---
language: anp
language_name: Angika
language_family: indoaryan_central
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-indoaryan_central
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: 3.777
  - name: best_isotropy
    type: isotropy
    value: 0.8298
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Angika** 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** | 3.298x | 3.30 | 0.1077% | 449,296 |
| **16k** | 3.575x | 3.58 | 0.1168% | 414,503 |
| **32k** | 3.777x 🏆 | 3.78 | 0.1234% | 392,298 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `साध्य रुप स॑ आइसलैण्ड दुनिया के सबसे पुराऽनो संसदीय लोकतंत्र छीकै। एकरा म॑ अभी 6...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁सा ध्य ▁रुप ▁स॑ ▁आइसलैण्ड ▁दुनिया ▁के ▁सबसे ▁पुरा ऽ ... (+26 more)` | 36 |
| 16k | `▁सा ध्य ▁रुप ▁स॑ ▁आइसलैण्ड ▁दुनिया ▁के ▁सबसे ▁पुरा ऽनो ... (+24 more)` | 34 |
| 32k | `▁साध्य ▁रुप ▁स॑ ▁आइसलैण्ड ▁दुनिया ▁के ▁सबसे ▁पुराऽनो ▁संसदीय ▁लोकतंत्र ... (+22 more)` | 32 |

**Sample 2:** `जनता दल एगो राष्ट्रीय दल छेकै। इतिहास एकरो देखौ बाहरी कड़ी संदर्भ`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁जनता ▁दल ▁एगो ▁राष्ट्रीय ▁दल ▁छेकै । ▁इतिहास ▁एकरो ▁देखौ ... (+3 more)` | 13 |
| 16k | `▁जनता ▁दल ▁एगो ▁राष्ट्रीय ▁दल ▁छेकै । ▁इतिहास ▁एकरो ▁देखौ ... (+3 more)` | 13 |
| 32k | `▁जनता ▁दल ▁एगो ▁राष्ट्रीय ▁दल ▁छेकै । ▁इतिहास ▁एकरो ▁देखौ ... (+3 more)` | 13 |

