---
language: lbe
language_name: Lak
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: 3.877
  - name: best_isotropy
    type: isotropy
    value: 0.2418
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lak** 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** | 3.286x | 3.29 | 0.1064% | 106,237 |
| **16k** | 3.645x | 3.65 | 0.1180% | 95,777 |
| **32k** | 3.877x 🏆 | 3.89 | 0.1255% | 90,045 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Маз – мазрай гъалгъатӀун ягу чичлан бикӀайссар. Маз дуссар гьарца миллатрал гьан...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁маз ▁– ▁мазрай ▁гъал гъ атӏ ун ▁ягу ▁чич лан ... (+9 more)` | 19 |
| 16k | `▁маз ▁– ▁мазрай ▁гъалгъ атӏун ▁ягу ▁чич лан ▁бикӏайссар . ... (+7 more)` | 17 |
| 32k | `▁маз ▁– ▁мазрай ▁гъалгъатӏун ▁ягу ▁чичлан ▁бикӏайссар . ▁маз ▁дуссар ... (+5 more)` | 15 |

**Sample 2:** `ХӀуриет ( «азадшиву») – Туркнал жяматийсса ва сиясийсса кказит Чил сайт кказитру`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁хӏ ури ет ▁( ▁« аз ад шиву ») ▁– ... (+8 more)` | 18 |
| 16k | `▁хӏ ури ет ▁( ▁« азадшиву ») ▁– ▁туркнал ▁жяматийсса ... (+6 more)` | 16 |
| 32k | `▁хӏуриет ▁( ▁« азадшиву ») ▁– ▁туркнал ▁жяматийсса ▁ва ▁сиясийсса ... (+4 more)` | 14 |

**Sample 3:** `(, ) — Дагъусттаннал Лакрал райондалун яруссаннал дазуйсса лакрал шяравалу. Бувч...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁(, ▁) ▁— ▁дагъусттаннал ▁лакрал ▁райондалун ▁яруссаннал ▁дазуй сса ▁лакрал ... (+5 more)` | 15 |
| 16k | `▁(, ▁) ▁— ▁дагъусттаннал ▁лакрал ▁райондалун ▁яруссаннал ▁дазуйсса ▁лакрал ▁шяравалу ... (+4 more)` | 14 |
| 32k | `▁(, ▁) ▁— ▁дагъусттаннал ▁лакрал ▁райондалун ▁яруссаннал ▁дазуйсса ▁лакрал ▁шяравалу ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 32k achieves 3.877x compression
- **Lowest UNK Rate:** 8k with 0.1064% 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 | 289 🏆 | 8.17 | 563 | 58.2% | 100.0% |
| **2-gram** | Subword | 491 | 8.94 | 1,956 | 53.7% | 96.1% |
| **3-gram** | Word | 292 | 8.19 | 637 | 57.5% | 100.0% |
| **3-gram** | Subword | 3,297 | 11.69 | 11,342 | 20.8% | 61.9% |
| **4-gram** | Word | 1,071 | 10.06 | 1,996 | 33.3% | 70.9% |
| **4-gram** | Subword | 10,634 | 13.38 | 32,543 | 12.1% | 40.2% |
| **5-gram** | Word | 991 | 9.95 | 1,708 | 32.8% | 74.0% |
| **5-gram** | Subword | 15,648 | 13.93 | 40,639 | 9.4% | 34.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `агьалинал аьдад` | 264 |
| 2 | `чил сайт` | 172 |
| 3 | `бувчӏин баву` | 165 |
| 4 | `инсан адимина` | 165 |
| 5 | `туркиянал статистикалул` | 152 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tüi̇k туркиянал статистикалул` | 152 |
| 2 | `туркиянал статистикалул департамент` | 152 |
| 3 | `туркиясса шагьру ва` | 140 |
| 4 | `примечания чил сайт` | 139 |
| 5 | `район агьалинал аьдад` | 138 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tüi̇k туркиянал статистикалул департамент` | 152 |
| 2 | `чил сайт къаймакъам муниципалитет` | 124 |
| 3 | `сайт къаймакъам муниципалитет шагьрурду` | 118 |
| 4 | `примечания чил сайт къаймакъам` | 116 |
| 5 | `статистикалул департамент агьалинал аьдад` | 90 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `чил сайт къаймакъам муниципалитет шагьрурду` | 118 |
| 2 | `примечания чил сайт къаймакъам муниципалитет` | 116 |
| 3 | `туркиянал статистикалул департамент агьалинал аьдад` | 90 |
| 4 | `tüi̇k туркиянал статистикалул департамент агьалинал` | 90 |
| 5 | `статистикалул департамент агьалинал аьдад шин` | 90 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а л` | 6,845 |
| 2 | `л _` | 5,250 |
| 3 | `а _` | 4,594 |
| 4 | `а н` | 4,356 |
| 5 | `с а` | 4,141 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а л _` | 3,177 |
| 2 | `с с а` | 2,851 |
| 3 | `н а л` | 2,180 |
| 4 | `с а _` | 1,620 |
| 5 | `_ б у` | 1,513 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н а л _` | 1,990 |
| 2 | `с с а _` | 1,561 |
| 3 | `с с а р` | 832 |
| 4 | `_ в а _` | 767 |
| 5 | `н н а л` | 632 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н н а л _` | 577 |
| 2 | `и н а л _` | 528 |
| 3 | `а г ь р у` | 514 |
| 4 | `ш а г ь р` | 509 |
| 5 | `_ ш а г ь` | 506 |


