---
language: ps
language_name: Pashto
language_family: iranian_eastern
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-iranian_eastern
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: 3.755
  - name: best_isotropy
    type: isotropy
    value: 0.8418
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Pashto** 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** | 3.070x | 3.07 | 0.0575% | 1,690,830 |
| **16k** | 3.354x | 3.35 | 0.0628% | 1,547,668 |
| **32k** | 3.584x | 3.58 | 0.0671% | 1,448,273 |
| **64k** | 3.755x 🏆 | 3.76 | 0.0703% | 1,382,248 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ډیلي د ختیځ تیمور هیواد پلازمینه یاد ښار د ختیځ تیمور اصلی بندر او تجارتی مرکز ګ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ډیلي ▁د ▁ختیځ ▁تیمور ▁هیواد ▁پلازمینه ▁یاد ▁ښار ▁د ▁ختیځ ... (+27 more)` | 37 |
| 16k | `▁ډیلي ▁د ▁ختیځ ▁تیمور ▁هیواد ▁پلازمینه ▁یاد ▁ښار ▁د ▁ختیځ ... (+25 more)` | 35 |
| 32k | `▁ډیلي ▁د ▁ختیځ ▁تیمور ▁هیواد ▁پلازمینه ▁یاد ▁ښار ▁د ▁ختیځ ... (+25 more)` | 35 |
| 64k | `▁ډیلي ▁د ▁ختیځ ▁تیمور ▁هیواد ▁پلازمینه ▁یاد ▁ښار ▁د ▁ختیځ ... (+24 more)` | 34 |

**Sample 2:** `د اشکامش ولسوالۍ د تخار ولايت یوه ولسوالۍ ده. په دغې ولسوالۍ کې د مېشتو خلکو شمې...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁د ▁اش کام ش ▁ولسوالۍ ▁د ▁تخار ▁ولايت ▁یوه ▁ولسوالۍ ... (+21 more)` | 31 |
| 16k | `▁د ▁اش کام ش ▁ولسوالۍ ▁د ▁تخار ▁ولايت ▁یوه ▁ولسوالۍ ... (+21 more)` | 31 |
| 32k | `▁د ▁اش کام ش ▁ولسوالۍ ▁د ▁تخار ▁ولايت ▁یوه ▁ولسوالۍ ... (+21 more)` | 31 |
| 64k | `▁د ▁اش کام ش ▁ولسوالۍ ▁د ▁تخار ▁ولايت ▁یوه ▁ولسوالۍ ... (+20 more)` | 30 |

