---
language: lez
language_name: Lezgian
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: 4.461
  - name: best_isotropy
    type: isotropy
    value: 0.8458
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lezgian** 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** | 3.556x | 3.56 | 0.2939% | 478,366 |
| **16k** | 3.921x | 3.92 | 0.3241% | 433,830 |
| **32k** | 4.233x | 4.24 | 0.3498% | 401,922 |
| **64k** | 4.461x 🏆 | 4.46 | 0.3687% | 381,358 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Кеферпатан грисбок (лат. Raphicerus sharpei) — антилопаяр хзандиз талукь тир гьа...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁кеферпатан ▁гр ис бок ▁( лат . ▁r aph ic ... (+14 more)` | 24 |
| 16k | `▁кеферпатан ▁гр исбок ▁( лат . ▁raphicerus ▁sh ar p ... (+10 more)` | 20 |
| 32k | `▁кеферпатан ▁грисбок ▁( лат . ▁raphicerus ▁sharpei ) ▁— ▁антилопаяр ... (+6 more)` | 16 |
| 64k | `▁кеферпатан ▁грисбок ▁( лат . ▁raphicerus ▁sharpei ) ▁— ▁антилопаяр ... (+6 more)` | 16 |

**Sample 2:** `Килова́тт-сят (кВт⋅ч) — гьасил ва я кардик кутунвай энергиядин кьадар, гьакӀни к...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁кил ова ́ т т - с ят ▁( к ... (+30 more)` | 40 |
| 16k | `▁кил ова ́т т - с ят ▁( кв т ... (+26 more)` | 36 |
| 32k | `▁кил ова ́т т - сят ▁( кв т ⋅ ... (+23 more)` | 33 |
| 64k | `▁кил ова ́т т - сят ▁( квт ⋅ ч ... (+22 more)` | 32 |

**Sample 3:** `йис (са агъзурни иридвишни яхцӀурницӀикьудлагьай йис) — чи эрадин йис. XVIII виш...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁йис ▁( са ▁агъзурни ▁иридвишни ▁яхцӏурницӏ икьудлагьай ▁йис ) ▁— ... (+20 more)` | 30 |
| 16k | `▁йис ▁( са ▁агъзурни ▁иридвишни ▁яхцӏурницӏ икьудлагьай ▁йис ) ▁— ... (+20 more)` | 30 |
| 32k | `▁йис ▁( са ▁агъзурни ▁иридвишни ▁яхцӏурницӏ икьудлагьай ▁йис ) ▁— ... (+20 more)` | 30 |
| 64k | `▁йис ▁( са ▁агъзурни ▁иридвишни ▁яхцӏурницӏ икьудлагьай ▁йис ) ▁— ... (+20 more)` | 30 |


### Key Findings

- **Best Compression:** 64k achieves 4.461x compression
- **Lowest UNK Rate:** 8k with 0.2939% 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 | 4,869 | 12.25 | 13,465 | 20.5% | 52.1% |
| **2-gram** | Subword | 378 🏆 | 8.56 | 3,725 | 59.9% | 97.5% |
| **3-gram** | Word | 4,928 | 12.27 | 15,118 | 20.8% | 53.1% |
| **3-gram** | Subword | 2,980 | 11.54 | 29,246 | 23.8% | 66.3% |
| **4-gram** | Word | 9,550 | 13.22 | 29,848 | 17.0% | 43.5% |
| **4-gram** | Subword | 13,090 | 13.68 | 130,341 | 12.8% | 40.9% |
| **5-gram** | Word | 8,440 | 13.04 | 24,720 | 17.7% | 44.1% |
| **5-gram** | Subword | 32,189 | 14.97 | 259,667 | 8.8% | 30.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `баянар элячӏунар` | 1,967 |
| 2 | `дагъустан республикадин` | 1,527 |
| 3 | `районда авай` | 1,079 |
| 4 | `райондин хуьрер` | 977 |
| 5 | `мусурманар я` | 936 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `на 1 января` | 911 |
| 2 | `суни мусурманар я` | 815 |
| 3 | `по муниципальным образованиям` | 767 |
| 4 | `1 января г` | 765 |
| 5 | `муниципальным образованиям на` | 741 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `на 1 января г` | 765 |
| 2 | `по муниципальным образованиям на` | 741 |
| 3 | `образованиям на 1 января` | 740 |
| 4 | `муниципальным образованиям на 1` | 740 |
| 5 | `российской федерации по муниципальным` | 582 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `по муниципальным образованиям на 1` | 740 |
| 2 | `муниципальным образованиям на 1 января` | 740 |
| 3 | `образованиям на 1 января г` | 707 |
| 4 | `российской федерации по муниципальным образованиям` | 582 |
| 5 | `населения российской федерации по муниципальным` | 582 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _` | 118,436 |
| 2 | `и н` | 101,992 |
| 3 | `д и` | 90,630 |
| 4 | `в а` | 85,472 |
| 5 | `а й` | 84,832 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `и н _` | 77,249 |
| 2 | `д и н` | 55,033 |
| 3 | `а й _` | 41,524 |
| 4 | `а р _` | 27,897 |
| 5 | `а н _` | 27,614 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `д и н _` | 50,137 |
| 2 | `х у ь р` | 18,492 |
| 3 | `_ х у ь` | 17,463 |
| 4 | `_ й и с` | 16,780 |
| 5 | `в а й _` | 14,217 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ х у ь р` | 16,863 |
| 2 | `р а й о н` | 10,265 |
| 3 | `_ р а й о` | 10,222 |
| 4 | `н д и н _` | 9,537 |
| 5 | `_ й и с а` | 8,563 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 378
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.7069 | 1.632 | 4.39 | 95,463 | 29.3% |
| **1** | Subword | 0.9092 | 1.878 | 7.01 | 1,497 | 9.1% |
| **2** | Word | 0.1745 | 1.129 | 1.35 | 418,311 | 82.5% |
| **2** | Subword | 0.9040 | 1.871 | 5.60 | 10,485 | 9.6% |
| **3** | Word | 0.0504 | 1.036 | 1.09 | 565,039 | 95.0% |
| **3** | Subword | 0.8361 | 1.785 | 3.99 | 58,647 | 16.4% |
| **4** | Word | 0.0209 🏆 | 1.015 | 1.04 | 611,226 | 97.9% |
| **4** | Subword | 0.6051 | 1.521 | 2.51 | 234,119 | 39.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ва промышленностдин институт я йисан эхирда француз чӏаларал манияр ягъунин сувар кваз постановление...`
2. `я додрас тӏвар ван авай хуьр вири санал ишлемиш жезвай орджоникидзедин тӏварунихъ галай макъаматдинн...`
3. `тир са чилин вине ала гадацӏийихуьруьн мягьлейрин тӏварар алимвилин дережадин мектебар кӏвалахзавай ...`

