---
language: mai
language_name: Maithili
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: 4.366
  - name: best_isotropy
    type: isotropy
    value: 0.8575
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Maithili** 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** | 3.443x | 3.45 | 0.1128% | 173,793 |
| **16k** | 3.812x | 3.82 | 0.1249% | 156,927 |
| **32k** | 4.113x | 4.12 | 0.1347% | 145,461 |
| **64k** | 4.366x 🏆 | 4.37 | 0.1430% | 137,033 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `एक अवधी व्यंजन छी। एकर मुख्य घटक बासमती चावल छी। भारत क खाना के व्यंजन`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁एक ▁अवधी ▁व्यंजन ▁छी । ▁एकर ▁मुख्य ▁घटक ▁बास मती ... (+8 more)` | 18 |
| 16k | `▁एक ▁अवधी ▁व्यंजन ▁छी । ▁एकर ▁मुख्य ▁घटक ▁बासमती ▁चावल ... (+7 more)` | 17 |
| 32k | `▁एक ▁अवधी ▁व्यंजन ▁छी । ▁एकर ▁मुख्य ▁घटक ▁बासमती ▁चावल ... (+7 more)` | 17 |
| 64k | `▁एक ▁अवधी ▁व्यंजन ▁छी । ▁एकर ▁मुख्य ▁घटक ▁बासमती ▁चावल ... (+7 more)` | 17 |

**Sample 2:** `एक पूर्वी भारतक उड़िया व्यंजन छी। सन्दर्भ सामग्रीसभ बाह्य जडीसभ एहो सभ देखी खानप...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁एक ▁पूर्वी ▁भारतक ▁उड़िया ▁व्यंजन ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ... (+8 more)` | 18 |
| 16k | `▁एक ▁पूर्वी ▁भारतक ▁उड़िया ▁व्यंजन ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ... (+8 more)` | 18 |
| 32k | `▁एक ▁पूर्वी ▁भारतक ▁उड़िया ▁व्यंजन ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ... (+8 more)` | 18 |
| 64k | `▁एक ▁पूर्वी ▁भारतक ▁उड़िया ▁व्यंजन ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ... (+8 more)` | 18 |

