---
language: pnb
language_name: Western Panjabi
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: 3.987
  - name: best_isotropy
    type: isotropy
    value: 0.8211
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Western Panjabi - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Western Panjabi** 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** | 3.374x | 3.35 | 0.0495% | 1,253,323 |
| **16k** | 3.663x | 3.64 | 0.0537% | 1,154,342 |
| **32k** | 3.861x | 3.84 | 0.0566% | 1,095,265 |
| **64k** | 3.987x 🏆 | 3.96 | 0.0585% | 1,060,503 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `<font size="+1" بلی size="1" : : : ناں : Pseudotriakis microdon size="1" تے پھرن...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁< font ▁size ="+ 1 " ▁بلی ▁size =" 1 ... (+26 more)` | 36 |
| 16k | `▁< font ▁size ="+ 1 " ▁بلی ▁size =" 1 ... (+25 more)` | 35 |
| 32k | `▁< font ▁size ="+ 1 " ▁بلی ▁size =" 1 ... (+22 more)` | 32 |
| 64k | `▁< font ▁size ="+ 1 " ▁بلی ▁size =" 1 ... (+22 more)` | 32 |

**Sample 2:** `واقعے جم موت ہور دیکھو ہجری شمسی عیسوی کیلنڈر ہجری کیلنڈر حوالے باہرلےجوڑ ہجری ت...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁واقعے ▁جم ▁موت ▁ہور ▁دیکھو ▁ہجری ▁شمسی ▁عیسوی ▁کیلنڈر ▁ہجری ... (+20 more)` | 30 |
| 16k | `▁واقعے ▁جم ▁موت ▁ہور ▁دیکھو ▁ہجری ▁شمسی ▁عیسوی ▁کیلنڈر ▁ہجری ... (+20 more)` | 30 |
| 32k | `▁واقعے ▁جم ▁موت ▁ہور ▁دیکھو ▁ہجری ▁شمسی ▁عیسوی ▁کیلنڈر ▁ہجری ... (+20 more)` | 30 |
| 64k | `▁واقعے ▁جم ▁موت ▁ہور ▁دیکھو ▁ہجری ▁شمسی ▁عیسوی ▁کیلنڈر ▁ہجری ... (+20 more)` | 30 |

**Sample 3:** `thumbnail یورپا مشتری پاندھی دا 6واں چند اے۔ ایہنوں 8 جنوری، وچ گلیلیو نے لبیا س...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁thumbnail ▁یورپ ا ▁مشت ری ▁پاندھی ▁دا ▁ 6 واں ... (+26 more)` | 36 |
| 16k | `▁thumbnail ▁یورپ ا ▁مشتری ▁پاندھی ▁دا ▁ 6 واں ▁چند ... (+23 more)` | 33 |
| 32k | `▁thumbnail ▁یورپ ا ▁مشتری ▁پاندھی ▁دا ▁ 6 واں ▁چند ... (+22 more)` | 32 |
| 64k | `▁thumbnail ▁یورپ ا ▁مشتری ▁پاندھی ▁دا ▁ 6 واں ▁چند ... (+21 more)` | 31 |