**Context Size 2:**

1. `баянар элячӏунар поселение село яраг казмаляр райондин хуьруьнсоветар ва абурук акатзавай хуьрер исп...`
2. `дагъустан республикадин гьукуматдин чӏал ава умуми са чӏал кьабулначир гьа а юкъуз ам москвадин бабу...`
3. `районда авай тунвай хуьр бугъда тепе тӏвар эцигнавай ухти араб чӏалал кхьенвай эсеррин кӏватӏал яз ч...`

**Context Size 3:**

1. `на 1 января г 2 475 33 численность постоянного населения российской федерации по муниципальным образ...`
2. `суни мусурманар я йисан урусат империядин агьалияр сиягьдиз къачунин нетижада уьлкведа къирицӏар ава...`
3. `по муниципальным образованиям на 1 января г йисан агьалияр сиягьриз къачунин нетижариз килигна хуьре...`

**Context Size 4:**

1. `на 1 января г йисан агьалияр сиягьриз къачунин нетижайриз килигна хуьре 472 касди уьумуьр ийизвайнас...`
2. `по муниципальным образованиям на 1 января г 32 113 33 численность постоянного населения республики д...`
3. `образованиям на 1 января г 54 786 35 численность постоянного населения российской федерации по муниц...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_пр_фияр_айта._и`
2. `агемен_вкрерагаг`
3. `испар_афен_йн_ст`

