README.md

---
language: ban
language_name: Balinese
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: 5.076
  - name: best_isotropy
    type: isotropy
    value: 0.8561
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Balinese** 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** | 4.067x | 4.07 | 0.1935% | 240,819 |
| **16k** | 4.471x | 4.48 | 0.2127% | 219,044 |
| **32k** | 4.812x | 4.82 | 0.2289% | 203,541 |
| **64k** | 5.076x 🏆 | 5.08 | 0.2415% | 192,952 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `920 921 922 923 924 925 926 927 928 929 Jadma Embas Seda Pustaka Pranala liyané ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 9 2 0 ▁ 9 2 1 ▁ 9 ... (+40 more)` | 50 |
| 16k | `▁ 9 2 0 ▁ 9 2 1 ▁ 9 ... (+40 more)` | 50 |
| 32k | `▁ 9 2 0 ▁ 9 2 1 ▁ 9 ... (+40 more)` | 50 |
| 64k | `▁ 9 2 0 ▁ 9 2 1 ▁ 9 ... (+40 more)` | 50 |

**Sample 2:** `Reutlingen (; Swabia: Reitlenga) inggih punika sinunggil kota ring Baden-Württem...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁re ut ling en ▁(; ▁sw ab ia : ▁re ... (+34 more)` | 44 |
| 16k | `▁re ut ling en ▁(; ▁sw ab ia : ▁re ... (+28 more)` | 38 |
| 32k | `▁re ut lingen ▁(; ▁sw abia : ▁re it l ... (+25 more)` | 35 |
| 64k | `▁reut lingen ▁(; ▁sw abia : ▁re it l enga ... (+22 more)` | 32 |

**Sample 3:** `Terneuzen () inggih punika kota miwah kotamadya ring sisi kelod kauh Belanda, ri...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ter ne uz en ▁() ▁inggih ▁punika ▁kota ▁miwah ▁kotamadya ... (+21 more)` | 31 |
| 16k | `▁ter ne uz en ▁() ▁inggih ▁punika ▁kota ▁miwah ▁kotamadya ... (+17 more)` | 27 |
| 32k | `▁ter ne uz en ▁() ▁inggih ▁punika ▁kota ▁miwah ▁kotamadya ... (+15 more)` | 25 |
| 64k | `▁ter ne uzen ▁() ▁inggih ▁punika ▁kota ▁miwah ▁kotamadya ▁ring ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 5.076x compression
- **Lowest UNK Rate:** 8k with 0.1935% 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 | 4,640 | 12.18 | 61,259 | 36.3% | 57.8% |
| **2-gram** | Subword | 223 🏆 | 7.80 | 8,004 | 73.6% | 99.2% |
| **3-gram** | Word | 5,627 | 12.46 | 79,401 | 34.2% | 56.0% |
| **3-gram** | Subword | 1,643 | 10.68 | 43,230 | 31.4% | 79.4% |
| **4-gram** | Word | 8,547 | 13.06 | 120,311 | 29.1% | 51.2% |
| **4-gram** | Subword | 7,491 | 12.87 | 210,661 | 18.4% | 54.1% |
| **5-gram** | Word | 8,777 | 13.10 | 92,971 | 25.7% | 49.1% |
| **5-gram** | Subword | 21,126 | 14.37 | 563,270 | 15.0% | 42.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `situs resmi` | 43,663 |
| 2 | `inggih punika` | 39,149 |
| 3 | `pusat statistik` | 24,769 |
| 4 | `badan pusat` | 24,755 |
| 5 | `silih tunggil` | 23,231 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `badan pusat statistik` | 24,753 |
| 2 | `pustaka pranala jaba` | 21,680 |
| 3 | `inggih punika silih` | 20,522 |
| 4 | `punika silih tunggil` | 20,156 |
| 5 | `pranala jaba situs` | 19,252 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `inggih punika silih tunggil` | 20,046 |
| 2 | `pranala jaba situs resmi` | 19,034 |
| 3 | `pustaka pranala jaba situs` | 18,664 |
| 4 | `dados kauahin ilang yening` | 15,610 |
| 5 | `kauahin ilang yening url` | 15,325 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pustaka pranala jaba situs resmi` | 18,475 |
| 2 | `dados kauahin ilang yening url` | 15,325 |
| 3 | `kauahin ilang yening url nenten` | 15,194 |
| 4 | `url dados kauahin ilang yening` | 15,039 |
| 5 | `ilang yening url nenten aktip` | 14,998 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n` | 914,478 |
| 2 | `n g` | 765,351 |
| 3 | `a _` | 556,979 |
| 4 | `i n` | 546,378 |
| 5 | `n _` | 539,027 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g _` | 376,926 |
| 2 | `a n _` | 301,627 |
| 3 | `i n g` | 300,756 |
| 4 | `a n g` | 227,744 |
| 5 | `_ k a` | 223,144 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i n g _` | 230,681 |
| 2 | `r i n g` | 152,062 |
| 3 | `_ r i n` | 133,355 |
| 4 | `a n g _` | 89,274 |
| 5 | `u n i k` | 75,300 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `r i n g _` | 149,014 |
| 2 | `_ r i n g` | 133,072 |
| 3 | `p u n i k` | 74,857 |
| 4 | `_ p u n i` | 72,286 |
| 5 | `b u p a t` | 70,377 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 223
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~43% 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 | 0.7231 | 1.651 | 5.15 | 258,667 | 27.7% |
| **1** | Subword | 0.9698 | 1.959 | 7.06 | 4,719 | 3.0% |
| **2** | Word | 0.2300 | 1.173 | 1.54 | 1,327,861 | 77.0% |
| **2** | Subword | 0.6130 | 1.529 | 3.55 | 33,296 | 38.7% |
| **3** | Word | 0.0751 | 1.053 | 1.14 | 2,029,547 | 92.5% |
| **3** | Subword | 0.5903 | 1.506 | 3.30 | 118,157 | 41.0% |
| **4** | Word | 0.0289 🏆 | 1.020 | 1.05 | 2,293,918 | 97.1% |
| **4** | Subword | 0.6581 | 1.578 | 2.95 | 389,827 | 34.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ring kabupatén manggarai univérsitas téknologi langkungan saking lis kediri propinsi jawa timur situ...`
2. `kabupatén bandar udara sipil negara wagian connecticut john musker dave akbarshah fikarno partai pol...`
3. `punika silih tunggil gampong ring panguntat warsa perang sane madaging aglomerasi pays blanc kawentu...`

