---
language: tt
language_name: Tatar
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: 3.888
  - name: best_isotropy
    type: isotropy
    value: 0.8039
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tatar** 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** | 2.518x | 2.52 | 1.8383% | 700,522 |
| **16k** | 3.065x | 3.07 | 2.2381% | 575,392 |
| **32k** | 3.505x | 3.51 | 2.5595% | 503,144 |
| **64k** | 3.888x 🏆 | 3.89 | 2.8391% | 453,599 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Вилья-Нвева () — Гватемаланың Гватемала департаментында урнашкан шәһәр. Тарих ел...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁вилья - н в ева ▁() ▁— ▁гватем ал аның ... (+14 more)` | 24 |
| 16k | `▁вилья - н в ева ▁() ▁— ▁гватем ал аның ... (+14 more)` | 24 |
| 32k | `▁вилья - н в ева ▁() ▁— ▁гватем ал аның ... (+14 more)` | 24 |
| 64k | `▁вилья - нв ева ▁() ▁— ▁гватем аланың ▁гватемала ▁департаментында ... (+12 more)` | 22 |

**Sample 2:** `Санта-Клара () — Кубаның Вилья-Клара правинсәсендә урнашкан шәһәр. Тарих елда ни...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁санта - к лар а ▁() ▁— ▁куб аның ▁вилья ... (+21 more)` | 31 |
| 16k | `▁санта - клар а ▁() ▁— ▁куб аның ▁вилья - ... (+17 more)` | 27 |
| 32k | `▁санта - клар а ▁() ▁— ▁куб аның ▁вилья - ... (+17 more)` | 27 |
| 64k | `▁санта - клара ▁() ▁— ▁кубаның ▁вилья - клара ▁правинсәсендә ... (+14 more)` | 24 |

**Sample 3:** `249 — Милади тәкъвим буенча I гасырга кергән ел. Б. э. к. 249 — безнең эрага кад...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 2 4 9 ▁— ▁милади ▁тәкъвим ▁буенча ▁i ▁гасырга ... (+29 more)` | 39 |
| 16k | `▁ 2 4 9 ▁— ▁милади ▁тәкъвим ▁буенча ▁i ▁гасырга ... (+29 more)` | 39 |
| 32k | `▁ 2 4 9 ▁— ▁милади ▁тәкъвим ▁буенча ▁i ▁гасырга ... (+29 more)` | 39 |
| 64k | `▁ 2 4 9 ▁— ▁милади ▁тәкъвим ▁буенча ▁i ▁гасырга ... (+29 more)` | 39 |


### Key Findings

- **Best Compression:** 64k achieves 3.888x compression
- **Lowest UNK Rate:** 8k with 1.8383% 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 | 5,605 | 12.45 | 336,396 | 17.6% | 56.9% |
| **2-gram** | Subword | 576 🏆 | 9.17 | 14,523 | 47.1% | 96.2% |
| **3-gram** | Word | 5,577 | 12.45 | 467,096 | 14.9% | 55.0% |
| **3-gram** | Subword | 3,878 | 11.92 | 124,619 | 17.9% | 58.8% |
| **4-gram** | Word | 6,302 | 12.62 | 904,172 | 13.6% | 53.3% |
| **4-gram** | Subword | 11,857 | 13.53 | 730,744 | 12.0% | 38.9% |
| **5-gram** | Word | 6,063 | 12.57 | 753,401 | 13.2% | 52.9% |
| **5-gram** | Subword | 22,534 | 14.46 | 2,199,517 | 9.5% | 31.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `торак пунктлары` | 511,989 |
| 2 | `торак пунктлар` | 358,682 |
| 3 | `буенча торак` | 358,322 |
| 4 | `искәрмәләр әдәбият` | 221,621 |
| 5 | `с isbn` | 214,931 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `буенча торак пунктлар` | 358,297 |
| 2 | `торак пунктлары буенча` | 187,674 |
| 3 | `пунктлары буенча торак` | 187,674 |
| 4 | `ред а м` | 153,676 |
| 5 | `торак пунктлары торак` | 129,977 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `пунктлары буенча торак пунктлар` | 187,674 |
| 2 | `торак пунктлары буенча торак` | 187,674 |
| 3 | `торак пунктлары торак пунктлары` | 129,976 |
| 4 | `пунктлары торак пунктлары буенча` | 129,287 |
| 5 | `словарь современных географических названий` | 106,362 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `торак пунктлары буенча торак пунктлар` | 187,674 |
| 2 | `пунктлары торак пунктлары буенча торак` | 129,287 |
| 3 | `торак пунктлары торак пунктлары буенча` | 129,287 |
| 4 | `ред акад в м котлякова` | 106,358 |
| 5 | `общ ред акад в м` | 106,358 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 11,023,264 |
| 2 | `а р` | 6,361,281 |
| 3 | `а _` | 5,311,741 |
| 4 | `а н` | 5,060,928 |
| 5 | `, _` | 5,060,574 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ — _` | 3,389,980 |
| 2 | `л а р` | 3,211,197 |
| 3 | `т о р` | 1,837,402 |
| 4 | `а р ы` | 1,689,146 |
| 5 | `а н _` | 1,646,751 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _ — _` | 1,375,605 |
| 2 | `л а р ы` | 1,366,265 |
| 3 | `_ т о р` | 1,190,607 |
| 4 | `р а к _` | 1,115,216 |
| 5 | `н ы ң _` | 1,092,167 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ т о р а` | 1,048,743 |
| 2 | `п у н к т` | 1,033,933 |
| 3 | `_ п у н к` | 1,033,877 |
| 4 | `т о р а к` | 998,550 |
| 5 | `о р а к _` | 998,164 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 576
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~32% 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 | 0.7595 | 1.693 | 6.53 | 995,401 | 24.0% |
| **1** | Subword | 0.9626 | 1.949 | 6.88 | 6,952 | 3.7% |
| **2** | Word | 0.2482 | 1.188 | 1.63 | 6,489,220 | 75.2% |
| **2** | Subword | 0.7481 | 1.680 | 5.47 | 47,775 | 25.2% |
| **3** | Word | 0.0818 | 1.058 | 1.16 | 10,550,818 | 91.8% |
| **3** | Subword | 0.7704 | 1.706 | 4.62 | 261,018 | 23.0% |
| **4** | Word | 0.0343 🏆 | 1.024 | 1.06 | 12,171,163 | 96.6% |
| **4** | Subword | 0.6961 | 1.620 | 3.36 | 1,206,914 | 30.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `торак пунктлары торак пунктлары районы торак пунктлар воеводалыгы торак пунктлар шәһәрләре буенча то...`
2. `м гуманитар изд центр владос 463 с isbn lutz d schmadel dictionary of minor planet names`
3. `в п история чехии периода феодализма v середина xvii в головина т гл ред акад в`

