---
language: pa
language_name: Punjabi
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: 4.042
  - name: best_isotropy
    type: isotropy
    value: 0.8342
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Punjabi** 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** | 3.344x | 3.35 | 0.0292% | 637,303 |
| **16k** | 3.646x | 3.65 | 0.0318% | 584,610 |
| **32k** | 3.881x | 3.88 | 0.0339% | 549,074 |
| **64k** | 4.042x 🏆 | 4.04 | 0.0353% | 527,239 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ਕਸੂੰਬੜੀ ਭਾਰਤੀ ਪੰਜਾਬ ਦੇ ਫ਼ਤਹਿਗੜ੍ਹ ਸਾਹਿਬ ਜ਼ਿਲ੍ਹੇ ਦੇ ਖੇੜਾ ਬਲਾਕ ਦਾ ਇੱਕ ਪਿੰਡ ਹੈ। ਹਵਾਲ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ਕਸ ੂੰ ਬ ੜੀ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਫ਼ਤਹਿਗੜ੍ਹ ▁ਸਾਹਿਬ ▁ਜ਼ਿਲ੍ਹੇ ... (+13 more)` | 23 |
| 16k | `▁ਕਸ ੂੰ ਬੜੀ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਫ਼ਤਹਿਗੜ੍ਹ ▁ਸਾਹਿਬ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ... (+12 more)` | 22 |
| 32k | `▁ਕਸ ੂੰ ਬੜੀ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਫ਼ਤਹਿਗੜ੍ਹ ▁ਸਾਹਿਬ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ... (+12 more)` | 22 |
| 64k | `▁ਕਸ ੂੰ ਬੜੀ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਫ਼ਤਹਿਗੜ੍ਹ ▁ਸਾਹਿਬ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ... (+12 more)` | 22 |

**Sample 2:** `ਚੂੰਗ ਭਾਰਤੀ ਪੰਜਾਬ ਦੇ ਤਰਨਤਾਰਨ ਜ਼ਿਲ੍ਹੇ ਦੇ ਬਲਾਕ ਭਿੱਖੀਵਿੰਡ ਦਾ ਇੱਕ ਪਿੰਡ ਹੈ। ਹਵਾਲੇ ਤਾਰਨ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ਚ ੂੰ ਗ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਤਰਨਤਾਰਨ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ... (+15 more)` | 25 |
| 16k | `▁ਚ ੂੰ ਗ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਤਰਨਤਾਰਨ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ... (+13 more)` | 23 |
| 32k | `▁ਚ ੂੰਗ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਤਰਨਤਾਰਨ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ▁ਭਿੱ ... (+12 more)` | 22 |
| 64k | `▁ਚੂੰਗ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਤਰਨਤਾਰਨ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ▁ਭਿੱਖੀਵਿੰਡ ▁ਦਾ ... (+9 more)` | 19 |

