RESEARCH_REPORT.md

# Moroccan Arabic — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **Moroccan 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** | 3.481x | 3.48 | 0.0910% | 300,053 |
| **16k** | 3.755x | 3.76 | 0.0982% | 278,145 |
| **32k** | 3.985x | 3.99 | 0.1041% | 262,127 |
| **64k** | 4.172x 🏆 | 4.18 | 0.1090% | 250,361 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `قريش هيا قبيلة ؤلا أجموع قبلي لي، علا حساب لمصادر لإسلامية، كانت ف مكة ؤ كاينتام...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ق ريش ▁هيا ▁قبيلة ▁ؤلا ▁أج موع ▁ق بلي ▁لي ... (+19 more)` | 29 |
| 16k | `▁قريش ▁هيا ▁قبيلة ▁ؤلا ▁أج موع ▁ق بلي ▁لي ، ... (+16 more)` | 26 |
| 32k | `▁قريش ▁هيا ▁قبيلة ▁ؤلا ▁أجموع ▁ق بلي ▁لي ، ▁علا ... (+15 more)` | 25 |
| 64k | `▁قريش ▁هيا ▁قبيلة ▁ؤلا ▁أجموع ▁قبلي ▁لي ، ▁علا ▁حساب ... (+14 more)` | 24 |

**Sample 2:** `آيت ميلك جماعة ترابية قروية كاينة في إقليم اشتوكة آيت باها، جهة سوس ماسة، ساكنين...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁آيت ▁ميل ك ▁جماعة ▁ترابية ▁قروية ▁كاينة ▁في ▁إقليم ▁اشتوكة ... (+16 more)` | 26 |
| 16k | `▁آيت ▁ميل ك ▁جماعة ▁ترابية ▁قروية ▁كاينة ▁في ▁إقليم ▁اشتوكة ... (+16 more)` | 26 |
| 32k | `▁آيت ▁ميل ك ▁جماعة ▁ترابية ▁قروية ▁كاينة ▁في ▁إقليم ▁اشتوكة ... (+16 more)` | 26 |
| 64k | `▁آيت ▁ميلك ▁جماعة ▁ترابية ▁قروية ▁كاينة ▁في ▁إقليم ▁اشتوكة ▁آيت ... (+15 more)` | 25 |