**Context Size 2:**

1. `торак пунктлары торак пунктлары буенча торак пунктлар буе воеводалыгы торак пунктлары калифорния тор...`
2. `буенча торак пунктлар виргиния торак пунктлары торак пунктлары буенча торак пунктлар воеводалыгы тор...`
3. `искәрмәләр әдәбият мексика словарь современных географических названий рус геогр о во моск центр под...`

**Context Size 3:**

1. `торак пунктлары буенча торак пунктлар торак пунктлары мәхәлләләре tr gölbaşı gördes vi gölbaşı görde...`
2. `пунктлары буенча торак пунктлар воеводалыгы торак пунктлары малопольське воєводство`
3. `ред а м родригеса м в пономарёва м гуманитар изд центр владос 463 с isbn сылтамалар мексика халкы`

**Context Size 4:**

1. `торак пунктлары буенча торак пунктлар воеводалыгы торак пунктлары люблінське воєводство`
2. `пунктлары торак пунктлары буенча торак пунктлар воеводалыгы торак пунктлары люблінське воєводство`
3. `торак пунктлары торак пунктлары буенча торак пунктлар воеводалыгы торак пунктлары люблінське воєводс...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_тла._маване_2_т`
2. `азьш_торабекы_че`
3. `рынь_скандәһәр,_`

