---
language: tyv
language_name: Tuvinian
language_family: turkic_siberian
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_siberian
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: 4.537
  - name: best_isotropy
    type: isotropy
    value: 0.8935
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tuvinian** 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** | 3.594x | 3.60 | 0.0328% | 531,182 |
| **16k** | 3.989x | 3.99 | 0.0364% | 478,519 |
| **32k** | 4.325x | 4.33 | 0.0394% | 441,354 |
| **64k** | 4.537x 🏆 | 4.54 | 0.0414% | 420,702 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `120 — илередип болур: 120 (сан) — 119 биле 121 аразында алыс сан. 120 чыл — григ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 1 2 0 ▁— ▁илередип ▁болур : ▁ 1 ... (+30 more)` | 40 |
| 16k | `▁ 1 2 0 ▁— ▁илередип ▁болур : ▁ 1 ... (+30 more)` | 40 |
| 32k | `▁ 1 2 0 ▁— ▁илередип ▁болур : ▁ 1 ... (+29 more)` | 39 |
| 64k | `▁ 1 2 0 ▁— ▁илередип ▁болур : ▁ 1 ... (+29 more)` | 39 |

**Sample 2:** `Волонтёр () – кандыг-ла бир мөөрей, шуулган азы улуг байырлалдарга акша-шалың дэ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁вол онт ёр ▁() ▁– ▁кандыг - ла ▁бир ▁мөөрей ... (+28 more)` | 38 |
| 16k | `▁вол онт ёр ▁() ▁– ▁кандыг - ла ▁бир ▁мөөрей ... (+25 more)` | 35 |
| 32k | `▁вол онтёр ▁() ▁– ▁кандыг - ла ▁бир ▁мөөрей , ... (+21 more)` | 31 |
| 64k | `▁волонтёр ▁() ▁– ▁кандыг - ла ▁бир ▁мөөрей , ▁шуулган ... (+20 more)` | 30 |

**Sample 3:** `Хертек, Артур Ойняр-оол-оглу (хх.хх.ххч. тор.) — Күнзегеш аттыг ном үндүрер төпт...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁хертек , ▁артур ▁ойн яр - оол - оглу ▁( ... (+19 more)` | 29 |
| 16k | `▁хертек , ▁артур ▁ойн яр - оол - оглу ▁( ... (+19 more)` | 29 |
| 32k | `▁хертек , ▁артур ▁ойн яр - оол - оглу ▁( ... (+18 more)` | 28 |
| 64k | `▁хертек , ▁артур ▁ойн яр - оол - оглу ▁( ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 4.537x compression
- **Lowest UNK Rate:** 8k with 0.0328% 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 | 12,431 | 13.60 | 23,023 | 9.7% | 31.7% |
| **2-gram** | Subword | 472 🏆 | 8.88 | 5,348 | 53.6% | 96.7% |
| **3-gram** | Word | 14,165 | 13.79 | 23,322 | 8.4% | 28.5% |
| **3-gram** | Subword | 4,204 | 12.04 | 40,268 | 18.3% | 58.9% |
| **4-gram** | Word | 28,047 | 14.78 | 43,599 | 6.7% | 21.1% |
| **4-gram** | Subword | 21,807 | 14.41 | 186,047 | 9.6% | 30.8% |
| **5-gram** | Word | 20,854 | 14.35 | 32,166 | 8.0% | 23.8% |
| **5-gram** | Subword | 64,567 | 15.98 | 403,526 | 6.4% | 20.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `бир дугаар` | 1,161 |
| 2 | `тыва республиканың` | 859 |
| 3 | `ынчалза даа` | 839 |
| 4 | `күш ажылдың` | 724 |
| 5 | `ссрэ ниң` | 721 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `социалистиг күш ажылдың` | 353 |
| 2 | `күш ажылдың маадыры` | 325 |
| 3 | `дөс тыва дылдың` | 280 |
| 4 | `чылдан чылга чедир` | 279 |
| 5 | `i наука новосибирск` | 268 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `социалистиг күш ажылдың маадыры` | 316 |
| 2 | `том i наука новосибирск` | 268 |
| 3 | `сөстүү словарь том i` | 240 |
| 4 | `словарь том i наука` | 240 |
| 5 | `ссрэ ниң дээди совединиң` | 190 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `сөстүү словарь том i наука` | 240 |
| 2 | `словарь том i наука новосибирск` | 240 |
| 3 | `ссрэ ниң дээди совединиң президиум` | 158 |
| 4 | `дөс тыва дылдың тайлыбыр сөстүү` | 154 |
| 5 | `тыва дылдың тайлыбыр сөстүү словарь` | 137 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а р` | 114,452 |
| 2 | `а _` | 112,817 |
| 3 | `а н` | 101,864 |
| 4 | `. _` | 94,390 |
| 5 | `_ к` | 90,647 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы ң _` | 33,971 |
| 2 | `ы л д` | 29,526 |
| 3 | `_ т у` | 28,537 |
| 4 | `д а _` | 28,076 |
| 5 | `т у р` | 27,698 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н ы ң _` | 25,621 |
| 2 | `_ т у р` | 23,645 |
| 3 | `_ ч ы л` | 20,602 |
| 4 | `ы л д а` | 19,319 |
| 5 | `_ б о л` | 18,075 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ч ы л д` | 16,920 |
| 2 | `ч ы л д а` | 12,964 |
| 3 | `п _ т у р` | 12,742 |
| 4 | `_ т у р г` | 12,031 |
| 5 | `б и л е _` | 11,388 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 472
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~21% 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 | 0.5460 | 1.460 | 3.63 | 203,818 | 45.4% |
| **1** | Subword | 0.0398 | 1.028 | 2.20 | 54,956 | 96.0% |
| **2** | Word | 0.1739 | 1.128 | 1.35 | 738,821 | 82.6% |
| **2** | Subword | 0.1135 | 1.082 | 1.59 | 120,839 | 88.7% |
| **3** | Word | 0.0508 | 1.036 | 1.08 | 995,160 | 94.9% |
| **3** | Subword | 0.3477 | 1.272 | 2.28 | 192,258 | 65.2% |
| **4** | Word | 0.0186 🏆 | 1.013 | 1.03 | 1,068,473 | 98.1% |
| **4** | Subword | 0.4488 | 1.365 | 2.19 | 438,273 | 55.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `биле олурар чаа ыяштар тудуп чиир буура даг советтериниң депутадынга соңгуткан чылда россияның элчин...`
2. `деп башкир педагогика институдунуң улуг хем тыва арат республиканың хөй кичээнгейин өөредилге эрткен...`
3. `чылда ол тываның ном үндүрер ажыл агый рынка развлечений игры в турции и 51 март 8`

