---
language: bo
language_name: Tibetan
language_family: tibetoburman_tibetic
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-tibetoburman_tibetic
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: 5.306
  - name: best_isotropy
    type: isotropy
    value: 0.8542
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tibetan** 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** | 4.069x | 4.07 | 0.3678% | 233,845 |
| **16k** | 4.567x | 4.57 | 0.4127% | 208,371 |
| **32k** | 4.989x | 4.99 | 0.4509% | 190,738 |
| **64k** | 5.306x 🏆 | 5.31 | 0.4795% | 179,358 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `གསེར་མོ་ནི་སྒོང་སྐྱེས་སྲོག་ཆགས་ཀྱི་རིགས་གཅིག་རེད། ལོ་རྒྱུས། པར་རིས་བར་འཁྱམས། ཟིན...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁གསེར་ མོ་ནི་ སྒོང་སྐྱེས་ སྲོག་ཆགས་ཀྱི་ རིགས་གཅིག་རེད། ▁ལོ་རྒྱུས། ▁པར་རིས་བར་ འཁྱམས། ▁ཟིན་ཐོ་ འམ་དཔྱད་གཞི། ... (+5 more)` | 15 |
| 16k | `▁གསེར་ མོ་ནི་ སྒོང་སྐྱེས་ སྲོག་ཆགས་ཀྱི་ རིགས་གཅིག་རེད། ▁ལོ་རྒྱུས། ▁པར་རིས་བར་ འཁྱམས། ▁ཟིན་ཐོ་ འམ་དཔྱད་གཞི། ... (+5 more)` | 15 |
| 32k | `▁གསེར་ མོ་ནི་ སྒོང་སྐྱེས་ སྲོག་ཆགས་ཀྱི་ རིགས་གཅིག་རེད། ▁ལོ་རྒྱུས། ▁པར་རིས་བར་ འཁྱམས། ▁ཟིན་ཐོ་ འམ་དཔྱད་གཞི། ... (+5 more)` | 15 |
| 64k | `▁གསེར་ མོ་ནི་ སྒོང་སྐྱེས་ སྲོག་ཆགས་ཀྱི་ རིགས་གཅིག་རེད། ▁ལོ་རྒྱུས། ▁པར་རིས་བར་ འཁྱམས། ▁ཟིན་ཐོ་ འམ་དཔྱད་གཞི། ... (+5 more)` | 15 |

**Sample 2:** `ཀྲོའུ་སི། ཞི་ལའི་ལྷ་སྒྲུང་ཁྲོད་ཀྱི་ལྷ་རེད། མི་ཚེ། པར་རིས་བར་འཁྱམས། ཟིན་ཐོ་འམ་དཔྱ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ཀྲ ོའུ་ སི། ▁ཞི་ ལའི་ ལྷ་ སྒྲུང་ ཁྲོད་ཀྱི་ ལྷ་ རེད། ... (+10 more)` | 20 |
| 16k | `▁ཀྲོའུ་ སི། ▁ཞི་ ལའི་ ལྷ་སྒྲུང་ ཁྲོད་ཀྱི་ ལྷ་རེད། ▁མི་ཚེ། ▁པར་རིས་བར་ འཁྱམས། ... (+7 more)` | 17 |
| 32k | `▁ཀྲོའུ་ སི། ▁ཞི་ ལའི་ ལྷ་སྒྲུང་ ཁྲོད་ཀྱི་ ལྷ་རེད། ▁མི་ཚེ། ▁པར་རིས་བར་ འཁྱམས། ... (+7 more)` | 17 |
| 64k | `▁ཀྲོའུ་ སི། ▁ཞི་ ལའི་ ལྷ་སྒྲུང་ ཁྲོད་ཀྱི་ ལྷ་རེད། ▁མི་ཚེ། ▁པར་རིས་བར་ འཁྱམས། ... (+7 more)` | 17 |