**Context Size 2:**

1. `situs resmi provinsi kalimantan timur indonésia pustaka pranala jaba of the betawi and their subordi...`
2. `inggih punika silih tunggil désa dinas sané magenah ring désa karimunjawa pulau karimunjawa gua sara...`
3. `pusat statistik provinsi lampung badan pusat statistik nusa tenggara timur ring panegara indonésia p...`

**Context Size 3:**

1. `badan pusat statistik provinsi lampung badan pusat statistik provinsi banten situs resmi pemerintah ...`
2. `pustaka pranala jaba situs resmi pamréntahan kota malang prodeskel binapemdes kemendagri banyuwangi ...`
3. `inggih punika silih tunggil kecamatan ring kabupatén tuban ring jawa timur ring panegara indonésia p...`

**Context Size 4:**

1. `inggih punika silih tunggil désa dinas sané magenah ring kecamatan pakem ring wawengkon kabupatén bo...`
2. `pranala jaba situs resmi pamréntahan propinsi kalimantan tengah badan pusat statistik propinsi kalim...`
3. `pustaka pranala jaba situs resmi pamrentahan propinsi jawa tengah badan pusat statistik propinsi daé...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `akraning_pa_dang`
2. `_pawewen,_ako_in`
3. `ngkang_l_parasih`