**Sample 3:** `اورګان آیالات (آورګان) یاهم (اوریګون) په انګلیسي Oregon) د امریکا متحده آیالاتون...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁اورګ ان ▁آیالات ▁( آ ور ګان ) ▁یاهم ▁( ... (+20 more)` | 30 |
| 16k | `▁اورګ ان ▁آیالات ▁( آ ور ګان ) ▁یاهم ▁( ... (+19 more)` | 29 |
| 32k | `▁اورګ ان ▁آیالات ▁( آ ور ګان ) ▁یاهم ▁( ... (+19 more)` | 29 |
| 64k | `▁اورګان ▁آیالات ▁( آ ورګان ) ▁یاهم ▁( ا وری ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 64k achieves 3.755x compression
- **Lowest UNK Rate:** 8k with 0.0575% 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 | 45,674 | 15.48 | 297,254 | 12.5% | 28.9% |
| **2-gram** | Subword | 413 🏆 | 8.69 | 15,507 | 59.5% | 95.4% |
| **3-gram** | Word | 171,855 | 17.39 | 538,733 | 5.2% | 14.6% |
| **3-gram** | Subword | 3,798 | 11.89 | 114,771 | 25.0% | 61.5% |
| **4-gram** | Word | 476,041 | 18.86 | 940,357 | 2.8% | 8.3% |
| **4-gram** | Subword | 23,206 | 14.50 | 601,330 | 12.4% | 33.8% |
| **5-gram** | Word | 400,777 | 18.61 | 620,569 | 2.6% | 7.4% |
| **5-gram** | Subword | 97,008 | 16.57 | 1,632,083 | 6.4% | 20.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `کې د` | 101,609 |
| 2 | `چې د` | 81,225 |
| 3 | `او د` | 75,622 |
| 4 | `چې په` | 35,921 |
| 5 | `په توګه` | 27,634 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `په کال کې` | 16,971 |
| 2 | `کال کې د` | 10,963 |
| 3 | `د کال د` | 7,888 |
| 4 | `په زکال کې` | 6,540 |
| 5 | `حال کې چې` | 6,283 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `په کال کې د` | 6,807 |
| 2 | `په داسې حال کې` | 5,964 |
| 3 | `په ز کال کې` | 5,740 |
| 4 | `داسې حال کې چې` | 5,705 |
| 5 | `په زکال کې د` | 2,929 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `په داسې حال کې چې` | 5,659 |
| 2 | `په ز کال کې د` | 2,507 |
| 3 | `داسې حال کې چې د` | 1,709 |
| 4 | `زکال څخه تر زکال پورې` | 656 |
| 5 | `له زکال څخه تر زکال` | 644 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ه _` | 2,871,045 |
| 2 | `_ د` | 1,942,072 |
| 3 | `ې _` | 1,592,102 |
| 4 | `و _` | 1,523,631 |
| 5 | `د _` | 1,482,416 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د _` | 1,230,113 |
| 2 | `پ ه _` | 685,331 |
| 3 | `_ پ ه` | 666,884 |
| 4 | `_ ا و` | 512,538 |
| 5 | `ا و _` | 430,611 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ پ ه _` | 666,254 |
| 2 | `_ ا و _` | 419,517 |
| 3 | `_ ک ې _` | 323,812 |
| 4 | `ې _ د _` | 278,354 |
| 5 | `_ چ ې _` | 264,546 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ې _ پ ه _` | 117,595 |
| 2 | `_ ک ې _ د` | 110,616 |
| 3 | `و _ پ ه _` | 102,895 |
| 4 | `ک ې _ د _` | 100,894 |
| 5 | `_ چ ې _ د` | 100,640 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 413
- **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 | 0.8526 | 1.806 | 8.06 | 503,287 | 14.7% |
| **1** | Subword | 1.0126 | 2.018 | 8.82 | 4,882 | 0.0% |
| **2** | Word | 0.3595 | 1.283 | 2.20 | 4,051,006 | 64.1% |
| **2** | Subword | 0.8406 | 1.791 | 5.62 | 43,065 | 15.9% |
| **3** | Word | 0.1526 | 1.112 | 1.34 | 8,883,549 | 84.7% |
| **3** | Subword | 0.7785 | 1.715 | 4.36 | 241,991 | 22.2% |
| **4** | Word | 0.0613 🏆 | 1.043 | 1.11 | 11,890,030 | 93.9% |
| **4** | Subword | 0.6609 | 1.581 | 3.11 | 1,054,058 | 33.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `د واقعیت کې په اصل د ناردرن پوهنتون کې په سیمه کي د سوریې د محاصرې`
2. `په او په بڼه پراخه ډله پالو جنگیالیو ویاړونه یې له طبیعي قانون هغه نور یې`
3. `او رازمحمد محمدی له زياتو اسنتياوو ځه زه يم چې له بدلون په خاطر رامنځته او`

**Context Size 2:**

1. `کې د ولسمشرۍ په ماڼۍ کي پيل کيژي اوداسد په مياشت كې كله پيسي زياتيږي او په`
2. `چې د سلطنتي کورنۍ تر نظارت لاندي زده کړي هغه په کاملو پاڼو کې لټوی او خپل`
3. `او د جاپان ریل پټلۍ ورغوي نور انجینري فلزي محصولات ۲۱ ۱ صف‌ ۲۱ ۲ ميليونه ټنونو`

