---
language: av
language_name: Avar
language_family: caucasian_northeast
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-caucasian_northeast
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: 4.685
  - name: best_isotropy
    type: isotropy
    value: 0.8604
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Avar** 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** | 3.628x | 3.63 | 0.0828% | 245,293 |
| **16k** | 4.030x | 4.03 | 0.0919% | 220,825 |
| **32k** | 4.383x | 4.39 | 0.1000% | 203,018 |
| **64k** | 4.685x 🏆 | 4.69 | 0.1069% | 189,944 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `19-абилеб Октябр — грегорианияб календаралда рекъон къо (високоснияб соналъ — св...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 1 9 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |
| 16k | `▁ 1 9 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |
| 32k | `▁ 1 9 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |
| 64k | `▁ 1 9 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |

**Sample 2:** `Пинкь яги ГьанамагӀ (латиназул мацӀалда bulla; Bullae) — гӀадамасул лага-черх. л...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁п ин кь ▁яги ▁гьан ам агӏ ▁( латиназул ▁мацӏалда ... (+18 more)` | 28 |
| 16k | `▁пин кь ▁яги ▁гьан амагӏ ▁( латиназул ▁мацӏалда ▁b ul ... (+15 more)` | 25 |
| 32k | `▁пин кь ▁яги ▁гьан амагӏ ▁( латиназул ▁мацӏалда ▁b ul ... (+14 more)` | 24 |
| 64k | `▁пинкь ▁яги ▁гьанамагӏ ▁( латиназул ▁мацӏалда ▁b ul la ; ... (+11 more)` | 21 |

**Sample 3:** `22-абилеб Октябр — грегорианияб календаралда рекъон къо (високоснияб соналъ — св...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 2 2 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |
| 16k | `▁ 2 2 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |
| 32k | `▁ 2 2 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |
| 64k | `▁ 2 2 - абилеб ▁октябр ▁— ▁грегорианияб ▁календаралда ▁рекъон ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 4.685x compression
- **Lowest UNK Rate:** 8k with 0.0828% 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 | 3,089 | 11.59 | 6,523 | 23.7% | 56.2% |
| **2-gram** | Subword | 424 🏆 | 8.73 | 4,120 | 58.0% | 96.7% |
| **3-gram** | Word | 2,775 | 11.44 | 6,745 | 26.4% | 58.9% |
| **3-gram** | Subword | 3,361 | 11.71 | 28,903 | 23.9% | 63.4% |
| **4-gram** | Word | 8,260 | 13.01 | 18,126 | 17.8% | 39.8% |
| **4-gram** | Subword | 15,393 | 13.91 | 119,191 | 12.7% | 37.5% |
| **5-gram** | Word | 7,813 | 12.93 | 15,673 | 16.8% | 39.4% |
| **5-gram** | Subword | 38,531 | 15.23 | 222,134 | 8.4% | 26.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `росу буго` | 710 |
| 2 | `география росу` | 660 |
| 3 | `мухъалъул росаби` | 578 |
| 4 | `буго мухъалъул` | 530 |
| 5 | `мухъалъул росу` | 523 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `география росу буго` | 645 |
| 2 | `росу буго мухъалъул` | 523 |
| 3 | `лъугьа бахъинал гьаруна` | 368 |
| 4 | `бахъинал гьаруна хвана` | 358 |
| 5 | `байрамал лъугьа бахъинал` | 353 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `география росу буго мухъалъул` | 513 |
| 2 | `лъугьа бахъинал гьаруна хвана` | 358 |
| 3 | `байрамал лъугьа бахъинал гьаруна` | 352 |
| 4 | `къо байрамал лъугьа бахъинал` | 351 |
| 5 | `бахъинал гьаруна хвана ишараби` | 349 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `къо байрамал лъугьа бахъинал гьаруна` | 350 |
| 2 | `лъугьа бахъинал гьаруна хвана ишараби` | 349 |
| 3 | `байрамал лъугьа бахъинал гьаруна хвана` | 348 |
| 4 | `демография ккола моноэтникияб авар росулъун` | 305 |
| 5 | `география росу буго мухъалъул марказ` | 279 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а л` | 85,368 |
| 2 | `л _` | 64,955 |
| 3 | `л ъ` | 53,561 |
| 4 | `а _` | 52,853 |
| 5 | `у л` | 50,828 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `у л _` | 34,266 |
| 2 | `л ъ у` | 31,682 |
| 3 | `ъ у л` | 26,429 |
| 4 | `а л ъ` | 24,583 |
| 5 | `_ г ь` | 22,014 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `л ъ у л` | 25,035 |
| 2 | `ъ у л _` | 22,571 |
| 3 | `а л ъ у` | 16,980 |
| 4 | `а л д а` | 11,684 |
| 5 | `_ г ь е` | 10,931 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `л ъ у л _` | 22,224 |
| 2 | `а л ъ у л` | 15,591 |
| 3 | `я л ъ у л` | 7,776 |
| 4 | `а л д а _` | 7,381 |
| 5 | `_ б у г о` | 5,843 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 424
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.6594 | 1.579 | 3.57 | 90,954 | 34.1% |
| **1** | Subword | 1.1677 | 2.247 | 9.26 | 1,148 | 0.0% |
| **2** | Word | 0.1264 | 1.092 | 1.22 | 323,475 | 87.4% |
| **2** | Subword | 0.9998 | 2.000 | 5.69 | 10,625 | 0.0% |
| **3** | Word | 0.0288 | 1.020 | 1.04 | 392,122 | 97.1% |
| **3** | Subword | 0.7938 | 1.734 | 3.67 | 60,414 | 20.6% |
| **4** | Word | 0.0121 🏆 | 1.008 | 1.02 | 406,770 | 98.8% |
| **4** | Subword | 0.5607 | 1.475 | 2.33 | 221,366 | 43.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ва испан фонология цогидал туркиял мацӏаз чанго шагьрияб гӏумру яшавалда хурхарал феодализм социум с...`
2. `буго республикалъул рутул мухъ буго шартіияб рикікіеналдалъун гьабураб бищун це б грузинский алфавит...`
3. `бугеб муниципалияб гӏуцӏи гъорлӏе рачуна чӏужуялда хурхарал цогидал киналго хвана ишараби мугъчӏваял...`

