---
language: az
language_name: Azerbaijani
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: 5.131
  - name: best_isotropy
    type: isotropy
    value: 0.8140
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Azerbaijani** 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** | 3.945x | 3.95 | 0.0962% | 1,248,644 |
| **16k** | 4.426x | 4.43 | 0.1079% | 1,113,127 |
| **32k** | 4.825x | 4.83 | 0.1176% | 1,021,125 |
| **64k** | 5.131x 🏆 | 5.13 | 0.1251% | 960,074 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `() — aləminin dəstəsinin fəsiləsinə aid bitki cinsi. Sinonimləri Heterotipik sin...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinə ▁aid ▁bitki ▁cinsi . ▁sinonimləri ... (+6 more)` | 16 |
| 16k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinə ▁aid ▁bitki ▁cinsi . ▁sinonimləri ... (+6 more)` | 16 |
| 32k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinə ▁aid ▁bitki ▁cinsi . ▁sinonimləri ... (+6 more)` | 16 |
| 64k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinə ▁aid ▁bitki ▁cinsi . ▁sinonimləri ... (+6 more)` | 16 |

**Sample 2:** `() — aləminin dəstəsinin fəsiləsinin cinsinə aid bitki növü. Sinonimləri Homotip...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+8 more)` | 18 |
| 16k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+8 more)` | 18 |
| 32k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+8 more)` | 18 |
| 64k | `▁() ▁— ▁aləminin ▁dəstəsinin ▁fəsiləsinin ▁cinsinə ▁aid ▁bitki ▁növü . ... (+8 more)` | 18 |

**Sample 3:** `.lr — Liberiyanın internet kodu. Xarici keçidlər IANA .lr whois information səvi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁. l r ▁— ▁li ber iyanın ▁internet ▁kodu . ... (+18 more)` | 28 |
| 16k | `▁. l r ▁— ▁liber iyanın ▁internet ▁kodu . ▁xarici ... (+13 more)` | 23 |
| 32k | `▁. lr ▁— ▁liber iyanın ▁internet ▁kodu . ▁xarici ▁keçidlər ... (+8 more)` | 18 |
| 64k | `▁. lr ▁— ▁liber iyanın ▁internet ▁kodu . ▁xarici ▁keçidlər ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 5.131x compression
- **Lowest UNK Rate:** 8k with 0.0962% 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 | 267,397 | 18.03 | 1,224,963 | 4.8% | 13.7% |
| **2-gram** | Subword | 404 🏆 | 8.66 | 18,219 | 58.1% | 97.7% |
| **3-gram** | Word | 584,031 | 19.16 | 1,748,154 | 4.1% | 9.8% |
| **3-gram** | Subword | 3,741 | 11.87 | 158,841 | 20.7% | 61.1% |
| **4-gram** | Word | 1,231,291 | 20.23 | 3,034,353 | 3.9% | 8.4% |
| **4-gram** | Subword | 21,126 | 14.37 | 962,195 | 10.3% | 32.7% |
| **5-gram** | Word | 931,111 | 19.83 | 2,270,890 | 4.5% | 9.8% |
| **5-gram** | Subword | 81,852 | 16.32 | 3,259,009 | 6.2% | 20.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `və ya` | 84,279 |
| 2 | `xarici keçidlər` | 65,570 |
| 3 | `həmçinin bax` | 61,824 |
| 4 | `i̇stinadlar xarici` | 45,903 |
| 5 | `i̇stinadlar həmçinin` | 30,953 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i̇stinadlar xarici keçidlər` | 45,411 |
| 2 | `i̇stinadlar həmçinin bax` | 30,925 |
| 3 | `fəsiləsinin cinsinə aid` | 20,614 |
| 4 | `dəstəsinin fəsiləsinin cinsinə` | 18,390 |
| 5 | `aid bitki növü` | 17,244 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dəstəsinin fəsiləsinin cinsinə aid` | 18,390 |
| 2 | `cinsinə aid bitki növü` | 17,225 |
| 3 | `fəsiləsinin cinsinə aid bitki` | 17,194 |
| 4 | `aləminin dəstəsinin fəsiləsinin cinsinə` | 14,711 |
| 5 | `növü i̇stinadlar həmçinin bax` | 10,186 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `fəsiləsinin cinsinə aid bitki növü` | 17,191 |
| 2 | `dəstəsinin fəsiləsinin cinsinə aid bitki` | 15,001 |
| 3 | `aləminin dəstəsinin fəsiləsinin cinsinə aid` | 14,711 |
| 4 | `cinsinə aid bitki növü i̇stinadlar` | 9,355 |
| 5 | `yeni ümumi kataloqda qeydə alınmış` | 8,316 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 8,039,357 |
| 2 | `ə _` | 6,502,225 |
| 3 | `i n` | 6,211,070 |
| 4 | `a r` | 5,368,955 |
| 5 | `ə r` | 5,307,819 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l ə r` | 2,430,392 |
| 2 | `l a r` | 2,275,096 |
| 3 | `d ə _` | 2,158,334 |
| 4 | `i n _` | 2,041,519 |
| 5 | `a n _` | 1,830,488 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ v ə _` | 1,480,720 |
| 2 | `l ə r i` | 1,249,750 |
| 3 | `l a r ı` | 1,061,145 |
| 4 | `i n d ə` | 1,055,926 |
| 5 | `n i n _` | 957,274 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i n i n _` | 790,811 |
| 2 | `l ə r i n` | 652,788 |
| 3 | `i n d ə _` | 641,243 |
| 4 | `l a r ı n` | 574,577 |
| 5 | `ı n d a _` | 522,632 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 404
- **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 | 0.9399 | 1.918 | 11.42 | 1,720,154 | 6.0% |
| **1** | Subword | 1.1732 | 2.255 | 8.01 | 8,102 | 0.0% |
| **2** | Word | 0.3192 | 1.248 | 1.95 | 19,621,953 | 68.1% |
| **2** | Subword | 0.7463 | 1.678 | 5.27 | 64,909 | 25.4% |
| **3** | Word | 0.1046 | 1.075 | 1.20 | 38,212,993 | 89.5% |
| **3** | Subword | 0.8107 | 1.754 | 4.76 | 342,087 | 18.9% |
| **4** | Word | 0.0352 🏆 | 1.025 | 1.06 | 45,793,057 | 96.5% |
| **4** | Subword | 0.7288 | 1.657 | 3.64 | 1,627,867 | 27.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `və 25 cilddə v əsr kilsələri keçmiş rodeziya adlı ilk britaniya və həyat və proqramlar efir`
2. `ildə fiziki cəhətdən əlverişsiz şərait yaratdı o təbriz universitetində asiya ölkələrinə marşal çini...`
3. `ilə yenidən tamaşaya qoyur və şirvanşahlar taxtında gözü ilə habelə qafqazın qərbi avropada və genos...`

