---
language: mad
language_name: Madurese
language_family: austronesian_other
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-austronesian_other
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: 4.690
  - name: best_isotropy
    type: isotropy
    value: 0.8668
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Madurese** 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** | 3.672x | 3.68 | 0.0762% | 283,323 |
| **16k** | 4.063x | 4.07 | 0.0844% | 255,999 |
| **32k** | 4.409x | 4.41 | 0.0915% | 235,937 |
| **64k** | 4.690x 🏆 | 4.69 | 0.0974% | 221,777 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Kolami iyâ arèya dhisa è Kacamadhân Walea Kapoloan, Tojo Una-Una, Sulawesi Tengn...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ko lami ▁iyâ ▁arèya ▁dhisa ▁è ▁kacamadhân ▁wa lea ▁kapoloan ... (+12 more)` | 22 |
| 16k | `▁ko lami ▁iyâ ▁arèya ▁dhisa ▁è ▁kacamadhân ▁walea ▁kapoloan , ... (+10 more)` | 20 |
| 32k | `▁ko lami ▁iyâ ▁arèya ▁dhisa ▁è ▁kacamadhân ▁walea ▁kapoloan , ... (+10 more)` | 20 |
| 64k | `▁kolami ▁iyâ ▁arèya ▁dhisa ▁è ▁kacamadhân ▁walea ▁kapoloan , ▁tojo ... (+9 more)` | 19 |

**Sample 2:** `jmpl Nyarang ojhen biasanah è kalakoh parappâèn bâdâ acara mantân`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁jmpl ▁ny arang ▁o jh en ▁biasanah ▁è ▁kala koh ... (+9 more)` | 19 |
| 16k | `▁jmpl ▁ny arang ▁o jh en ▁biasanah ▁è ▁kala koh ... (+8 more)` | 18 |
| 32k | `▁jmpl ▁ny arang ▁o jhen ▁biasanah ▁è ▁kala koh ▁para ... (+6 more)` | 16 |
| 64k | `▁jmpl ▁nyarang ▁ojhen ▁biasanah ▁è ▁kalakoh ▁parappâ èn ▁bâdâ ▁acara ... (+1 more)` | 11 |

**Sample 3:** `jmpl cer bawang, iâ area kakanan dâri Mekasân, Madhurâ. èghâbây dâri teppong bân...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁jmpl ▁cer ▁ba wang , ▁i â ▁area ▁kakanan ▁dâri ... (+13 more)` | 23 |
| 16k | `▁jmpl ▁cer ▁bawang , ▁i â ▁area ▁kakanan ▁dâri ▁me ... (+11 more)` | 21 |
| 32k | `▁jmpl ▁cer ▁bawang , ▁iâ ▁area ▁kakanan ▁dâri ▁me kasân ... (+10 more)` | 20 |
| 64k | `▁jmpl ▁cer ▁bawang , ▁iâ ▁area ▁kakanan ▁dâri ▁mekasân , ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 64k achieves 4.690x compression
- **Lowest UNK Rate:** 8k with 0.0762% 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 | 7,660 | 12.90 | 15,927 | 15.5% | 38.8% |
| **2-gram** | Subword | 284 🏆 | 8.15 | 2,917 | 65.5% | 99.2% |
| **3-gram** | Word | 8,331 | 13.02 | 12,743 | 10.9% | 33.7% |
| **3-gram** | Subword | 2,475 | 11.27 | 21,754 | 25.0% | 69.0% |
| **4-gram** | Word | 11,782 | 13.52 | 16,213 | 9.8% | 26.2% |
| **4-gram** | Subword | 14,165 | 13.79 | 105,104 | 11.2% | 37.1% |
| **5-gram** | Word | 6,142 | 12.58 | 8,427 | 13.4% | 34.7% |
| **5-gram** | Subword | 47,465 | 15.53 | 258,432 | 7.5% | 23.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `iyâ arèya` | 3,079 |
| 2 | `è taon` | 2,005 |
| 3 | `sala sèttong` | 1,545 |
| 4 | `è bâkto` | 1,201 |
| 5 | `ka angghuy` | 1,038 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `panèka sala sèttong` | 583 |
| 2 | `al qur an` | 334 |
| 3 | `sè bâḍâ è` | 250 |
| 4 | `arèya sala sèttong` | 249 |
| 5 | `iyâ arèya sala` | 218 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `iyâ arèya sala sèttong` | 205 |
| 2 | `sala sèttong naghârâ è` | 116 |
| 3 | `sè tamaso ka ḍâlem` | 114 |
| 4 | `tamaso ka ḍâlem famili` | 112 |
| 5 | `panèka sala sèttong sastrawan` | 106 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sè tamaso ka ḍâlem famili` | 111 |
| 2 | `panèka sala sèttong naghârâ è` | 97 |
| 3 | `arèya tombuwân sè tamaso ka` | 83 |
| 4 | `iyâ arèya tombuwân sè tamaso` | 81 |
| 5 | `panèka sala sèttong sastrawan bân` | 76 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n` | 135,108 |
| 2 | `a _` | 111,120 |
| 3 | `n _` | 106,453 |
| 4 | `n g` | 96,416 |
| 5 | `_ s` | 84,557 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a` | 39,553 |
| 2 | `a n _` | 38,801 |
| 3 | `â n _` | 37,878 |
| 4 | `n g _` | 34,520 |
| 5 | `a n g` | 34,407 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `b â n _` | 25,412 |
| 2 | `_ s è _` | 23,221 |
| 3 | `_ b â n` | 22,209 |
| 4 | `_ p a n` | 12,960 |
| 5 | `g h i _` | 12,282 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ b â n _` | 19,896 |
| 2 | `a g h i _` | 10,512 |
| 3 | `a n g g h` | 7,941 |
| 4 | `a n è k a` | 6,131 |
| 5 | `r è y a _` | 6,117 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 284
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.8768 | 1.836 | 5.67 | 85,149 | 12.3% |
| **1** | Subword | 0.9174 | 1.889 | 5.75 | 1,785 | 8.3% |
| **2** | Word | 0.2172 | 1.162 | 1.45 | 481,154 | 78.3% |
| **2** | Subword | 0.7767 | 1.713 | 4.61 | 10,251 | 22.3% |
| **3** | Word | 0.0556 | 1.039 | 1.08 | 694,348 | 94.4% |
| **3** | Subword | 0.8058 | 1.748 | 3.95 | 47,246 | 19.4% |
| **4** | Word | 0.0147 🏆 | 1.010 | 1.02 | 750,067 | 98.5% |
| **4** | Subword | 0.6526 | 1.572 | 2.80 | 186,332 | 34.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `è sosol empa kecamaḍhân bone èkennal mènangka am jungen rhein è ḍâlem ghâbâyânna james tautan sè`
2. `sè ajhârâ neng pernata dhârurat politik filsafat tiongkok akennalaghi kendaraan rèya kalabân lo polo...`
3. `bân sayatan è tèmor gedenken an panèka èlakonè marèna dâpa sè terlibat ḍâlem abentu pandhengngan man...`