**Context Size 2:**

1. `росу буго мухъалъул марказ лъаратӏаса 22 км лъ жанубияб бакъбаккудехун ралъдал гьурматӏаса 968 метра...`
2. `география росу буго мухъалъул марказ лъаратӏаса 0 5 41 9 12 гуржиял 617 401 253 10 0`
3. `буго мухъалъул центер уркарахъалдаса бакътӏерхьудехун демография референсал мухъалъул росаби мухъ ро...`

**Context Size 3:**

1. `география росу буго мухъалъул марказ лъаратӏаса 22 км алъ демография ккола моноэтникияб авар росулъу...`
2. `росу буго мухъалъул центер уркарахъалдаса жанубияб бакътӏерхьудехун ралъдал гьурматӏаса борхалъи буг...`
3. `лъугьа бахъинал гьаруна хвана ишараби мугъчӏваял гь балагье трактат адабият тайпаби изданиял`

**Context Size 4:**

1. `география росу буго мухъалъул марказ лъаратӏаса 5 км алъ шималалиябгин бакъбаккудехун аваргӏоралъул ...`
2. `байрамал лъугьа бахъинал гьаруна хвана ишараби мугъчӏваял гь балагье`
3. `къо байрамал лъугьа бахъинал гьаруна хвана ишараби мугъчӏваял гь балагье`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ссва_—_1_вадаре`
2. `ан._ия_в._тӏавар`
3. `лдацӏиялъухъуск;`

**Context Size 2:**

1. `алдастияб_6_киябр`
2. `л_джибацӏаниякеап`
3. `лъул_бакъго_рахъе`

**Context Size 3:**

1. `ул_намен_гьеб_раса`
2. `лъулго_справенция)`
3. `ъул_яги_перации_«г`

**Context Size 4:**

1. `лъул_ассив_гьел_ккв`
2. `ъул_ківар_география`
3. `алъулалде._борхалъу`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (221,366 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 | 34,315 |
| Total Tokens | 413,611 |
| Mean Frequency | 12.05 |
| Median Frequency | 3 |
| Frequency Std Dev | 77.17 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ва | 7,138 |
| 2 | буго | 5,684 |
| 3 | бугеб | 2,903 |
| 4 | ккола | 2,872 |
| 5 | росу | 2,838 |
| 6 | мухъалъул | 2,671 |
| 7 | гьеб | 2,178 |
| 8 | росдал | 1,902 |
| 9 | the | 1,812 |
| 10 | цо | 1,800 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | уркутамахьи | 2 |
| 2 | континуумалде | 2 |
| 3 | къулецӏмаги | 2 |
| 4 | гьаркӏасуниб | 2 |
| 5 | махӏарги | 2 |
| 6 | пилибхиталъул | 2 |
| 7 | заповедникалда | 2 |
| 8 | пилибхит | 2 |
| 9 | лъалъадул | 2 |
| 10 | хӏанчӏи | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9572 |
| R² (Goodness of Fit) | 0.993745 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 23.1% |
| Top 1,000 | 51.6% |
| Top 5,000 | 74.2% |
| Top 10,000 | 83.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9937 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 23.1% of corpus
- **Long Tail:** 24,315 words needed for remaining 16.4% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 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 | 0.8604 | 0.3207 | N/A | N/A |
| **mono_64d** | 64 | 0.7367 | 0.2711 | N/A | N/A |
| **mono_128d** | 128 | 0.2721 | 0.2530 | N/A | N/A |
| **aligned_32d** | 32 | 0.8604 🏆 | 0.3335 | 0.0200 | 0.1400 |
| **aligned_64d** | 64 | 0.7367 | 0.2791 | 0.0280 | 0.1780 |
| **aligned_128d** | 128 | 0.2721 | 0.2649 | 0.0820 | 0.2540 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8604 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2870. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.2% 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 | **0.488** | 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 |
|--------|----------|
| `-ба` | батӏалъуда, батӏа, бахъинаро |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-л` | субтропикиял, кумикал, риччалел |
| `-а` | лъараца, тіалъиялда, анатолиялдаса |
| `-ул` | агьлулъиялъул, кипралъул, урарталъул |
| `-ъул` | агьлулъиялъул, кипралъул, урарталъул |
| `-лъул` | агьлулъиялъул, кипралъул, урарталъул |
| `-да` | тіалъиялда, текстазда, батӏалъуда |
| `-ал` | кумикал, туарегал, я́сал |
| `-ги` | тахшагьарлъунги, яги, фортисги |