**Sample 3:** `एक दक्षिण भारतीय खाना छी। सन्दर्भ सामग्रीसभ बाह्य जडीसभ एहो सभ देखी भारतीय खाना`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁एक ▁दक्षिण ▁भारतीय ▁खाना ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ▁जडीसभ ... (+5 more)` | 15 |
| 16k | `▁एक ▁दक्षिण ▁भारतीय ▁खाना ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ▁जडीसभ ... (+5 more)` | 15 |
| 32k | `▁एक ▁दक्षिण ▁भारतीय ▁खाना ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ▁जडीसभ ... (+5 more)` | 15 |
| 64k | `▁एक ▁दक्षिण ▁भारतीय ▁खाना ▁छी । ▁सन्दर्भ ▁सामग्रीसभ ▁बाह्य ▁जडीसभ ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.366x compression
- **Lowest UNK Rate:** 8k with 0.1128% 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 | 4,297 | 12.07 | 22,467 | 28.2% | 54.7% |
| **2-gram** | Subword | 1,743 🏆 | 10.77 | 25,848 | 38.2% | 73.9% |
| **3-gram** | Word | 3,810 | 11.90 | 23,927 | 27.9% | 59.1% |
| **3-gram** | Subword | 11,518 | 13.49 | 110,689 | 17.8% | 44.5% |
| **4-gram** | Word | 5,211 | 12.35 | 40,011 | 25.0% | 57.3% |
| **4-gram** | Subword | 36,978 | 15.17 | 333,125 | 13.4% | 32.8% |
| **5-gram** | Word | 4,223 | 12.04 | 29,488 | 24.4% | 60.5% |
| **5-gram** | Subword | 56,327 | 15.78 | 426,789 | 12.2% | 28.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `सन्दर्भ सामग्रीसभ` | 11,778 |
| 2 | `एहो सभ` | 10,279 |
| 3 | `सभ देखी` | 8,741 |
| 4 | `बाह्य जडीसभ` | 8,199 |
| 5 | `सामग्रीसभ बाह्य` | 7,108 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `एहो सभ देखी` | 8,735 |
| 2 | `सन्दर्भ सामग्रीसभ बाह्य` | 7,108 |
| 3 | `सामग्रीसभ बाह्य जडीसभ` | 6,649 |
| 4 | `जडीसभ एहो सभ` | 3,689 |
| 5 | `बाह्य जडीसभ एहो` | 3,676 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `सन्दर्भ सामग्रीसभ बाह्य जडीसभ` | 6,649 |
| 2 | `बाह्य जडीसभ एहो सभ` | 3,674 |
| 3 | `सामग्रीसभ बाह्य जडीसभ एहो` | 3,561 |
| 4 | `सन्दर्भ सामग्रीसभ एहो सभ` | 3,438 |
| 5 | `जडीसभ एहो सभ देखी` | 3,273 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `सन्दर्भ सामग्रीसभ बाह्य जडीसभ एहो` | 3,561 |
| 2 | `सामग्रीसभ बाह्य जडीसभ एहो सभ` | 3,559 |
| 3 | `बाह्य जडीसभ एहो सभ देखी` | 3,259 |
| 4 | `सन्दर्भ सामग्रीसभ एहो सभ देखी` | 2,498 |
| 5 | `जनवरी मार्च अप्रैल जुन जुलाई` | 2,163 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `क _` | 121,319 |
| 2 | `_ अ` | 91,240 |
| 3 | `ल _` | 72,637 |
| 4 | `_ स` | 70,074 |
| 5 | `स भ` | 66,192 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `स भ _` | 47,639 |
| 2 | `_ अ छि` | 30,922 |
| 3 | `_ । _` | 30,370 |
| 4 | `_ ए क` | 19,980 |
| 5 | `_ आ _` | 19,191 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ अ छि _` | 18,176 |
| 2 | `अ छि _ ।` | 13,864 |
| 3 | `छि _ । _` | 13,497 |
| 4 | `_ ए क _` | 13,064 |
| 5 | `_ स न्द र्भ` | 12,821 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ अ छि _ ।` | 13,854 |
| 2 | `अ छि _ । _` | 13,399 |
| 3 | `_ स न्द र्भ _` | 12,640 |
| 4 | `स न्द र्भ _ सा` | 12,376 |
| 5 | `न्द र्भ _ सा म` | 11,966 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 1,743
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.7362 | 1.666 | 4.91 | 124,145 | 26.4% |
| **1** | Subword | 0.8265 | 1.773 | 10.76 | 7,745 | 17.3% |
| **2** | Word | 0.1969 | 1.146 | 1.43 | 607,477 | 80.3% |
| **2** | Subword | 0.5739 | 1.489 | 3.94 | 83,321 | 42.6% |
| **3** | Word | 0.0593 | 1.042 | 1.10 | 864,728 | 94.1% |
| **3** | Subword | 0.4893 | 1.404 | 2.75 | 328,318 | 51.1% |
| **4** | Word | 0.0220 🏆 | 1.015 | 1.04 | 952,209 | 97.8% |
| **4** | Subword | 0.3124 | 1.242 | 1.75 | 902,200 | 68.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `अछि सन्दर्भ सामग्रीसभ बाह्य जडीसभ एहो सभ देखी खानपान एवं सांस्कृतिक जीवनक समस्यामे वन ट्री हिल`
2. `आ कोशलपुर पर जापान टोक्यो जापानी लड़ाकू विमान जे आब विवाद सन् मे टन ओर्का आ`
3. `छी जे किछ समयक लेल निश्चित भेल छल आ जिन के नाम महाबिर पब्लिशर्स कार्य कर्नाटक`

**Context Size 2:**

1. `सन्दर्भ सामग्रीसभ बाह्य जडीसभ एहो सभ देखी जिलाक गाउँपालिकासभ गाउँपालिकासभ`
2. `एहो सभ देखी जिलाक गाउँपालिकासभ गाउँपालिकासभ`
3. `बाह्य जडीसभ जिला समन्वय समितिक कार्यालय सुनसरी नेपाल एहो सभ देखी गगनचुम्बी गगनचुम्बी भवनसभ पूरा भेल ...`