**Sample 3:** `ਭੇਲ ਭਾਰਤੀ ਪੰਜਾਬ ਦੇ ਜਲੰਧਰ ਜ਼ਿਲ੍ਹੇ ਦੇ ਬਲਾਕ ਆਦਮਪੁਰ ਦਾ ਇੱਕ ਪਿੰਡ ਹੈ। ਹਵਾਲੇ ਜ਼ਿਲ੍ਹੇ ਦੇ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ਭ ੇਲ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਜਲੰਧਰ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ▁ਆਦ ... (+10 more)` | 20 |
| 16k | `▁ਭ ੇਲ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਜਲੰਧਰ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ▁ਆਦਮਪੁਰ ... (+9 more)` | 19 |
| 32k | `▁ਭ ੇਲ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਜਲੰਧਰ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ▁ਆਦਮਪੁਰ ... (+9 more)` | 19 |
| 64k | `▁ਭੇਲ ▁ਭਾਰਤੀ ▁ਪੰਜਾਬ ▁ਦੇ ▁ਜਲੰਧਰ ▁ਜ਼ਿਲ੍ਹੇ ▁ਦੇ ▁ਬਲਾਕ ▁ਆਦਮਪੁਰ ▁ਦਾ ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.042x compression
- **Lowest UNK Rate:** 8k with 0.0292% 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 | 65,512 | 16.00 | 395,139 | 9.9% | 25.1% |
| **2-gram** | Subword | 1,824 🏆 | 10.83 | 65,167 | 38.3% | 74.2% |
| **3-gram** | Word | 226,610 | 17.79 | 723,559 | 4.6% | 13.1% |
| **3-gram** | Subword | 17,627 | 14.11 | 426,051 | 16.0% | 37.7% |
| **4-gram** | Word | 595,990 | 19.18 | 1,217,646 | 2.1% | 7.1% |
| **4-gram** | Subword | 101,454 | 16.63 | 1,977,133 | 8.3% | 22.6% |
| **5-gram** | Word | 481,395 | 18.88 | 795,359 | 2.0% | 6.8% |
| **5-gram** | Subword | 336,559 | 18.36 | 3,786,103 | 4.3% | 14.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ਜਾਂਦਾ ਹੈ` | 51,096 |
| 2 | `ਗਿਆ ਸੀ` | 36,408 |
| 3 | `ਤੌਰ ਤੇ` | 36,131 |
| 4 | `ਹੈ ਅਤੇ` | 35,656 |
| 5 | `ਕੀਤਾ ਗਿਆ` | 30,014 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ਕੀਤਾ ਗਿਆ ਸੀ` | 16,375 |
| 2 | `ਦੇ ਰੂਪ ਵਿੱਚ` | 11,064 |
| 3 | `ਕਿਹਾ ਜਾਂਦਾ ਹੈ` | 9,910 |
| 4 | `ਦੇ ਤੌਰ ਤੇ` | 7,251 |
| 5 | `ਆਮ ਤੌਰ ਤੇ` | 7,156 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ਸਾਲ ਦੀ ਉਮਰ ਵਿੱਚ` | 4,687 |
| 2 | `ਦਾ ਇੱਕ ਪਿੰਡ ਹੈ` | 4,498 |
| 3 | `ਹਵਾਲੇ ਜ਼ਿਲ੍ਹੇ ਦੇ ਪਿੰਡ` | 3,112 |
| 4 | `ਵੀ ਕਿਹਾ ਜਾਂਦਾ ਹੈ` | 2,917 |