**Context Size 2:**

1. `və ya yalan olan bir cismin səthinin digər cismin səthi arasındakı əlaqəni araşdırır i̇sbat nəzəriyy...`
2. `xarici keçidlər ssr xalq hərbi dəniz nazirinin köməkçisi içləyib ilin iyun ayında çimkent şəhəri res...`
3. `i̇stinadlar xarici keçidlər yanvar kaltenbrunner bir parade videosu nuremberg duruşmasında kaltenbru...`

**Context Size 3:**

1. `i̇stinadlar xarici keçidlər profile at sport resutls org kişi velosipedçilər sürücüləri yay olimpiya...`
2. `fəsiləsinin cinsinə aid bitki növü sinonimləri heterotipik sinonimləri i̇stinadlar həmçinin bax i̇ra...`
3. `dəstəsinin fəsiləsinin cinsinə aid bitki növü i̇stinadlar həmçinin bax nizami süleymanov kərrar əbil...`

**Context Size 4:**

1. `dəstəsinin fəsiləsinin cinsinə aid heyvan növü i̇stinadlar həmçinin bax ildə təsvir edilən sərtqanad...`
2. `cinsinə aid bitki növü təbii yayılması botaniki təsviri ekologiyası azərbaycanda yayılması i̇stifadə...`
3. `fəsiləsinin cinsinə aid bitki növü i̇stinadlar həmçinin bax ildə təsvir edilən bitkilər ildə təsvir ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_sindırə,_ke_enı`
2. `ak,_xşdinrmisə_i`
3. `inı_bondəkilayaq`

