---
language: id
language_name: Indonesian
language_family: austronesian_malay
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_malay
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: 5.355
  - name: best_isotropy
    type: isotropy
    value: 0.6446
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-13
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Indonesian** 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** | 4.240x | 4.24 | 0.0805% | 2,784,763 |
| **16k** | 4.730x | 4.73 | 0.0899% | 2,496,316 |
| **32k** | 5.099x | 5.10 | 0.0969% | 2,315,931 |
| **64k** | 5.355x 🏆 | 5.36 | 0.1017% | 2,205,288 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Marga Karya adalah salah satu desa di kecamatan Kulisusu Barat, Kabupaten Buton ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁marga ▁karya ▁adalah ▁salah ▁satu ▁desa ▁di ▁kecamatan ▁k ulis ... (+14 more)` | 24 |
| 16k | `▁marga ▁karya ▁adalah ▁salah ▁satu ▁desa ▁di ▁kecamatan ▁k ulis ... (+13 more)` | 23 |
| 32k | `▁marga ▁karya ▁adalah ▁salah ▁satu ▁desa ▁di ▁kecamatan ▁k ulis ... (+12 more)` | 22 |
| 64k | `▁marga ▁karya ▁adalah ▁salah ▁satu ▁desa ▁di ▁kecamatan ▁k ulis ... (+12 more)` | 22 |

**Sample 2:** `Sukamaju adalah desa di kecamatan Majalaya, Bandung, Jawa Barat, Indonesia. Refe...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁suk ama ju ▁adalah ▁desa ▁di ▁kecamatan ▁maj alaya , ... (+10 more)` | 20 |
| 16k | `▁suk ama ju ▁adalah ▁desa ▁di ▁kecamatan ▁maj alaya , ... (+10 more)` | 20 |
| 32k | `▁sukamaju ▁adalah ▁desa ▁di ▁kecamatan ▁maj alaya , ▁bandung , ... (+8 more)` | 18 |
| 64k | `▁sukamaju ▁adalah ▁desa ▁di ▁kecamatan ▁majalaya , ▁bandung , ▁jawa ... (+7 more)` | 17 |

**Sample 3:** `Sukarapih adalah desa di kecamatan Sukarame, Tasikmalaya, Jawa Barat, Indonesia....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁suk arap ih ▁adalah ▁desa ▁di ▁kecamatan ▁sukar ame , ... (+11 more)` | 21 |
| 16k | `▁suk arap ih ▁adalah ▁desa ▁di ▁kecamatan ▁sukar ame , ... (+9 more)` | 19 |
| 32k | `▁suk arap ih ▁adalah ▁desa ▁di ▁kecamatan ▁sukar ame , ... (+9 more)` | 19 |
| 64k | `▁suk arap ih ▁adalah ▁desa ▁di ▁kecamatan ▁sukarame , ▁tasikmalaya ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 5.355x compression
- **Lowest UNK Rate:** 8k with 0.0805% 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 | 352,571 | 18.43 | 3,589,156 | 5.5% | 15.7% |
| **2-gram** | Subword | 237 🏆 | 7.89 | 60,775 | 71.6% | 99.3% |
| **3-gram** | Word | 1,403,108 | 20.42 | 7,774,768 | 5.0% | 12.0% |
| **3-gram** | Subword | 2,119 | 11.05 | 298,247 | 28.5% | 73.3% |
| **4-gram** | Word | 2,339,176 | 21.16 | 12,102,231 | 6.6% | 13.7% |
| **4-gram** | Subword | 13,149 | 13.68 | 1,501,572 | 14.3% | 40.9% |
| **5-gram** | Word | 1,091,988 | 20.06 | 7,805,199 | 10.1% | 20.0% |
| **5-gram** | Subword | 56,499 | 15.79 | 5,070,685 | 8.4% | 25.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pada tahun` | 570,229 |
| 2 | `pranala luar` | 330,544 |
| 3 | `bagian dari` | 220,724 |
| 4 | `salah satu` | 204,094 |
| 5 | `referensi pranala` | 188,446 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referensi pranala luar` | 188,236 |
| 2 | `merupakan bagian dari` | 173,920 |
| 3 | `ini juga merupakan` | 121,570 |
| 4 | `juga merupakan bagian` | 118,712 |
| 5 | `spesies ini juga` | 82,513 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `juga merupakan bagian dari` | 118,623 |
| 2 | `ini juga merupakan bagian` | 118,088 |
| 3 | `spesies ini juga merupakan` | 82,160 |
| 4 | `merupakan bagian dari genus` | 74,651 |
| 5 | `kelas insecta filum arthropoda` | 71,731 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ini juga merupakan bagian dari` | 118,072 |
| 2 | `spesies ini juga merupakan bagian` | 82,150 |
| 3 | `kelas insecta filum arthropoda dan` | 71,731 |
| 4 | `filum arthropoda dan kingdom animalia` | 71,725 |
| 5 | `insecta filum arthropoda dan kingdom` | 71,724 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n` | 49,403,346 |
| 2 | `n _` | 31,170,947 |
| 3 | `a _` | 27,237,962 |
| 4 | `_ d` | 23,894,955 |
| 5 | `n g` | 23,074,425 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n _` | 24,307,048 |
| 2 | `a n g` | 11,583,028 |
| 3 | `_ m e` | 10,082,401 |
| 4 | `_ d a` | 9,885,365 |
| 5 | `n g _` | 9,758,169 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n g _` | 7,357,567 |
| 2 | `k a n _` | 6,126,631 |
| 3 | `_ m e n` | 5,037,208 |
| 4 | `_ d a n` | 4,774,956 |
| 5 | `d a n _` | 4,773,132 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a n _` | 4,636,764 |
| 2 | `y a n g _` | 4,351,516 |
| 3 | `_ y a n g` | 4,285,242 |
| 4 | `n g a n _` | 2,901,020 |
| 5 | `p a d a _` | 2,514,636 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 237
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.8593 | 1.814 | 13.13 | 2,962,654 | 14.1% |
| **1** | Subword | 0.4616 | 1.377 | 5.47 | 82,539 | 53.8% |
| **2** | Word | 0.4377 | 1.354 | 2.70 | 38,824,783 | 56.2% |
| **2** | Subword | 0.4117 | 1.330 | 2.64 | 451,148 | 58.8% |
| **3** | Word | 0.1831 | 1.135 | 1.41 | 104,699,371 | 81.7% |
| **3** | Subword | 0.4412 | 1.358 | 2.78 | 1,192,939 | 55.9% |
| **4** | Word | 0.0695 🏆 | 1.049 | 1.12 | 147,775,338 | 93.1% |
| **4** | Subword | 0.5403 | 1.454 | 3.03 | 3,321,158 | 46.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `dan inlandsch schrijver semua lautan mazhab chicago medical top akan tetapi istrinya musik dan yogya...`
2. `yang dirilis pada tahun pembangunan talud pembangunan ii orthomolybdate feo h2 lebih mudah teroksida...`
3. `di india jakarta ichtiar baru seri televisi abc nbc selama lamanya yang mendorong serta melumasi lap...`