| 5 | `ਹੈ ਹਵਾਲੇ ਜ਼ਿਲ੍ਹੇ ਦੇ` | 2,408 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ਹੈ ਹਵਾਲੇ ਜ਼ਿਲ੍ਹੇ ਦੇ ਪਿੰਡ` | 2,358 |
| 2 | `ਦਾ ਇੱਕ ਪਿੰਡ ਹੈ ਹਵਾਲੇ` | 2,190 |
| 3 | `ਪਿੰਡ ਹੈ ਹਵਾਲੇ ਜ਼ਿਲ੍ਹੇ ਦੇ` | 1,587 |
| 4 | `ਇੱਕ ਪਿੰਡ ਹੈ ਹਵਾਲੇ ਜ਼ਿਲ੍ਹੇ` | 1,551 |
| 5 | `ਜੂਨ ਜੁਲਾਈ ਸਤੰਬਰ ਅਕਤੂਬਰ ਦਸੰਬਰ` | 1,224 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ਰ _` | 970,300 |
| 2 | `_ ਅ` | 824,969 |
| 3 | `, _` | 781,870 |
| 4 | `ਨ _` | 746,764 |
| 5 | `। _` | 733,291 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ਵਿੱ ਚ` | 572,750 |
| 2 | `ਵਿੱ ਚ _` | 533,677 |
| 3 | `_ ਦੇ _` | 530,516 |
| 4 | `ਅ ਤੇ _` | 432,213 |
| 5 | `_ ਅ ਤੇ` | 431,849 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ਵਿੱ ਚ _` | 533,074 |
| 2 | `_ ਅ ਤੇ _` | 431,071 |
| 3 | `_ ਹੈ । _` | 249,093 |
| 4 | `_ ਇੱ ਕ _` | 216,221 |
| 5 | `_ ਲ ਈ _` | 135,834 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ਹ ਨ । _` | 79,400 |
| 2 | `ਦਾ _ ਹੈ । _` | 69,651 |
| 3 | `_ ਕ ਰ ਨ _` | 56,253 |
| 4 | `_ ਉ ਸ ਨੇ _` | 53,553 |
| 5 | `_ ਹੈ । _ ਇ` | 51,650 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 1,824
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~14% 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 | 0.7819 | 1.719 | 8.40 | 605,913 | 21.8% |
| **1** | Subword | 0.7222 | 1.650 | 10.75 | 17,141 | 27.8% |
| **2** | Word | 0.3690 | 1.291 | 2.26 | 5,085,870 | 63.1% |
| **2** | Subword | 0.7395 | 1.670 | 6.01 | 184,279 | 26.0% |
| **3** | Word | 0.1540 | 1.113 | 1.34 | 11,467,166 | 84.6% |
| **3** | Subword | 0.5675 | 1.482 | 3.86 | 1,107,278 | 43.2% |
| **4** | Word | 0.0639 🏆 | 1.045 | 1.11 | 15,379,661 | 93.6% |
| **4** | Subword | 0.4313 | 1.348 | 2.39 | 4,276,620 | 56.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ਵਿੱਚ ਫੁੱਟਾਂ ਦੀ ਵਕਾਲਤ ਵੀ ਹਨ ਨਿੱਜੀ ਅਤੇ ਫਿਰ ਹੈਵੀ ਕੇਕ ਵਿੱਚ ਮਾਰੀਆਂ ਜਾਂਦੀਆਂ ਹਨ ਜਨਮ`
2. `ਦੇ ਨਾਲ ਸਨਮਾਨਿਤ ਕੀਤਾ ਤਾਂ ਦੇਵੀ ਮਹਾਤਮਯਮ ਅਨੁਸਾਰ ਉਸਨੇ ਊਰਜਾ ਕੁਸ਼ਲਤਾ ਨਾਲ ਹਰਾਇਆ 24 ਵਿੱਚ ਪੈਸਾ`
3. `ਹੈ 3 october egyptclay sai jayalakshmy jayaram montinee tangphong thassha december retrieved 25 ਸ੍ਰੀ...`