**Sample 3:** `خديجة بنت علي بن أبي طالب، هي بنت علي بن أبي طالب. مصادر د نسا`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁خديجة ▁بنت ▁علي ▁بن ▁أبي ▁طالب ، ▁هي ▁بنت ▁علي ... (+7 more)` | 17 |
| 16k | `▁خديجة ▁بنت ▁علي ▁بن ▁أبي ▁طالب ، ▁هي ▁بنت ▁علي ... (+7 more)` | 17 |
| 32k | `▁خديجة ▁بنت ▁علي ▁بن ▁أبي ▁طالب ، ▁هي ▁بنت ▁علي ... (+7 more)` | 17 |
| 64k | `▁خديجة ▁بنت ▁علي ▁بن ▁أبي ▁طالب ، ▁هي ▁بنت ▁علي ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.172x compression
- **Lowest UNK Rate:** 8k with 0.0910% 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 | 7,415 | 12.86 | 40,208 | 22.8% | 50.4% |
| **2-gram** | Subword | 428 🏆 | 8.74 | 5,913 | 57.8% | 96.3% |
| **3-gram** | Word | 5,775 | 12.50 | 44,139 | 27.3% | 56.7% |
| **3-gram** | Subword | 3,823 | 11.90 | 44,840 | 23.0% | 60.5% |
| **4-gram** | Word | 8,149 | 12.99 | 71,489 | 27.3% | 53.3% |
| **4-gram** | Subword | 20,320 | 14.31 | 222,645 | 11.9% | 35.8% |
| **5-gram** | Word | 7,702 | 12.91 | 59,669 | 28.3% | 52.6% |
| **5-gram** | Subword | 63,356 | 15.95 | 533,903 | 7.3% | 24.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `واصلة ل` | 8,540 |
| 2 | `نسبة د` | 7,170 |
| 3 | `ف لمغريب` | 6,310 |
| 4 | `ف إقليم` | 6,015 |
| 5 | `ف نسبة` | 4,265 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ف نسبة د` | 4,264 |
| 2 | `فيها مصدر و` | 3,235 |
| 3 | `و نسبة د` | 2,894 |
| 4 | `مصدر و بايت` | 2,855 |
| 5 | `اللي خدامين ف` | 2,761 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `فيها مصدر و بايت` | 2,855 |
| 2 | `نسبة نّاس اللي خدامين` | 2,705 |
| 3 | `نّاس اللي خدامين ف` | 2,595 |
| 4 | `على حساب لإحصاء الرسمي` | 2,501 |
| 5 | `لمغريب هاد دّوار كينتامي` | 2,500 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `نسبة نّاس اللي خدامين ف` | 2,594 |
| 2 | `ف لمغريب هاد دّوار كينتامي` | 2,500 |
| 3 | `لمغريب هاد دّوار كينتامي ل` | 2,500 |
| 4 | `هاد دّوار كينتامي ل مشيخة` | 2,500 |
| 5 | `حساب لإحصاء الرسمي د عام` | 2,500 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ا ل` | 348,897 |
| 2 | `_ ل` | 282,523 |
| 3 | `ة _` | 230,243 |
| 4 | `_ ا` | 221,714 |
| 5 | `_ م` | 157,830 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ا ل` | 216,894 |
| 2 | `_ ف _` | 84,068 |
| 3 | `ا ت _` | 64,715 |
| 4 | `_ و _` | 60,577 |
| 5 | `ي ة _` | 60,370 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د ي ا` | 48,269 |
| 2 | `د ي ا ل` | 48,014 |
| 3 | `ي ا ل _` | 33,434 |
| 4 | `د _ ا ل` | 33,075 |
| 5 | `_ م ن _` | 29,173 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ د ي ا ل` | 47,884 |
| 2 | `د ي ا ل _` | 33,006 |
| 3 | `_ ع ل ى _` | 19,658 |
| 4 | `_ ا ل ل ي` | 18,939 |
| 5 | `ا ل ل ي _` | 18,733 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 428
- **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 | 0.8581 | 1.813 | 5.40 | 180,421 | 14.2% |
| **1** | Subword | 1.1243 | 2.180 | 8.36 | 2,159 | 0.0% |
| **2** | Word | 0.2267 | 1.170 | 1.49 | 973,633 | 77.3% |
| **2** | Subword | 0.8165 | 1.761 | 5.10 | 18,051 | 18.4% |
| **3** | Word | 0.0619 | 1.044 | 1.10 | 1,450,643 | 93.8% |
| **3** | Subword | 0.8035 | 1.745 | 4.14 | 92,103 | 19.7% |
| **4** | Word | 0.0207 🏆 | 1.014 | 1.04 | 1,595,675 | 97.9% |
| **4** | Subword | 0.6627 | 1.583 | 2.87 | 381,563 | 33.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ف ايكنان نقص ب سباب غتيال لماليك لأمازيغي ؤ ولّا على المنطق والبحث كان حتا زلزال`
2. `و نسبة نّاس اللي سبق ليهوم مصادر ربحو جايزة أحسن 10 سنين موراها تولّا لحكم الداتي`
3. `د لميداليات ف إقليم لحوز جهة مراكش آسفي ف المغرب من بعد باللي كان نتر خيالي`

**Context Size 2:**

1. `واصلة ل 3 ف لعقد ديال عوام كيوافق ف تّقويم لهيجري ؤ ف تّقويم لڭريڭوري بدا نهار`
2. `نسبة د الشوماج واصلة ل 6 6 044 0 290 يوكطوتانية هيدروجين 7 7 و لخصوبة لكاملة`
3. `ف لمغريب هاد دّوار كينتامي ل مشيخة أيت قضني لي كتضم 9 د دّواور لعاداد د سّكان`