### Key Findings

- **Best Perplexity:** 2-gram (word) with 289
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.5464 | 1.460 | 2.38 | 14,824 | 45.4% |
| **1** | Subword | 1.4264 | 2.688 | 9.63 | 447 | 0.0% |
| **2** | Word | 0.0829 | 1.059 | 1.13 | 35,065 | 91.7% |
| **2** | Subword | 1.0905 | 2.130 | 5.40 | 4,302 | 0.0% |
| **3** | Word | 0.0248 | 1.017 | 1.04 | 39,281 | 97.5% |
| **3** | Subword | 0.7425 | 1.673 | 2.86 | 23,223 | 25.7% |
| **4** | Word | 0.0131 🏆 | 1.009 | 1.02 | 40,171 | 98.7% |
| **4** | Subword | 0.4036 | 1.323 | 1.73 | 66,320 | 59.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ва къазах кирил алфавит جثتپباذدڅخحچشسژڗزرعظطضڝصکقڢفڠغنملگݤګيوه усларал алфавит алеут лугъат хъанай ...`
2. `аьдад 27 освенцим кӏану бугьлай бушиву му бакъа бувну бачи учирчагу жу дурсса чӏумал бикӏу гьануну`
3. `бур иш тагьар щищал ссащал ттущал вищал танащал жущал зущал тайннащал кӏанттул улклухсса ччаврин бут...`

**Context Size 2:**

1. `агьалинал аьдад шин шагьру шяравалу total 9 008 18 646 27 654 6 102 24 227 30`
2. `чил сайт къаймакъам муниципалитет шагьрурду`
3. `инсан адимина 23 058 хъамитайпа 23 710 tüi̇k туркиянал статистикалул департамент агьалинал аьдад 434...`

**Context Size 3:**

1. `tüi̇k туркиянал статистикалул департамент примечания чил сайт къаймакъам муниципалитет шагьрурду`
2. `туркиянал статистикалул департамент примечания чил сайт къаймакъам муниципалитет шагьрурду`
3. `туркиясса шагьру ва артвин ильданул центр район агьалинал аьдад 18 072 инсан адимина 9 211 хъамитайп...`

**Context Size 4:**

1. `tüi̇k туркиянал статистикалул департамент районну адыяман adıyaman merkez бесни besni челикхан çelik...`
2. `чил сайт къаймакъам муниципалитет шагьрурду`
3. `примечания чил сайт къаймакъам муниципалитет шагьрурду`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_xvilstücaziulyu`
2. `азивуххагьанун_w`
3. `укумаласаймесаль`