**Context Size 2:**

1. `pada tahun dengan bubarnya laskar jihad by noorhaidi hasan s ip center sikka 4 maria sharapova dan`
2. `pranala luar film rusia tahun berikutnya penyelidik ufo dapat berupa kuantitatif misalnya dalam bent...`
3. `bagian dari ordo diptera kelas insecta filum arthropoda dan kingdom animalia larva kumbang ini biasa...`

**Context Size 3:**

1. `merupakan bagian dari genus bulbophyllum nama ilmiah dari spesies ini didasarkan pada laporan dua or...`
2. `referensi pranala luar air alps armada air alps telah mencakup pesawat berikut ini per agustus armad...`
3. `ini juga merupakan bagian dari genus menemerus dan ordo araneae nama ilmiah dari spesies ini pertama...`

**Context Size 4:**

1. `juga merupakan bagian dari genus neoitamus ordo diptera kelas insecta filum arthropoda dan kingdom a...`
2. `ini juga merupakan bagian dari ordo poales spesies cyperus paniceus sendiri merupakan bagian dari ge...`
3. `spesies ini juga merupakan bagian dari genus megopis ordo coleoptera kelas insecta filum arthropoda ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `ani_arasebeladan`
2. `_kani,_"tatryang`
3. `ng_mbantundidmbk`

**Context Size 2:**

1. `angnyangala_pest.`
2. `n_gi,_ision_untif`
3. `a_bah_res_porah_a`

**Context Size 3:**

1. `an_:_dan_ada_yang_`
2. `angan_mencanyimnya`
3. `_merurandah_dengka`

**Context Size 4:**

1. `ang_dirand_prättige`
2. `kan_dises_p._london`
3. `_menyata_panason_me`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (3,321,158 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 | 1,224,888 |
| Total Tokens | 195,423,598 |
| Mean Frequency | 159.54 |
| Median Frequency | 4 |
| Frequency Std Dev | 8831.73 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | dan | 4,660,597 |
| 2 | yang | 4,306,521 |
| 3 | di | 3,661,285 |
| 4 | pada | 2,304,326 |
| 5 | dari | 2,124,901 |
| 6 | dengan | 1,729,322 |
| 7 | ini | 1,681,032 |
| 8 | untuk | 1,457,185 |
| 9 | dalam | 1,438,758 |
| 10 | adalah | 1,350,786 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | melanthiales | 2 |
| 2 | trilliales | 2 |
| 3 | medeolaceae | 2 |
| 4 | alstroemeriales | 2 |
| 5 | burmanniales | 2 |
| 6 | amaryllidales | 2 |
| 7 | dioscoreanae | 2 |
| 8 | arecanae | 2 |
| 9 | mewstadz | 2 |
| 10 | bithorax | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0756 |
| R² (Goodness of Fit) | 0.989157 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 29.0% |
| Top 1,000 | 56.7% |
| Top 5,000 | 76.2% |
| Top 10,000 | 83.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9892 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 29.0% of corpus
- **Long Tail:** 1,214,888 words needed for remaining 17.0% 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 | 0.6145 | 0.3978 | N/A | N/A |
| **mono_64d** | 64 | 0.6446 | 0.3232 | N/A | N/A |
| **mono_128d** | 128 | 0.6017 | 0.2493 | N/A | N/A |
| **aligned_32d** | 32 | 0.6145 | 0.3840 | 0.5320 | 0.8980 |
| **aligned_64d** | 64 | 0.6446 🏆 | 0.3083 | 0.7760 | 0.9520 |
| **aligned_128d** | 128 | 0.6017 | 0.2548 | 0.8760 | 0.9860 |