**Sample 3:** `མྱང་འདས་གཞན་ནས་སྒྲུབ་ཏུ་མེད། མྱ་ངན་ལས་འདས་པ་སྟེ་ཐར་པ་དང་། ཐམས་ཅད་མཁྱེན་པའི་གོ་འཕ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁མྱང་ འདས་ གཞན་ ནས་ སྒྲུབ་ ཏུ་ མེད། ▁མྱ་ངན་ ལས་འདས་ པ་སྟེ་ ... (+15 more)` | 25 |
| 16k | `▁མྱང་འདས་ གཞན་ ནས་ སྒྲུབ་ ཏུ་ མེད། ▁མྱ་ངན་ ལས་འདས་ པ་སྟེ་ ཐར་ ... (+13 more)` | 23 |
| 32k | `▁མྱང་འདས་ གཞན་ནས་ སྒྲུབ་ ཏུ་ མེད། ▁མྱ་ངན་ ལས་འདས་ པ་སྟེ་ ཐར་ པ་དང་། ... (+10 more)` | 20 |
| 64k | `▁མྱང་འདས་ གཞན་ནས་ སྒྲུབ་ ཏུ་ མེད། ▁མྱ་ངན་ལས་འདས་ པ་སྟེ་ ཐར་ པ་དང་། ▁ཐམས་ཅད་ ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 5.306x compression
- **Lowest UNK Rate:** 8k with 0.3678% 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 | 35,575 | 15.12 | 163,426 | 8.0% | 26.6% |
| **2-gram** | Subword | 468 🏆 | 8.87 | 14,902 | 58.0% | 90.7% |
| **3-gram** | Word | 208,497 | 17.67 | 499,603 | 3.7% | 11.0% |
| **3-gram** | Subword | 3,697 | 11.85 | 87,521 | 25.1% | 62.9% |
| **4-gram** | Word | 574,996 | 19.13 | 1,035,818 | 3.2% | 7.7% |
| **4-gram** | Subword | 21,129 | 14.37 | 395,961 | 12.1% | 36.3% |
| **5-gram** | Word | 554,814 | 19.08 | 896,814 | 3.6% | 8.0% |
| **5-gram** | Subword | 85,765 | 16.39 | 872,546 | 6.0% | 20.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `པ དང` | 28,306 |
| 2 | `བ དང` | 12,858 |
| 3 | `པ ལ` | 12,495 |
| 4 | `ཐམས ཅད` | 12,121 |
| 5 | `པ ནི` | 11,602 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `སྤྱོད འཇུག གི` | 4,094 |
| 2 | `ཞེས བྱ བ` | 3,742 |
| 3 | `ད དུང གཟིགས` | 3,594 |
| 4 | `ཕྱོགས དྲ མཐུད` | 3,563 |
| 5 | `ཕྱི ཕྱོགས དྲ` | 3,563 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ཕྱི ཕྱོགས དྲ མཐུད` | 3,562 |
| 2 | `དཔྱད གཞིའི དཀར ཆག` | 3,391 |
| 3 | `ཟིན ཐོ འམ དཔྱད` | 2,805 |
| 4 | `ཐོ འམ དཔྱད གཞི` | 2,802 |
| 5 | `དུང གཟིགས ཕྱི ཕྱོགས` | 2,789 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ཟིན ཐོ འམ དཔྱད གཞི` | 2,802 |
| 2 | `ད དུང གཟིགས ཕྱི ཕྱོགས` | 2,789 |
| 3 | `གཟིགས ཕྱི ཕྱོགས དྲ མཐུད` | 2,779 |
| 4 | `དཀར ཆག ད དུང གཟིགས` | 2,777 |
| 5 | `དཔྱད གཞིའི དཀར ཆག ད` | 2,776 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ས ་` | 1,109,782 |
| 2 | `། _` | 814,181 |
| 3 | `ང ་` | 726,970 |
| 4 | `ན ་` | 605,125 |
| 5 | `་ བ` | 601,943 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `་ པ ་` | 233,799 |
| 2 | `ག ས ་` | 214,635 |
| 3 | `། _ །` | 181,451 |
| 4 | `ས ་ པ` | 169,152 |
| 5 | `་ ད ང` | 160,512 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `་ ད ང ་` | 137,863 |
| 2 | `་ པ འི ་` | 114,983 |
| 3 | `ང ་ ། _` | 88,853 |
| 4 | `ས ་ པ ་` | 77,821 |
| 5 | `་ པ ར ་` | 67,023 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ད ང ་ ། _` | 50,908 |
| 2 | `་ ད ང ་ །` | 50,893 |
| 3 | `ས ་ པ འི ་` | 39,175 |
| 4 | `་ རྣ མ ས ་` | 29,571 |
| 5 | `་ སོ ག ས ་` | 28,140 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 468
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~20% 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 | 0.9206 | 1.893 | 17.76 | 45,103 | 7.9% |
| **1** | Subword | 0.8281 | 1.775 | 6.83 | 8,393 | 17.2% |
| **2** | Word | 0.7033 | 1.628 | 3.81 | 800,524 | 29.7% |
| **2** | Subword | 0.4670 | 1.382 | 4.11 | 57,328 | 53.3% |
| **3** | Word | 0.2921 | 1.224 | 1.62 | 3,051,550 | 70.8% |
| **3** | Subword | 0.4481 | 1.364 | 3.28 | 235,662 | 55.2% |
| **4** | Word | 0.1112 🏆 | 1.080 | 1.18 | 4,929,019 | 88.9% |
| **4** | Subword | 0.3733 | 1.295 | 2.38 | 773,603 | 62.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `པ ཡིད གཉིས གདན ཤོ མིག གསུམ རྫིང བུར ལན གསུམ པ ལ མཱུ ཥི ཏ`
2. `དང སུམ གཉིས ཀྱི ཞབས ལྕགས རིགས སུ བཞུགས པ ཆེན མོ གཉིས ཀྱི ཚད ལས`
3. `ལ བོད ཤན ནམ ཞིག ལུས ལ སོགས པའི མིང པེལ རེས མོས བརྡུང བའི སྐུ`