**Context Size 2:**

1. `an_punisi_ka_ma_i`
2. `ng_doh_for,_namas`
3. `a_matasur_sur_jaj`

**Context Size 3:**

1. `ng_pamréntahan_kaa`
2. `an_sumelaya,_propi`
3. `ing_richoir,_jani_`

**Context Size 4:**

1. `ing_lis._gresik_pun`
2. `ring_radeship_himse`
3. `_ring_soroh_jaya_be`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (389,827 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 | 98,403 |
| Total Tokens | 3,677,636 |
| Mean Frequency | 37.37 |
| Median Frequency | 3 |
| Frequency Std Dev | 767.63 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ring | 133,161 |
| 2 | kabupatén | 61,962 |
| 3 | punika | 52,592 |
| 4 | situs | 47,934 |
| 5 | sané | 47,011 |
| 6 | resmi | 44,807 |
| 7 | inggih | 39,587 |
| 8 | saking | 39,350 |
| 9 | url | 35,045 |
| 10 | propinsi | 33,485 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ᬧᬳᬗᬿ | 2 |
| 2 | ᬧᬓᬓ᭄ | 2 |
| 3 | ᬮᬸᬦᬸᬓ᭄ | 2 |
| 4 | ᬫᭂᬭᬜ᭄ᬘᬂ | 2 |
| 5 | patonangi | 2 |
| 6 | ᬩᬩᬭᬶᬲ᭄ | 2 |
| 7 | ᬢᬢᬓᬦ᭄ | 2 |
| 8 | ᬳᬮᬢ᭄ | 2 |
| 9 | ᬩᬤᭁᬦ᭄ | 2 |
| 10 | ᬩᬮᬸᬓᬸᬂ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1326 |
| R² (Goodness of Fit) | 0.997911 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 45.3% |
| Top 1,000 | 69.2% |
| Top 5,000 | 83.1% |
| Top 10,000 | 88.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9979 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 45.3% of corpus
- **Long Tail:** 88,403 words needed for remaining 12.0% 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 | 0.8561 🏆 | 0.3559 | N/A | N/A |
| **mono_64d** | 64 | 0.8453 | 0.2824 | N/A | N/A |
| **mono_128d** | 128 | 0.8108 | 0.2152 | N/A | N/A |
| **aligned_32d** | 32 | 0.8561 | 0.3499 | 0.0500 | 0.3000 |
| **aligned_64d** | 64 | 0.8453 | 0.2791 | 0.1160 | 0.4180 |
| **aligned_128d** | 128 | 0.8108 | 0.2217 | 0.1860 | 0.5760 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8561 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2840. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 18.6% 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 | **0.148** | 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 |
|--------|----------|
| `-ka` | kaumahné, kambilo, karangdinoyo |
| `-ma` | maseosan, matogu, manufaktur |
| `-pa` | papadun, palmerah, pacing |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | alien, gejeran, hughenden |
| `-an` | gejeran, maseosan, matangnyan |
| `-ng` | wyoming, siung, yèning |
| `-ang` | nelebang, renang, hilirundang |

### 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 |
|------|----------|------------------|----------|
| `anga` | 1.63x | 366 contexts | angar, ranga, manga |
| `nten` | 1.91x | 86 contexts | inten, enten, wnten |
| `atan` | 1.68x | 151 contexts | batan, vatan, patan |
| `ngan` | 1.50x | 185 contexts | ingan, angan, ringan |
| `akin` | 1.95x | 42 contexts | makin, dakin, yakin |
| `ungg` | 1.47x | 120 contexts | tungg, ungga, unggak |
| `nggi` | 1.58x | 77 contexts | anggi, nggih, ninggi |
| `taha` | 1.86x | 33 contexts | tahan, tahai, tahar |
| `ados` | 2.09x | 21 contexts | dados, sados, padosa |
| `ggih` | 1.99x | 22 contexts | nggih, inggih, lnggih |
| `stat` | 1.88x | 20 contexts | state, stats, istat |
| `isti` | 1.56x | 37 contexts | sistim, bistik, mistik |

### 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` | 119 words | kapribadian, kaanyarin |
| `-pa` | `-n` | 117 words | palimanan, pawedaran |
| `-pa` | `-an` | 104 words | palimanan, pawedaran |
| `-ka` | `-ng` | 90 words | kagampilang, kalaliang |
| `-ka` | `-ang` | 75 words | kagampilang, kalaliang |
| `-ka` | `-an` | 68 words | kapribadian, kalanguan |
| `-ma` | `-n` | 45 words | malun, maroon |
| `-ma` | `-an` | 36 words | madénan, mabinaan |
| `-ma` | `-ng` | 34 words | mamantang, mahondang |
| `-ma` | `-ang` | 20 words | mamantang, mahondang |

### 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 |
|------|-----------------|------------|------|
| patarungan | **`pa-taru-ng-an`** | 7.5 | `taru` |
| kalédangan | **`ka-léda-ng-an`** | 7.5 | `léda` |
| malimongan | **`ma-limo-ng-an`** | 7.5 | `limo` |
| kasemaran | **`ka-semar-an`** | 6.0 | `semar` |
| kaasosiasiang | **`ka-asosiasi-ang`** | 6.0 | `asosiasi` |
| kadaftarang | **`ka-daftar-ang`** | 6.0 | `daftar` |
| malaibang | **`ma-laib-ang`** | 6.0 | `laib` |
| kasunanan | **`ka-sunan-an`** | 6.0 | `sunan` |
| kawarisang | **`ka-waris-ang`** | 6.0 | `waris` |
| pangabdian | **`pa-ngabdi-an`** | 6.0 | `ngabdi` |
| palaibang | **`pa-laib-ang`** | 6.0 | `laib` |
| kabudayaan | **`ka-budaya-an`** | 6.0 | `budaya` |
| mapangangge | **`ma-pa-ngangge`** | 6.0 | `ngangge` |
| mapontang | **`ma-pont-ang`** | 6.0 | `pont` |
| kajegegan | **`ka-jegeg-an`** | 6.0 | `jegeg` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Balinese 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 (5.08x) |
| N-gram | **2-gram** | Lowest perplexity (223) |
| Markov | **Context-4** | Highest predictability (97.1%) |
| 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: 2026-01-03 18:39:33*