---
language: he
language_name: Hebrew
language_family: semitic_hebrew
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-semitic_hebrew
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: 4.191
  - name: best_isotropy
    type: isotropy
    value: 0.8057
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-13
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Hebrew** 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** | 3.129x | 3.13 | 0.0482% | 4,188,199 |
| **16k** | 3.502x | 3.50 | 0.0540% | 3,742,094 |
| **32k** | 3.872x | 3.87 | 0.0597% | 3,384,734 |
| **64k** | 4.191x 🏆 | 4.19 | 0.0646% | 3,127,199 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `אייזנשטיין או איזנשטין (Eisenstein), שם משפחה גרמני ושם יהודי אשכנזי נפוץ. פירוש...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁אייז נשטיין ▁או ▁איז נ שט ין ▁( e is ... (+26 more)` | 36 |
| 16k | `▁אייז נשטיין ▁או ▁איז נשט ין ▁( e is en ... (+20 more)` | 30 |
| 32k | `▁אייז נשטיין ▁או ▁איז נשט ין ▁( e is en ... (+19 more)` | 29 |
| 64k | `▁אייזנשטיין ▁או ▁איז נשט ין ▁( e is enstein ), ... (+17 more)` | 27 |

**Sample 2:** `שטיבל היא צורת הקטנה של המילה היידית שטוב ("בית" או "חדר"). משפחה משפחה אשכנזיים`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁שט יבל ▁היא ▁צורת ▁הקטנה ▁של ▁המילה ▁הי ידית ▁שט ... (+13 more)` | 23 |
| 16k | `▁שט יבל ▁היא ▁צורת ▁הקטנה ▁של ▁המילה ▁הי ידית ▁שט ... (+12 more)` | 22 |
| 32k | `▁שט יבל ▁היא ▁צורת ▁הקטנה ▁של ▁המילה ▁הי ידית ▁שט ... (+11 more)` | 21 |
| 64k | `▁שטיבל ▁היא ▁צורת ▁הקטנה ▁של ▁המילה ▁היידית ▁שט וב ▁(" ... (+9 more)` | 19 |