**Context Size 2:**

1. `н_«тр_ста_чӏерди_`
2. `ин_панчесифар_арв`
3. `ди_авуз_кутурдара`

**Context Size 3:**

1. `ин_ибрин_диделено_`
2. `дин_халкь_типпадин`
3. `ай_халкӏ_муниципал`

**Context Size 4:**

1. `дин_пешерра_азербай`
2. `хуьрер_я._адан_кесп`
3. `_хуьруьн_агьалияр_д`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (234,119 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 | 36,658 |
| Total Tokens | 697,569 |
| Mean Frequency | 19.03 |
| Median Frequency | 3 |
| Frequency Std Dev | 143.41 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ва | 11,171 |
| 2 | я | 10,219 |
| 3 | тир | 5,987 |
| 4 | авай | 5,477 |
| 5 | йисан | 5,251 |
| 6 | райондин | 4,964 |
| 7 | йисуз | 4,832 |
| 8 | хуьр | 4,422 |
| 9 | и | 3,952 |
| 10 | агьалияр | 3,896 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | сч | 2 |
| 2 | элкъюрун | 2 |
| 3 | кюмекдин | 2 |
| 4 | солферино | 2 |
| 5 | солферинодикай | 2 |
| 6 | хкинар | 2 |
| 7 | ӏӏӏ | 2 |
| 8 | тюкӏюриз | 2 |
| 9 | яцин | 2 |
| 10 | къанавдин | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0501 |
| R² (Goodness of Fit) | 0.994687 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 28.8% |
| Top 1,000 | 60.5% |
| Top 5,000 | 80.5% |
| Top 10,000 | 88.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9947 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 28.8% of corpus
- **Long Tail:** 26,658 words needed for remaining 11.9% 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 | 0.8458 | 0.3324 | N/A | N/A |
| **mono_64d** | 64 | 0.7103 | 0.2681 | N/A | N/A |
| **mono_128d** | 128 | 0.3532 | 0.2524 | N/A | N/A |
| **aligned_32d** | 32 | 0.8458 🏆 | 0.3332 | 0.0120 | 0.1080 |
| **aligned_64d** | 64 | 0.7103 | 0.2750 | 0.0260 | 0.1320 |
| **aligned_128d** | 128 | 0.3532 | 0.2570 | 0.0300 | 0.1680 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8458 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2863. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.0% 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 | **0.451** | 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 |
|--------|----------|
| `-к` | киривияр, коллективди, красноярского |
| `-а` | аспирант, авахьзавай, артём |
| `-с` | смомпк, селевкидрин, сидань |
| `-м` | мценск, мадридда, мирзебутай |
| `-г` | гьапутрихъ, гьадахъ, городе |
| `-т` | технический, туркменар, тахсиркарвилиз |
| `-ма` | мадридда, магьарамдхуьруьн, малумдай |
| `-ка` | канвондо, кайтаги, камер |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ин` | хъчарин, еревандин, селевкидрин |
| `-н` | хъчарин, еревандин, шагьан |
| `-а` | мадридда, чарара, хтанва |
| `-и` | россии, коллективди, гвардияди |
| `-й` | эгьлийрилай, технический, авахьзавай |
| `-ай` | эгьлийрилай, авахьзавай, лежбервилелай |
| `-р` | туркменар, киривияр, ярукьвалар |
| `-ар` | туркменар, ярукьвалар, бизнесменар |

### 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 |
|------|----------|------------------|----------|
| `ияди` | 2.07x | 37 contexts | унияди, данияди, армияди |
| `адин` | 1.72x | 58 contexts | мадина, чкадин, эрадин |
| `алди` | 1.74x | 50 contexts | далди, чӏалди, идалди |
| `айон` | 2.02x | 28 contexts | район, районы, района |
| `уьре` | 1.65x | 44 contexts | гуьре, уьрер, хуьре |
| `егье` | 1.78x | 33 contexts | зегье, вегьей, тегьер |
| `ьруь` | 2.06x | 20 contexts | хуьруь, куьруь, хуьруьк |
| `ндин` | 1.78x | 30 contexts | диндин, иондин, фондин |
| `райо` | 2.10x | 17 contexts | район, районы, района |
| `зава` | 1.63x | 39 contexts | завал, язава, завай |
| `агьа` | 1.52x | 48 contexts | агьан, багьа, шагьа |
| `йонд` | 2.24x | 10 contexts | районда, районди, райондал |

### 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 |
|--------|--------|-----------|----------|
| `-к` | `-н` | 194 words | кӏвачерин, кьакьанвилин |
| `-к` | `-ин` | 141 words | кӏвачерин, кьакьанвилин |
| `-к` | `-й` | 121 words | ксаривай, кхьирагрикай |
| `-г` | `-н` | 119 words | градусдин, гьикаятдин |
| `-а` | `-н` | 117 words | алимдин, астрахан |
| `-м` | `-н` | 114 words | муьгьуьдин, муьжуьгьафтеран |
| `-к` | `-р` | 112 words | къайдаяр, кьар |
| `-к` | `-а` | 112 words | канда, куьреда |
| `-к` | `-и` | 107 words | конституции, къирицӏви |
| `-к` | `-ай` | 101 words | ксаривай, кхьирагрикай |

### 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 |
|------|-----------------|------------|------|
| полковник | **`полков-н-ик`** | 7.5 | `н` |
| рекьерихъ | **`рекьер-и-хъ`** | 7.5 | `и` |
| уьзбекистанда | **`уьзбекиста-н-да`** | 7.5 | `н` |
| туьхкӏуьрунин | **`туьхкӏуьру-н-ин`** | 7.5 | `н` |
| бизнесменар | **`бизнесме-н-ар`** | 7.5 | `н` |
| кьурагьрин | **`кьурагь-р-ин`** | 7.5 | `р` |
| давамарда | **`давам-ар-да`** | 7.5 | `ар` |
| упражнения | **`упражне-н-ия`** | 7.5 | `н` |
| футболкаяр | **`футболк-а-яр`** | 7.5 | `а` |
| тӏварарик | **`тӏвар-ар-ик`** | 7.5 | `ар` |
| алакьунин | **`алакьу-н-ин`** | 7.5 | `н` |
| октябрьдилай | **`октябрьди-л-ай`** | 7.5 | `л` |
| туьхкӏуьрна | **`туьхкӏуьр-н-а`** | 7.5 | `н` |
| общественная | **`обществен-н-ая`** | 7.5 | `н` |
| туькӏуьрдалди | **`туькӏуьрд-ал-ди`** | 7.5 | `ал` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lezgian 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 (4.46x) |
| N-gram | **2-gram** | Lowest perplexity (378) |
| Markov | **Context-4** | Highest predictability (97.9%) |
| 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 10:28:15*