**Context Size 2:**

1. `ਜਾਂਦਾ ਹੈ ਮੁਗ਼ਲ ਸਮਰਾਟ ਅਕਬਰ ਦੀ ਮੁੱਖ ਭੂਮਿਕਾ ਵਿੱਚ ਲਿਖਦੇ ਹਨ ਕਿ ਆਜ਼ਾਦੀ ਤੋਂ ਬਾਅਦ ਉਸਨੂੰ ਗਿਆਨ`
2. `ਗਿਆ ਸੀ ਵਿੱਚ ਇਸ ਸਥਿਤੀ ਨੂੰ ਖਤਮ ਹੋ ਗਿਆ ਇਸ ਗੱਲ ਦੀ ਪੁਸ਼ਟੀ ਕੀਤੀ ਕਿ ਸਾਰਾ ਨੇ`
3. `ਤੌਰ ਤੇ ਰਾਜ ਬਿਹਾਰ ਵਿੱਚ ਚੋਖੇ ਸੁਧਾਰ ਦੇ ਸਮੇਂ ਤੋਂ ਇੱਥੇ ਆ ਕੇ ਜਾਂ ਮਿਰਚਾਂ ਸ਼ਾਮਲ ਕਰਦਾ`

**Context Size 3:**

1. `ਕੀਤਾ ਗਿਆ ਸੀ ਮਹਾਰਾਸ਼ਟਰ ਸਰਕਾਰ ਨੇ ਸਮਾਜਿਕ ਵਿਗਿਆਨ ਵਿੱਚ ਦੇਸ਼ ਦਾ ਸਭ ਤੋਂ ਮਕਬੂਲ ਕਹਾਣੀ big two hearted`
2. `ਦੇ ਰੂਪ ਵਿੱਚ ਸ਼ਾਮਲ ਕੀਤਾ ਗਿਆ ਹੈ ਜਿਸ ਵਿੱਚ ਫਾਰਸੀ ਅਤੇ ਯੂਨਾਨੀਆਂ ਨੇ ਮਸ਼ਹੂਰ ਕਾਨਾ ਜੋ ਮਧੂਮੱਖੀਆਂ ਤੋਂ`
3. `ਕਿਹਾ ਜਾਂਦਾ ਹੈ ਪਰੰਪਰਾ ਦੇ ਸੰਬੰਧ ਵਿੱਚ ਕੈਂਬਰਿਜ ਯੂਨੀਵਰਸਿਟੀ ਦੇ ਹਿਸਾਬਦਾਨ ਐੱਚ ਐੱਫ਼ ਬੇਕਰ ਅਤੇ ਈ ਡਬਲਿਊ ਹੌਬਸਨ`

**Context Size 4:**

1. `ਸਾਲ ਦੀ ਉਮਰ ਵਿੱਚ ਉਸਦੀ ਮੌਤ ਹੋ ਗਈ ਉਸਨੇ ਆਪਣਾ ਜੀਵਨ ਆਪਣੇ ਪਤੀ ਅਤੇ ਇੱਕ ਬੇਟੇ ਨਾਲ ਕੈਨੇਡਾ ਦੇ`
2. `ਦਾ ਇੱਕ ਪਿੰਡ ਹੈ ਹਵਾਲੇ ਜ਼ਿਲ੍ਹੇ ਦੇ ਪਿੰਡ ਬਲਾਕ ਦੇ ਪਿੰਡ`
3. `ਵੀ ਕਿਹਾ ਜਾਂਦਾ ਹੈ ਦੁਆਰਾ ਵਰਤੀ ਜਾਂਦੀ ਇੱਕ ਵੱਖਰੀ ਕਿਸਮ ਦੀ ਕਿਤਾਬ ਹੈ ਜਿਸ ਗੀਹੋਨ ਦਰਿਆ ਮੰਨਿਆ ਗਿਆ ਹੈ`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_rstederishjh_ਗ੍ਰਾ`
2. `ਰ_ਮੁੱਖ_ਵਿਚ_they:_ਮਾਂ_`
3. `ਸਨੇ_ਪੈਦਾ_ਅਭਿਨੇ_ਸੀ।_ਹੈ।_`

**Context Size 2:**

1. `ਰ_ਬਣੀ_ਸੰਗ੍ਰਹਿਣ_ਵਾਈਆਂ_ਬਾਹ`
2. `_ਅਤੇ_ਜ਼ੈਨ_ਯੂਨੀਵਰਮ_ਜਿਸਨੂੰ_`
3. `,_ਖੇਡਾਂ_ਵਿੱਚ_ਉਹ_ਕੁਮਾ_ਪੜ੍ਹਾ`

**Context Size 3:**

1. `_ਵਿੱਚ_ਪੋਲੀਆਂ_ਹਨ।_ਉਹ_ਆਪਣੇ`
2. `ਵਿੱਚ_ਹੋਇਆ_ਅਤੇ_ਰਸਮੀ)_ਜਾਂ_ਬ`
3. `_ਦੇ_ਨਾਲ_ਸੰਬੰਧ_ਰੱਖਦੇ_ਹਨ।_`