**Sample 3:** `לאופרד הוא התעתיק העברי למילה Leopard, הקיימת במספר שפות ומשמעותה היא נמר (בעל ח...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁לא ופר ד ▁הוא ▁הת עתיק ▁העברי ▁למ ילה ▁le ... (+21 more)` | 31 |
| 16k | `▁לא ופר ד ▁הוא ▁הת עתיק ▁העברי ▁למילה ▁le op ... (+17 more)` | 27 |
| 32k | `▁לאופר ד ▁הוא ▁הת עתיק ▁העברי ▁למילה ▁le op ard ... (+15 more)` | 25 |
| 64k | `▁לאופר ד ▁הוא ▁התעתיק ▁העברי ▁למילה ▁le opard , ▁הקיימת ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.191x compression
- **Lowest UNK Rate:** 8k with 0.0482% 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 | 839,907 | 19.68 | 4,883,996 | 3.8% | 9.8% |
| **2-gram** | Subword | 388 🏆 | 8.60 | 45,811 | 57.3% | 98.0% |
| **3-gram** | Word | 2,460,970 | 21.23 | 7,456,944 | 1.9% | 5.1% |
| **3-gram** | Subword | 4,159 | 12.02 | 320,573 | 19.8% | 57.8% |
| **4-gram** | Word | 6,086,424 | 22.54 | 12,242,689 | 1.3% | 3.3% |
| **4-gram** | Subword | 31,153 | 14.93 | 1,768,539 | 7.8% | 25.6% |
| **5-gram** | Word | 5,115,710 | 22.29 | 8,563,842 | 1.1% | 3.0% |
| **5-gram** | Subword | 174,825 | 17.42 | 6,204,970 | 3.7% | 13.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `על ידי` | 619,385 |
| 2 | `קישורים חיצוניים` | 326,599 |
| 3 | `הערות שוליים` | 252,301 |
| 4 | `ארצות הברית` | 176,732 |
| 5 | `על פי` | 148,464 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `קישורים חיצוניים הערות` | 115,186 |
| 2 | `חיצוניים הערות שוליים` | 115,178 |
| 3 | `של ארצות הברית` | 67,555 |
| 4 | `של המאה ה` | 45,554 |
| 5 | `המאה ה 20` | 39,531 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `קישורים חיצוניים הערות שוליים` | 115,165 |
| 2 | `של המאה ה 20` | 24,487 |
| 3 | `שבהם תבנית בריטניקה אינה` | 19,413 |
| 4 | `תבנית בריטניקה אינה מתאימה` | 19,413 |
| 5 | `את הופעת הבכורה שלו` | 16,388 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `שבהם תבנית בריטניקה אינה מתאימה` | 19,413 |
| 2 | `ערך את הופעת הבכורה שלו` | 11,486 |
| 3 | `הערות שוליים שבהם תבנית בריטניקה` | 10,724 |
| 4 | `שוליים שבהם תבנית בריטניקה אינה` | 10,724 |
| 5 | `בית הנבחרים של ארצות הברית` | 7,604 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ה` | 39,073,833 |
| 2 | `ת _` | 29,026,407 |
| 3 | `_ ב` | 24,932,558 |
| 4 | `ה _` | 24,128,474 |
| 5 | `ם _` | 21,592,884 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `י ם _` | 13,358,320 |
| 2 | `ו ת _` | 11,186,966 |
| 3 | `ת _ ה` | 8,271,610 |
| 4 | `_ ש ל` | 6,687,390 |
| 5 | `ש ל _` | 5,737,360 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ש ל _` | 5,452,714 |
| 2 | `_ א ת _` | 2,964,460 |
| 3 | `ו ת _ ה` | 2,726,223 |
| 4 | `_ ע ל _` | 2,650,017 |
| 5 | `י י ם _` | 2,272,182 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ש ל _ ה` | 1,545,782 |
| 2 | `_ ה ו א _` | 1,326,505 |
| 3 | `_ א ת _ ה` | 1,316,470 |
| 4 | `ה _ ש ל _` | 1,085,085 |
| 5 | `ו _ ש ל _` | 843,378 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 388
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~13% 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 | 1.1002 | 2.144 | 22.34 | 2,985,722 | 0.0% |
| **1** | Subword | 0.8730 | 1.831 | 7.49 | 25,039 | 12.7% |
| **2** | Word | 0.3737 | 1.296 | 2.25 | 66,677,134 | 62.6% |
| **2** | Subword | 0.6573 | 1.577 | 4.43 | 187,480 | 34.3% |
| **3** | Word | 0.1205 | 1.087 | 1.25 | 150,136,299 | 87.9% |
| **3** | Subword | 0.6833 | 1.606 | 3.99 | 829,497 | 31.7% |
| **4** | Word | 0.0427 🏆 | 1.030 | 1.07 | 187,719,110 | 95.7% |
| **4** | Subword | 0.6743 | 1.596 | 3.51 | 3,312,743 | 32.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `של היציע היו מפסיקים לעבוד כמכונאי רכב שעברו לפורטלנד מיין ושרד רוחות האקליפס שם השיר הפשוט`
2. `את סגן אלוף אלה אטלנטית לאחר הפסקה מהנורמה איסוף המידע שלו וכן מעל שכבה ארכאולוגית במחנה`
3. `על מצדה השמאלי מחזיק באזרחות צרפתית ערבית לפיה ניתן למרלן דיטריך בביקור בהודו נאבקו למצוא תשובות`

**Context Size 2:**

1. `על ידי מחשב ובכך להסיר את שלטון הטרור מרדכי מיררג ס חזנה של העיר נהפכו ללא רלוונטיות`
2. `קישורים חיצוניים הערות שוליים ילידי אוקראינה בעלת קול סופרן אלט טנור מקהלהsing unto godאלט טנור סופר...`
3. `הערות שוליים כדורגל סעודיות מועדוני כדורגל באזור כורדיסטן שבעיראק עם קהילות האם שלהן אף יותר מהסירוס...`

**Context Size 3:**

1. `קישורים חיצוניים הערות שוליים קנדים החברה המלכותית זרים בחברה המלכותית יהודים בחברה המלכותית המדליה ...`
2. `חיצוניים הערות שוליים קולנוע וטלוויזיה צ יליאניות תקשורת צ יליאנים טלוויזיה צ יליאנים קולנוע וטלוויז...`
3. `של ארצות הברית בהתבסס על סקרים על הקרקע ועל תצלומי אוויר שצולמו ממטוסי משלחת החקר האנטארקטית הבריטית...`

