥныут ... (+25 more)` | 35 |

**Sample 2:** `Эски Чечкаб (, ) — јурт Россияда Татарстан Республиканыҥ Кайбыч аймагында кирет....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁эски ▁че ч ка б ▁(, ▁) ▁— ▁јурт ▁россияда ... (+12 more)` | 22 |
| 16k | `▁эски ▁чечкаб ▁(, ▁) ▁— ▁јурт ▁россияда ▁татарстан ▁республиканыҥ ▁кайбыч ... (+7 more)` | 17 |

**Sample 3:** `Танк - темирле јабылган тебингиштерлӱ јуучыл машина.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁танк ▁- ▁темир ле ▁ја б ылган ▁тебин ги ш ... (+6 more)` | 16 |
| 16k | `▁танк ▁- ▁темирле ▁јабылган ▁тебингиштерлӱ ▁јуучыл ▁машина .` | 8 |


### Key Findings

- **Best Compression:** 16k achieves 3.686x compression
- **Lowest UNK Rate:** 8k with 0.3992% 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 | 4,423 | 12.11 | 11,976 | 16.5% | 55.6% |
| **2-gram** | Subword | 413 🏆 | 8.69 | 2,708 | 55.2% | 98.2% |
| **3-gram** | Word | 5,471 | 12.42 | 16,254 | 15.6% | 52.1% |
| **3-gram** | Subword | 3,292 | 11.68 | 22,428 | 19.5% | 62.9% |
| **4-gram** | Word | 8,010 | 12.97 | 27,702 | 15.3% | 46.3% |
| **4-gram** | Subword | 14,003 | 13.77 | 96,467 | 10.5% | 35.7% |
| **5-gram** | Word | 7,318 | 12.84 | 24,542 | 16.3% | 46.7% |
| **5-gram** | Subword | 33,559 | 15.03 | 198,894 | 7.1% | 25.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `республики алтай` | 1,479 |
| 2 | `ј чык` | 1,391 |
| 3 | `горно алтайск` | 1,246 |
| 4 | `алтай республиканыҥ` | 1,220 |
| 5 | `ј бож` | 1,072 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `јылдыҥ ӱлӱрген айыныҥ` | 755 |
| 2 | `ӱлӱрген айыныҥ 15` | 730 |
| 3 | `алтайск ау ра` | 511 |
| 4 | `горно алтайск ау` | 511 |
| 5 | `јон јаткан јерлери` | 503 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `јылдыҥ ӱлӱрген айыныҥ 15` | 730 |
| 2 | `горно алтайск ау ра` | 511 |
| 3 | `болгон јылдыҥ ӱлӱрген айыныҥ` | 367 |
| 4 | `айыныҥ 15 кӱнине јетире` | 365 |
| 5 | `аайынча јылдыҥ ӱлӱрген айыныҥ` | 365 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `юлиан кӱнтизӱ аайынча јылдыҥ ӱлӱрген` | 365 |
| 2 | `кӱнтизӱ аайынча јылдыҥ ӱлӱрген айыныҥ` | 365 |
| 3 | `кӱнине јетире болгон јылдыҥ ӱлӱрген` | 365 |
| 4 | `юлиан кӱнтизӱни 13 кӱнге озолоп` | 365 |
| 5 | `кӱнтизӱ юлиан кӱнтизӱни 13 кӱнге` | 365 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ к` | 74,208 |
| 2 | `, _` | 64,571 |
| 3 | `_ ј` | 55,512 |
| 4 | `а _` | 55,147 |
| 5 | `ҥ _` | 53,924 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы ҥ _` | 34,158 |
| 2 | `д а _` | 16,990 |
| 3 | `_ — _` | 16,847 |
| 4 | `н ы ҥ` | 15,805 |
| 5 | `_ к а` | 15,039 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н ы ҥ _` | 15,207 |
| 2 | `д ы ҥ _` | 13,173 |
| 3 | `_ к ӱ н` | 11,135 |
| 4 | `а л т а` | 9,624 |
| 5 | `_ ј ы л` | 9,304 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а л т а й` | 8,736 |
| 2 | `_ ј ы л д` | 7,756 |
| 3 | `с к и й _` | 7,663 |
| 4 | `_ а л т а` | 6,748 |
| 5 | `й д ы ҥ _` | 5,904 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 413
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.7265 | 1.655 | 4.23 | 64,260 | 27.4% |
| **1** | Subword | 1.6376 | 3.112 | 16.04 | 301 | 0.0% |
| **2** | Word | 0.1676 | 1.123 | 1.34 | 271,928 | 83.2% |
| **2** | Subword | 1.3152 | 2.488 | 8.04 | 4,828 | 0.0% |
| **3** | Word | 0.0551 | 1.039 | 1.10 | 364,496 | 94.5% |
| **3** | Subword | 0.8837 | 1.845 | 4.16 | 38,825 | 11.6% |
| **4** | Word | 0.0265 🏆 | 1.019 | 1.05 | 400,428 | 97.3% |
| **4** | Subword | 0.6047 | 1.521 | 2.55 | 161,528 | 39.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ла ӧскӧ кижиниҥ адын масс системы но строеніемъ мерзокъ всё спишет вермахт понёс 90 км јаш`
2. `ле јолдоры јуртта 9 кӱнинде москвада в в ломоносова јылда гаагада переплётчик бичиктер берестяная гр...`
3. `алтай республика хакасия монголия горно алтайск гагу ныҥ јарымјылдык курстарына аткарылган оныҥ адыл...`