### Key Findings

- **Best Compression:** 64k achieves 3.987x compression
- **Lowest UNK Rate:** 8k with 0.0495% 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 | 75,798 | 16.21 | 740,485 | 13.0% | 25.5% |
| **2-gram** | Subword | 455 🏆 | 8.83 | 31,574 | 58.1% | 95.3% |
| **3-gram** | Word | 362,363 | 18.47 | 1,592,960 | 4.5% | 12.9% |
| **3-gram** | Subword | 4,157 | 12.02 | 200,891 | 24.0% | 60.3% |
| **4-gram** | Word | 1,268,078 | 20.27 | 3,340,374 | 2.5% | 7.4% |
| **4-gram** | Subword | 25,110 | 14.62 | 1,043,941 | 12.3% | 32.8% |
| **5-gram** | Word | 1,264,061 | 20.27 | 2,644,505 | 2.5% | 7.3% |
| **5-gram** | Subword | 106,026 | 16.69 | 3,000,396 | 7.2% | 21.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `د ی` | 636,166 |
| 2 | `تو ں` | 423,885 |
| 3 | `نو ں` | 352,128 |
| 4 | `ا ے` | 155,281 |
| 5 | `دے لئی` | 102,000 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `اس د ی` | 29,046 |
| 2 | `انہاں د ی` | 27,692 |
| 3 | `انہاں نو ں` | 24,454 |
| 4 | `font size 1` | 24,402 |
| 5 | `د ی طرف` | 22,242 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ی وجہ تو ں` | 15,972 |
| 2 | `د ی وجہ تو` | 15,769 |
| 3 | `font size 1 size` | 9,010 |
| 4 | `size 1 color black` | 8,781 |
| 5 | `دے ناں تو ں` | 8,743 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `د ی وجہ تو ں` | 15,758 |
| 2 | `font size 1 size 1` | 8,428 |
| 3 | `د ی طرف تو ں` | 7,772 |
| 4 | `size 1 size 1 color` | 6,657 |
| 5 | `1 size 1 color black` | 5,232 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ے _` | 5,428,043 |
| 2 | `ی _` | 4,517,358 |
| 3 | `_ ا` | 4,456,935 |
| 4 | `_ د` | 3,754,809 |
| 5 | `ں _` | 3,049,226 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `د ے _` | 1,633,658 |
| 2 | `ا ں _` | 1,428,031 |
| 3 | `_ د ے` | 1,418,307 |
| 4 | `ت ے _` | 1,198,221 |
| 5 | `_ و چ` | 983,245 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د ے _` | 1,415,850 |
| 2 | `_ و چ _` | 931,900 |
| 3 | `_ ت ے _` | 767,638 |
| 4 | `‏ ‏ ی _` | 616,950 |
| 5 | `د ‏ ‏ ی` | 612,667 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د ‏ ‏ ی` | 612,245 |
| 2 | `د ‏ ‏ ی _` | 604,110 |
| 3 | `_ ت و ‏ ں` | 423,919 |
| 4 | `ت و ‏ ں _` | 421,873 |
| 5 | `و ‏ ‏ ں _` | 329,449 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 455
- **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 | 0.7943 | 1.734 | 9.73 | 826,993 | 20.6% |
| **1** | Subword | 0.7157 | 1.642 | 6.80 | 15,827 | 28.4% |
| **2** | Word | 0.3933 | 1.313 | 2.41 | 8,042,106 | 60.7% |
| **2** | Subword | 0.6609 | 1.581 | 4.50 | 107,498 | 33.9% |
| **3** | Word | 0.1776 | 1.131 | 1.44 | 19,356,492 | 82.2% |
| **3** | Subword | 0.6554 | 1.575 | 3.88 | 483,762 | 34.5% |
| **4** | Word | 0.0843 🏆 | 1.060 | 1.16 | 27,821,467 | 91.6% |
| **4** | Subword | 0.6318 | 1.550 | 3.14 | 1,876,646 | 36.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `دے مطابق لکڑی چھوٹی انتظامی ونڈ سمیں روچک کھیڈ کلب وغیرہ مسجد تعمیر کیتے اکبر خان`
2. `ں ختم ہوئے گئے جتھے تک نوبت وی کِسے نظام الدین جنرل دے لئی جو تپسیا`
3. `وچ ریک تو ں اپنے تعلق اُتے محمول منقول مشاہدہ کرنا چاہندا سی جو عورتاں د`

**Context Size 2:**

1. `د ی قدیم تریخ دی تریخ ہندستان دی ونڈ پیکنگ اوپیرا چین دا سارا دار و مدار`
2. `تو ں انہاں دا ناں خرزادہ سی اصل وچ کمانڈر کمیسار تے ممبر ملکاں د ی فیکٹری`
3. `نو ں جدید بناؤن لئی ورتے جاسکدے نیں کیلیفورنیا وچ اک آفریدی پشتون معاشرے دے رہنماواں تو`

