RESEARCH_REPORT.md

# Arabic — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **Arabic** Wikipedia data by [Wikilangs](https://wikilangs.org).

👈 [Back to README](README.md)

## 📋 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** | 3.251x | 3.25 | 0.0702% | 5,509,050 |
| **16k** | 3.654x | 3.65 | 0.0788% | 4,901,830 |
| **32k** | 4.033x | 4.03 | 0.0870% | 4,440,712 |
| **64k** | 4.347x 🏆 | 4.35 | 0.0938% | 4,120,770 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `استوديوهات أفلام والت ديزني أفلام والت ديزني منتجع والت ديزني العالمي ديزني لاند...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁است ودي وه ات ▁أفلام ▁والت ▁دي ز ني ▁أفلام ... (+22 more)` | 32 |
| 16k | `▁است ودي وهات ▁أفلام ▁والت ▁ديزني ▁أفلام ▁والت ▁ديزني ▁منت ... (+10 more)` | 20 |
| 32k | `▁استوديوهات ▁أفلام ▁والت ▁ديزني ▁أفلام ▁والت ▁ديزني ▁منتجع ▁والت ▁ديزني ... (+7 more)` | 17 |
| 64k | `▁استوديوهات ▁أفلام ▁والت ▁ديزني ▁أفلام ▁والت ▁ديزني ▁منتجع ▁والت ▁ديزني ... (+7 more)` | 17 |

**Sample 2:** `باسكال قد تعني: الباسكال، وحدة قياس الضغط لغة باسكال، لغة برمجة الفيلسوف باسكال،...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁با سك ال ▁قد ▁تعني : ▁البا سك ال ، ... (+29 more)` | 39 |
| 16k | `▁باسكال ▁قد ▁تعني : ▁الباسك ال ، ▁وحدة ▁قياس ▁الضغط ... (+18 more)` | 28 |
| 32k | `▁باسكال ▁قد ▁تعني : ▁الباسك ال ، ▁وحدة ▁قياس ▁الضغط ... (+15 more)` | 25 |
| 64k | `▁باسكال ▁قد ▁تعني : ▁الباسك ال ، ▁وحدة ▁قياس ▁الضغط ... (+15 more)` | 25 |

**Sample 3:** `جمهورية الكونغو الديمقراطية، زائير سابقًا، عاصمتها كينشاسا. جمهورية الكونغو، عاص...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁جمهورية ▁الكون غو ▁الديمقراطية ، ▁ز ائ ير ▁سابق ًا ... (+21 more)` | 31 |
| 16k | `▁جمهورية ▁الكونغو ▁الديمقراطية ، ▁ز ائ ير ▁سابقًا ، ▁عاصمتها ... (+16 more)` | 26 |
| 32k | `▁جمهورية ▁الكونغو ▁الديمقراطية ، ▁زائ ير ▁سابقًا ، ▁عاصمتها ▁كينشاسا ... (+12 more)` | 22 |
| 64k | `▁جمهورية ▁الكونغو ▁الديمقراطية ، ▁زائير ▁سابقًا ، ▁عاصمتها ▁كينشاسا . ... (+10 more)` | 20 |