**Context Size 2:**

1. `iyâ arèya katettapân ḍâri allah kaangghuy ngalakonè imsak molaè bâkto teknologi transistor mulaè a n...`
2. `è taon schrödinger dhâddhi asisten exner sombher`
3. `sala sèttong naghârâ è èropa lao provinsi kapolowan kanary ceuta melilla è afrika kantor perserikata...`

**Context Size 3:**

1. `panèka sala sèttong sastrawan bân panolès inḍonèsia karjâ buku bidadari untuk dewa assalamualaikum b...`
2. `al qur an bapa èn serring nghâjhâk potra potrana akompol samarèna maghrib kaângguy abahas tafsir al ...`
3. `sè bâḍâ è antara kompolan polo polo è tèmorra polo maḍhurâ sapuḍi aropa aghi polo palèng lowas nomer`

**Context Size 4:**

1. `iyâ arèya sala sèttong ghunong wisata sè baḍâ è banyuwangi bân bândâbâsa jhâbâ tèmor inḍonèsia sè an...`
2. `sala sèttong naghârâ è èropa bârâ antillen belanda provinsi bonaire sint eustatius bân saba è amerik...`
3. `sè tamaso ka ḍâlem famili cucurbitaceae tombuwân arèya èkoca kèya jambu bol inḍonesia malay apple in...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ewây_bâtè_se_pa`
2. `a'_jon_è._kana_l`
3. `n_-la_al_paasèra`

