---
language: inh
language_name: Ingush
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: 4.589
  - name: best_isotropy
    type: isotropy
    value: 0.7882
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ingush** 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** | 3.549x | 3.56 | 0.1349% | 201,601 |
| **16k** | 3.935x | 3.94 | 0.1496% | 181,782 |
| **32k** | 4.258x | 4.27 | 0.1619% | 168,012 |
| **64k** | 4.589x 🏆 | 4.60 | 0.1745% | 155,892 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ме́ксика ( ), официальни — Мексикахой Хетта ШтаташМИД России | | МЕКСИКА () — па...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ме ́ кс ика ▁( ▁), ▁официальни ▁— ▁мекс ика ... (+19 more)` | 29 |
| 16k | `▁ме ́ кс ика ▁( ▁), ▁официальни ▁— ▁мексика хой ... (+17 more)` | 27 |
| 32k | `▁ме ́ кс ика ▁( ▁), ▁официальни ▁— ▁мексика хой ... (+16 more)` | 26 |
| 64k | `▁ме́ксика ▁( ▁), ▁официальни ▁— ▁мексикахой ▁хетта ▁штаташмид ▁россии ▁| ... (+11 more)` | 21 |

**Sample 2:** `Нотр-Дам-де-Пари е Парижа Даьла Наьна Элгац (, ) — Париже йоалла католикий элгац...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁н от р - дам - де - п ари ... (+27 more)` | 37 |
| 16k | `▁нот р - дам - де - пари ▁е ▁пари ... (+21 more)` | 31 |
| 32k | `▁нот р - дам - де - пари ▁е ▁парижа ... (+20 more)` | 30 |
| 64k | `▁нотр - дам - де - пари ▁е ▁парижа ▁даьла ... (+18 more)` | 28 |

**Sample 3:** `«Нийсхо» (я) () — шера гӀалгӀашкара хьаяьккха́ ГӀалме шахьар юха ГӀалгӀай Респуб...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁« нийс хо » ▁( я ) ▁() ▁— ▁шера ... (+25 more)` | 35 |
| 16k | `▁« нийс хо » ▁( я ) ▁() ▁— ▁шера ... (+20 more)` | 30 |
| 32k | `▁« нийсхо » ▁( я ) ▁() ▁— ▁шера ▁гӏалгӏаш ... (+17 more)` | 27 |
| 64k | `▁« нийсхо » ▁( я ) ▁() ▁— ▁шера ▁гӏалгӏашкара ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.589x compression
- **Lowest UNK Rate:** 8k with 0.1349% 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 | 2,700 | 11.40 | 4,486 | 18.1% | 59.8% |
| **2-gram** | Subword | 374 🏆 | 8.55 | 2,693 | 59.4% | 97.6% |
| **3-gram** | Word | 2,178 | 11.09 | 4,133 | 19.5% | 65.5% |
| **3-gram** | Subword | 3,053 | 11.58 | 18,826 | 23.3% | 64.6% |
| **4-gram** | Word | 4,659 | 12.19 | 9,587 | 15.7% | 49.4% |
| **4-gram** | Subword | 14,259 | 13.80 | 75,178 | 11.2% | 36.9% |
| **5-gram** | Word | 3,632 | 11.83 | 7,779 | 17.6% | 54.3% |
| **5-gram** | Subword | 35,588 | 15.12 | 140,686 | 7.5% | 25.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `белгалдаккхар тӏатовжамаш` | 415 |
| 2 | `гӏалгӏай мехка` | 328 |
| 3 | `з хь` | 315 |
| 4 | `вай з` | 307 |
| 5 | `хьажа иштта` | 255 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `вай з хь` | 307 |
| 2 | `шераш вай з` | 232 |
| 3 | `нах баха моттигаш` | 153 |
| 4 | `хь шераш вай` | 130 |
| 5 | `з хь шераш` | 130 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `шераш вай з хь` | 232 |
| 2 | `вай з хь шераш` | 130 |
| 3 | `з хь шераш вай` | 130 |
| 4 | `хь шераш вай з` | 130 |
| 5 | `шахьара нах баха моттигаш` | 130 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `вай з хь шераш вай` | 130 |
| 2 | `з хь шераш вай з` | 130 |
| 3 | `хь шераш вай з хь` | 130 |
| 4 | `шераш вай з хь шераш` | 117 |
| 5 | `гӏа шераш вай з хь` | 100 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 75,922 |
| 2 | `а р` | 27,088 |
| 3 | `ӏ а` | 26,314 |
| 4 | `а л` | 24,378 |
| 5 | `р а` | 24,271 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `х ь а` | 13,086 |
| 2 | `г ӏ а` | 13,029 |
| 3 | `а ш _` | 11,108 |
| 4 | `р а _` | 10,332 |
| 5 | `ч а _` | 9,547 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а р а _` | 4,962 |
| 2 | `а ч а _` | 4,074 |
| 3 | `_ х ь а` | 3,915 |
| 4 | `г ӏ а л` | 3,870 |
| 5 | `а г ӏ а` | 3,736 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `х и н н а` | 3,488 |
| 2 | `_ х и н н` | 3,331 |
| 3 | `г ӏ а л г` | 3,121 |
| 4 | `ӏ а л г ӏ` | 3,119 |
| 5 | `а л г ӏ а` | 3,111 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 374
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | Word | 0.6550 | 1.575 | 3.54 | 50,260 | 34.5% |
| **1** | Subword | 1.2189 | 2.328 | 9.47 | 622 | 0.0% |
| **2** | Word | 0.1442 | 1.105 | 1.26 | 177,219 | 85.6% |
| **2** | Subword | 1.1111 | 2.160 | 6.21 | 5,892 | 0.0% |
| **3** | Word | 0.0357 | 1.025 | 1.05 | 221,229 | 96.4% |
| **3** | Subword | 0.8323 | 1.781 | 3.70 | 36,562 | 16.8% |
| **4** | Word | 0.0120 🏆 | 1.008 | 1.02 | 230,572 | 98.8% |
| **4** | Subword | 0.5706 | 1.485 | 2.34 | 135,317 | 42.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `а долаш ший йоазонашта юкъе лелаш хул цхьайолча хана денз цун бизнес дегӏакхувлара дукха мехкарий ам...`
2. `я лоам жӏайраха шахьаре я аьдагӏий мотт хьехаш аьлте юрта хьисапе моттиг хиннай шера мальсагов дошлу...`
3. `гӏалгӏай мохк баьккха́ ва́гӏача моастагӏчунга паргӏата ма дарра аьлча гӏалгӏаша къаьстта кубчий пхьа...`