### Key Findings

- **Best Compression:** 64k achieves 4.347x compression
- **Lowest UNK Rate:** 8k with 0.0702% 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 | 359,826 | 18.46 | 2,030,200 | 4.4% | 13.3% |
| **2-gram** | Subword | 426 🏆 | 8.73 | 44,225 | 56.3% | 96.2% |
| **3-gram** | Word | 775,988 | 19.57 | 2,900,317 | 3.0% | 10.9% |
| **3-gram** | Subword | 4,163 | 12.02 | 321,654 | 24.3% | 56.3% |
| **4-gram** | Word | 1,494,234 | 20.51 | 4,693,107 | 2.8% | 10.2% |
| **4-gram** | Subword | 27,277 | 14.74 | 1,666,030 | 13.3% | 31.5% |
| **5-gram** | Word | 1,059,510 | 20.01 | 3,368,028 | 3.6% | 11.9% |
| **5-gram** | Subword | 133,736 | 17.03 | 5,324,551 | 5.8% | 18.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `في عام` | 137,432 |
| 2 | `في القرن` | 92,611 |
| 3 | `كرة قدم` | 88,053 |
| 4 | `العديد من` | 65,695 |
| 5 | `الولايات المتحدة` | 63,417 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `في القرن 20` | 27,502 |
| 2 | `في الولايات المتحدة` | 25,188 |
| 3 | `على الرغم من` | 25,111 |
| 4 | `في القرن 21` | 20,515 |
| 5 | `بما في ذلك` | 18,931 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `كرة قدم مغتربون في` | 15,717 |
| 2 | `تحت سن الثامنة عشر` | 13,585 |
| 3 | `على الرغم من أن` | 8,756 |
| 4 | `في الألعاب الأولمبية الصيفية` | 5,980 |
| 5 | `عام بلغ عدد سكان` | 5,886 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `تعداد عام بلغ عدد سكان` | 5,588 |
| 2 | `بحسب تعداد عام وبلغ عدد` | 5,569 |
| 3 | `تعداد عام وبلغ عدد الأسر` | 5,569 |
| 4 | `نسمة بحسب تعداد عام وبلغ` | 5,566 |
| 5 | `في الفئة العمرية ما بين` | 5,561 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ا ل` | 27,516,669 |
| 2 | `_ ا` | 23,616,110 |
| 3 | `ة _` | 13,152,069 |
| 4 | `ن _` | 9,255,735 |
| 5 | `ي _` | 9,009,959 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ا ل` | 22,248,047 |
| 2 | `ا ل م` | 4,149,844 |
| 3 | `ي ة _` | 4,126,642 |
| 4 | `_ ف ي` | 4,065,816 |
| 5 | `ف ي _` | 3,976,227 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ف ي _` | 3,688,677 |
| 2 | `ة _ ا ل` | 3,625,657 |
| 3 | `_ ا ل م` | 3,573,633 |
| 4 | `ن _ ا ل` | 2,468,103 |
| 5 | `_ م ن _` | 2,362,149 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ف ي _ ا ل` | 1,266,206 |
| 2 | `_ ف ي _ ا` | 1,245,053 |
| 3 | `ا ت _ ا ل` | 1,085,180 |
| 4 | `_ ع ل ى _` | 1,078,435 |
| 5 | `ي ة _ ا ل` | 1,036,752 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 426
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~18% 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 | 1.0468 | 2.066 | 15.08 | 2,190,668 | 0.0% |
| **1** | Subword | 1.2063 | 2.307 | 11.28 | 11,477 | 0.0% |
| **2** | Word | 0.3256 | 1.253 | 2.03 | 33,010,787 | 67.4% |
| **2** | Subword | 0.8269 | 1.774 | 5.80 | 129,485 | 17.3% |
| **3** | Word | 0.1052 | 1.076 | 1.21 | 67,054,969 | 89.5% |
| **3** | Subword | 0.7049 | 1.630 | 4.15 | 751,177 | 29.5% |
| **4** | Word | 0.0350 🏆 | 1.025 | 1.06 | 81,123,579 | 96.5% |
| **4** | Subword | 0.6481 | 1.567 | 3.38 | 3,113,652 | 35.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `في الألعاب الآسيوية خاض جهادًا فالأقدر قتالًا شديدًا تولَّى من حيث كانوا في المناهج العلاجية في`
2. `من حيث منعت استخدام مصطلح من الخلايا battery of america bureau of the baskervilles العديد من`
3. `على التلال وهي عضو النادي مبارياته الدولية بعد فوز فرنسا بيافرا التي عززت المظهر الخارجي للمبنى`

**Context Size 2:**

1. `في عام وقد انتقل بعض أفراد فرقته إلى فرقة المسرح الكويتي مسرح الرواد في هذا المجال غونار`
2. `في القرن 20 يابانيون في القرن 20 ذكور في سينيما ماراثية من دلهي النحات الرئيسي والمسؤول الرئيسي`
3. `كرة قدم مغتربون في الولايات المتحدة وبريطانيا العظمى والهجينة على مركبة فضائية مأهولة في منطقة كوم ا...`