**Context Size 2:**

1. `бир дугаар улуг хуралы ооӊ мурнунда турган календарьны эрги санның деп ылгап тодарадыр моол астроном...`
2. `тыва республиканың өөредилге болгаш эртем яамызының хүндүлел бижии за заслуги перед чувашской респуб...`
3. `ынчалза даа чылдарда экономиканың буурааны биле ол ийи эртемниң үндезин шинчилээр чүүлү кижи бир дуг...`

**Context Size 3:**

1. `социалистиг күш ажылдың маадыры намдары 3 сентябрь чылда көдээ суур гагида гальского района төрүттүн...`
2. `күш ажылдың маадыры атты тывыскан ленин ордени тыпсыры база серп биле молот медальдар продолжала и д...`
3. `дөс тыва дылдың тайлыбыр сөстүү словарь том i наука новосибирск г г г`

**Context Size 4:**

1. `социалистиг күш ажылдың маадыры намдары 6 октябрь чылда в кишлаке паткинаб бо үеде дарвазского район...`
2. `том i наука новосибирск в в`
3. `сөстүү словарь том i наука новосибирск й й`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_4_биң_штүнаннус`
2. `ажы_绨_андезэрган`
3. `рфелар._доюн_тту`

**Context Size 2:**

1. `аряның_и_учшен._т`
2. `а_эвеспей_кий_урь`
3. `анолга_өөгүдегенг`

**Context Size 3:**

1. `ың_ордение_памяти_`
2. `ылдайджанның_демде`
3. `_тур;_калгаш_улуг-`

**Context Size 4:**

1. `ның_саң-хөөн,_өөрүп`
2. `_тура_шөлүглер_атка`
3. `_чылдың_монгуш,_а_«`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (438,273 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 | 62,436 |
| Total Tokens | 1,039,813 |
| Mean Frequency | 16.65 |
| Median Frequency | 3 |
| Frequency Std Dev | 134.66 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | биле | 11,983 |
| 2 | деп | 8,474 |
| 3 | чылда | 8,314 |
| 4 | турган | 8,262 |
| 5 | в | 7,660 |
| 6 | болгаш | 7,220 |
| 7 | ол | 7,087 |
| 8 | база | 7,027 |
| 9 | турар | 6,804 |
| 10 | и | 5,739 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 𥼊 | 2 |
| 2 | 𥼋 | 2 |
| 3 | 𥼌 | 2 |
| 4 | 𥼍 | 2 |
| 5 | 𥼎 | 2 |
| 6 | 𥼏 | 2 |
| 7 | 361 | 2 |
| 8 | 359 | 2 |
| 9 | moons | 2 |
| 10 | пегас | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9998 |
| R² (Goodness of Fit) | 0.992471 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 23.1% |
| Top 1,000 | 51.4% |
| Top 5,000 | 72.7% |
| Top 10,000 | 81.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9925 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 23.1% of corpus
- **Long Tail:** 52,436 words needed for remaining 19.0% 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 | 0.8935 | 0.3132 | N/A | N/A |
| **mono_64d** | 64 | 0.8586 | 0.2437 | N/A | N/A |
| **mono_128d** | 128 | 0.5600 | 0.2029 | N/A | N/A |
| **aligned_32d** | 32 | 0.8935 🏆 | 0.3180 | 0.0200 | 0.1780 |
| **aligned_64d** | 64 | 0.8586 | 0.2406 | 0.0320 | 0.1860 |
| **aligned_128d** | 128 | 0.5600 | 0.2028 | 0.0720 | 0.2540 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8935 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2535. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 7.2% 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 | **0.159** | Low formulaic 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 |
|--------|----------|
| `-с` | сэ, суперлиги, сөөртүр |