**Context Size 3:**

1. `په کال کې په همدې کنفرانس کې تقریبآ ۳۵۰ملی او نړيوالو چینلونو او رسنیو له خوا د ۳۰`
2. `کال کې د دوهم وېلهليم لخوا د اوټو ون بسمارک د حکومت مشر او د چين له حکومت`
3. `د کال د جولای په ۲۸ یې د پيلوټۍ شمېره تصدیقنامه او د کال تر جنورۍ پورې یې`

**Context Size 4:**

1. `په کال کې د bienvenue à monseigneur le duc d anjou په نوم د ماشومانو لپاره په کابل کې`
2. `په داسې حال کې چې پلازمېنه يې د سيوډاډ ډي پورټو ريکو شتمن بندري ښار نومېږي بالاخره سوداګرو او`
3. `په ز کال کې فواره تر څنډو fountain overflows دا رښتينې شپه this real night چې له مړينې څخه`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_«_ر_(_زړيخیاړیق`
2. `ور_خه_څخه_نګو_او`
3. `ارسیېرد_کاسې_ځام`

**Context Size 2:**

1. `ه_هم_وکرښت_ده_يا_`
2. `_د_بری_ژونکي_او_ا`
3. `ې_ځړانسولى_دو_له_`

**Context Size 3:**

1. `_د_معبدالقرنيو_سره`
2. `په_طبیعي_سره_تعریف`
3. `_په_هغې_د_انسان_کړ`

**Context Size 4:**

1. `_په_توګه_يې_ادب_په_`
2. `_او_21_cfr_pass_emp`
3. `_کې_دا_بڼو_او_اړخون`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,054,058 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 | 217,546 |
| Total Tokens | 14,149,518 |
| Mean Frequency | 65.04 |
| Median Frequency | 4 |
| Frequency Std Dev | 3465.58 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | د | 1,254,743 |
| 2 | په | 675,956 |
| 3 | او | 421,489 |
| 4 | کې | 342,021 |
| 5 | چې | 274,692 |
| 6 | له | 235,307 |
| 7 | ته | 126,758 |
| 8 | سره | 101,317 |
| 9 | هغه | 92,015 |
| 10 | څخه | 87,815 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | زېډ | 2 |
| 2 | تیموری | 2 |
| 3 | الأحمر | 2 |
| 4 | البشتون | 2 |
| 5 | بیټسمینانو | 2 |
| 6 | فیبوناسي | 2 |
| 7 | لسیال | 2 |
| 8 | بوګیا | 2 |
| 9 | abridgement | 2 |
| 10 | needhams | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0558 |
| R² (Goodness of Fit) | 0.993922 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 43.4% |
| Top 1,000 | 64.5% |
| Top 5,000 | 80.5% |
| Top 10,000 | 86.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9939 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 43.4% of corpus
- **Long Tail:** 207,546 words needed for remaining 13.7% 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 | 0.8418 | 0.3831 | N/A | N/A |
| **mono_64d** | 64 | 0.8348 | 0.3051 | N/A | N/A |
| **mono_128d** | 128 | 0.8087 | 0.2314 | N/A | N/A |
| **aligned_32d** | 32 | 0.8418 🏆 | 0.3891 | 0.0500 | 0.2360 |
| **aligned_64d** | 64 | 0.8348 | 0.3128 | 0.1100 | 0.3720 |
| **aligned_128d** | 128 | 0.8087 | 0.2225 | 0.1160 | 0.3960 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8418 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3073. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 11.6% 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 | **-0.638** | 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 |
|--------|----------|
| `-ا` | اقاخان, امویانو, الکینو |
| `-د` | داراز, دانګوروشراب, دسروالجيانو |
| `-م` | مالټ, منځنۍ, مگزين |
| `-او` | اوباسو, اوتوبيوګرافي, اورونوکنترول |
| `-ال` | الکینو, الشعرا, الګوري |
| `-و` | وايى, وطنونه, وبسایټ |
| `-ب` | بوډا, بيلولو, برېـښي |
| `-س` | سوخوی, سیکھ, سرای |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-و` | امویانو, ليدو, الکینو |
| `-ه` | رواده, خايسته, وطنونه |
| `-ي` | پيداکیږي, شېرعلي, اوتوبيوګرافي |
| `-نو` | امویانو, الکینو, ګابېنونو |
| `-ن` | اقاخان, هېډن, چمپین |
| `-s` | eats, specimens, dinosaurs |
| `-نه` | وطنونه, ختنه, ټيپونه |
| `-ې` | پياوړې, سوړې, کرايې |