**Context Size 4:**

1. `_ਵਿੱਚ_ਇੱਕ_ਸਰੋਤ_ਜਿਸ_ਵਿੱਚ_ਲਿਆ`
2. `_ਅਤੇ_ਕਰਨੈਲ_ਨਪੋਲੀਅਨ(20_ਫੁੱ`
3. `_ਹੈ।_ਮੁਫਤ_ਸਿਰਾਜ-ਉਦ-ਦੌਲਾ_ਦੀ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (4,276,620 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 | 242,047 |
| Total Tokens | 18,725,732 |
| Mean Frequency | 77.36 |
| Median Frequency | 4 |
| Frequency Std Dev | 2689.48 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ਵਿੱਚ | 572,433 |
| 2 | ਦੇ | 531,722 |
| 3 | ਹੈ | 471,753 |
| 4 | ਅਤੇ | 432,771 |
| 5 | ਦੀ | 370,327 |
| 6 | ਨੂੰ | 275,364 |
| 7 | ਦਾ | 267,922 |
| 8 | ਸੀ | 222,609 |
| 9 | ਇੱਕ | 219,966 |
| 10 | ਤੋਂ | 188,860 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ਸੁੰਦਰਨਰ | 2 |
| 2 | ਚੱਕਰਾਈ | 2 |
| 3 | divyakirti | 2 |
| 4 | csie | 2 |
| 5 | ਵਿਟਾਲੀ | 2 |
| 6 | ਸ਼ਮਤੀਕੋਵ | 2 |
| 7 | bvsc | 2 |
| 8 | mvph | 2 |
| 9 | ਉੱਲੀਮਾਰਾਂ | 2 |
| 10 | sarkaryawah | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1016 |
| R² (Goodness of Fit) | 0.993300 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 40.3% |
| Top 1,000 | 64.7% |
| Top 5,000 | 81.6% |
| Top 10,000 | 87.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9933 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 40.3% of corpus
- **Long Tail:** 232,047 words needed for remaining 12.7% 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 | 0.8342 🏆 | 0.3762 | N/A | N/A |
| **mono_64d** | 64 | 0.8303 | 0.3067 | N/A | N/A |
| **mono_128d** | 128 | 0.8116 | 0.2410 | N/A | N/A |
| **aligned_32d** | 32 | 0.8342 | 0.3832 | 0.0760 | 0.3300 |
| **aligned_64d** | 64 | 0.8303 | 0.3087 | 0.1300 | 0.4120 |
| **aligned_128d** | 128 | 0.8116 | 0.2355 | 0.1700 | 0.4920 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8342 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3085. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 17.0% 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 | **-0.529** | 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 |
|--------|----------|
| `-ਸ` | ਸੱਬਲਕਸ਼ਮੀ, ਸਪਿਨੋਜ਼ਾ, ਸਵਰੋ |
| `-ਕ` | ਕਿਸਮੇਟ, ਕੋਲਵਿਨ, ਕੀਮਾਰ |
| `-ਮ` | ਮੰਡੀ, ਮਾਰਟਨੀ, ਮੋਹਨਕਾਧਲ |
| `-ਬ` | ਬਿਭੂਤੀਭੂਸ਼ਣ, ਬੈਰੂਨੀ, ਬਚਾਏ |
| `-ਪ` | ਪਲੱਕਡ਼, ਪੀਡਬਲਯੂਏ, ਪੱਟਮੱਲ |
| `-ਅ` | ਅਤਨੂ, ਅਸਾਂਜ, ਅਵਾਰਡxbiz |
| `-ਰ` | ਰਾਏਚੂਰ, ਰੇਸ਼ੇਬਾਜ਼, ਰਵਾਇਤੀ |
| `-ਵ` | ਵਲੱਲੀ, ਵਿਸਾਯਨ, ਵਿਦਆਉਟ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ਨ` | ਦਵੈਪਾਇਨ, ਜੁਬੀਨ, ਫਾਰੇਨ |
| `-ਰ` | ਗੁਰਬੀਰ, ਯੋਗਤਾਸੁਪਰ, ਆਲਿਵਰ |
| `-ਸ` | ਓਵਰਟੋਨਸ, ਟੈਨਿਨਸ, ਜੋਨਜਸ |
| `-s` | missions, legs, democracies |
| `-ਲ` | ਮੋਹਨਕਾਧਲ, ਸਕੂਲ, ਪੱਟਮੱਲ |
| `-ਕ` | ਨਾਸਤਾਲਿਕ, ਓਟਕ, ਅਕ |
| `-ਮ` | ਦੇਮ, ਨਿਮਾਜਨਮ, ਭਾਗਮ |
| `-n` | anchan, broughton, ceylon |