**Context Size 3:**

1. `اس د ی معرفت کہیا گیا سی کہ علم مثلثات کوریاضی دے اک علیحدہ موضوع دے طورپرمتعارف کروائے`
2. `انہاں د ی نظر تو ں مضمون دے مسودہ نگاراں وچو ں اک برج د ی شناخت دا`
3. `انہاں نو ں عذاب خدا دے ذریعہ سزا یافتہ افراد وچو ں چار ملکہ بطور ملکہ نيں پہلی`

**Context Size 4:**

1. `ی وجہ تو ں غیر واضح نيں حالاں کہ تبت دے ناں نو ں شری حمیرہ لکھیا گیا سی`
2. `د ی وجہ تو ں قیدیاں نو ں قتل کر دتا فرانسیسی گورنر ڈوپلے نے مظفر جنگ کيت ی`
3. `font size 1 size 1 color black lonoke county arkansas font 250px دیس صوبہ ساؤتھ ڈیکوٹا راجکعر کلیر ل...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_راٹی،_اٹہہد_حمی`
2. `اوچ_وہنے_منی_و‏ں`
3. `یالأنیدے_آشدھ_مب`

**Context Size 2:**

1. `ے_علیسانہار_کيتاں`
2. `ی_اک_صد_نے_آخری_ش`
3. `_اپنے_بھ_کيتائنگ_`

**Context Size 3:**

1. `دے_لفظاں_وچ_انہ_مظ`
2. `اں_دار_تے_اس_گئی۔_`
3. `_دے_نيں_کہ_ہوری_بی`

**Context Size 4:**

1. `_دے_خیبر_پانی_ھود_ک`
2. `_وچ_سرکارڈ_،_क्रिस_कुलथा`
3. `_تے_انہاں_دے_ہور_اے`


### Key Findings

- **Best Predictability:** Context-4 (word) with 91.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,876,646 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 | 354,441 |
| Total Tokens | 38,365,731 |
| Mean Frequency | 108.24 |
| Median Frequency | 4 |
| Frequency Std Dev | 4606.26 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | دے | 1,417,871 |
| 2 | ں | 946,354 |
| 3 | وچ | 938,439 |
| 4 | تے | 775,429 |
| 5 | ی | 685,094 |
| 6 | د | 647,998 |
| 7 | دا | 502,834 |
| 8 | نے | 448,856 |
| 9 | اے | 445,649 |
| 10 | تو | 435,054 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | گوکلے | 2 |
| 2 | gokula | 2 |
| 3 | سہورا | 2 |
| 4 | سنسنوار | 2 |
| 5 | کٹھمبر | 2 |
| 6 | آغر | 2 |
| 7 | انیردھ | 2 |
| 8 | imadus | 2 |
| 9 | چورامان | 2 |
| 10 | بُندیل | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1062 |
| R² (Goodness of Fit) | 0.989961 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.9% |
| Top 1,000 | 64.4% |
| Top 5,000 | 82.1% |
| Top 10,000 | 87.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9900 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.9% of corpus
- **Long Tail:** 344,441 words needed for remaining 12.1% 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 | 0.8211 🏆 | 0.4072 | N/A | N/A |
| **mono_64d** | 64 | 0.8095 | 0.3302 | N/A | N/A |
| **mono_128d** | 128 | 0.7605 | 0.2826 | N/A | N/A |
| **aligned_32d** | 32 | 0.8211 | 0.3992 | 0.0680 | 0.2880 |
| **aligned_64d** | 64 | 0.8095 | 0.3176 | 0.1360 | 0.4980 |
| **aligned_128d** | 128 | 0.7605 | 0.2618 | 0.2180 | 0.6080 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8211 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3331. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 21.8% 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 | **-0.655** | 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 |
|--------|----------|
| `-ال` | الحرکۃ, الرُّکنِ, الجارود |
| `-ا` | اثرہويا, اورسرکشی, انورؔ |
| `-م` | مستنگ, مولاناعبدالرؤف, مرحمت |
| `-ب` | بیشکتاش, بیوکس, بانسری |
| `-ک` | کومچ, کاراگنڈا, کیبی |
| `-س` | سفین, سپردگی, سامع |
| `-و` | والصلۃ, ویلفئیر, وطواط |
| `-پ` | پرفائزتھے, پیچیدگى, پستاں |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ی` | گھمری, کیبی, کوتای |
| `-ں` | دواخاناں, پستاں, تکبراں |
| `-ا` | کاراگنڈا, شانامتا, اثرہويا |
| `-ن` | ڈینوبیئن, سفین, ٹراجن |
| `-اں` | دواخاناں, پستاں, تکبراں |
| `-s` | uvs, hylocereus, sectors |
| `-ر` | جَور, نذير, فچنر |
| `-ہ` | آئنہ, تےحملہ, ریاضشہزادہ |

