---
language: ks
language_name: Kashmiri
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: 4.330
  - name: best_isotropy
    type: isotropy
    value: 0.8234
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kashmiri** 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** | 3.063x | 3.07 | 0.4060% | 110,104 |
| **16k** | 3.479x | 3.49 | 0.4611% | 96,950 |
| **32k** | 3.906x | 3.92 | 0.5177% | 86,347 |
| **64k** | 4.330x 🏆 | 4.34 | 0.5739% | 77,888 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `خال حر چھُ جۆم تہٕ کٔشیٖر ہٕنٛدِ اَنَنت ناگ ضِلہٕ کہِ کۄکَرناگ تَحصیٖلُک اَکھ گا...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁خال ▁حر ▁چھُ ▁جۆم ▁تہٕ ▁کٔشیٖر ▁ہٕنٛدِ ▁اَنَنت ▁ناگ ▁ضِلہٕ ... (+9 more)` | 19 |
| 16k | `▁خال ▁حر ▁چھُ ▁جۆم ▁تہٕ ▁کٔشیٖر ▁ہٕنٛدِ ▁اَنَنت ▁ناگ ▁ضِلہٕ ... (+9 more)` | 19 |
| 32k | `▁خال ▁حر ▁چھُ ▁جۆم ▁تہٕ ▁کٔشیٖر ▁ہٕنٛدِ ▁اَنَنت ▁ناگ ▁ضِلہٕ ... (+9 more)` | 19 |
| 64k | `▁خال ▁حر ▁چھُ ▁جۆم ▁تہٕ ▁کٔشیٖر ▁ہٕنٛدِ ▁اَنَنت ▁ناگ ▁ضِلہٕ ... (+9 more)` | 19 |

**Sample 2:** `<div class="mw-content-ltr" lang="en" dir="ltr"> फ़न छु आख अिनसٲनय आसार.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁< div ▁class =" mw - content - ltr " ... (+24 more)` | 34 |
| 16k | `▁< div ▁class =" mw - content - ltr " ... (+20 more)` | 30 |
| 32k | `▁< div ▁class =" mw - content - ltr " ... (+16 more)` | 26 |
| 64k | `▁< div ▁class =" mw - content - ltr " ... (+16 more)` | 26 |

