---
language: gag
language_name: Gagauz
language_family: turkic_oghuz
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_oghuz
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: 3.538
  - name: best_isotropy
    type: isotropy
    value: 0.8240
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Gagauz** 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** | 2.876x | 2.88 | 0.0916% | 443,197 |
| **16k** | 3.120x | 3.12 | 0.0994% | 408,594 |
| **32k** | 3.336x | 3.34 | 0.1062% | 382,142 |
| **64k** | 3.538x 🏆 | 3.54 | 0.1127% | 360,274 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Üülen Dakota — Amerika Birleşik Devletläri Viliyatı`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁üülen ▁dak ota ▁— ▁amerika ▁birleşik ▁devletläri ▁viliyatı` | 8 |
| 16k | `▁üülen ▁dakota ▁— ▁amerika ▁birleşik ▁devletläri ▁viliyatı` | 7 |
| 32k | `▁üülen ▁dakota ▁— ▁amerika ▁birleşik ▁devletläri ▁viliyatı` | 7 |
| 64k | `▁üülen ▁dakota ▁— ▁amerika ▁birleşik ▁devletläri ▁viliyatı` | 7 |

**Sample 2:** `Gasımuşağı halıları () — Azerbaycan halısı. Dış baalantılar Araşdırmalar "Qasımu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁g ası muş a ğı ▁h alılar ı ▁() ▁— ... (+27 more)` | 37 |
| 16k | `▁g ası muş ağı ▁h alılar ı ▁() ▁— ▁azerbaycan ... (+25 more)` | 35 |
| 32k | `▁g asımuşağı ▁halıları ▁() ▁— ▁azerbaycan ▁hal ısı . ▁dış ... (+14 more)` | 24 |
| 64k | `▁gasımuşağı ▁halıları ▁() ▁— ▁azerbaycan ▁halısı . ▁dış ▁baalantılar ▁ar ... (+9 more)` | 19 |

**Sample 3:** `Önemli Olaylar Dünnää Gagauz Doğmâk Ölenler kategori:Günler`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁önemli ▁olaylar ▁dünnää ▁gagauz ▁doğmâk ▁ölenler ▁kategori : günler` | 9 |
| 16k | `▁önemli ▁olaylar ▁dünnää ▁gagauz ▁doğmâk ▁ölenler ▁kategori : günler` | 9 |
| 32k | `▁önemli ▁olaylar ▁dünnää ▁gagauz ▁doğmâk ▁ölenler ▁kategori : günler` | 9 |
| 64k | `▁önemli ▁olaylar ▁dünnää ▁gagauz ▁doğmâk ▁ölenler ▁kategori : günler` | 9 |