**Context Size 2:**

1. `республики алтай от 3 марта года n 9 6 о языках народов проживающих на территории республики алтай`
2. `ј чык совет ле россий орнитолог јурукчы анималист бу кӱнде божогондор ајарулар 27 айдыҥ 27 кӱни юлиа...`
3. `горно алтайск алтайдыҥ бичиктер чыгарар изд возы 1 эл опт диск cd rom на алт яз б`

**Context Size 3:**

1. `јылдыҥ ӱлӱрген айыныҥ 15 кӱнинеҥ ала тулаан айдыҥ 29 кӱнинде артист россияныҥ театрал ишчилериниҥ би...`
2. `ӱлӱрген айыныҥ 15 кӱнинеҥ ала кандык айдыҥ 15 кӱни юлиан кӱнтизӱ аайынча јылдыҥ ӱлӱрген айыныҥ 15 кӱ...`
3. `алтайск ау ра литературно издательский дом алтын туу сууда балык кезем астаган да болзо корулу јерле...`

**Context Size 4:**

1. `јылдыҥ ӱлӱрген айыныҥ 15 кӱнине јетире болгон јылдыҥ ӱлӱрген айыныҥ 15 кӱнине јетире болгон јылдыҥ ӱ...`
2. `горно алтайск ау ра литературно издательский дом алтын туу јайдыҥ бойында аркалары койу ла бийик ӧлӧ...`
3. `болгон јылдыҥ ӱлӱрген айыныҥ 15 кӱнинеҥ ала кӱӱк айдыҥ 6 кӱни григориан кӱнтизӱде јылдыҥ 360 кӱни ви...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_гатӱли»)_јектич`
2. `аканамикет_јыхих`
3. `ртакклан_онла_бь`

**Context Size 2:**

1. `_кыл,_баснов_кылг`
2. `,_29_21,97_малтал`
3. `_јуртиреспублик_а`

**Context Size 3:**

1. `ыҥ_кодондо_инфранс`
2. `да_православ_башка`
3. `_—_titus_liefs_asb`

**Context Size 4:**

1. `ныҥ_кандыра_агып_ба`
2. `дыҥ_физиканыҥ_ӱӱрел`
3. `_кӱнтизӱле_кӱни_гри`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (161,528 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 | 26,328 |
| Total Tokens | 565,164 |
| Mean Frequency | 21.47 |
| Median Frequency | 3 |
| Frequency Std Dev | 124.45 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ла | 6,601 |
| 2 | ле | 4,964 |
| 3 | алтай | 4,646 |
| 4 | деп | 3,903 |
| 5 | с | 3,881 |
| 6 | јылда | 3,745 |
| 7 | айдыҥ | 3,441 |
| 8 | болгон | 3,230 |
| 9 | км | 3,151 |
| 10 | јурт | 3,140 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | таскадуларды | 2 |
| 2 | туузаланат | 2 |
| 3 | узаныш | 2 |
| 4 | эрессейде | 2 |
| 5 | метеметике | 2 |
| 6 | јеткилдери | 2 |
| 7 | кӧмпӱтерлик | 2 |
| 8 | чоотош | 2 |
| 9 | кошлык | 2 |
| 10 | програмалары | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1627 |
| R² (Goodness of Fit) | 0.985919 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 27.1% |
| Top 1,000 | 65.7% |
| Top 5,000 | 85.9% |
| Top 10,000 | 92.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9859 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 27.1% of corpus
- **Long Tail:** 16,328 words needed for remaining 7.6% 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 | 0.8419 | 0.3607 | N/A | N/A |
| **mono_64d** | 64 | 0.7375 | 0.3054 | N/A | N/A |
| **mono_128d** | 128 | 0.3603 | 0.2810 | N/A | N/A |
| **aligned_32d** | 32 | 0.8419 🏆 | 0.3554 | 0.0260 | 0.1460 |
| **aligned_64d** | 64 | 0.7375 | 0.2999 | 0.0660 | 0.2980 |
| **aligned_128d** | 128 | 0.3603 | 0.2823 | 0.1580 | 0.4340 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8419 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3141. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 15.8% 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 | **0.854** | 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 |
|--------|----------|
| `-ка` | калькутта, калба, кацукава |
| `-ко` | контр, козерёкова, кожондоп |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ыҥ` | филармонияныҥ, транспорттыҥ, британияныҥ |
| `-ий` | белорусский, макарьевский, исетский |
| `-кий` | белорусский, макарьевский, исетский |
| `-ский` | белорусский, макарьевский, исетский |
| `-ныҥ` | филармонияныҥ, британияныҥ, наралканыҥ |
| `-иҥ` | јеезезиниҥ, изӱзиниҥ, ӱренчиктердиҥ |
| `-да` | ордында, совхозында, садуда |
| `-ый` | государственный, музейный, тёплый |