**Context Size 2:**

1. `an_kaapès_jaktunt`
2. `a_bia_al_nèkentuh`
3. `n_ton:_enta_pem-m`

**Context Size 3:**

1. `_kaoḍi’_“propa_kuf`
2. `an_krèpublik_ngalo`
3. `ân_sè_labân_kapa_l`

**Context Size 4:**

1. `bân_smp_3_ḍésémber_`
2. `_sè_abârra_sala_oli`
3. `_bân_bân_demi_abhâr`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (186,332 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 | 37,097 |
| Total Tokens | 741,682 |
| Mean Frequency | 19.99 |
| Median Frequency | 4 |
| Frequency Std Dev | 232.38 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | è | 23,535 |
| 2 | sè | 23,401 |
| 3 | bân | 20,011 |
| 4 | ka | 7,685 |
| 5 | panèka | 5,706 |
| 6 | taon | 5,597 |
| 7 | ḍâri | 4,979 |
| 8 | kalabân | 4,663 |
| 9 | arèya | 4,306 |
| 10 | orèng | 4,157 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | eghunaaghin | 2 |
| 2 | pengatorannah | 2 |
| 3 | ngelaksanaaghin | 2 |
| 4 | sampèr | 2 |
| 5 | geluk | 2 |
| 6 | tekuk | 2 |
| 7 | rasmè | 2 |
| 8 | maddhekka | 2 |
| 9 | uttarkashi | 2 |
| 10 | spillway | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0120 |
| R² (Goodness of Fit) | 0.991547 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 31.6% |
| Top 1,000 | 58.3% |
| Top 5,000 | 79.8% |
| Top 10,000 | 87.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9915 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 31.6% of corpus
- **Long Tail:** 27,097 words needed for remaining 12.2% 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 | 0.8668 🏆 | 0.3020 | N/A | N/A |
| **mono_64d** | 64 | 0.6062 | 0.2632 | N/A | N/A |
| **mono_128d** | 128 | 0.1633 | 0.2527 | N/A | N/A |
| **aligned_32d** | 32 | 0.8668 | 0.3113 | 0.0380 | 0.2740 |
| **aligned_64d** | 64 | 0.6062 | 0.2737 | 0.0720 | 0.3700 |
| **aligned_128d** | 128 | 0.1633 | 0.2516 | 0.1100 | 0.4080 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8668 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2757. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 11.0% 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 | **0.495** | 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 |
|--------|----------|
| `-a` | advokasi, aobâna, alias |
| `-s` | sekabbhinna, sahabatta, salajâ |
| `-ka` | kakosongan, kapalana, kaodi |
| `-ma` | macmillan, marapi, mareh |
| `-k` | kemaluan, kakosongan, khadijah |
| `-pa` | paragraf, parsiapân, panyâbâb |
| `-b` | berry, biography, bhâdâ |
| `-p` | penolès, paragraf, parsiapân |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | kemaluan, kakosongan, parsiapân |
| `-a` | sekabbhinna, sahabatta, aobâna |
| `-an` | kemaluan, kakosongan, macmillan |
| `-i` | èghâdhui, advokasi, ègabungaghi |
| `-hi` | ègabungaghi, aningghâlaghi, èdebataghi |
| `-na` | sekabbhinna, aobâna, rilisna |
| `-s` | waprès, penolès, cutlass |
| `-ng` | gâmpang, tambâng, torkaḍâng |

### 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 |
|------|----------|------------------|----------|
| `angk` | 1.72x | 122 contexts | angka, angko, èangka |
| `nggh` | 1.57x | 158 contexts | ongghe, èngghi, èngghâ |
| `gghu` | 1.88x | 60 contexts | agghu, negghu, ongghu |
| `ngka` | 1.55x | 131 contexts | angka, èangka, mengka |
| `angg` | 1.47x | 151 contexts | anggâ, anggun, rangga |
| `ddhi` | 1.98x | 37 contexts | eddhi, seddhi, deddhi |
| `gghâ` | 1.73x | 63 contexts | cegghâ, èngghâ, logghâ |
| `tton` | 2.08x | 25 contexts | ottone, èttong, button |
| `âddh` | 2.13x | 16 contexts | bâddhâ, ḍâddhi, sâddhi |
| `hâdd` | 2.12x | 15 contexts | dhâddi, dhâddih, dhâddhi |
| `aren` | 1.66x | 33 contexts | karen, arena, areng |
| `labâ` | 1.84x | 22 contexts | labân, alabân, labâng |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-n` | 162 words | pangobhâdhân, panganjhuân |
| `-pa` | `-n` | 161 words | pangobhâdhân, panganjhuân |
| `-ka` | `-n` | 154 words | kabendherran, kaodhiân |
| `-s` | `-a` | 130 words | sèvilla, sadaja |
| `-k` | `-n` | 124 words | kabendherran, kaodhiân |
| `-p` | `-an` | 122 words | pakarangan, pangamatan |
| `-pa` | `-an` | 106 words | pakarangan, pangamatan |
| `-k` | `-an` | 99 words | kabendherran, karegghingan |
| `-a` | `-i` | 91 words | adhâddiyaghi, azeri |
| `-ka` | `-an` | 90 words | kabendherran, karegghingan |

### 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 |
|------|-----------------|------------|------|
| bertasbih | **`bertasb-i-h`** | 7.5 | `i` |
| pertamina | **`pertam-i-na`** | 7.5 | `i` |
| fakultassa | **`fakultas-s-a`** | 7.5 | `s` |
| pendukungnga | **`pendukung-ng-a`** | 7.5 | `ng` |
| parèntana | **`parènt-an-a`** | 7.5 | `an` |
| terlarang | **`terla-ra-ng`** | 7.5 | `ra` |
| kebijaksanaan | **`kebijaksa-na-an`** | 7.5 | `na` |
| ibukottana | **`ibukott-an-a`** | 7.5 | `an` |
| kapotosanna | **`kapotos-an-na`** | 7.5 | `an` |
| rangsangan | **`rangsa-ng-an`** | 7.5 | `ng` |
| pangangghuy | **`pa-ng-angghuy`** | 7.5 | `angghuy` |
| tangghungan | **`tangghu-ng-an`** | 7.5 | `ng` |
| polinesia | **`poline-si-a`** | 7.5 | `si` |
| pematangan | **`pe-ma-tangan`** | 7.5 | `tangan` |
| ètampilkan | **`ètampil-k-an`** | 7.5 | `k` |

### 6.6 Linguistic Interpretation

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

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.69x) |
| N-gram | **2-gram** | Lowest perplexity (284) |
| Markov | **Context-4** | Highest predictability (98.5%) |
| 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: 2026-01-10 11:30:57*