**Context Size 3:**

1. `ف نسبة د التسكويل واصلة ل 90 8 و نسبة د لأمية واصلة ل 50 33 لخدمة ف`
2. `فيها مصدر و بايت على حساب النوع د لحنش التشلال التنفوسي فشلان لكبدة لكوما و bites a d`
3. `و نسبة د الشوماج واصلة ل 18 4 و لموعدّال د لعمر عند الجواج اللولاني هوّ 23 87`

**Context Size 4:**

1. `نسبة نّاس اللي خدامين في لقطاع لخاص 39 1 مصادر الرباط سلا القنيطرة قروية ف إقليم لخميسات مسكونين ف`
2. `نّاس اللي خدامين ف لپريڤي 57 1 مصادر الرباط سلا القنيطرة قروية ف إقليم سيدي إيفني جهة ݣلميم واد`
3. `على حساب لإحصاء الرسمي د عام نوطات مصادر ف لمغريب ف إقليم تارودانت زادهوم داريجابوت`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_أو_جة_م_-اسبش_د`
2. `الاف_ف،_عية_لحدا`
3. `لعة_ل_وعبر،_اليب`

**Context Size 2:**

1. `الجديات)._عنصاد_ا`
2. `_لخمسيوسيحطولا_صر`
3. `ة_ديال_لهي_بزرقة_`

**Context Size 3:**

1. `_اللي_خمائيات_ديال`
2. `_ف_لجمهورية_الطابل`
3. `ات_(گاع_ل_من_مابين`

**Context Size 4:**

1. `_ديال_المرسى_ديال_ا`
2. `ديالهوم_مصادر_فيهم_`
3. `يال_شيحد_من_بعد_فـ_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (381,563 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 | 79,667 |
| Total Tokens | 2,057,009 |
| Mean Frequency | 25.82 |
| Median Frequency | 4 |
| Frequency Std Dev | 518.98 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ف | 84,381 |
| 2 | و | 60,856 |
| 3 | د | 60,420 |
| 4 | ديال | 32,966 |
| 5 | من | 29,503 |
| 6 | ل | 23,808 |
| 7 | على | 19,757 |
| 8 | لي | 18,777 |
| 9 | ب | 17,745 |
| 10 | اللي | 17,410 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ختيلال | 2 |
| 2 | تسطية | 2 |
| 3 | التخمار | 2 |
| 4 | لمركزين | 2 |
| 5 | تعلاف | 2 |
| 6 | الروضيو | 2 |
| 7 | رِد | 2 |
| 8 | وينغز | 2 |
| 9 | تايغرز | 2 |
| 10 | كلتة | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0203 |
| R² (Goodness of Fit) | 0.998917 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 38.4% |
| Top 1,000 | 62.8% |
| Top 5,000 | 77.7% |
| Top 10,000 | 84.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9989 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 38.4% of corpus
- **Long Tail:** 69,667 words needed for remaining 15.9% 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 | 0.8215 🏆 | 0.3275 | N/A | N/A |
| **mono_64d** | 64 | 0.8006 | 0.2538 | N/A | N/A |
| **mono_128d** | 128 | 0.6555 | 0.2039 | N/A | N/A |
| **aligned_32d** | 32 | 0.8215 | 0.3276 | 0.0080 | 0.1080 |
| **aligned_64d** | 64 | 0.8006 | 0.2565 | 0.0380 | 0.2000 |
| **aligned_128d** | 128 | 0.6555 | 0.2044 | 0.0440 | 0.2420 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8215 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2623. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.4% 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 | **1.121** | 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 |
|--------|----------|
| `-ال` | القوميين, الاحتياطية, الطابلة |
| `-ل` | لعضان, لكرواتي, لعاميد |
| `-ت` | تقرا, تحقيقات, تشارلي |
| `-م` | ميطاكا, معاهد, موليكيلة |
| `-لم` | لمحلولة, لمقبولين, لمطلوق |
| `-و` | والهيئات, والطرقان, وبطريقة |
| `-الم` | المركب, المعروفين, المناخية |
| `-ب` | بنشليخة, بيئات, بلمارشالية |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ت` | والهيئات, تحقيقات, لبويرات |
| `-ة` | بنشليخة, وبطريقة, عشبة |
| `-ات` | والهيئات, تحقيقات, لبويرات |
| `-ن` | لعضان, والطرقان, القوميين |
| `-ية` | أكترية, الاحتياطية, والاشتراكية |
| `-ا` | ميطاكا, تقرا, سيينا |
| `-ي` | ؤطوماتيكي, لكرواتي, سينتشي |
| `-ين` | القوميين, پيسّين, مشهورين |

