---
language: krc
language_name: Karachay-Balkar
language_family: turkic_kipchak
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_kipchak
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: 4.721
  - name: best_isotropy
    type: isotropy
    value: 0.8818
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Karachay-Balkar - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Karachay-Balkar** 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** | 3.832x | 3.84 | 0.1001% | 359,596 |
| **16k** | 4.195x | 4.20 | 0.1096% | 328,464 |
| **32k** | 4.446x | 4.45 | 0.1162% | 309,925 |
| **64k** | 4.721x 🏆 | 4.72 | 0.1233% | 291,915 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `.va — Ватиканны огъары дараджаны интернет домениди. доменле sv:Toppdomän#V`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁. va ▁— ▁ват ик анны ▁огъары ▁дараджаны ▁интернет ▁домениди ... (+7 more)` | 17 |
| 16k | `▁. va ▁— ▁ват иканны ▁огъары ▁дараджаны ▁интернет ▁домениди . ... (+6 more)` | 16 |
| 32k | `▁. va ▁— ▁ватиканны ▁огъары ▁дараджаны ▁интернет ▁домениди . ▁доменле ... (+5 more)` | 15 |
| 64k | `▁. va ▁— ▁ватиканны ▁огъары ▁дараджаны ▁интернет ▁домениди . ▁доменле ... (+5 more)` | 15 |

**Sample 2:** `.cu — Кубаны огъары дараджаны интернет домени. доменле sv:Toppdomän#C`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁. c u ▁— ▁куб аны ▁огъары ▁дараджаны ▁интернет ▁домени ... (+7 more)` | 17 |
| 16k | `▁. cu ▁— ▁кубаны ▁огъары ▁дараджаны ▁интернет ▁домени . ▁доменле ... (+5 more)` | 15 |
| 32k | `▁. cu ▁— ▁кубаны ▁огъары ▁дараджаны ▁интернет ▁домени . ▁доменле ... (+5 more)` | 15 |
| 64k | `▁. cu ▁— ▁кубаны ▁огъары ▁дараджаны ▁интернет ▁домени . ▁доменле ... (+5 more)` | 15 |

**Sample 3:** `.it — Италияны огъары дараджаны интернет домени. доменле he:סיומת אינטרנט#טבלת ס...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁. it ▁— ▁италияны ▁огъары ▁дараджаны ▁интернет ▁домени . ▁доменле ... (+13 more)` | 23 |
| 16k | `▁. it ▁— ▁италияны ▁огъары ▁дараджаны ▁интернет ▁домени . ▁доменле ... (+13 more)` | 23 |
| 32k | `▁. it ▁— ▁италияны ▁огъары ▁дараджаны ▁интернет ▁домени . ▁доменле ... (+13 more)` | 23 |
| 64k | `▁. it ▁— ▁италияны ▁огъары ▁дараджаны ▁интернет ▁домени . ▁доменле ... (+13 more)` | 23 |