### 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` | 3.07x | 58 contexts | tiong, action, kition |
| `ادشا` | 2.58x | 40 contexts | پادشا, ادشاہ, بادشا |
| `بادش` | 2.73x | 27 contexts | بادشا, بادشان, بادشاہ |
| `ھارت` | 2.32x | 48 contexts | طھارت, دھارت, مھارت |
| `یتاں` | 1.94x | 74 contexts | حیتاں, گیتاں, جیتاں |
| `مریک` | 2.32x | 35 contexts | امریک, مریکل, مریکہ |
| `لاقے` | 3.13x | 12 contexts | غلاقے, علاقے, علاقےِ |
| `ردار` | 1.66x | 119 contexts | كردار, قردار, کردار |
| `کومت` | 2.34x | 28 contexts | حکومت, کومتے, ہکومت |
| `حکوم` | 2.07x | 43 contexts | حکومت, حکومٹ, حکومۃ |
| `سلطن` | 2.35x | 26 contexts | سلطنت, سلطنة, سلطنتِ |
| `ستعم` | 2.21x | 26 contexts | مستعمل, استعمی, ستعمال |

### 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 |
|--------|--------|-----------|----------|
| `-ا` | `-ی` | 59 words | ابچلی, البیرنی |
| `-ال` | `-ی` | 41 words | البیرنی, السلیمی |
| `-ا` | `-ں` | 40 words | ایواناں, اخواندیاں |
| `-ا` | `-ا` | 37 words | اڈاندا, اینٹونیا |
| `-ا` | `-اں` | 35 words | ایواناں, اخواندیاں |
| `-م` | `-ی` | 33 words | مائکرونیشی, مرزاجانی |
| `-ک` | `-ی` | 32 words | کابلی, کوریری |
| `-س` | `-ی` | 32 words | سرکھائی, سنگتراشی |
| `-ک` | `-ا` | 28 words | کانازاوا, کيتاگیاتھا |
| `-ا` | `-ن` | 27 words | اوزگین, اکورگان |

### 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 |
|------|-----------------|------------|------|
| انقلابیان | **`انقلاب-ی-ان`** | 7.5 | `ی` |
| حبیریمنیا | **`حبیریم-ن-یا`** | 7.5 | `ن` |
| منموہنیاں | **`منموہن-ی-اں`** | 7.5 | `ی` |
| بناچاہندے | **`ب-نا-چاہندے`** | 7.5 | `چاہندے` |
| والزیارات | **`و-ال-زیارات`** | 6.0 | `زیارات` |
| یونانیدیس | **`یونانی-دی-س`** | 6.0 | `یونانی` |
| protestants | **`protestant-s`** | 4.5 | `protestant` |
| destinations | **`destination-s`** | 4.5 | `destination` |
| والانحطاط | **`و-الانحطاط`** | 4.5 | `الانحطاط` |
| reprinted | **`reprint-ed`** | 4.5 | `reprint` |
| ناخوشگوار | **`نا-خوشگوار`** | 4.5 | `خوشگوار` |
| بازنطینیاں | **`بازنطینی-اں`** | 4.5 | `بازنطینی` |
| اسماعیلاں | **`اسماعیل-اں`** | 4.5 | `اسماعیل` |
| respected | **`respect-ed`** | 4.5 | `respect` |
| اندازاًجنوب | **`ان-د-ازاًجنوب`** | 4.5 | `ازاًجنوب` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Western Panjabi 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 (3.99x) |
| N-gram | **2-gram** | Lowest perplexity (455) |
| Markov | **Context-4** | Highest predictability (91.6%) |
| 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 21:07:05*