### Key Findings

- **Best Compression:** 64k achieves 3.538x compression
- **Lowest UNK Rate:** 8k with 0.0916% 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 | 1,971 | 10.94 | 4,598 | 31.2% | 63.5% |
| **2-gram** | Subword | 446 🏆 | 8.80 | 3,286 | 54.9% | 97.3% |
| **3-gram** | Word | 1,822 | 10.83 | 5,238 | 34.0% | 64.5% |
| **3-gram** | Subword | 4,206 | 12.04 | 22,902 | 18.5% | 57.6% |
| **4-gram** | Word | 5,954 | 12.54 | 16,618 | 24.1% | 43.7% |
| **4-gram** | Subword | 22,619 | 14.47 | 104,362 | 9.2% | 29.9% |
| **5-gram** | Word | 5,006 | 12.29 | 14,499 | 25.9% | 45.6% |
| **5-gram** | Subword | 56,179 | 15.78 | 204,429 | 6.6% | 21.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hem bak` | 1,043 |
| 2 | `dış baalantılar` | 677 |
| 3 | `dili laf` | 581 |
| 4 | `türk dili` | 554 |
| 5 | `laf edelir` | 538 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dili laf edelir` | 538 |
| 2 | `hem bak türkiye` | 514 |
| 3 | `türkiye kasabalar listesi` | 511 |
| 4 | `bak türkiye türkiye` | 504 |
| 5 | `türk dili laf` | 503 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hem bak türkiye türkiye` | 504 |
| 2 | `türkiye türkiye kasabalar listesi` | 501 |
| 3 | `bak türkiye türkiye kasabalar` | 500 |
| 4 | `türk dili laf edelir` | 500 |
| 5 | `resmi türk dili laf` | 500 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `bak türkiye türkiye kasabalar listesi` | 500 |
| 2 | `hem bak türkiye türkiye kasabalar` | 500 |
| 3 | `resmi türk dili laf edelir` | 500 |
| 4 | `türkiye resmi türk dili laf` | 500 |
| 5 | `bu kasabade türkiye resmi türk` | 499 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a r` | 35,710 |
| 2 | `a n` | 34,563 |
| 3 | `a _` | 34,248 |
| 4 | `n _` | 31,040 |
| 5 | `l a` | 29,285 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a r` | 14,140 |
| 2 | `_ k a` | 11,046 |
| 3 | `a r _` | 9,987 |
| 4 | `a n _` | 9,910 |
| 5 | `_ b a` | 7,607 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a r _` | 6,472 |
| 2 | `_ d i l` | 4,896 |
| 3 | `t ü r k` | 4,490 |
| 4 | `_ t ü r` | 4,397 |
| 5 | `_ k a s` | 4,301 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t ü r k` | 4,273 |
| 2 | `k a s a b` | 3,998 |
| 3 | `a s a b a` | 3,997 |
| 4 | `_ k a s a` | 3,991 |
| 5 | `_ h e m _` | 3,823 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 446
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.6215 | 1.538 | 3.19 | 70,858 | 37.9% |
| **1** | Subword | 1.1311 | 2.190 | 8.91 | 872 | 0.0% |
| **2** | Word | 0.1089 | 1.078 | 1.18 | 224,953 | 89.1% |
| **2** | Subword | 1.0438 | 2.062 | 5.90 | 7,767 | 0.0% |
| **3** | Word | 0.0312 | 1.022 | 1.05 | 265,002 | 96.9% |
| **3** | Subword | 0.8545 | 1.808 | 3.91 | 45,790 | 14.5% |
| **4** | Word | 0.0143 🏆 | 1.010 | 1.02 | 275,839 | 98.6% |
| **4** | Subword | 0.6677 | 1.589 | 2.56 | 178,853 | 33.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `hem gezdii erlerdä da var küüyün 2 baskı evindä bulunan derneklär bütün poêtlar ya halk respublikası`
2. `dili laf edelir görüntüler hem ki evli dört kuruluş evresinde üye tam olarak seçerkendorfman alberto...`
3. `bir suçtan mahkûm oldu nereiyi bütün gün moldovanın çiftçi pidoş kendi yaratmalarınnan katıldılar av...`

**Context Size 2:**

1. `hem bak laos laoslular laos dili vientiane times i̇ngiliz dili yazı latin alfaviti 50px latin dili l...`
2. `dış baalantılar en wikipedia turkey kasabalari`
3. `dili laf edelir görüntüler hem bak türkiye türkiye kasabalar listesi dış baalantılar en wikipedia tu...`

**Context Size 3:**

1. `dili laf edelir görüntüler hem bak türkiye türkiye kasabalar listesi dış baalantılar en wikipedia tu...`
2. `hem bak türkiye türkiye kasabalar listesi dış baalantılar en wikipedia turkey kasabalari`
3. `türkiye kasabalar listesi dış baalantılar en wikipedia turkey kasabalari`

**Context Size 4:**

1. `hem bak türkiye türkiye kasabalar listesi dış baalantılar en wikipedia turkey kasabalari`
2. `türkiye türkiye kasabalar listesi dış baalantılar en wikipedia turkey kasabalari`
3. `bak türkiye türkiye kasabalar listesi dış baalantılar en wikipedia turkey kasabalari`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_stısızar_la_köl`
2. `asekome_()_serne`
3. `i_iyovi,840_9-_k`