**Context Size 4:**

1. `קישורים חיצוניים הערות שוליים מסדר עמיתי הכבוד אנגלים אנגלים ממוצא ולשי שנולדו`
2. `של המאה ה 20 הנפיקו מניות ונרשמו למסחר בבורסה עשרות חברות מישראל בין השאר אמבלייז הונפקה לראשונה בבו...`
3. `שבהם תבנית בריטניקה אינה מתאימה פיזיקליים חסרי ממדים של מעגלים חשמליים`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_עלטואם_קרוריזם_`
2. `יקרו._קואול_הימח`
3. `וחותוריהדיעם_שלך`

**Context Size 2:**

1. `_הראלץ,_וין._בכות`
2. `ת_בה_השמוד_המחזק_`
3. `_בחרו,_את_מא/נקרת`

**Context Size 3:**

1. `ים_דיאנה_תוכן_רקוס`
2. `ות_בציה_ישראליפורי`
3. `ת_המקיינת_45_דאולו`

**Context Size 4:**

1. `_של_חיים)_שמחוץ_לדח`
2. `_את_כלל_במגזין_הטרי`
3. `ות_הראשון_הישיבה_סי`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (3,312,743 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 | 1,343,537 |
| Total Tokens | 218,728,300 |
| Mean Frequency | 162.80 |
| Median Frequency | 5 |
| Frequency Std Dev | 6864.53 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | של | 5,459,894 |
| 2 | את | 2,971,688 |
| 3 | על | 2,703,880 |
| 4 | הוא | 1,339,510 |
| 5 | עם | 1,154,254 |
| 6 | ב | 905,656 |
| 7 | בשנת | 775,632 |
| 8 | ה | 760,765 |
| 9 | גם | 682,600 |
| 10 | היה | 665,182 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | markomannen | 2 |
| 2 | traditiones | 2 |
| 3 | possessionesque | 2 |
| 4 | bisterem | 2 |
| 5 | אנוויגאדו | 2 |
| 6 | קרואטיתאנטה | 2 |
| 7 | קרואטיתאיוון | 2 |
| 8 | מנדאריץ | 2 |
| 9 | סקסאפאהו | 2 |
| 10 | בסקסאפאהו | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8691 |
| R² (Goodness of Fit) | 0.995091 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 18.7% |
| Top 1,000 | 39.8% |
| Top 5,000 | 60.2% |
| Top 10,000 | 69.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9951 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 18.7% of corpus
- **Long Tail:** 1,333,537 words needed for remaining 30.2% 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 | 0.8057 | 0.3812 | N/A | N/A |
| **mono_64d** | 64 | 0.7873 | 0.2918 | N/A | N/A |
| **mono_128d** | 128 | 0.7406 | 0.2357 | N/A | N/A |
| **aligned_32d** | 32 | 0.8057 🏆 | 0.3678 | 0.1680 | 0.6000 |
| **aligned_64d** | 64 | 0.7873 | 0.2944 | 0.3600 | 0.7620 |
| **aligned_128d** | 128 | 0.7406 | 0.2283 | 0.4900 | 0.8080 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8057 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2999. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 49.0% 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 | **-0.772** | 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 |
|--------|----------|
| `-ו` | ופריסה, וחדאת, והסטודנטים |
| `-ה` | היידון, הברבריזציה, האגיטטורים |
| `-מ` | ממגין, מלביץ, מרעשי |
| `-ב` | באנצ, בהרמוניקות, בהמלצת |
| `-ל` | לספקי, להסגברה, לאירופים |
| `-ש` | שהטלגרף, שהתיוג, שואלר |
| `-וה` | והסטודנטים, והראווה, והריסת |
| `-א` | איטיטאווי, אנטיפוסופוליפידית, אֶצְבְּעוֹנִי |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ם` | והסטודנטים, האגיטטורים, לאירופים |
| `-ה` | כמוכה, ופריסה, הברבריזציה |
| `-ת` | נווטות, וחדאת, אנטיפוסופוליפידית |
| `-ים` | והסטודנטים, האגיטטורים, לאירופים |
| `-ות` | נווטות, פרקיםאחיות, בהרמוניקות |
| `-י` | איטיטאווי, זולנסקי, לספקי |
| `-ן` | דריגיטשין, היידון, ממגין |
| `-s` | lugares, wootens, hijras |