### 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` | 3.19x | 58 contexts | aktion, option, cation |
| `وونک` | 1.73x | 355 contexts | کوونک, وونکی, وونکو |
| `دونک` | 1.76x | 186 contexts | دونکی, یدونکی, ندونکي |
| `وادو` | 2.00x | 64 contexts | موادو, وادوڅ, دموادو |
| `رسره` | 2.39x | 29 contexts | ترسره, درسره, ورسره |
| `تاری` | 2.18x | 39 contexts | تاریخ, تاریم, تاریځ |
| `ځانګ` | 2.13x | 39 contexts | ځانګړ, ځانګو, ځانګې |
| `ادون` | 1.67x | 100 contexts | مادون, يادون, یادون |
| `وړان` | 1.80x | 63 contexts | وړانی, وړانګ, وړاند |
| `ولای` | 1.67x | 87 contexts | كولای, دولای, کولای |
| `غانس` | 2.97x | 11 contexts | افغانست, فغانستان, افغانستا |
| `وموړ` | 2.18x | 28 contexts | وموړې, نوموړ, نوموړﺉ |

### 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` | `-ي` | 94 words | امازوني, اوپاتي |
| `-ا` | `-ن` | 60 words | الکافرون, الجنون |
| `-م` | `-و` | 56 words | مرخيړيو, ملېشو |
| `-ا` | `-ه` | 56 words | اخلاقپوه, ایونونه |
| `-ا` | `-و` | 55 words | انجيلو, اليساندرو |
| `-د` | `-و` | 46 words | دکوندو, دیلانو |
| `-د` | `-ه` | 44 words | دډيروخلکولپاره, درنه |
| `-م` | `-ه` | 42 words | ماړه, ماډله |
| `-ک` | `-و` | 37 words | کرهنیزو, کټګوریو |
| `-و` | `-ه` | 35 words | واه, وځلوله |

### 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 |
|------|-----------------|------------|------|
| ماشومانوته | **`ماشومانو-ت-ه`** | 7.5 | `ت` |
| دماشينونو | **`دماشي-نو-نو`** | 7.5 | `نو` |
| سلوبونوکي | **`سلوبو-نو-کي`** | 7.5 | `نو` |
| دالکینونو | **`دالکی-نو-نو`** | 7.5 | `نو` |
| ميلیونونه | **`ميلیو-نو-نه`** | 7.5 | `نو` |
| تصمیم‌نیوونې | **`تصمیم‌نیو-و-نې`** | 7.5 | `و` |
| مسلمانانود | **`مسلمانا-نو-د`** | 7.5 | `نو` |
| فزیکپوهنه | **`فزیکپو-ه-نه`** | 7.5 | `ه` |
| بیتکوینونه | **`بیتکوی-نو-نه`** | 7.5 | `نو` |
| سازمونونه | **`سازمو-نو-نه`** | 7.5 | `نو` |
| مېلمستونونه | **`مېلمستو-نو-نه`** | 7.5 | `نو` |
| مالکیتونو | **`مالکیت-و-نو`** | 7.5 | `و` |
| بریتانیوی | **`بریتانی-و-ی`** | 7.5 | `و` |
| نورکارونه | **`ن-ور-کارونه`** | 6.0 | `کارونه` |
| الوتونکيو | **`ال-وتونکي-و`** | 6.0 | `وتونکي` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Pashto 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 (3.76x) |
| N-gram | **2-gram** | Lowest perplexity (413) |
| Markov | **Context-4** | Highest predictability (93.9%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-10 19:12:45*