### Key Findings

- **Best Isotropy:** aligned_64d with 0.6446 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3196. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 87.6% 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 | **-0.225** | 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 |
|--------|----------|
| `-s` | sarmizegetusa, sounkyoensis, savoia |
| `-a` | anakboru, analdie, aerotaxi |
| `-ma` | mantellodon, mariarosa, manaruh |
| `-m` | mengahruskan, muhadatsatul, menyalahkan |
| `-k` | khathib, kunžak, kar98k |
| `-p` | parungi, perusaahaan, pinsot |
| `-b` | burdi, bumbong, bagiab |
| `-t` | theridioides, teymourtash, talana |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | westa, grazilla, lefkosia |
| `-n` | discrimination, jörn, mengahruskan |
| `-s` | gomphrenoides, zimdars, sounkyoensis |
| `-i` | parungi, burdi, aerotaxi |
| `-e` | analdie, herne, iratsume |
| `-an` | mengahruskan, fatchurohman, perusaahaan |
| `-ya` | bungkusnya, oksidatifnya, berkembangbiaknya |
| `-r` | vbr, legitimator, sattar |

### 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 |
|------|----------|------------------|----------|
| `engu` | 1.64x | 240 contexts | cengu, dengu, wengu |
| `ebag` | 2.05x | 77 contexts | sebag, tebag, lebaga |
| `gkan` | 1.83x | 118 contexts | ingkan, ongkan, tigkan |
| `ebua` | 2.11x | 62 contexts | sebua, ebuah, zebua |
| `rkan` | 1.74x | 146 contexts | arkan, mrkan, erkan |
| `egar` | 1.61x | 200 contexts | jegar, degar, cegar |
| `rseb` | 2.00x | 68 contexts | terseb, ersebut, trsebut |
| `njad` | 2.11x | 51 contexts | njadi, anjad, anjadi |
| `ingk` | 1.37x | 376 contexts | singk, hingk, ingky |
| `menj` | 1.88x | 63 contexts | menju, menja, menje |
| `terb` | 1.49x | 188 contexts | terbai, terbis, terbat |
| `nnya` | 1.65x | 106 contexts | annya, ionnya, lannya |

### 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` | 117 words | pankorben, pembumian |
| `-p` | `-a` | 104 words | puncumania, paradera |
| `-s` | `-a` | 93 words | sylviatata, saaka |
| `-a` | `-a` | 85 words | ajidarma, anisotricha |
| `-k` | `-n` | 82 words | kipin, kylián |
| `-p` | `-an` | 81 words | pembumian, pacinan |
| `-k` | `-a` | 78 words | kreuta, kepemimpinanya |
| `-m` | `-n` | 77 words | mistakon, mengkonsentrasikan |
| `-s` | `-n` | 74 words | sajikdan, saefudin |
| `-t` | `-a` | 72 words | tubicinella, typhlonyphia |

### 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 |
|------|-----------------|------------|------|
| coelosphaeridae | **`coelosphaerid-a-e`** | 7.5 | `a` |
| iguanidae | **`iguanid-a-e`** | 7.5 | `a` |
| wijayaanwar | **`wijayaanw-a-r`** | 7.5 | `a` |
| kerarajaan | **`keraraj-a-an`** | 7.5 | `a` |
| pandjhoerit | **`pandjhoer-i-t`** | 7.5 | `i` |
| fauthouxsandrine | **`fauthouxsandri-n-e`** | 7.5 | `n` |
| retnowati | **`retnow-a-ti`** | 7.5 | `a` |
| encontrar | **`encontr-a-r`** | 7.5 | `a` |
| prasekolah | **`p-ra-sekolah`** | 7.5 | `sekolah` |
| penamamaan | **`penama-ma-an`** | 7.5 | `ma` |
| samatorsemarang | **`samatorsemar-a-ng`** | 7.5 | `a` |
| keshavrao | **`keshavr-a-o`** | 7.5 | `a` |
| mencatatnya | **`mencatat-n-ya`** | 7.5 | `n` |
| interkelasi | **`interke-la-si`** | 7.5 | `la` |
| siberpunk | **`siberpu-n-k`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Indonesian 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 (5.35x) |
| N-gram | **2-gram** | Lowest perplexity (237) |
| Markov | **Context-4** | Highest predictability (93.1%) |
| 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: 2026-01-13 19:55:01*