### Key Findings

- **Best Compression:** 64k achieves 4.721x compression
- **Lowest UNK Rate:** 8k with 0.1001% 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 | 4,346 | 12.09 | 7,787 | 17.8% | 47.9% |
| **2-gram** | Subword | 391 🏆 | 8.61 | 3,511 | 58.8% | 97.5% |
| **3-gram** | Word | 3,291 | 11.68 | 5,584 | 20.4% | 49.5% |
| **3-gram** | Subword | 2,989 | 11.55 | 26,299 | 24.2% | 65.9% |
| **4-gram** | Word | 5,701 | 12.48 | 8,855 | 16.2% | 35.7% |
| **4-gram** | Subword | 13,131 | 13.68 | 110,221 | 13.2% | 39.9% |
| **5-gram** | Word | 3,634 | 11.83 | 5,566 | 18.4% | 42.8% |
| **5-gram** | Subword | 33,332 | 15.02 | 206,967 | 8.3% | 27.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `алай а` | 1,099 |
| 2 | `эм уллу` | 508 |
| 3 | `абш ны` | 438 |
| 4 | `бла бирге` | 404 |
| 5 | `халкъла арасы` | 386 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `огъары дараджаны интернет` | 255 |
| 2 | `болгъан ишле туугъанла` | 240 |
| 3 | `григориан орузламада джылны` | 236 |
| 4 | `байрамла болгъан ишле` | 236 |
| 5 | `джылны ахырына дери` | 235 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `кюнюдю джылны ахырына дери` | 235 |
| 2 | `кюн къалады байрамла болгъан` | 234 |
| 3 | `къалады байрамла болгъан ишле` | 234 |
| 4 | `байрамла болгъан ишле туугъанла` | 229 |
| 5 | `болгъан ишле туугъанла ёлгенле` | 228 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `кюн къалады байрамла болгъан ишле` | 234 |
| 2 | `къалады байрамла болгъан ишле туугъанла` | 227 |
| 3 | `байрамла болгъан ишле туугъанла ёлгенле` | 224 |
| 4 | `чи кюнюдю джылны ахырына дери` | 117 |
| 5 | `огъары дараджаны интернет домениди доменле` | 91 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 83,938 |
| 2 | `а н` | 76,834 |
| 3 | `л а` | 72,803 |
| 4 | `_ б` | 61,892 |
| 5 | `_ к` | 60,105 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `г ъ а` | 32,934 |
| 2 | `н ы _` | 32,399 |
| 3 | `д а _` | 31,775 |
| 4 | `_ д ж` | 26,820 |
| 5 | `_ к ъ` | 25,061 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `г ъ а н` | 18,270 |
| 2 | `а н ы _` | 14,240 |
| 3 | `л г ъ а` | 12,066 |
| 4 | `_ б о л` | 11,397 |
| 5 | `_ б л а` | 11,168 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `л г ъ а н` | 10,519 |
| 2 | `_ б л а _` | 10,384 |
| 3 | `г ъ а н д` | 8,413 |
| 4 | `_ д ж ы л` | 8,226 |
| 5 | `ъ а н д ы` | 8,219 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 391
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.7669 | 1.702 | 4.45 | 81,464 | 23.3% |
| **1** | Subword | 0.8973 | 1.863 | 7.38 | 1,256 | 10.3% |
| **2** | Word | 0.1558 | 1.114 | 1.29 | 361,983 | 84.4% |
| **2** | Subword | 0.9642 | 1.951 | 5.73 | 9,247 | 3.6% |
| **3** | Word | 0.0339 | 1.024 | 1.05 | 465,485 | 96.6% |
| **3** | Subword | 0.8243 | 1.771 | 3.79 | 52,874 | 17.6% |
| **4** | Word | 0.0094 🏆 | 1.007 | 1.01 | 486,649 | 99.1% |
| **4** | Subword | 0.5763 | 1.491 | 2.38 | 200,334 | 42.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `бла джакъланнганды джыл сыйлы окъу письмо diwan press isbn гл ред в 3 de sɛˈʃɛl сейш`
2. `эмда сумода иги тюбейдиле эмда джерли эмда тамалладан халкъла арасы илишкиле джылда 0 0 3 2`
3. `да тыярыкъбыз израилге мисирни сегиз компания ингилизлиле къыбыла кюнбатыш орус алим публицист байра...`

**Context Size 2:**

1. `алай а ол хакъла бек адаргы болгъандыла къулну къайнагъы джангы къазауат людовикни хорламы бла битед...`
2. `эм уллу эмда ара хунтагъа 150 белгили адамладан къуралгъан тамал депутатциясын джыяргъа буйрукъ берг...`
3. `абш ны къуралгъанындан джюз джылдан артыкъны тургъанды джыл къыбыла каролина къыбылада флорида ачыкъ...`

**Context Size 3:**

1. `огъары дараджаны интернет домени доменле sv toppdomän n`
2. `болгъан ишле туугъанла ёлгенле а09`
3. `григориан орузламада джылны 58 чи кюнюдю джылны ахырына дери 216 кюн къалады байрамла болгъан ишле т...`

**Context Size 4:**

1. `кюнюдю джылны ахырына дери 364 кюн високос джыллада 365 кюн къалады байрамла болгъан ишле туугъанла ...`
2. `къалады байрамла болгъан ишле туугъанла ёлгенле б09`
3. `кюн къалады байрамла болгъан ишле туугъанла ёлгенле а09`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_рган_1_ghat._ге`
2. `а_агъарекатайраш`
3. `нтгелюны_олене_т`