**Sample 3:** `कोनो रोग सॆं मनुष्य के बचाव लेली जे विधि अपनैलॊ जाय छै, वोकरा चिकित्सा कहलॊ जाय ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁कोनो ▁रोग ▁सॆं ▁मनुष्य ▁के ▁बच ाव ▁लेली ▁जे ▁विधि ... (+14 more)` | 24 |
| 16k | `▁कोनो ▁रोग ▁सॆं ▁मनुष्य ▁के ▁बचाव ▁लेली ▁जे ▁विधि ▁अपन ... (+12 more)` | 22 |
| 32k | `▁कोनो ▁रोग ▁सॆं ▁मनुष्य ▁के ▁बचाव ▁लेली ▁जे ▁विधि ▁अपनैलॊ ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 32k achieves 3.777x compression
- **Lowest UNK Rate:** 8k with 0.1077% 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 | 5,133 | 12.33 | 15,401 | 20.6% | 52.0% |
| **2-gram** | Subword | 1,763 🏆 | 10.78 | 18,130 | 37.8% | 73.7% |
| **3-gram** | Word | 4,136 | 12.01 | 14,976 | 21.1% | 59.7% |
| **3-gram** | Subword | 12,510 | 13.61 | 74,071 | 14.6% | 40.2% |
| **4-gram** | Word | 6,638 | 12.70 | 28,729 | 18.3% | 55.5% |
| **4-gram** | Subword | 43,295 | 15.40 | 212,245 | 8.3% | 26.6% |
| **5-gram** | Word | 4,565 | 12.16 | 20,947 | 20.4% | 62.1% |
| **5-gram** | Subword | 74,529 | 16.19 | 271,380 | 5.9% | 20.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `के लिए` | 1,987 |
| 2 | `के अनुसार` | 1,711 |
| 3 | `छै जे` | 1,664 |
| 4 | `छै जेकरा` | 1,521 |
| 5 | `के औसत` | 1,421 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `छै जेकरा म` | 1,240 |
| 2 | `जनगणना के अनुसार` | 1,231 |
| 3 | `के रूप में` | 796 |
| 4 | `परिवार रहै छै` | 789 |
| 5 | `म स्थित ऐगो` | 690 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `छै जेकरा म कुल` | 638 |
| 2 | `के औसत लिंग अनुपात` | 559 |
| 3 | `छै जनगणना के अनुसार` | 535 |
| 4 | `के जनगणना के अनुसार` | 498 |
| 5 | `गाँव छै जेकरा म` | 479 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `गाँव छै जेकरा म कुल` | 476 |
| 2 | `छै के जनगणना के अनुसार` | 438 |
| 3 | `0 6 आयु वर्ग के` | 436 |
| 4 | `6 आयु वर्ग के बच्चा` | 435 |
| 5 | `आयु वर्ग के बच्चा के` | 432 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `र _` | 44,141 |
| 2 | `_ के` | 43,544 |
| 3 | `के _` | 39,889 |
| 4 | `, _` | 27,806 |
| 5 | `। _` | 27,568 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ के _` | 37,379 |
| 2 | `_ में _` | 14,100 |
| 3 | `_ की _` | 9,283 |
| 4 | `_ औ र` | 9,137 |
| 5 | `औ र _` | 9,133 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ औ र _` | 9,104 |
| 2 | `_ है । _` | 6,415 |
| 3 | `_ छै । _` | 6,096 |
| 4 | `_ ए क _` | 4,687 |
| 5 | `_ छै , _` | 3,618 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ छै , _ जे` | 2,233 |
| 2 | `_ भा र त _` | 2,072 |
| 3 | `ता _ है । _` | 2,029 |
| 4 | `_ अ नु सा र` | 2,019 |
| 5 | `_ के _ लि ए` | 1,986 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 1,763
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~21% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | Word | 0.8698 | 1.827 | 5.82 | 59,321 | 13.0% |
| **1** | Subword | 0.9730 | 1.963 | 11.48 | 4,665 | 2.7% |
| **2** | Word | 0.2523 | 1.191 | 1.56 | 344,866 | 74.8% |
| **2** | Subword | 0.5491 | 1.463 | 3.85 | 53,547 | 45.1% |
| **3** | Word | 0.0707 | 1.050 | 1.12 | 537,872 | 92.9% |
| **3** | Subword | 0.4976 | 1.412 | 2.68 | 206,241 | 50.2% |
| **4** | Word | 0.0212 🏆 | 1.015 | 1.03 | 599,865 | 97.9% |
| **4** | Subword | 0.3012 | 1.232 | 1.72 | 551,827 | 69.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `के महिमा बहुत थोड़ा या एक क्षेत्र क साबुन कारखानों में है प्रेमचंद अध्यापक फ्रांसिस प्रथम`
2. `में छै जेकरा मॅॆ कुल 650 महिला छै देवनागरी लिपि शब्दावली लिपि केरौ अधिकार प्राप्त छै`
3. `छै उदाहरणतः x11 रंगों के मौखिक संचार प्रतीक समूह भी पंचवटी प्रसिद्ध हुआ आज १५० से`

**Context Size 2:**

1. `के लिए मिस्र पर विजय प्राप्त करै छीयै जे कणोज स॑ भी अधिक अलग अलग रूप दिया`
2. `के अनुसार पत्रांग गांव के आबादी 105 छै जे गाँव के जनसंख्या छै जेकरा म 147 पुरुष`
3. `छै जे उत्तर प्रदेश राज्य मँ स्थित छै मानदंड के अनुसार कुंदरी सोन कुरहा हरला के कुल`

**Context Size 3:**

1. `छै जेकरा म 118 पुरुष आरु जबकि महिला छै तेलबाद्रो गांव म 0 6 आयु वर्ग के बच्चा`
2. `जनगणना के अनुसार हरवाडीह के बाल लिंग अनुपात 915 छै जे उत्तर प्रदेश के मिर्ज़ापुर जिले की बेलन`
3. `के रूप में देखा जाता है किंतु पाप के सभी परिणाम नष्ट नहीं होते उसके परिणाम दूर करने`

**Context Size 4:**

1. `छै जेकरा म कुल 72 पुरुष छै जबकि 80 महिला छै जैसनो कि के जनगणना म बतैलो गेलो छै`
2. `के औसत लिंग अनुपात 835 स कम छै`
3. `छै जनगणना के अनुसार सरोख गांव के आबादी 673 छेलै जेकरा म॑ स॑ 613 पुरुष आरू 503 महिला छै`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_(मेल_उत्पत्ति_सूत्रों_के_के_`
2. `र_हैं_रानर्जी_सम्परिसबना_दो`
3. `क_दौराजलड़कई_साथ_कुल_`

**Context Size 2:**

1. `र_के_इस_छै।_मुआविष्कार_दि`
2. `_के_ठीक_यौगिक_रक्षा_आवासी_`
3. `के_अध्ययन_में_लैटिन_का_दार्श`

**Context Size 3:**

1. `_के_भाई_थे_और_माना_जाता_है`
2. `_में_5%_छै।_जनताँत्रिक_रूप_`
3. `_की_जाती_हैं_जो_लगन_की_किता`