**Context Size 2:**

1. `._а._y._—_ростары`
2. `арда_кой_//_пункт`
3. `а_җәсер_сынынтраз`

**Context Size 3:**

1. `_—_lerinava,_the_n`
2. `лар_мәхәлләр_чык_с`
3. `торак_пунктлар_ист`

**Context Size 4:**

1. `._—_isbn_љубоја,_бр`
2. `лары_өлкәләр_әдәбия`
3. `_торак_пункт._геогр`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,206,914 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 | 443,760 |
| Total Tokens | 70,749,793 |
| Mean Frequency | 159.43 |
| Median Frequency | 3 |
| Frequency Std Dev | 4837.60 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | торак | 998,246 |
| 2 | м | 917,540 |
| 3 | в | 885,385 |
| 4 | һәм | 800,090 |
| 5 | с | 768,930 |
| 6 | урнашкан | 631,181 |
| 7 | буенча | 609,080 |
| 8 | а | 543,019 |
| 9 | искәрмәләр | 532,743 |
| 10 | пунктлары | 512,045 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | плзень | 2 |
| 2 | бобровски | 2 |
| 3 | шумперк | 2 |
| 4 | unscop | 2 |
| 5 | agreste | 2 |
| 6 | серпер | 2 |
| 7 | мөлдір | 2 |
| 8 | бұлақ | 2 |
| 9 | қамшыгер | 2 |
| 10 | алғашқы | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.5672 |
| R² (Goodness of Fit) | 0.955579 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.8% |
| Top 1,000 | 73.9% |
| Top 5,000 | 91.6% |
| Top 10,000 | 93.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9556 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.8% of corpus
- **Long Tail:** 433,760 words needed for remaining 6.1% 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 | 0.8039 🏆 | 0.3550 | N/A | N/A |
| **mono_64d** | 64 | 0.7762 | 0.3573 | N/A | N/A |
| **mono_128d** | 128 | 0.7182 | 0.2748 | N/A | N/A |
| **aligned_32d** | 32 | 0.8039 | 0.3711 | 0.0220 | 0.1680 |
| **aligned_64d** | 64 | 0.7762 | 0.3654 | 0.0620 | 0.3380 |
| **aligned_128d** | 128 | 0.7182 | 0.2805 | 0.1200 | 0.4000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8039 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3340. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 12.0% 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 | **0.677** | 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` | көндәшсез, көчләрне, колбукаро |
| `-ка` | калибровочную, кандәһләви, кардези |
| `-с` | сердә, спацавенто, смольниця |
| `-а` | айдиал, артыкка, артефактларның |
| `-ко` | колбукаро, коце, кояметла |
| `-б` | борап, быш, борганино |
| `-т` | таден, типографик, ташлау |
| `-ма` | мај, маркето, маһирлыгын |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | фалерна, генриэтта, нугуманова |
| `-н` | таден, гөлләреннән, узуларын |
| `-е` | көчләрне, физиологияне, коце |
| `-ы` | друиды, бурычларны, ярашлыгы |
| `-ың` | юлайның, артефактларның, тарасовның |
| `-ң` | юлайның, артефактларның, тарасовның |
| `-р` | дәфтәрләр, борепер, рифмир |
| `-о` | колбукаро, нефтяного, кваральио |

### 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 |
|------|----------|------------------|----------|
| `екси` | 2.66x | 45 contexts | лекси, лексик, лексин |
| `скәр` | 2.50x | 46 contexts | әскәр, искәр, яскәр |
| `мәлә` | 2.05x | 76 contexts | мәләш, мәләлә, өмәләр |
| `шкан` | 2.12x | 65 contexts | ашкан, нашкан, лашкан |
| `әләр` | 1.68x | 188 contexts | әләрә, дәләр, тәләр |
| `имат` | 2.26x | 47 contexts | тимати, иматра, алимат |
| `рнаш` | 2.61x | 27 contexts | борнаш, бурнаш, урнаша |
| `тлар` | 1.49x | 284 contexts | ютлар, тлары, утлар |
| `ункт` | 2.49x | 20 contexts | пункт, пункте, пункту |
| `уенч` | 2.54x | 17 contexts | уенча, буенч, уенчы |
| `пунк` | 2.31x | 21 contexts | пункт, пункте, пункту |
| `нашк` | 2.44x | 17 contexts | нашкан, урнашка, анашкин |

### 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` | 141 words | касыймга, кога |
| `-к` | `-н` | 75 words | киселешеннән, канкин |
| `-а` | `-а` | 74 words | амперга, азияда |
| `-к` | `-ы` | 72 words | кабатланмаучы, контрастлы |
| `-с` | `-а` | 72 words | сарданьола, сребрна |
| `-б` | `-а` | 59 words | букинага, барглувка |
| `-т` | `-а` | 59 words | тулыландыруга, тромпета |
| `-п` | `-а` | 54 words | продуктларга, планичка |
| `-т` | `-ы` | 50 words | тарминалы, тотышканчы |
| `-к` | `-е` | 50 words | конуктепе, кавакдере |

### 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 |
|------|-----------------|------------|------|
| диэлектрик | **`диэлектр-и-к`** | 7.5 | `и` |
| катнашучының | **`катнашучы-н-ың`** | 7.5 | `н` |
| датчиклары | **`датчикл-ар-ы`** | 7.5 | `ар` |
| канатында | **`ка-на-тында`** | 7.5 | `тында` |
| кулланылаалынма | **`кулланылаалын-м-а`** | 7.5 | `м` |
| ансамбленың | **`ансамбле-н-ың`** | 7.5 | `н` |
| шрикантешвара | **`шрикантешв-ар-а`** | 7.5 | `ар` |
| ятьмәләрнең | **`ятьмәләр-н-ең`** | 7.5 | `н` |
| полифоник | **`полифон-и-к`** | 7.5 | `и` |
| тласмалак | **`тласма-ла-к`** | 7.5 | `ла` |
| балачагын | **`ба-ла-чагын`** | 7.5 | `чагын` |
| каланчага | **`каланч-а-га`** | 7.5 | `а` |
| шикләнергә | **`шикләне-р-гә`** | 7.5 | `р` |
| страфорини | **`страфори-н-и`** | 7.5 | `н` |
| тургайлары | **`тургай-ла-ры`** | 7.5 | `ла` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tatar 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 (3.89x) |
| N-gram | **2-gram** | Lowest perplexity (576) |
| Markov | **Context-4** | Highest predictability (96.6%) |
| 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: 2026-01-11 04:28:46*