**Context Size 3:**

1. `एहो सभ देखी क्रिकेट विश्वकप क्रिकेट विश्वकप प्रतियोगिताक पाँचम क्रिकेट विश्वकप छल ई प्रतियोगिता २२ फ...`
2. `सन्दर्भ सामग्रीसभ बाह्य जडीसभ www dorw gov np www wikipedia org रेलवे`
3. `सामग्रीसभ बाह्य जडीसभ युनेस्को विश्व सम्पदा क्षेत्रमा समावेश कएल गेल वर्ष आ मापदण्ड विवरण सम्पदा क्ष...`

**Context Size 4:**

1. `सन्दर्भ सामग्रीसभ बाह्य जडीसभ एहो सभ देखी मन्दिरसभ विश्व सम्पदा क्षेत्रसभ संरक्षित क्षेत्रसभ दरवारसभ`
2. `बाह्य जडीसभ एहो सभ देखु लोक में बनाएल वा सुधारल लेखसभ नगरपालिकासभ`
3. `सामग्रीसभ बाह्य जडीसभ एहो सभ देखी पात्रसभ देवीसभ`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_गि_खोलासमूदर_(४०३,_`
2. `कएकस्बेलज़ार_रासन्दर्भ_ज_क्षे`
3. `सञ्चालिभिनेपागर्मी_प्रयोगिरि_सँ_`

**Context Size 2:**

1. `क_नामक_प्रदेश_नं_ये_जे_म`
2. `_अनुसारथिसभ_बाह्य_जनवरी_`
3. `ल_जभण्डारीक_योद्धा_रहस्य'_लि`

**Context Size 3:**

1. `सभ_एहो_सभ_खोजा।soekmo`
2. `_अछि।_ओहिक_राष्ट्रिय_वालेंसियाई`
3. `_।_एतय_मुख्यमन्त्रीसभ_बाह्य_ज`

**Context Size 4:**

1. `_अछि_।_भूगोल_सन्दर्भ_सामग्री_नि`
2. `अछि_।_सन्दर्भ_सामग्रीसभ_एहो_स`
3. `छि_।_वर्तमान_बौद्ध_विहार_राज्यक`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (902,200 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 | 49,509 |
| Total Tokens | 1,264,926 |
| Mean Frequency | 25.55 |
| Median Frequency | 3 |
| Frequency Std Dev | 294.44 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | अछि | 30,903 |
| 2 | आ | 19,409 |
| 3 | छी | 15,249 |
| 4 | एक | 14,560 |
| 5 | के | 13,574 |
| 6 | सन्दर्भ | 12,693 |
| 7 | छल | 12,679 |
| 8 | मे | 12,000 |
| 9 | सामग्रीसभ | 11,793 |
| 10 | ई | 11,492 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | रॉबर्ट्स | 2 |
| 2 | आरोहित | 2 |
| 3 | पिलरक | 2 |
| 4 | हिमनदीय | 2 |
| 5 | मिलिकए | 2 |
| 6 | हाइक | 2 |
| 7 | मेलुङ्त्से | 2 |
| 8 | तासी | 2 |
| 9 | तासिलाप्चा | 2 |
| 10 | भजनसभ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1297 |
| R² (Goodness of Fit) | 0.992103 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.1% |
| Top 1,000 | 64.5% |
| Top 5,000 | 82.8% |
| Top 10,000 | 88.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9921 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.1% of corpus
- **Long Tail:** 39,509 words needed for remaining 11.3% 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 | 0.8575 | 0.3363 | N/A | N/A |
| **mono_64d** | 64 | 0.7955 | 0.2720 | N/A | N/A |
| **mono_128d** | 128 | 0.4568 | 0.2464 | N/A | N/A |
| **aligned_32d** | 32 | 0.8575 🏆 | 0.3402 | 0.0080 | 0.0880 |
| **aligned_64d** | 64 | 0.7955 | 0.2672 | 0.0260 | 0.1060 |
| **aligned_128d** | 128 | 0.4568 | 0.2394 | 0.0320 | 0.1580 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8575 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2836. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.2% 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 | **1.089** | 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 |
|--------|----------|
| `-स` | सरदर, सोरेन, सियामी |
| `-क` | कराल, करतै, कुडिग्राम |
| `-ब` | बसोबास, बर्गक, बहिनसँ |
| `-म` | मोनेटा, मङ्सिर, मम |
| `-प` | पश्चिमे, परैत, पाउन्डक |
| `-ज` | जोडेत, जाम, जालघर |
| `-अ` | अन्तर्देशीय, अवधमे, अपराधमे |
| `-र` | रीति, रचनाकार, रम्य |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-क` | पाउन्डक, बर्गक, राजनैतिक |
| `-र` | सरदर, विरुधुनगर, रचनाकार |
| `-न` | उपप्रधान, सोरेन, विमान |
| `-सभ` | वंशसभ, संहितासभ, फिल्मसभ |
| `-त` | परैत, जोडेत, इसलेत |
| `-भ` | वंशसभ, संहितासभ, फिल्मसभ |
| `-ल` | थाङपाल, कराल, निकैल |
| `-स` | गेट्स, बसोबास, बस |