**Sample 3:** `پۄژھٕ لوو ( کٲشُر : /pɔt͡sʰɨ loːw/ ) چھُ اَکھ کۄکُٹ جانوَر۔ یێمِس چھِ آسان دٔرِ ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁پۄ ژھ ٕ ▁ل وو ▁( ▁کٲشُر ▁: ▁/ p ... (+32 more)` | 42 |
| 16k | `▁پۄ ژھ ٕ ▁ل وو ▁( ▁کٲشُر ▁: ▁/ p ... (+28 more)` | 38 |
| 32k | `▁پۄ ژھ ٕ ▁لوو ▁( ▁کٲشُر ▁: ▁/ p ɔ ... (+25 more)` | 35 |
| 64k | `▁پۄ ژھ ٕ ▁لوو ▁( ▁کٲشُر ▁: ▁/ pɔt͡shɨ ▁lo ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 64k achieves 4.330x compression
- **Lowest UNK Rate:** 8k with 0.4060% 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 | 4,270 | 12.06 | 13,008 | 27.0% | 51.9% |
| **2-gram** | Subword | 717 🏆 | 9.49 | 8,087 | 50.2% | 89.7% |
| **3-gram** | Word | 3,328 | 11.70 | 13,076 | 34.6% | 54.3% |
| **3-gram** | Subword | 5,676 | 12.47 | 43,674 | 18.9% | 53.4% |
| **4-gram** | Word | 3,583 | 11.81 | 18,210 | 38.3% | 53.4% |
| **4-gram** | Subword | 24,823 | 14.60 | 157,731 | 11.7% | 32.1% |
| **5-gram** | Word | 1,886 | 10.88 | 11,592 | 46.3% | 62.4% |
| **5-gram** | Subword | 55,080 | 15.75 | 271,155 | 8.5% | 25.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `مَنٛز چھِ` | 2,057 |
| 2 | `یَتھ مَنٛز` | 1,812 |
| 3 | `چھِ اَکھ` | 1,547 |
| 4 | `تہٕ کٔشیٖر` | 1,382 |
| 5 | `جۆم تہٕ` | 1,348 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `جۆم تہٕ کٔشیٖر` | 1,312 |
| 2 | `چھُ جۆم تہٕ` | 1,188 |
| 3 | `تہٕ کٔشیٖر ہٕنٛدِ` | 1,093 |
| 4 | `تَحصیٖلُک اَکھ گام` | 1,088 |
| 5 | `حَوالہٕ ضِلٕک گام` | 793 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `چھُ جۆم تہٕ کٔشیٖر` | 1,184 |
| 2 | `جۆم تہٕ کٔشیٖر ہٕنٛدِ` | 1,093 |
| 3 | `حَوالہٕ لوٗکھ فِلِم اَداکارہ` | 785 |
| 4 | `فِلمی دور حَوالہٕ لوٗکھ` | 782 |
| 5 | `دور حَوالہٕ لوٗکھ فِلِم` | 782 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `چھُ جۆم تہٕ کٔشیٖر ہٕنٛدِ` | 1,090 |
| 2 | `فِلمی دور حَوالہٕ لوٗکھ فِلِم` | 782 |
| 3 | `دور حَوالہٕ لوٗکھ فِلِم اَداکارہ` | 782 |
| 4 | `فِلمَن مَنٛز چھِ کٲم کَران` | 780 |
| 5 | `یۄس فِلمَن مَنٛز چھِ کٲم` | 780 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ہٕ _` | 56,082 |
| 2 | `ی _` | 51,513 |
| 3 | `ن _` | 50,007 |
| 4 | `س _` | 46,753 |
| 5 | `_ ک` | 41,465 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `نٛ ز _` | 27,467 |
| 2 | `ت ہٕ _` | 26,266 |
| 3 | `_ مَ نٛ` | 25,790 |
| 4 | `مَ نٛ ز` | 25,779 |
| 5 | `_ ت ہٕ` | 20,498 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ مَ نٛ ز` | 25,766 |
| 2 | `مَ نٛ ز _` | 23,974 |
| 3 | `_ ت ہٕ _` | 20,358 |
| 4 | `س _ مَ نٛ` | 12,638 |
| 5 | `_ اَ ک ھ` | 10,503 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ مَ نٛ ز _` | 23,963 |
| 2 | `س _ مَ نٛ ز` | 12,634 |
| 3 | `_ اَ ک ھ _` | 9,937 |
| 4 | `حَ و ا ل ہٕ` | 6,016 |
| 5 | `_ حَ و ا ل` | 6,015 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 717
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.7411 | 1.671 | 4.61 | 79,386 | 25.9% |
| **1** | Subword | 1.0067 | 2.009 | 8.33 | 2,814 | 0.0% |
| **2** | Word | 0.2063 | 1.154 | 1.44 | 364,441 | 79.4% |
| **2** | Subword | 0.7176 | 1.644 | 4.49 | 23,416 | 28.2% |
| **3** | Word | 0.0596 | 1.042 | 1.10 | 521,272 | 94.0% |
| **3** | Subword | 0.5951 | 1.511 | 3.13 | 105,115 | 40.5% |
| **4** | Word | 0.0192 🏆 | 1.013 | 1.03 | 566,067 | 98.1% |
| **4** | Subword | 0.4756 | 1.391 | 2.20 | 328,354 | 52.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `مَنٛز سارِوٕے کھوتہٕ زیٛادٕ گَژھَن ماس کمیونیکیشن مصنوعات کھیوان ٲسؠ پنٕنؠ بناونِک لاگت آیہ زنانہٕ پ...`
2. `تہٕ مَنٛز کَنٹراسٹ ایجَنٹُک اِنجَکشَن کَرنہٕ آمژ وسیع علاقہٕ جموں و سلم پیشین گوئی سیتھ بنییٛے`
3. `اَکھ علاقہٕ جموں و کشمیر نیشنل میوزیم بیکتاشی آرڈرٕچ خۄدمۄختار مُلکٕک پٲٹھؠ صوفی سنت أمس پننس`

**Context Size 2:**

1. `مَنٛز چھِ واریاہ لکھ چھ شب برات تہوارس غلطی کران تکیاز یہِ چھ ہیری پوٹر رون ویٖضلی`
2. `یَتھ مَنٛز تَمام جِسمٕچ خوٗن رَگہٕ شٲمِل چھِ یِمن پرٛؠتھ أکِس پنٕنؠ مزاحیہ مہم جوئی آسان ییٚلہِ`
3. `چھِ اَکھ بھرپور سۄنہٕ زرد رنگ چھُ فراہم کران ڈُوَلنگو چھِ بأتن پیٚٹھ کورسز پیش کران سہ`