**Context Size 2:**

1. `алеххаврал_ин_т_к`
2. `л_шинатни._чиви._`
3. `а_лакӏалуну_дусса`

**Context Size 3:**

1. `ал_жуж_xvii—xvi_el`
2. `сса_гьаейссавних_ш`
3. `нал_шярава_26_эски`

**Context Size 4:**

1. `нал_маз_(аьрабнал_а`
2. `сса_щарая_ингилис_b`
3. `ссар._агьалинал_ста`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (66,320 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 | 5,374 |
| Total Tokens | 38,623 |
| Mean Frequency | 7.19 |
| Median Frequency | 3 |
| Frequency Std Dev | 21.50 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ва | 771 |
| 2 | аьдад | 394 |
| 3 | бур | 362 |
| 4 | инсан | 309 |
| 5 | шагьру | 295 |
| 6 | шинал | 274 |
| 7 | агьалинал | 267 |
| 8 | маз | 217 |
| 9 | чил | 217 |
| 10 | ягу | 194 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | спорт | 2 |
| 2 | нурмагомедов | 2 |
| 3 | гренландия | 2 |
| 4 | советских | 2 |
| 5 | социалистических | 2 |
| 6 | республик | 2 |
| 7 | адолф | 2 |
| 8 | гьитлер | 2 |
| 9 | саллатіир | 2 |
| 10 | сталинград | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8339 |
| R² (Goodness of Fit) | 0.982815 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.5% |
| Top 1,000 | 67.1% |
| Top 5,000 | 98.1% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9828 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.5% of corpus
- **Long Tail:** -4,626 words needed for remaining 100.0% 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 | 0.2418 | 0.5099 | N/A | N/A |
| **mono_64d** | 64 | 0.0556 | 0.4959 | N/A | N/A |
| **mono_128d** | 128 | 0.0084 | 0.4715 | N/A | N/A |
| **aligned_32d** | 32 | 0.2418 🏆 | 0.4977 | 0.0178 | 0.1869 |
| **aligned_64d** | 64 | 0.0556 | 0.4695 | 0.0445 | 0.1869 |
| **aligned_128d** | 128 | 0.0084 | 0.4738 | 0.0386 | 0.2285 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.2418 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4864. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.5% 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 | **1.143** | 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` | комаровлул, конья, ккули |
| `-а` | аллагьнал, аьлил, апрель |
| `-б` | бакъахьурча, баглар, буру |
| `-м` | мазсулейман, мукьилчинмур, мармара |
| `-д` | дянив, даву, дишайссар |
| `-с` | сарычам, сахих, стакан |
| `-бу` | буру, буллалаву, буххлаххиссар |
| `-ба` | бакъахьурча, баглар, бакӏрал |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-л` | комаровлул, аллагьнал, аьлил |
| `-а` | цукунчӏавсса, бакъахьурча, хауса |
| `-ал` | аллагьнал, бакӏрал, бакӏчитал |
| `-у` | хӏакьину, буру, чичрурду |
| `-са` | цукунчӏавсса, хауса, гъансса |
| `-н` | ттуйн, стакан, ттун |
| `-р` | баглар, невшехир, мукьилчинмур |
| `-ул` | комаровлул, барзул, мургул |

### 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 |
|------|----------|------------------|----------|
| `айсс` | 1.77x | 27 contexts | байсса, дайсса, шайсса |
| `ссар` | 1.82x | 19 contexts | дуссар, ухссар, буссар |
| `йсса` | 1.69x | 14 contexts | байсса, дайсса, шайсса |
| `хъан` | 1.89x | 9 contexts | хъанан, хъанай, ляхъан |
| `улла` | 1.59x | 12 contexts | дуллан, буллай, арулла |
| `мазр` | 1.82x | 8 contexts | мазри, мазру, мазрай |
| `унна` | 1.51x | 12 contexts | кунна, сунна, куннал |
| `аьра` | 1.81x | 7 contexts | аьрал, аьраб, аьрали |
| `лчин` | 1.69x | 8 contexts | цалчин, цалчинми, цалчинмур |
| `нсса` | 1.90x | 6 contexts | бансса, чансса, гъансса |
| `ннал` | 1.68x | 8 contexts | куннал, миннал, ханнал |
| `асса` | 1.66x | 8 contexts | чассаг, кьасса, журасса |

### 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 |
|--------|--------|-----------|----------|
| `-а` | `-л` | 45 words | аллагьнал, аьлил |
| `-к` | `-л` | 42 words | комаровлул, къарачайнал |
| `-б` | `-а` | 35 words | бакъахьурча, ба |
| `-б` | `-у` | 35 words | буру, буллалаву |
| `-а` | `-ал` | 33 words | аллагьнал, арантурал |
| `-м` | `-а` | 32 words | мармара, муратпаша |
| `-б` | `-л` | 30 words | бакӏрал, барзул |
| `-к` | `-ал` | 30 words | къарачайнал, куннал |
| `-к` | `-н` | 27 words | камерун, къаплан |
| `-б` | `-р` | 27 words | баглар, буххлаххиссар |

### 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 |
|------|-----------------|------------|------|
| къабивкӏун | **`къ-а-бивкӏун`** | 7.5 | `бивкӏун` |
| советская | **`советск-а-я`** | 7.5 | `а` |
| балайрдаву | **`балайрд-а-ву`** | 7.5 | `а` |
| макьаларду | **`макьал-ар-ду`** | 7.5 | `ар` |
| бартольдлул | **`бартольд-л-ул`** | 6.0 | `бартольд` |
| агьрамнал | **`агьрам-н-ал`** | 6.0 | `агьрам` |
| миллатиял | **`миллат-ия-л`** | 6.0 | `миллат` |
| къаяевлул | **`къаяев-л-ул`** | 6.0 | `къаяев` |
| республикалул | **`республик-ал-ул`** | 6.0 | `республик` |
| бакъанугу | **`бакъа-ну-гу`** | 6.0 | `бакъа` |
| ущущулгъилун | **`ущущулгъи-л-ун`** | 6.0 | `ущущулгъи` |
| дунияллул | **`дуниял-л-ул`** | 6.0 | `дуниял` |
| абумуслим | **`а-бу-муслим`** | 6.0 | `муслим` |
| шамхалнал | **`шамхал-н-ал`** | 6.0 | `шамхал` |
| закуевлул | **`закуев-л-ул`** | 6.0 | `закуев` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lak 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 | **32k BPE** | Best compression (3.88x) |
| N-gram | **2-gram** | Lowest perplexity (289) |
| Markov | **Context-4** | Highest predictability (98.7%) |
| 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 10:21:18*