**Context Size 2:**

1. `а_ню_блай_прундыл`
2. `ан_соломод_бламал`
3. `ласын_джомони_изд`

**Context Size 3:**

1. `гъатда,_архительви`
2. `ны_джылгъа_кенге_б`
3. `да_политиканы_сима`

**Context Size 4:**

1. `гъаны_мийик_тилде_д`
2. `аны_биринчиси_болад`
3. `лгъан_джылда_джерле`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (200,334 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 | 31,984 |
| Total Tokens | 462,833 |
| Mean Frequency | 14.47 |
| Median Frequency | 3 |
| Frequency Std Dev | 100.73 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | бла | 11,098 |
| 2 | эмда | 6,281 |
| 3 | да | 3,753 |
| 4 | эм | 2,789 |
| 5 | джылны | 2,622 |
| 6 | бир | 2,539 |
| 7 | болгъанды | 2,365 |
| 8 | ол | 2,214 |
| 9 | уллу | 2,174 |
| 10 | аны | 2,033 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | уотер | 2 |
| 2 | килбрайд | 2 |
| 3 | камбернолд | 2 |
| 4 | сайлангъанды | 2 |
| 5 | стив | 2 |
| 6 | зохран | 2 |
| 7 | мамдани | 2 |
| 8 | mamdani | 2 |
| 9 | плейнс | 2 |
| 10 | джеральд | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9853 |
| R² (Goodness of Fit) | 0.993593 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.2% |
| Top 1,000 | 54.9% |
| Top 5,000 | 77.2% |
| Top 10,000 | 86.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9936 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.2% of corpus
- **Long Tail:** 21,984 words needed for remaining 13.7% 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 | 0.8818 | 0.2934 | N/A | N/A |
| **mono_64d** | 64 | 0.6138 | 0.2510 | N/A | N/A |
| **mono_128d** | 128 | 0.1461 | 0.2598 | N/A | N/A |
| **aligned_32d** | 32 | 0.8818 🏆 | 0.2916 | 0.0080 | 0.1040 |
| **aligned_64d** | 64 | 0.6138 | 0.2543 | 0.0200 | 0.1400 |
| **aligned_128d** | 128 | 0.1461 | 0.2580 | 0.0360 | 0.1920 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8818 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2680. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.6% 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 | **0.553** | 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` | кеси, кёбчюлюкню, къалмайды |
| `-а` | агъымладан, арий, анжучу |
| `-с` | стандартланы, сомовну, синхрон |
| `-т` | том, тюрлениуде, тизгинде |
| `-б` | бкъб, билдириргенди, берлингтон |
| `-м` | мисирни, меридианыны, мадам |
| `-д` | джерлешгендиле, джауладан, документальный |
| `-дж` | джерлешгендиле, джауладан, джукъугъа |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | ра, ачхада, наполеоннга |
| `-ы` | идеологияланы, апианы, прибалтиканы |
| `-ны` | идеологияланы, апианы, прибалтиканы |
| `-н` | агъымладан, джауладан, берлингтон |
| `-и` | кеси, мисирни, эспри |
| `-ла` | гарнизонла, алынмагъандыла, тутадыла |
| `-е` | джерлешгендиле, пэрле, тюрлениуде |
| `-да` | ачхада, манитобада, галилеяда |

### 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 |
|------|----------|------------------|----------|
| `генд` | 1.95x | 60 contexts | юзгенди, легенды, дегенди |
| `лени` | 1.69x | 65 contexts | ленин, члени, ишлени |
| `ърал` | 2.34x | 17 contexts | кърал, къралы, къралды |
| `лгъа` | 1.59x | 67 contexts | алгъа, залгъа, нолгъа |
| `гъан` | 1.42x | 107 contexts | дагъан, ойгъан, озгъан |
| `ргъа` | 1.80x | 38 contexts | ургъан, баргъа, ояргъа |
| `къур` | 1.99x | 26 contexts | къурд, къуру, къурч |
| `ланы` | 1.64x | 53 contexts | планы, уланы, аланы |
| `къра` | 2.29x | 13 contexts | кърал, къралы, къралды |
| `лыкъ` | 1.67x | 36 contexts | балыкъ, палыкъ, ачлыкъ |
| `алгъ` | 1.56x | 34 contexts | алгъы, алгъа, залгъа |
| `енди` | 1.81x | 19 contexts | эфенди, афенди, доменди |

### 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` | `-а` | 215 words | къонакъгъа, къабатла |
| `-к` | `-ы` | 195 words | къуралгъаны, къойгъанды |
| `-а` | `-а` | 173 words | арба, аздыла |
| `-а` | `-ы` | 142 words | анты, айтымланы |
| `-б` | `-а` | 136 words | булутлада, браганса |
| `-к` | `-н` | 128 words | кетерилген, кючледен |
| `-д` | `-ы` | 121 words | джууукълашады, дараджасыны |
| `-к` | `-и` | 116 words | киргизиледи, келди |
| `-к` | `-е` | 110 words | корее, кавказские |
| `-д` | `-а` | 108 words | дахауда, джаратыргъа |

### 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 |
|------|-----------------|------------|------|
| къошулмау | **`къошулм-а-у`** | 7.5 | `а` |
| дараджада | **`дарадж-а-да`** | 7.5 | `а` |
| спектральная | **`спектральн-а-я`** | 7.5 | `а` |
| кириллицада | **`кириллиц-а-да`** | 7.5 | `а` |
| ашырылгъанды | **`ашырылгъ-ан-ды`** | 7.5 | `ан` |
| кафедраны | **`кафедр-а-ны`** | 7.5 | `а` |
| температураны | **`температур-а-ны`** | 7.5 | `а` |
| аякъланнганла | **`аякъланнг-ан-ла`** | 7.5 | `ан` |
| тохтатады | **`тохтат-а-ды`** | 7.5 | `а` |
| чыкъгъанда | **`чыкъгъ-ан-да`** | 7.5 | `ан` |
| къуршаланады | **`къуршалан-а-ды`** | 7.5 | `а` |
| тоналгъанды | **`тоналгъ-ан-ды`** | 7.5 | `ан` |
| тизгиннге | **`тизгин-н-ге`** | 7.5 | `н` |
| сёлешелле | **`сёлеше-л-ле`** | 7.5 | `л` |
| механиканы | **`механик-а-ны`** | 7.5 | `а` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Karachay-Balkar 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 (4.72x) |
| N-gram | **2-gram** | Lowest perplexity (391) |
| Markov | **Context-4** | Highest predictability (99.1%) |
| 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 08:32:24*