**Context Size 3:**

1. `جۆم تہٕ کٔشیٖر ہٕنٛدِ جۆم ضِلہٕ کہِ رنبیر سِنگھ پورہ تَحصیٖلُک اَکھ گام اَتھ گامَس مَنٛز چھِ 107`
2. `چھُ جۆم تہٕ کٔشیٖر ہٕنٛدِ جۆم ضِلہٕ کہِ رنبیر سِنگھ پورہ تَحصیٖلُک اَکھ گام حَوالہٕ ناگ ضِلٕک گام`
3. `تہٕ کٔشیٖر ہٕنٛدِ اَنَنت ناگ ضِلہٕ کہِ ڈورو تَحصیٖلُک اَکھ گام اَتھ گامَس مَنٛز چھِ 92 گَرٕ اَمہِ`

**Context Size 4:**

1. `چھُ جۆم تہٕ کٔشیٖر ہٕنٛدِ جۆم ضِلہٕ کہِ رنبیر سِنگھ پورہ تَحصیٖلُک اَکھ گام اَتھ گامَس مَنٛز چھِ 20`
2. `جۆم تہٕ کٔشیٖر ہٕنٛدِ اَنَنت ناگ ضِلہٕ کہِ لارنوٗ تَحصیٖلُک اَکھ گام حَوالہٕ ناگ ضِلٕک گام ناگ ذِلٕک...`
3. `دور حَوالہٕ لوٗکھ فِلِم اَداکارہ لوٗکھ صٔدی ہٕنٛد ہِندوستٲنؠ گُلوکار لوٗکہٕ گُلوکار زَنان لوٗکہٕ گُل...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ند_کھ_kegutrees`
2. `البے۔_حال_ادینعٲ`
3. `یکین_رٗکٗنہٕ_و۔_اَمق`

**Context Size 2:**

1. `ہٕ_یاہیم_زٕ_100_زَبا`
2. `ی_پیٚٹھ_زیٛادٕ_ؤرِیائ`
3. `ن_خیاہندگی_سائزس_`

**Context Size 3:**

1. `نٛز_غصہٕک_قٔطیُک_مولوج`
2. `تہٕ_کہِ_رپورٹرین_تہٕ_`
3. `_مَنٛز_سِکیمیانہٕ_خٲطرٕ`

**Context Size 4:**

1. `_مَنٛز_شۆروٗع_آمژ،_خاص`
2. `مَنٛز_اَکھ_گام_تَحصیٖلُک_`
3. `_تہٕ_ہندی_ٹی_ویژن_اد`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (328,354 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 | 32,062 |
| Total Tokens | 620,162 |
| Mean Frequency | 19.34 |
| Median Frequency | 3 |
| Frequency Std Dev | 238.99 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | مَنٛز | 25,769 |
| 2 | تہٕ | 20,507 |
| 3 | اَکھ | 10,418 |
| 4 | چھِ | 10,313 |
| 5 | چھ | 10,180 |
| 6 | چھُ | 9,013 |
| 7 | حَوالہٕ | 6,011 |
| 8 | پؠٹھ | 5,446 |
| 9 | سٟتؠ | 5,087 |
| 10 | اوس | 3,680 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | چھوٗٹؠ | 2 |
| 2 | سیٖلو | 2 |
| 3 | تِلوان | 2 |
| 4 | واگور | 2 |
| 5 | تِعدادس | 2 |
| 6 | لوُکھ | 2 |
| 7 | jund | 2 |
| 8 | جند | 2 |
| 9 | سیلیوٹ | 2 |
| 10 | آتمٲیی | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0333 |
| R² (Goodness of Fit) | 0.995367 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.8% |
| Top 1,000 | 63.0% |
| Top 5,000 | 82.2% |
| Top 10,000 | 89.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9954 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.8% of corpus
- **Long Tail:** 22,062 words needed for remaining 10.5% 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 | 0.8234 | 0.3376 | N/A | N/A |
| **mono_64d** | 64 | 0.5243 | 0.3031 | N/A | N/A |
| **mono_128d** | 128 | 0.1285 | 0.2958 | N/A | N/A |
| **aligned_32d** | 32 | 0.8234 🏆 | 0.3329 | 0.0140 | 0.1300 |
| **aligned_64d** | 64 | 0.5243 | 0.3029 | 0.0340 | 0.1640 |
| **aligned_128d** | 128 | 0.1285 | 0.2888 | 0.0360 | 0.1480 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8234 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3102. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.6% 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 | **1.461** | 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 |
|--------|----------|
| `-ا` | اینیمیشن, امانت, اتھس |
| `-م` | مُقَدَس, مَشِرقَس, موبایل |
| `-ک` | کٔٔر, کمپیوٹیڈ, کارٕبٲری |
| `-ب` | بجائے, برخاست, بٕڑِبَب |
| `-س` | سٹیٹس, سوراخ, سوفوکلیس |
| `-پ` | پرٛانہ, پُنِم, پٮ۪ٹھمِس |
| `-و` | وُڈٕر, ویزلی, وارفرین |
| `-ت` | تِہنٛزِ, تؠمِس, تراناہٕچ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ن` | اینیمیشن, گولڈن, گزینن |
| `-ی` | ندوی, أندی, ؤنی |
| `-س` | سٹیٹس, سوفوکلیس, پٮ۪ٹھمِس |
| `-ک` | پیسِفِک, یمُک, جِسمُک |
| `-ر` | کٔٔر, اِنکار, تشہیر |
| `-ا` | سنیہا, ہانجوٗرا, کَٹریٖنا |
| `-ہ` | پرٛانہ, گولِہ, ساراہ |
| `-ت` | امانت, برخاست, گوٚمُت |