### 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 |
|------|----------|------------------|----------|
| `ский` | 2.17x | 43 contexts | омский, окский, юрский |
| `ында` | 1.53x | 51 contexts | мында, айында, сындар |
| `ыныҥ` | 1.68x | 30 contexts | мыныҥ, зыныҥ, угыныҥ |
| `лтай` | 1.85x | 21 contexts | алтай, шылтай, алтайды |
| `лгон` | 2.21x | 12 contexts | толгон, болгон, болгонм |
| `лган` | 1.70x | 23 contexts | алган, калган, салган |
| `осси` | 2.03x | 13 contexts | россия, россию, россии |
| `аныҥ` | 1.67x | 23 contexts | оканыҥ, сшаныҥ, эраныҥ |
| `олго` | 1.66x | 22 contexts | колго, волго, голго |
| `алта` | 1.49x | 26 contexts | алтай, алтан, алтам |
| `јылд` | 1.77x | 15 contexts | јылда, јылды, јылдын |
| `ылда` | 1.63x | 19 contexts | тылда, дылда, јылда |

### 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 |
|--------|--------|-----------|----------|
| `-ка` | `-ыҥ` | 21 words | казакстанныҥ, кайырлыктыҥ |
| `-ко` | `-ыҥ` | 20 words | конституцияныҥ, конкурстардыҥ |
| `-ка` | `-ий` | 14 words | кадетский, карский |
| `-ко` | `-ый` | 13 words | консалтинговый, командный |
| `-ка` | `-ныҥ` | 11 words | казакстанныҥ, канаданыҥ |
| `-ко` | `-ныҥ` | 11 words | конституцияныҥ, колхозыныҥ |
| `-ко` | `-ий` | 10 words | комментарий, ковалевский |
| `-ка` | `-кий` | 10 words | кадетский, карский |
| `-ка` | `-ский` | 10 words | кадетский, карский |
| `-ко` | `-да` | 9 words | косметологияда, коруда |

### 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 |
|------|-----------------|------------|------|
| планеталарында | **`планеталарын-да`** | 4.5 | `планеталарын` |
| актуруныҥ | **`актуру-ныҥ`** | 4.5 | `актуру` |
| покровский | **`покров-ский`** | 4.5 | `покров` |
| искусствоныҥ | **`искусство-ныҥ`** | 4.5 | `искусство` |
| думазыныҥ | **`думазы-ныҥ`** | 4.5 | `думазы` |
| медицинада | **`медицина-да`** | 4.5 | `медицина` |
| балдарыныҥ | **`балдары-ныҥ`** | 4.5 | `балдары` |
| португалияда | **`португалия-да`** | 4.5 | `португалия` |
| программада | **`программа-да`** | 4.5 | `программа` |
| аймагыныҥ | **`аймагы-ныҥ`** | 4.5 | `аймагы` |
| академияда | **`академия-да`** | 4.5 | `академия` |
| авиацияныҥ | **`авиация-ныҥ`** | 4.5 | `авиация` |
| шотландский | **`шотланд-ский`** | 4.5 | `шотланд` |
| киргизияныҥ | **`киргизия-ныҥ`** | 4.5 | `киргизия` |
| регрессияныҥ | **`регрессия-ныҥ`** | 4.5 | `регрессия` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Southern Altai 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 | **16k BPE** | Best compression (3.69x) |
| N-gram | **2-gram** | Lowest perplexity (413) |
| Markov | **Context-4** | Highest predictability (97.3%) |
| 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: 2026-01-03 16:17:03*