### 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 |
|------|----------|------------------|----------|
| `תפקי` | 2.54x | 314 contexts | תפקיע, בתפקי, תפקיר |
| `ופיע` | 2.45x | 92 contexts | ופיעה, מופיע, הופיע |
| `טלוו` | 2.81x | 51 contexts | טלווב, טלווה, טלווג |
| `עילו` | 1.93x | 275 contexts | עילות, עילום, העילו |
| `גרמנ` | 2.21x | 126 contexts | גרמני, גרמנה, גרמנו |
| `יצונ` | 2.23x | 120 contexts | זיצונג, חיצונה, קיצונה |
| `תקופ` | 2.13x | 149 contexts | תקופת, בתקופ, תקופה |
| `מדינ` | 1.90x | 259 contexts | מדינם, מדינת, מדינצ |
| `קיימ` | 1.95x | 203 contexts | קיימו, קיימה, קיימת |
| `וגרפ` | 1.73x | 292 contexts | וגרפה, וגרפי, וגרפו |
| `תוכנ` | 1.69x | 272 contexts | תוכנה, תוכנם, תוכנן |
| `רסיט` | 2.40x | 45 contexts | ברסיט, רסיטל, גרסיט |

### 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 |
|--------|--------|-----------|----------|
| `-ה` | `-ת` | 158 words | המפלסות, ההזדווגות |
| `-ו` | `-ת` | 158 words | וכמראיינת, ובמשאיות |
| `-ה` | `-ם` | 154 words | הגזברים, הטאטארים |
| `-ו` | `-ם` | 144 words | וניכוסם, וברציפים |
| `-ה` | `-ים` | 136 words | הגזברים, הטאטארים |
| `-ו` | `-ה` | 114 words | ותראקיה, וונרה |
| `-ו` | `-ים` | 110 words | וברציפים, ומייסדים |
| `-ו` | `-ות` | 105 words | ובמשאיות, ורציונליות |
| `-מ` | `-ם` | 90 words | ממחניים, מהפארקים |
| `-מ` | `-ת` | 85 words | מהקלוריות, מתעשרת |

### 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 |
|------|-----------------|------------|------|
| sipstrassi | **`sipstras-s-i`** | 7.5 | `s` |
| אברדינשייר | **`אברדינשי-י-ר`** | 7.5 | `י` |
| האנטינגדונשייר | **`האנטינגדונשי-י-ר`** | 7.5 | `י` |
| ובסטנדרטים | **`וב-סטנדרט-ים`** | 6.0 | `סטנדרט` |
| ותינוקותיהן | **`ותינוקות-יה-ן`** | 6.0 | `ותינוקות` |
| שבאפשרותם | **`שב-אפשרות-ם`** | 6.0 | `אפשרות` |
| השתקפויותיהם | **`השתקפויות-יה-ם`** | 6.0 | `השתקפויות` |
| מפרוותיהם | **`מפרוות-יה-ם`** | 6.0 | `מפרוות` |
| והארכאולוגים | **`וה-ארכאולוג-ים`** | 6.0 | `ארכאולוג` |
| התייבשותה | **`התייבש-ות-ה`** | 6.0 | `התייבש` |
| עקרונותיהן | **`עקרונות-יה-ן`** | 6.0 | `עקרונות` |
| שבמדבריות | **`שב-מדברי-ות`** | 6.0 | `מדברי` |
| מראשוניותו | **`מראשוני-ות-ו`** | 6.0 | `מראשוני` |
| ממחלותיהם | **`ממחלות-יה-ם`** | 6.0 | `ממחלות` |
| הפנולוגיה | **`ה-פנולוג-יה`** | 6.0 | `פנולוג` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Hebrew 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 (4.19x) |
| N-gram | **2-gram** | Lowest perplexity (388) |
| Markov | **Context-4** | Highest predictability (95.7%) |
| 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: 2026-01-13 14:18:23*