**Context Size 3:**

1. `في القرن 20 أمريكيون في القرن 21 هـ في القاهرة 923 هـ في القاهرة بالعربية في القرن 7`
2. `على الرغم من محدودية علمهم ومستواهما الثقافي إلا أنهما كانا تابعين لأمير بلدة فيدين البلغاري ميخائيل...`
3. `في الولايات المتحدة تصغير يسار ترجمة لاتينية عمرها خمس مائة عام لكتاب القانون في الطب لابن سينا وقال`

**Context Size 4:**

1. `كرة قدم مغتربون في فرنسا كيداه منتخب ماليزيا لكرة القدم روابط خارجية مراجع رجال ناميبيون في القرن 21...`
2. `تحت سن الثامنة عشر ونسبة 18 3 في الخامسة والستين من العمر وما فوق تعداد عام بلغ عدد سكان`
3. `على الرغم من أن الاكتشافات الأثرية لا تدعم هذه النظرية حيث أن تسمية الألوان الأساسية طبقا للتطور الت...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_التفيهالرزين_ول`
2. `اقاتية_إلوعتحروب`
3. `ل_ب_ي_الجة_الجة_`

**Context Size 2:**

1. `البية_عصرية_على_أ`
2. `_الزهربية._إره_مق`
3. `ة_التعلى_المية_ال`

**Context Size 3:**

1. `_البحر_من_أصبحت_حر`
2. `المصر_السنّة_-_فقد_`
3. `ية_في_wirtugust_ha`

**Context Size 4:**

1. `_في_جنوبيَّة_من_ناثـر`
2. `ة_الممثلين_على_نفسه`
3. `_المسيحيون_فلوريدا.`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (3,113,652 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 | 986,324 |
| Total Tokens | 94,902,130 |
| Mean Frequency | 96.22 |
| Median Frequency | 4 |
| Frequency Std Dev | 4980.31 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | في | 3,714,132 |
| 2 | من | 2,378,870 |
| 3 | على | 1,085,920 |
| 4 | إلى | 833,112 |
| 5 | أن | 489,978 |
| 6 | عام | 455,946 |
| 7 | التي | 369,985 |
| 8 | عن | 368,235 |
| 9 | أو | 366,818 |
| 10 | مع | 331,151 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | وساريكات | 2 |
| 2 | نهايةالمدةفترة | 2 |
| 3 | valachi | 2 |
| 4 | فالمختصون | 2 |
| 5 | المتأسفين | 2 |
| 6 | والمنشغلين | 2 |
| 7 | انحسبت | 2 |
| 8 | غيوان | 2 |
| 9 | moji | 2 |
| 10 | إيمجوي | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9151 |
| R² (Goodness of Fit) | 0.992048 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.0% |
| Top 1,000 | 43.4% |
| Top 5,000 | 63.5% |
| Top 10,000 | 72.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9920 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.0% of corpus
- **Long Tail:** 976,324 words needed for remaining 27.9% 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 | 0.8111 | 0.3617 | N/A | N/A |
| **mono_64d** | 64 | 0.7841 | 0.2928 | N/A | N/A |
| **mono_128d** | 128 | 0.7556 | 0.2345 | N/A | N/A |
| **aligned_32d** | 32 | 0.8111 🏆 | 0.3646 | 0.1340 | 0.4860 |
| **aligned_64d** | 64 | 0.7841 | 0.2939 | 0.2860 | 0.6560 |
| **aligned_128d** | 128 | 0.7556 | 0.2339 | 0.3720 | 0.7660 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8111 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2969. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 37.2% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.353** | 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` | الماكر, الويجرية, العرقيه |
| `-وال` | والمسكيت, والمأذون, والرسو |
| `-و` | وَصِيف, وخلافاً, وبالكيفية |
| `-الم` | الماكر, المحيطان, المتوسِّط |
| `-بال` | بالمدين, بالجماع, بالتأثر |
| `-ب` | بِالنيابة, بالمدين, بقاءة |
| `-ل` | للتمتع, لجرح, لقزم |
| `-م` | مصصم, معاملات, مناظرا |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ا` | تعرضها, مناظرا, فقابلا |
| `-ن` | بالمدين, والمأذون, المحيطان |
| `-ة` | بِالنيابة, الويجرية, وبالكيفية |
| `-ت` | معاملات, والمسكيت, ومُؤسسات |
| `-ي` | اخصابي, الثانيةفي, بيبيمي |
| `-ين` | بالمدين, الغلامين, للهيروجين |
| `-ات` | معاملات, ومُؤسسات, الألقابسنوات |
| `-م` | تسكينهم, مصصم, لقزم |