**Context Size 2:**

1. `ar_önek_:_kar_uş_`
2. `an_türkçek_won_ge`
3. `a_bar_maal_döndad`

**Context Size 3:**

1. `lar_i̇ngilleriyada_`
2. `_kan_ay_habesinder`
3. `ar_da,_rayequezdıl`

**Context Size 4:**

1. `lar_list_verdi._bun`
2. `_dillerinizm,_bir_l`
3. `türk_koordinatnarı_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (178,853 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 | 26,154 |
| Total Tokens | 288,661 |
| Mean Frequency | 11.04 |
| Median Frequency | 3 |
| Frequency Std Dev | 61.28 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | hem | 3,845 |
| 2 | dili | 2,983 |
| 3 | bir | 2,801 |
| 4 | da | 2,704 |
| 5 | 1 | 1,883 |
| 6 | türkiye | 1,882 |
| 7 | ay | 1,737 |
| 8 | bu | 1,733 |
| 9 | gagauz | 1,519 |
| 10 | o | 1,516 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | vanların | 2 |
| 2 | derecede | 2 |
| 3 | varlığından | 2 |
| 4 | biolojik | 2 |
| 5 | koreyada | 2 |
| 6 | cejuan | 2 |
| 7 | günümüzdä | 2 |
| 8 | toscano | 2 |
| 9 | şenubi | 2 |
| 10 | grübüdur | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9373 |
| R² (Goodness of Fit) | 0.991888 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.1% |
| Top 1,000 | 53.2% |
| Top 5,000 | 76.4% |
| Top 10,000 | 86.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9919 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.1% of corpus
- **Long Tail:** 16,154 words needed for remaining 13.4% 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 | 0.8240 | 0.3585 | N/A | N/A |
| **mono_64d** | 64 | 0.5076 | 0.3424 | N/A | N/A |
| **mono_128d** | 128 | 0.1196 | 0.3318 | N/A | N/A |
| **aligned_32d** | 32 | 0.8240 🏆 | 0.3601 | 0.0340 | 0.1900 |
| **aligned_64d** | 64 | 0.5076 | 0.3378 | 0.0780 | 0.3180 |
| **aligned_128d** | 128 | 0.1196 | 0.3296 | 0.1000 | 0.4120 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8240 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3434. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.0% 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 | **1.113** | 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 |
|--------|----------|
| `-ka` | kafasını, kastela, kaçanik |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | asirin, sarıboyun, bolton |
| `-an` | ardından, hazırlanan, komrattan |
| `-ar` | aaraştırerlar, aznar, aktrisalar |
| `-er` | çalışer, techner, muzaffer |
| `-da` | olgularında, sţenasında, moskvada |

### 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 |
|------|----------|------------------|----------|
| `leri` | 1.84x | 88 contexts | lerik, ileri, galeri |
| `ları` | 1.73x | 87 contexts | onları, otları, yuları |
| `ller` | 2.12x | 36 contexts | aller, moller, ullern |
| `asın` | 1.72x | 59 contexts | basın, klasın, alasın |
| `anın` | 1.83x | 39 contexts | canın, hanın, sanını |
| `nnar` | 1.90x | 32 contexts | onnar, onnara, gunnar |
| `ille` | 1.85x | 29 contexts | lille, pille, ville |
| `arın` | 1.82x | 30 contexts | uların, karının, boyarın |
| `ında` | 1.62x | 40 contexts | sında, adında, ilında |
| `gauz` | 2.18x | 14 contexts | gagauz, gauzlar, gagauzça |
| `nsan` | 1.75x | 19 contexts | insan, insanı, insana |
| `evle` | 2.10x | 11 contexts | devlet, evleri, devleti |

### 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 |
|--------|--------|-----------|----------|
| `-ka` | `-n` | 36 words | kantakuzenin, karaçoban |
| `-ka` | `-ar` | 28 words | katılannar, karaullar |
| `-ka` | `-an` | 16 words | karaçoban, karannıktan |
| `-ka` | `-da` | 13 words | kasabalarda, katkıda |
| `-ka` | `-er` | 6 words | kaybettiler, kazaner |

### 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 |
|------|-----------------|------------|------|
| argentinada | **`argentina-da`** | 4.5 | `argentina` |
| tehnikada | **`tehnika-da`** | 4.5 | `tehnika` |
| bakannıında | **`bakannıın-da`** | 4.5 | `bakannıın` |
| konferenţiyada | **`konferenţiya-da`** | 4.5 | `konferenţiya` |
| devletlerinda | **`devletlerin-da`** | 4.5 | `devletlerin` |
| delegaţiyada | **`delegaţiya-da`** | 4.5 | `delegaţiya` |
| vyetnamda | **`vyetnam-da`** | 4.5 | `vyetnam` |
| kasabalarda | **`ka-sabal-ar-da`** | 4.5 | `sabal` |
| forrester | **`forrest-er`** | 4.5 | `forrest` |
| vakıdında | **`vakıdın-da`** | 4.5 | `vakıdın` |
| karıştırêrlar | **`ka-rıştırêrl-ar`** | 3.0 | `rıştırêrl` |
| çayırlarda | **`çayırl-ar-da`** | 3.0 | `çayırl` |
| karikaturacılar | **`ka-rikaturacıl-ar`** | 3.0 | `rikaturacıl` |
| karşılaşan | **`ka-rşılaş-an`** | 3.0 | `rşılaş` |
| katılaceklar | **`ka-tılacekl-ar`** | 3.0 | `tılacekl` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Gagauz 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 (3.54x) |
| N-gram | **2-gram** | Lowest perplexity (446) |
| Markov | **Context-4** | Highest predictability (98.6%) |
| 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: 2026-01-04 14:49:17*