### 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 |
|------|----------|------------------|----------|
| `ستان` | 1.61x | 50 contexts | استان, داستان, استانن |
| `شمیر` | 1.97x | 19 contexts | کشمیر, کشمیرس, کَشمیر |
| `اوان` | 1.68x | 32 contexts | باوان, راوان, ہاوان |
| `اندا` | 1.64x | 31 contexts | اندام, انداز, اندازہ |
| `مریک` | 1.94x | 15 contexts | امریکن, امریکی, امریکا |
| `امری` | 1.86x | 17 contexts | امریش, رامری, امریکن |
| `کشمی` | 1.78x | 19 contexts | کشمیر, لکشمی, لَکشمی |
| `اداک` | 2.01x | 12 contexts | اداکٲر, اداکار, اداکأر |
| `وستا` | 1.85x | 15 contexts | وستاد, ووستاد, دوستانہٕ |
| `اکار` | 1.71x | 19 contexts | ناکارٕ, اداکار, کلاکار |
| `علاق` | 1.78x | 16 contexts | علاقک, علاقو, علاقن |
| `داکا` | 1.93x | 12 contexts | اداکار, اداکاری, اداکارہ |

### 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` | 72 words | انڈسٹری, ایلی |
| `-ا` | `-ن` | 56 words | اخترَن, الدين |
| `-ا` | `-س` | 53 words | اہمیتَس, الاسدس |
| `-ا` | `-ک` | 39 words | البانیاک, اجتیہادک |
| `-م` | `-ن` | 37 words | مٲدانَن, موضوٗعن |
| `-م` | `-ی` | 30 words | مہدی, میلوڈی |
| `-پ` | `-ن` | 26 words | پکچرن, پروڈکشن |
| `-ب` | `-ی` | 25 words | بدعنوانی, بازی |
| `-ک` | `-ن` | 24 words | کوئن, کٔرٕن |
| `-ا` | `-ا` | 22 words | اِنٛدرا, ازولا |

### 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 |
|------|-----------------|------------|------|
| پٲکِستانکین | **`پٲکِستانک-ی-ن`** | 7.5 | `ی` |
| پاکستانکس | **`پاکستان-ک-س`** | 7.5 | `ک` |
| کانٛگرٛیس | **`کانٛگرٛ-ی-س`** | 7.5 | `ی` |
| ایسوسیشنن | **`ایسوسیش-ن-ن`** | 7.5 | `ن` |
| ہِندوستانس | **`ہِندوستان-س`** | 4.5 | `ہِندوستان` |
| کارپوریشنس | **`کارپوریشن-س`** | 4.5 | `کارپوریشن` |
| خاندانٕکؠ | **`خاندانٕک-ؠ`** | 4.5 | `خاندانٕک` |
| برٹھاکُرن | **`برٹھاکُر-ن`** | 4.5 | `برٹھاکُر` |
| یوٗٹیٛوٗبس | **`یوٗٹیٛوٗب-س`** | 4.5 | `یوٗٹیٛوٗب` |
| انٛگریٖزی | **`انٛگریٖز-ی`** | 4.5 | `انٛگریٖز` |
| ٹورنامنٹن | **`ٹورنامنٹ-ن`** | 4.5 | `ٹورنامنٹ` |
| پارلیمنٹس | **`پارلیمنٹ-س`** | 4.5 | `پارلیمنٹ` |
| ایوروپِیَن | **`ای-و-روپِیَن`** | 4.5 | `روپِیَن` |
| فِراعوٗنن | **`فِراعوٗن-ن`** | 4.5 | `فِراعوٗن` |
| ہندوستانٕکی | **`ہندوستانٕک-ی`** | 4.5 | `ہندوستانٕک` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kashmiri 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 (4.33x) |
| N-gram | **2-gram** | Lowest perplexity (717) |
| Markov | **Context-4** | Highest predictability (98.1%) |
| 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 08:34:21*