### 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 |
|------|----------|------------------|----------|
| `ستخد` | 2.56x | 420 contexts | ستخدم, يستخد, تستخد |
| `التع` | 1.70x | 417 contexts | التعس, التعب, التعمد |
| `مجمو` | 2.12x | 120 contexts | مجموة, مجمود, مجموع |
| `استخ` | 1.97x | 149 contexts | استخف, استخم, استخد |
| `تحدة` | 2.82x | 26 contexts | متحدة, ومتحدة, لمتحدة |
| `المق` | 1.38x | 607 contexts | المقد, المقل, المقص |
| `ارات` | 1.31x | 739 contexts | كارات, تارات, دارات |
| `لمنا` | 1.38x | 514 contexts | ظلمنا, حلمنا, لمنار |
| `المج` | 1.39x | 473 contexts | المجل, المجد, المجن |
| `امعة` | 2.14x | 53 contexts | قامعة, دامعة, سامعة |
| `لعال` | 1.76x | 115 contexts | العال, لعالم, لعالي |
| `الحا` | 1.34x | 492 contexts | الحاد, الحاق, الحاف |

### 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 |
|--------|--------|-----------|----------|
| `-ال` | `-ة` | 297 words | المحميّة, العقاقيرية |
| `-ال` | `-ن` | 179 words | القطبيتان, المحتشدين |
| `-ال` | `-ي` | 167 words | السيجومي, الازدي |
| `-و` | `-ا` | 138 words | والكوسا, ومجتهدًا |
| `-ال` | `-ية` | 129 words | العقاقيرية, المُغطية |
| `-ال` | `-ت` | 113 words | الأستكشافات, المتغيِّرات |
| `-ال` | `-ين` | 98 words | المحتشدين, المتخاذلين |
| `-ال` | `-ات` | 97 words | الأستكشافات, المتغيِّرات |
| `-وال` | `-ة` | 72 words | والحرورية, والضرورية |
| `-م` | `-ا` | 64 words | مُؤديًا, مأمونًا |

### 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 |
|------|-----------------|------------|------|
| الهوسيتية | **`الهوسي-ت-ية`** | 7.5 | `ت` |
| وتحويلتين | **`وتحويل-ت-ين`** | 7.5 | `ت` |
| القراخانيين | **`القراخان-ي-ين`** | 7.5 | `ي` |
| فیروزآباد | **`فیروزآب-ا-د`** | 7.5 | `ا` |
| الارسالية | **`الا-رسال-ية`** | 6.0 | `رسال` |
| والمتعلمة | **`وال-متعلم-ة`** | 6.0 | `متعلم` |
| والكيكونغو | **`و-ال-كيكونغو`** | 6.0 | `كيكونغو` |
| والسويسريين | **`و-ال-سويسريين`** | 6.0 | `سويسريين` |
| والنازحون | **`و-ال-نازحون`** | 6.0 | `نازحون` |
| القترائية | **`الق-ترائ-ية`** | 6.0 | `ترائ` |
| للنوميديين | **`لل-نوميدي-ين`** | 6.0 | `نوميدي` |
| والفاندال | **`و-ال-فاندال`** | 6.0 | `فاندال` |
| وبالإجراءات | **`و-بال-إجراءات`** | 6.0 | `إجراءات` |
| بالهليكوبتر | **`ب-ال-هليكوبتر`** | 6.0 | `هليكوبتر` |
| والاستقلابية | **`و-ال-استقلابية`** | 6.0 | `استقلابية` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Arabic 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 (4.35x) |
| N-gram | **2-gram** | Lowest perplexity (426) |
| Markov | **Context-4** | Highest predictability (96.5%) |
| 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 |

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*Generated by Wikilangs Pipeline · 2026-03-04 14:57:25*