### 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 |
|------|----------|------------------|----------|
| `алъу` | 1.88x | 101 contexts | алъул, далъун, малъун |
| `ялъу` | 2.05x | 41 contexts | ялъул, ялъуни, аялъул |
| `ьабу` | 2.11x | 29 contexts | гьабу, гьабун, кьабун |
| `агьа` | 1.75x | 59 contexts | багьа, дагьа, шагьав |
| `иялъ` | 1.85x | 36 contexts | химиялъ, биялъул, армиялъ |
| `анал` | 1.48x | 70 contexts | канал, ханал, данал |
| `иялд` | 1.69x | 36 contexts | сиялда, азиялде, азиялда |
| `огра` | 1.87x | 22 contexts | географ, фотограф, этнограф |
| `азда` | 1.67x | 31 contexts | гьазда, ишазда, раздан |
| `налд` | 1.64x | 31 contexts | иналда, доналд, иналде |
| `гъор` | 2.15x | 13 contexts | гъорлі, гъорлъ, гъорлӏ |
| `лдас` | 2.01x | 15 contexts | лдаса, ялдаса, алдаса |

### 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 |
|--------|--------|-----------|----------|
| `-ба` | `-л` | 36 words | багьадурасул, бакътӏерхьул |
| `-ба` | `-а` | 34 words | багъа, батӏалъана |
| `-ба` | `-ул` | 17 words | багьадурасул, бакътӏерхьул |
| `-ба` | `-ун` | 16 words | бахчун, бахъбаккудехун |
| `-ба` | `-да` | 16 words | бащалъуда, балазда |
| `-ба` | `-ал` | 11 words | бахӏсал, бакъбаккулал |
| `-ба` | `-ъул` | 8 words | бавариялъул, баталйоналъул |
| `-ба` | `-лда` | 8 words | бахъиялда, бахшалда |
| `-ба` | `-ги` | 6 words | бакӏалъулги, бахӏарзабиги |
| `-ба` | `-лъул` | 6 words | бавариялъул, баталйоналъул |

### 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 |
|------|-----------------|------------|------|
| къуръаналги | **`къуръан-ал-ги`** | 6.0 | `къуръан` |
| ханасдаги | **`ханас-да-ги`** | 6.0 | `ханас` |
| элементалги | **`элемент-ал-ги`** | 6.0 | `элемент` |
| гьелъулги | **`гьел-ъул-ги`** | 6.0 | `гьел` |
| гьармониялда | **`гьармония-лда`** | 4.5 | `гьармония` |
| гьолокьги | **`гьолокь-ги`** | 4.5 | `гьолокь` |
| хьондасебги | **`хьондасеб-ги`** | 4.5 | `хьондасеб` |
| районазул | **`районаз-ул`** | 4.5 | `районаз` |
| аскаразда | **`аскараз-да`** | 4.5 | `аскараз` |
| экономикаги | **`экономика-ги`** | 4.5 | `экономика` |
| процессазул | **`процессаз-ул`** | 4.5 | `процессаз` |
| насрудиницаги | **`насрудиница-ги`** | 4.5 | `насрудиница` |
| бугиланги | **`бугилан-ги`** | 4.5 | `бугилан` |
| рагьаразул | **`рагьараз-ул`** | 4.5 | `рагьараз` |
| минскалъул | **`минска-лъул`** | 4.5 | `минска` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Avar 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 (4.69x) |
| N-gram | **2-gram** | Lowest perplexity (424) |
| Markov | **Context-4** | Highest predictability (98.8%) |
| 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 18:29:30*