### 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 |
|------|----------|------------------|----------|
| `indi` | 3.26x | 45 contexts | indic, hindi, indie |
| `ress` | 3.17x | 50 contexts | cress, press, dress |
| `atio` | 3.32x | 38 contexts | ratio, lation, nation |
| `vers` | 3.08x | 47 contexts | versa, verso, verse |
| `nter` | 3.08x | 45 contexts | enter, inter, unter |
| `tion` | 3.01x | 48 contexts | lation, option, nation |
| `ment` | 3.15x | 37 contexts | mente, mentem, cement |
| `stor` | 3.11x | 35 contexts | astor, jstor, stork |
| `ture` | 3.05x | 34 contexts | mature, nature, future |
| `iver` | 3.13x | 29 contexts | diver, river, giver |
| `ctio` | 3.05x | 25 contexts | action, auction, section |
| `mber` | 3.12x | 22 contexts | ember, amber, number |

### 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 |
|--------|--------|-----------|----------|
| `-ਕ` | `-ਨ` | 41 words | ਕੈਲੇਡੋਨੀਅਨ, ਕਰਤੱਵਪੂਰਨ |
| `-ਸ` | `-ਨ` | 37 words | ਸੰਰਚਨ, ਸਿਵਨ |
| `-ਸ` | `-ਰ` | 31 words | ਸੇਲਾਂਗੋਰ, ਸਾਰਤ੍ਰ |
| `-ਸ` | `-ਕ` | 26 words | ਸਮਾਨਆਰਥਕ, ਸਕੈਪਟਿਕ |
| `-ਕ` | `-ਰ` | 26 words | ਕੈਨਰ, ਕੈਬਰ |
| `-ਮ` | `-ਨ` | 19 words | ਮੇਰੀਨ, ਮੁਕੁੰਦਨ |
| `-ਮ` | `-ਰ` | 17 words | ਮੰਜਰੇਕਰ, ਮਿਊਰ |
| `-ਬ` | `-ਨ` | 17 words | ਬੈਗੁਈਸੇਨ, ਬ੍ਰੇਮੇਨ |
| `-ਪ` | `-ਨ` | 16 words | ਪੋਥਨ, ਪ੍ਰਸਾਸਨ |
| `-ਰ` | `-ਨ` | 16 words | ਰੂਪਵਾਨ, ਰਘੂਨਾਥਨ |

### 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 |
|------|-----------------|------------|------|
| intentions | **`intention-s`** | 4.5 | `intention` |
| ਅਤਾਉੱਲ੍ਹਾ | **`ਅ-ਤ-ਾਉੱਲ੍ਹਾ`** | 4.5 | `ਾਉੱਲ੍ਹਾ` |
| orientale | **`oriental-e`** | 4.5 | `oriental` |
| presented | **`present-ed`** | 4.5 | `present` |
| ecosystems | **`ecosystem-s`** | 4.5 | `ecosystem` |
| ਵਿਸ਼ਵੰਭਰਨ | **`ਵਿਸ਼ਵੰਭਰ-ਨ`** | 4.5 | `ਵਿਸ਼ਵੰਭਰ` |
| commissioner | **`commission-er`** | 4.5 | `commission` |
| potentials | **`potential-s`** | 4.5 | `potential` |
| ਅਜ਼ਹੇਂਦਰਾ | **`ਅ-ਜ-਼ਹੇਂਦਰਾ`** | 4.5 | `਼ਹੇਂਦਰਾ` |
| manhattans | **`manhattan-s`** | 4.5 | `manhattan` |
| neighbors | **`neighbor-s`** | 4.5 | `neighbor` |
| ਹਾਰਪਰਕੋਲਿਨਸ | **`ਹਾਰਪਰਕੋਲਿਨ-ਸ`** | 4.5 | `ਹਾਰਪਰਕੋਲਿਨ` |
| audiobooks | **`audiobook-s`** | 4.5 | `audiobook` |
| capitalists | **`capitalist-s`** | 4.5 | `capitalist` |
| ਇਲੈਕਟ੍ਰਾਨ | **`ਇਲੈਕਟ੍ਰਾ-ਨ`** | 4.5 | `ਇਲੈਕਟ੍ਰਾ` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Punjabi 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 (4.04x) |
| N-gram | **2-gram** | Lowest perplexity (1,824) |
| Markov | **Context-4** | Highest predictability (93.6%) |
| 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 19:32:35*