**Context Size 2:**

1. `белгалдаккхар тӏатовжамаш чеботарев а и робакидзеи даьча тохкамех фаьппий кхаькхалоех е ӏадатех а е ...`
2. `гӏалгӏай мехка паччахьалкъен филармони хамхой ахьмада цӏерагӏа я юрт ларс жӏайрахой баьха моттиг улл...`
3. `з хь 590 гӏа шераш 390 гӏа шераш vii бӏаьшу 600 гӏа шераш вай з хь xcix`

**Context Size 3:**

1. `вай з хь шераш вай з хь xxx xxix xxviii xxvii xxvi xxv xxiv xxiii xxii xxi 2`
2. `шераш вай з хь 830 гӏа шераш вай з хь шераш вай з хь 7 шу i бӏаьшера`
3. `з хь шераш вай з хь шераш вай з хь шераш вай з хь шераш вай з хь`

**Context Size 4:**

1. `шераш вай з хь 720 гӏа шераш вай з хь 50 гӏа шераш вай з хь шераш вай з`
2. `хь шераш вай з хь шераш вай з хь 400 гӏа шераш вай з хь шераш вай з хь`
3. `з хь шераш вай з хь xiv бӏаьшу вай з хь тӏатовжамаш`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `аш_дндолега_афал`
2. `_коа,_—_«цхьерми`
3. `оаллг_пргӏе._мап`