### 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` | 2.90x | 12 contexts | motion, nation, action |
| `atio` | 2.93x | 9 contexts | nation, nations, station |
| `कसभक` | 1.87x | 16 contexts | लोकसभक, घटकसभक, अंकसभक |

### 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 |
|--------|--------|-----------|----------|
| `-स` | `-क` | 95 words | समलैंगिक, स्मारकक |
| `-प` | `-क` | 90 words | पाठकक, परमेश्वरक |
| `-म` | `-क` | 54 words | मैथुनक, माउसक |
| `-क` | `-क` | 44 words | कामरानक, कृपाचार्यक |
| `-व` | `-क` | 40 words | विधेयक, वानरसभक |
| `-न` | `-क` | 35 words | निबन्धक, नाइजेरियाक |
| `-स` | `-र` | 35 words | सितम्बर, सङ्गीतकार |
| `-अ` | `-क` | 35 words | अंगूरक, अप्सराक |
| `-क` | `-र` | 31 words | कमान्डर, कर्मकार |
| `-म` | `-र` | 30 words | मोतीपुर, मंडोर |

### 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 |
|------|-----------------|------------|------|
| इलेक्ट्रिकल | **`इलेक्ट्रि-क-ल`** | 7.5 | `क` |
| विश्वविद्यालय | **`विश्वविद्या-ल-य`** | 7.5 | `ल` |
| जनकद्वारा | **`जन-क-द्वारा`** | 7.5 | `द्वारा` |
| राष्ट्रीयकरण | **`राष्ट्रीय-क-रण`** | 7.5 | `क` |
| महासञ्चालकक | **`महासञ्चाल-क-क`** | 7.5 | `क` |
| समयअनुसार | **`सम-य-अनुसार`** | 7.5 | `अनुसार` |
| ज़्यादातर | **`ज़्यादा-त-र`** | 7.5 | `त` |
| समर्थकसभक | **`समर्थ-क-सभक`** | 7.5 | `क` |
| उपजिलासभक | **`उप-जिला-सभक`** | 6.0 | `जिला` |
| मिलियनेयरक | **`मिलियनेयर-क`** | 4.5 | `मिलियनेयर` |
| मन्त्रिमण्डल | **`म-न-्त्रिमण्डल`** | 4.5 | `्त्रिमण्डल` |
| विष्फोटनक | **`विष्फोटन-क`** | 4.5 | `विष्फोटन` |
| गाजियाबादक | **`गाजियाबाद-क`** | 4.5 | `गाजियाबाद` |
| गिरफ्तारीक | **`गिरफ्तारी-क`** | 4.5 | `गिरफ्तारी` |
| religions | **`religion-s`** | 4.5 | `religion` |

### 6.6 Linguistic Interpretation

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

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.37x) |
| N-gram | **2-gram** | Lowest perplexity (1,743) |
| Markov | **Context-4** | Highest predictability (97.8%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 11:39:06*