### 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 |
|------|----------|------------------|----------|
| `انية` | 1.84x | 68 contexts | سانية, تانية, غانية |
| `النا` | 1.79x | 63 contexts | الناي, الناس, النار |
| `لمغر` | 2.03x | 30 contexts | لمغرب, المغرب, لمغربي |
| `جماع` | 1.89x | 37 contexts | جماعة, إجماع, جماعي |
| `اللو` | 1.66x | 61 contexts | اللون, اللور, اللوز |
| `الات` | 1.59x | 65 contexts | صالات, حالات, سالات |
| `مغري` | 2.11x | 18 contexts | مغرية, مغريب, لمغريب |
| `دهوم` | 2.19x | 16 contexts | ضدهوم, يردهوم, جهدهوم |
| `إحصا` | 2.09x | 17 contexts | إحصاء, لإحصا, إحصائي |
| `حصاء` | 2.23x | 14 contexts | إحصاء, ليحصاء, لإحصاء |
| `قليم` | 2.08x | 16 contexts | إقليم, فقليم, اقليم |
| `لجوا` | 1.76x | 26 contexts | لجواب, الجوا, لجواد |

### 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` | 281 words | الرواقية, القهوة |
| `-ل` | `-ة` | 184 words | لفريسة, للمنصة |
| `-ال` | `-ت` | 170 words | المجموعات, الصوتيات |
| `-ال` | `-ات` | 164 words | المجموعات, الصوتيات |
| `-ال` | `-ية` | 142 words | الرواقية, السيادية |
| `-ل` | `-ت` | 131 words | لقمقومات, لپوطوات |
| `-ل` | `-ات` | 125 words | لقمقومات, لپوطوات |
| `-ل` | `-ن` | 124 words | لعيّان, لخيشوميين |
| `-ال` | `-ن` | 119 words | الكربون, الفريقين |
| `-ل` | `-ية` | 116 words | لعدمية, لبيولوجية |

### 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 |
|------|-----------------|------------|------|
| والعمالات | **`و-ال-عمالات`** | 7.5 | `عمالات` |
| والراشيدية | **`و-ال-راشيدية`** | 7.5 | `راشيدية` |
| والمشروبات | **`و-ال-مشروبات`** | 7.5 | `مشروبات` |
| والمؤرخين | **`و-ال-مؤرخين`** | 7.5 | `مؤرخين` |
| والمسيحية | **`و-ال-مسيحية`** | 7.5 | `مسيحية` |
| فالسعودية | **`ف-ال-سعودية`** | 7.5 | `سعودية` |
| بالفرنسية | **`ب-ال-فرنسية`** | 7.5 | `فرنسية` |
| بالكيلوݣرام | **`ب-ال-كيلوݣرام`** | 7.5 | `كيلوݣرام` |
| والأساتذة | **`و-ال-أساتذة`** | 7.5 | `أساتذة` |
| والأقاليم | **`و-ال-أقاليم`** | 7.5 | `أقاليم` |
| باللاتينية | **`ب-ال-لاتينية`** | 7.5 | `لاتينية` |
| باليونانية | **`ب-ال-يونانية`** | 7.5 | `يونانية` |
| لبزقوليين | **`لبزقول-ي-ين`** | 7.5 | `ي` |
| فالجورنال | **`ف-ال-جورنال`** | 7.5 | `جورنال` |
| بالصيناعة | **`ب-ال-صيناعة`** | 7.5 | `صيناعة` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Moroccan Arabic 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 (4.17x) |
| N-gram | **2-gram** | Lowest perplexity (428) |
| Markov | **Context-4** | Highest predictability (97.9%) |
| 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 |

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*Generated by Wikilangs Pipeline · 2026-03-02 12:03:50*