**Context Size 2:**

1. `а_сийчеи_бе._хьа_`
2. `архойиха_худжамаӏ`
3. `ӏайча_хаязыкнофи_`

**Context Size 3:**

1. `хьалкхар_тӏа_—_«бӏ`
2. `гӏалаходкуменна_ба`
3. `аш_лелал_ха́ннай._б`

**Context Size 4:**

1. `ара_арахой_2_обозна`
2. `ача_между_из,_нохчи`
3. `_хьаяхача_багарга_х`


### 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 (135,317 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 | 19,260 |
| Total Tokens | 235,079 |
| Mean Frequency | 12.21 |
| Median Frequency | 3 |
| Frequency Std Dev | 72.65 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | а | 6,393 |
| 2 | я | 2,455 |
| 3 | гӏалгӏай | 2,253 |
| 4 | из | 2,010 |
| 5 | шера | 1,966 |
| 6 | да | 1,931 |
| 7 | и | 1,329 |
| 8 | белгалдаккхар | 1,258 |
| 9 | в | 1,233 |
| 10 | тӏа | 1,139 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ориентальни | 2 |
| 2 | балтий | 2 |
| 3 | лорала́ | 2 |
| 4 | кхерамзеи | 2 |
| 5 | wie | 2 |
| 6 | дарбанчаш | 2 |
| 7 | легализаци | 2 |
| 8 | целители | 2 |
| 9 | практикаш | 2 |
| 10 | лоралгахь | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0116 |
| R² (Goodness of Fit) | 0.991479 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 28.1% |
| Top 1,000 | 59.7% |
| Top 5,000 | 82.4% |
| Top 10,000 | 91.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9915 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 28.1% of corpus
- **Long Tail:** 9,260 words needed for remaining 8.7% 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 | 0.7882 🏆 | 0.3485 | N/A | N/A |
| **mono_64d** | 64 | 0.3727 | 0.3608 | N/A | N/A |
| **mono_128d** | 128 | 0.0496 | 0.3296 | N/A | N/A |
| **aligned_32d** | 32 | 0.7882 | 0.3541 | 0.0140 | 0.1220 |
| **aligned_64d** | 64 | 0.3727 | 0.3473 | 0.0180 | 0.1180 |
| **aligned_128d** | 128 | 0.0496 | 0.3275 | 0.0380 | 0.1560 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7882 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3446. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.8% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **1.160** | 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 |
|--------|----------|
| `-д` | дийхка, довта, даьржаи |
| `-к` | классификациям, кӏориганаькъан, кодекса |
| `-с` | сулак, сомали, статьяш |
| `-б` | бунак, берашта, белгалъеш |
| `-м` | мусульманами, мухтарова, мальта |
| `-а` | астрале, аьтта, амхарой |
| `-т` | тӏахьелхаш, тайпового, тийна |
| `-хьа` | хьалхадоахаш, хьалхашкарча, хьаста |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | община, мухтарова, юххьанцарча |
| `-и` | мусульманами, жигули, экзотермически |
| `-й` | лезгинский, регулярный, амхарой |
| `-аш` | тӏахьелхаш, воагӏаш, яхараш |
| `-ш` | тӏахьелхаш, воагӏаш, яхараш |
| `-е` | астрале, йолае, ӏомаде |
| `-ий` | лезгинский, къарший, советский |
| `-ча` | юххьанцарча, йолалуча, хьогденнача |

### 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 |
|------|----------|------------------|----------|
| `ккха` | 1.67x | 69 contexts | яккха, йоккха, аьккха |
| `ькъа` | 1.96x | 30 contexts | шаькъа, ӏаькъа, даькъа |
| `хьар` | 1.58x | 67 contexts | пхьар, хьарп, хьарме |
| `амаш` | 1.70x | 45 contexts | тамаш, замаш, ӏамаш |
| `хача` | 1.85x | 28 contexts | яхача, ухача, кхача |
| `инна` | 1.92x | 24 contexts | хинна, шинна, хиннар |
| `аькъ` | 1.78x | 30 contexts | наькъ, даькъ, шаькъа |
| `аккх` | 1.89x | 24 contexts | боаккх, воаккх, чаккхе |
| `кхар` | 1.70x | 33 contexts | кхарт, декхар, акхаре |
| `ахьа` | 1.38x | 55 contexts | кхахьа, арахьа, дахьаш |
| `лгал` | 1.78x | 21 contexts | кулгал, белгал, белгала |
| `хинн` | 1.93x | 16 contexts | хинна, хиннар, хиннад |

### 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 |
|--------|--------|-----------|----------|
| `-д` | `-а` | 176 words | длина, дешагара |
| `-к` | `-а` | 148 words | кӏезигагӏа, кепагӏа |
| `-б` | `-а` | 110 words | баьлча, бийтта |
| `-м` | `-а` | 104 words | малхбоалега, мукха |
| `-г` | `-а` | 91 words | гӏалгӏайченна, галашкархоша |
| `-т` | `-а` | 80 words | тайпарча, тӏаргамара |
| `-а` | `-а` | 79 words | арадийна, арахецарца |
| `-п` | `-а` | 67 words | принципаца, произведенеша |
| `-с` | `-а` | 61 words | секретара, сша |
| `-к` | `-и` | 59 words | клавиши, критически |

### 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 |
|------|-----------------|------------|------|
| шоллагӏчох | **`шоллагӏч-о-х`** | 7.5 | `о` |
| кепатехача | **`кепатех-а-ча`** | 7.5 | `а` |
| кулгалдара | **`кулгалд-а-ра`** | 7.5 | `а` |
| баьцакомар | **`баьцако-м-ар`** | 7.5 | `м` |
| дӏатиллай | **`дӏатилл-а-й`** | 7.5 | `а` |
| наькъахои | **`наькъах-о-и`** | 7.5 | `о` |
| исбахьлен | **`исбахь-л-ен`** | 7.5 | `л` |
| кириллицай | **`кириллиц-а-й`** | 7.5 | `а` |
| латтандаь | **`латтанд-а-ь`** | 7.5 | `а` |
| гӏалгӏашкара | **`гӏалгӏаш-ка-ра`** | 7.5 | `ка` |
| гӏоазотаца | **`гӏоазот-а-ца`** | 7.5 | `а` |
| моттигашкара | **`моттигаш-ка-ра`** | 7.5 | `ка` |
| хьаракаца | **`хьара-ка-ца`** | 7.5 | `ка` |
| малхбоалехьаи | **`малхбоалехь-а-и`** | 7.5 | `а` |
| республикаца | **`республик-а-ца`** | 7.5 | `а` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ingush 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 (4.59x) |
| N-gram | **2-gram** | Lowest perplexity (374) |
| 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: 2026-01-10 04:22:21*