**Context Size 2:**

1. `པ དང གདམ ང མ གཉིས གཉིས གཉིས ཡོད ཤར ཕོགས ཀི པཎི ཏ ཨ བྷི ཥིཉྩ`
2. `བ དང མནའ སྐྱེལ ཞིང དབྱར ཀ རི ཀ སྤྱི མཐུན རྒྱལ ཁབ དེ རུ བཞག གོ`
3. `པ ལ བཞུགས པར ཞལ གྱིས བཞེས པ ནས འབྲས བུ ཉེ ཟ དེའི བྱེ བྲག པ`

**Context Size 3:**

1. `སྤྱོད འཇུག གི དཀའ འགྲེལ ཤིང དཔར ཞེས གསུངས པ ནི འདོད པ ཁྱབ ཁོངས ཡངས པ དེ`
2. `ཞེས བྱ བ ལ སོགས པ གཞན མ ཡིན ནོ རབ འབར དགྲ ཡི དབང དུ ཟད འཕེལ`
3. `ད དུང གཟིགས ཕྱི ཕྱོགས དྲ མཐུད ལྕེ དཔྱད གཞིའི དཀར ཆག ད དུང གཟིགས ཀྱེ རྡོ རྗེ`

**Context Size 4:**

1. `དཔྱད གཞིའི དཀར ཆག ད དུང གཟིགས ཕྱི ཕྱོགས དྲ མཐུད དབྱིན ཇིའི རླུང འཕྲིན ཀུང སིས ཉིན དེར`
2. `ཟིན ཐོ འམ དཔྱད གཞི དཔྱད གཞིའི དཀར ཆག ད དུང གཟིགས ཕྱི ཕྱོགས དྲ མཐུད bdrc buddhist digital`
3. `ཐོ འམ དཔྱད གཞི དཔྱད གཞིའི དཀར ཆག ད དུང གཟིགས གེ སར རྒྱལ པོ རྒྱ ནག ཏུ ཕེབས`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `་དུ་མོ་སྦྱངས་མསལ་ཁྲི་ཁ`
2. `ས་ཉིས།_ཞནང་ཀྱིས།_དང`
3. `གས་ཆེན་ནི་ཡོད་འ༔_།_`

**Context Size 2:**

1. `ས་དངོས་ཀྱི་ལྷས་ད་ེ_རྣམས`
2. `།_ཁེངས་བཞིན་པའི་སྡུག་ཡི`
3. `ང་།_ད་གཉིས།_དྲངས་པར`

**Context Size 3:**

1. `་པ་ལ་དྲིས་ན་ནི་_ལོའི་རྒྱུད`
2. `གས་པ་གླིང་བཙན་པོ་དབྱིངས`
3. `།_།བྱས་ཀྱང་རུང་།_མི་དང`

**Context Size 4:**

1. `་དང་།_།མཐུ་སྟོབས་རྒྱས་མཛེ`
2. `་པའི་ཚུལ་བཻ་སེར་པོ་འཁོར་ཡ`
3. `ང་།_བཞི་པ།_སྟོན་པ་སྒྲུབ་པ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 88.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (773,603 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 | 18,977 |
| Total Tokens | 7,591,805 |
| Mean Frequency | 400.05 |
| Median Frequency | 5 |
| Frequency Std Dev | 3886.00 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | པ | 277,831 |
| 2 | དང | 165,810 |
| 3 | ལ | 150,300 |
| 4 | བ | 127,823 |
| 5 | པའི | 118,705 |
| 6 | མ | 92,873 |
| 7 | དེ | 80,387 |
| 8 | ནི | 78,884 |
| 9 | ཀྱི | 76,665 |
| 10 | དུ | 73,981 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | སུམྦྷའི | 2 |
| 2 | བིཀྲ | 2 |
| 3 | jayasena | 2 |
| 4 | ཤུདྡྷཿསརྦྦ | 2 |
| 5 | ཧྲོཾ | 2 |
| 6 | ཝརྞཱ | 2 |
| 7 | caryā | 2 |
| 8 | gīti | 2 |
| 9 | caryāgītivṛtti | 2 |
| 10 | དཀྲྀཏ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 2.0091 |
| R² (Goodness of Fit) | 0.961368 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 47.6% |
| Top 1,000 | 90.6% |
| Top 5,000 | 99.1% |
| Top 10,000 | 99.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9614 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 47.6% of corpus
- **Long Tail:** 8,977 words needed for remaining 0.3% 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 | 0.8542 🏆 | 0.3709 | N/A | N/A |
| **mono_64d** | 64 | 0.8068 | 0.3078 | N/A | N/A |
| **mono_128d** | 128 | 0.6072 | 0.2915 | N/A | N/A |
| **aligned_32d** | 32 | 0.8542 | 0.3660 | 0.0160 | 0.1720 |
| **aligned_64d** | 64 | 0.8068 | 0.3152 | 0.0740 | 0.2780 |
| **aligned_128d** | 128 | 0.6072 | 0.2869 | 0.1820 | 0.3900 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8542 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3231. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 18.2% 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 | **-0.603** | 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.

*No productive affixes detected.*


### 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.

*No significant bound stems detected.*


### 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`).

*Insufficient data for recursive segmentation.*


### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tibetan 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 (5.31x) |
| N-gram | **2-gram** | Lowest perplexity (468) |
| Markov | **Context-4** | Highest predictability (88.9%) |
| 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 19:39:42*