**Context Size 2:**

1. `n_bələ_hüsymətliq`
2. `ə_onlan_ehrə_il_m`
3. `indlaşı_atınd_eds`

**Context Size 3:**

1. `lər_kuboku_olanmas`
2. `lar._söz_əlaqədi_b`
3. `də_yabr_ilə_yer,_r`

**Context Size 4:**

1. `_və_təhsili_ilə_çıx`
2. `lərini_100_mində_il`
3. `indən_yazdı,_lakin_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,627,867 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 | 756,239 |
| Total Tokens | 53,635,250 |
| Mean Frequency | 70.92 |
| Median Frequency | 4 |
| Frequency Std Dev | 2293.39 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | və | 1,485,732 |
| 2 | ildə | 413,531 |
| 3 | ilə | 412,011 |
| 4 | bir | 365,123 |
| 5 | bu | 360,987 |
| 6 | də | 230,701 |
| 7 | üçün | 222,167 |
| 8 | azərbaycan | 221,202 |
| 9 | olan | 220,810 |
| 10 | sonra | 181,029 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | gallaghers | 2 |
| 2 | liamın | 2 |
| 3 | liamla | 2 |
| 4 | backstab | 2 |
| 5 | antonioi | 2 |
| 6 | nipissinq | 2 |
| 7 | votivkirche | 2 |
| 8 | pirtle | 2 |
| 9 | takaxasinin | 2 |
| 10 | caporael | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9645 |
| R² (Goodness of Fit) | 0.992387 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 20.8% |
| Top 1,000 | 45.3% |
| Top 5,000 | 65.5% |
| Top 10,000 | 73.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9924 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 20.8% of corpus
- **Long Tail:** 746,239 words needed for remaining 26.3% 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 | 0.8140 🏆 | 0.3681 | N/A | N/A |
| **mono_64d** | 64 | 0.8077 | 0.2833 | N/A | N/A |
| **mono_128d** | 128 | 0.7661 | 0.2223 | N/A | N/A |
| **aligned_32d** | 32 | 0.8140 | 0.3594 | 0.1680 | 0.4820 |
| **aligned_64d** | 64 | 0.8077 | 0.2928 | 0.2820 | 0.7100 |
| **aligned_128d** | 128 | 0.7661 | 0.2246 | 0.4440 | 0.7780 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8140 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2918. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 44.4% 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 | **-0.527** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | kinopovestin, kristofferson, morfologiyasının |
| `-a` | metraja, irradiyasiya, razumovskaya |
| `-in` | kinopovestin, kriolitin, şikin |
| `-ın` | morfologiyasının, başın, buxtaların |
| `-an` | mozaikasından, qaçmazdan, tsiklopropan |
| `-ar` | vəzifəsimajoritar, yaratmışlar, tubalar |
| `-ən` | pərakəndəliyindən, gərginləşməsindən, birincidən |
| `-nın` | morfologiyasının, tistanın, andrianın |

### 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 |
|------|----------|------------------|----------|
| `ərba` | 2.70x | 42 contexts | ərbaa, ərbab, lərba |
| `rbay` | 2.38x | 53 contexts | orbay, arbay, erbay |
| `arix` | 2.17x | 73 contexts | larix, tarix, farix |
| `ayca` | 2.82x | 24 contexts | cayca, tayca, sayca |
| `mişd` | 1.65x | 164 contexts | mişdi, emişdi, mişdir |
| `nlar` | 1.37x | 429 contexts | anlar, nları, onlar |
| `ərəf` | 1.80x | 86 contexts | şərəf, ərəfə, tərəf |
| `lmiş` | 1.76x | 94 contexts | ölmiş, almiş, olmiş |
| `mışd` | 1.60x | 142 contexts | mışdı, mışdır, camışda |
| `ycan` | 2.94x | 13 contexts | aycan, bəycan, beycan |
| `qlar` | 1.45x | 196 contexts | aqlar, qlarn, lıqlar |
| `əfin` | 1.66x | 97 contexts | rəfin, dəfin, səfinə |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| foneminin | **`fonem-in-in`** | 6.0 | `fonem` |
| təmsillərinin | **`təmsillər-in-in`** | 6.0 | `təmsillər` |
| qətiyyətinin | **`qətiyyət-in-in`** | 6.0 | `qətiyyət` |
| büküşlərinin | **`büküşlər-in-in`** | 6.0 | `büküşlər` |
| hədisçilərinin | **`hədisçilər-in-in`** | 6.0 | `hədisçilər` |
| planlaşdırmaqda | **`planlaşdırmaq-da`** | 4.5 | `planlaşdırmaq` |
| bölmələrimizin | **`bölmələrimiz-in`** | 4.5 | `bölmələrimiz` |
| heteranın | **`hetera-nın`** | 4.5 | `hetera` |
| somervillin | **`somervill-in`** | 4.5 | `somervill` |
| tanımanın | **`tanıma-nın`** | 4.5 | `tanıma` |
| meyitlərin | **`meyitlər-in`** | 4.5 | `meyitlər` |
| kameralizmin | **`kameralizm-in`** | 4.5 | `kameralizm` |
| burnettin | **`burnett-in`** | 4.5 | `burnett` |
| mussadıqın | **`mussadıq-ın`** | 4.5 | `mussadıq` |
| qalaçanın | **`qalaça-nın`** | 4.5 | `qalaça` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Azerbaijani 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 (5.13x) |
| N-gram | **2-gram** | Lowest perplexity (404) |
| Markov | **Context-4** | Highest predictability (96.5%) |
| 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 14:36:36*