**Context Size 4:**

1. `_और_गैर-न्यायिक_सदन_की_आवृ`
2. `_है।_व्यापक_छै_तs_आखरी_सांस`
3. `_छै।_इतिहास_के_बाद_उसको_स`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (551,827 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 | 27,495 |
| Total Tokens | 705,736 |
| Mean Frequency | 25.67 |
| Median Frequency | 4 |
| Frequency Std Dev | 313.78 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | के | 37,476 |
| 2 | में | 14,866 |
| 3 | छै | 13,486 |
| 4 | है | 12,172 |
| 5 | की | 9,675 |
| 6 | और | 9,147 |
| 7 | का | 7,600 |
| 8 | से | 7,248 |
| 9 | को | 5,485 |
| 10 | हैं | 5,201 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | zeros | 2 |
| 2 | ignored | 2 |
| 3 | dmy | 2 |
| 4 | mdy | 2 |
| 5 | paren | 2 |
| 6 | breaking | 2 |
| 7 | inserted | 2 |
| 8 | values | 2 |
| 9 | separator | 2 |
| 10 | days | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1206 |
| R² (Goodness of Fit) | 0.994934 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.9% |
| Top 1,000 | 69.2% |
| Top 5,000 | 86.8% |
| Top 10,000 | 92.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9949 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.9% of corpus
- **Long Tail:** 17,495 words needed for remaining 7.2% 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 | 0.8298 🏆 | 0.3551 | N/A | N/A |
| **mono_64d** | 64 | 0.7019 | 0.2957 | N/A | N/A |
| **mono_128d** | 128 | 0.3519 | 0.2719 | N/A | N/A |
| **aligned_32d** | 32 | 0.8298 | 0.3586 | 0.0160 | 0.0940 |
| **aligned_64d** | 64 | 0.7019 | 0.2950 | 0.0180 | 0.1240 |
| **aligned_128d** | 128 | 0.3519 | 0.2673 | 0.0300 | 0.1420 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8298 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3073. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.0% 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 | **1.980** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ों` | चक्रवातों, अनुक्रमों, मोहरों |

### 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 |
|------|----------|------------------|----------|
| `tion` | 2.65x | 15 contexts | motion, action, edition |
| `atio` | 2.66x | 12 contexts | nations, station, national |
| `stat` | 2.68x | 6 contexts | state, status, statue |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

*No significant affix co-occurrences detected.*


### 6.5 Recursive Morpheme Segmentation

Using **Recursive Hierarchical Substitutability**, we decompose complex words into their constituent morphemes. This approach handles nested affixes (e.g., `prefix-prefix-root-suffix`).

| Word | Suggested Split | Confidence | Stem |
|------|-----------------|------------|------|
| अविष्कारों | **`अविष्कार-ों`** | 4.5 | `अविष्कार` |
| रूपान्तरणों | **`रूपान्तरण-ों`** | 4.5 | `रूपान्तरण` |
| महाविद्यालयों | **`महाविद्यालय-ों`** | 4.5 | `महाविद्यालय` |
| यूरोपियनों | **`यूरोपियन-ों`** | 4.5 | `यूरोपियन` |
| प्रकाशकों | **`प्रकाशक-ों`** | 4.5 | `प्रकाशक` |
| अनुक्रमों | **`अनुक्रम-ों`** | 4.5 | `अनुक्रम` |
| सम्मेलनों | **`सम्मेलन-ों`** | 4.5 | `सम्मेलन` |
| सुल्तानों | **`सुल्तान-ों`** | 4.5 | `सुल्तान` |
| गणितज्ञों | **`गणितज्ञ-ों`** | 4.5 | `गणितज्ञ` |
| पुस्तकालयों | **`पुस्तकालय-ों`** | 4.5 | `पुस्तकालय` |
| महाकाव्यों | **`महाकाव्य-ों`** | 4.5 | `महाकाव्य` |
| गुणसूत्रों | **`गुणसूत्र-ों`** | 4.5 | `गुणसूत्र` |
| शास्त्रों | **`शास्त्र-ों`** | 4.5 | `शास्त्र` |
| संग्रहालयों | **`संग्रहालय-ों`** | 4.5 | `संग्रहालय` |
| कार्यालयों | **`कार्यालय-ों`** | 4.5 | `कार्यालय` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Angika 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 | **32k BPE** | Best compression (3.78x) |
| N-gram | **2-gram** | Lowest perplexity (1,763) |
| Markov | **Context-4** | Highest predictability (97.9%) |
| 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 16:32:35*