| `-к` | колесников, каразымаар, көрейлер |
| `-а` | арыглаашкын, адагылаар, ааска |
| `-д` | диалектилериниң, действительно, давала |
| `-б` | будут, барбас, буддистериниң |
| `-т` | тыважыдып, турачыларын, тиде |
| `-м` | методологиязын, макрон, моего |
| `-ка` | каразымаар, карлык, каттышканының |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | шипилина, давала, гарсонкуба |
| `-н` | арыглаашкын, яшин, турачыларын |
| `-ң` | оюннарның, диалектилериниң, фадеевтиң |
| `-р` | ынаныр, каразымаар, көрейлер |
| `-ың` | оюннарның, башкызының, чырыктың |
| `-е` | эктинде, привычное, отставке |
| `-ы` | шыгжамыры, будды, опереттазы |
| `-и` | ниитилелдери, суперлиги, офицерлерни |

### 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 |
|------|----------|------------------|----------|
| `ының` | 1.96x | 48 contexts | зының, атының, цзының |
| `угаа` | 2.04x | 40 contexts | чугаа, угаап, угаан |
| `алда` | 1.66x | 93 contexts | валда, алдан, талда |
| `аның` | 1.81x | 57 contexts | чаның, ханың, ааның |
| `иниң` | 1.92x | 43 contexts | зиниң, линиң, ивиниң |
| `азын` | 1.44x | 151 contexts | чазын, назын, сазын |
| `лдар` | 1.51x | 108 contexts | алдар, салдар, холдар |
| `лган` | 1.67x | 66 contexts | алган, клган, салган |
| `ылды` | 1.76x | 49 contexts | кылды, хылды, чылды |
| `ерге` | 1.61x | 67 contexts | берге, терге, серге |
| `урга` | 1.50x | 80 contexts | турга, уурга, ургаш |
| `рган` | 1.47x | 87 contexts | орган, трган, арган |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-к` | `-н` | 97 words | каналын, карьеразын |
| `-к` | `-а` | 96 words | калбаа, кикбокска |
| `-а` | `-а` | 76 words | азыралга, анкарага |
| `-ч` | `-н` | 70 words | чугаазын, чазын |
| `-с` | `-а` | 70 words | сывында, салчака |
| `-к` | `-ң` | 70 words | кохтуң, консерваториязының |
| `-с` | `-ң` | 60 words | сонуургалдарының, сезонунуң |
| `-т` | `-н` | 57 words | тын, турин |
| `-к` | `-е` | 56 words | күштелдиреринге, кезекте |
| `-б` | `-н` | 55 words | бригадазын, бакалаврын |

### 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 |
|------|-----------------|------------|------|
| археологтары | **`археологт-а-ры`** | 7.5 | `а` |
| үндезинниң | **`үндезин-н-иң`** | 7.5 | `н` |
| картинная | **`картин-н-ая`** | 7.5 | `н` |
| областьаар | **`область-а-ар`** | 7.5 | `а` |
| чедирислам | **`чедирисл-а-м`** | 7.5 | `а` |
| украинада | **`украин-а-да`** | 7.5 | `а` |
| бадырыптар | **`бадырып-т-ар`** | 7.5 | `т` |
| неделяларга | **`неделял-ар-га`** | 7.5 | `ар` |
| делегейнин | **`делегей-н-ин`** | 7.5 | `н` |
| медалдары | **`медал-да-ры`** | 7.5 | `да` |
| областьта | **`область-т-а`** | 7.5 | `т` |
| чурттапкан | **`чурттап-ка-н`** | 7.5 | `ка` |
| загадочная | **`загадоч-н-ая`** | 7.5 | `н` |
| областная | **`област-н-ая`** | 7.5 | `н` |
| сыктывкаре | **`сыктывк-ар-е`** | 7.5 | `ар` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tuvinian shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.54x) |
| N-gram | **2-gram** | Lowest perplexity (472) |
| Markov | **Context-4** | Highest predictability (98.1%) |
| 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: 2026-01-11 02:16:25*