# Wikilangs Models: Comprehensive Research Report
## ARY - Full Ablation Study

This report presents a comprehensive evaluation of language models trained on ARY Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/01_tokenizer_compression.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 3.134x | 3.09 | 0.0472% | 379,309 |
| **16k** | 3.346x | 3.30 | 0.0504% | 355,311 |
| **32k** | 3.535x | 3.49 | 0.0532% | 336,296 |
| **64k** | 3.683x 🏆 | 3.64 | 0.0555% | 322,761 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `نينڭ بايزورا بنت الشيخ حمزة أولا نينڭ بايزورا هي مومتيلة وموغنية ماليزية.

 مصاد...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ن ينڭ ▁باي ز ورا ▁بنت ▁الشيخ ▁حم زة ▁أولا ... (+32 more)` | 42 |
| 16k | `▁ن ينڭ ▁باي ز ورا ▁بنت ▁الشيخ ▁حمزة ▁أولا ▁ن ... (+29 more)` | 39 |
| 32k | `▁ن ينڭ ▁باي ز ورا ▁بنت ▁الشيخ ▁حمزة ▁أولا ▁ن ... (+29 more)` | 39 |
| 64k | `▁ن ينڭ ▁باي ز ورا ▁بنت ▁الشيخ ▁حمزة ▁أولا ▁ن ... (+27 more)` | 37 |

**Sample 2:** `هادي صفحة د التوضيح، كلمة بركان يمكن يكونو عندها هاد لمعاني:

 بْرْكان: مدينة مغ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁هادي ▁صفحة ▁د ▁التوضيح ، ▁كلمة ▁بركان ▁يمكن ▁يكونو ▁عندها ... (+26 more)` | 36 |
| 16k | `▁هادي ▁صفحة ▁د ▁التوضيح ، ▁كلمة ▁بركان ▁يمكن ▁يكونو ▁عندها ... (+25 more)` | 35 |
| 32k | `▁هادي ▁صفحة ▁د ▁التوضيح ، ▁كلمة ▁بركان ▁يمكن ▁يكونو ▁عندها ... (+24 more)` | 34 |
| 64k | `▁هادي ▁صفحة ▁د ▁التوضيح ، ▁كلمة ▁بركان ▁يمكن ▁يكونو ▁عندها ... (+22 more)` | 32 |

**Sample 3:** `أسيل عمران (مزيودة ف 1989) هي مغنية و ممتلة سعودية كتعيش ف لإمارات.

 مصادر 

تص...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁أس يل ▁عمر ان ▁( مزيودة ▁ف ▁ 1 9 ... (+36 more)` | 46 |
| 16k | `▁أس يل ▁عمر ان ▁( مزيودة ▁ف ▁ 1 9 ... (+32 more)` | 42 |
| 32k | `▁أس يل ▁عمران ▁( مزيودة ▁ف ▁ 1 9 8 ... (+28 more)` | 38 |
| 64k | `▁أس يل ▁عمران ▁( مزيودة ▁ف ▁ 1 9 8 ... (+28 more)` | 38 |


### Key Findings

- **Best Compression:** 64k achieves 3.683x compression
- **Lowest UNK Rate:** 8k with 0.0472% 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/05_ngram_perplexity.png)

![N-gram Coverage](visualizations/07_ngram_coverage.png)

### Results

| N-gram | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | 7,187 🏆 | 12.81 | 56,749 | 24.4% | 53.2% |
| **2-gram** | 486 🏆 | 8.93 | 6,227 | 54.9% | 95.4% |
| **3-gram** | 8,812 | 13.11 | 76,888 | 21.3% | 52.8% |
| **3-gram** | 4,295 | 12.07 | 51,256 | 22.1% | 58.7% |
| **4-gram** | 12,168 | 13.57 | 124,859 | 20.1% | 50.4% |
| **4-gram** | 22,008 | 14.43 | 260,844 | 12.0% | 35.5% |

### Top 5 N-grams by Size

**2-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `تصنيف :` | 37,187 |
| 2 | `، و` | 18,746 |
| 3 | `ن ّ` | 10,639 |
| 4 | `) :` | 10,185 |
| 5 | `مصادر تصنيف` | 10,087 |

**3-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `مصادر تصنيف :` | 10,087 |
| 2 | `تصنيف : مقالات` | 7,001 |
| 3 | `ن ّ اس` | 6,981 |
| 4 | `ل ّ ي` | 6,914 |
| 5 | `: دوار ف` | 5,007 |

**4-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `تصنيف : دوار ف` | 5,005 |
| 2 | `نسبة ن ّ اس` | 4,061 |
| 3 | `. مصادر تصنيف :` | 3,827 |
| 4 | `تصنيف : مقالات زادهوم` | 3,506 |
| 5 | `: مقالات زادهوم داريجابوت` | 3,506 |


### Key Findings

- **Best Perplexity:** 2-gram with 486
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/09_markov_entropy.png)

![Markov Branching](visualizations/10_markov_branching.png)

### Results

| Context | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | 0.7813 | 1.719 | 5.36 | 189,320 | 21.9% |
| **1** | 1.1519 | 2.222 | 8.71 | 1,931 | 0.0% |
| **2** | 0.2761 | 1.211 | 1.68 | 1,014,676 | 72.4% |
| **2** | 0.9863 | 1.981 | 6.24 | 16,826 | 1.4% |
| **3** | 0.0931 | 1.067 | 1.18 | 1,701,309 | 90.7% |
| **3** | 0.8744 | 1.833 | 4.33 | 104,928 | 12.6% |
| **4** | 0.0366 🏆 | 1.026 | 1.07 | 2,000,181 | 96.3% |
| **4** | 0.6731 🏆 | 1.594 | 2.82 | 454,694 | 32.7% |

### Generated Text Samples

Below are text samples generated from each Markov chain model:

**Context Size 1:**

1. `. قرات لانفورماتيك ، وحسبوهم النسابون المسلمين ) غايب مجموعntnən ( قائم الزاوية هو ، الطابلو`
2. `، كان ل 6 % ، ولكن ماكخون ( ولا لبيطاليين اللي سبق ليهوم خدمو )`
3. `ف كتاب " ف جماعة قروية ف دوك لي جاو فالغرب د لكورة تا نتيجة لاندماج`

**Context Size 2:**

1. `تصنيف : عوام د تقويم لميلادي تصنيف : نهارات د لعام تصنيف : كتاتبيا مغاربا د لقرن`
2. `، و صدرات منو أغنية rip , love . الديسك خرج رسميا ً paypal holdings inc .`
3. `ن ّ اس ن ّ شيطين ( ل ّ ي قاريين فوق الليسي ( ليسي و جامعة`

**Context Size 3:**

1. `مصادر تصنيف : يناير تصنيف : نهارات د لعام تصنيف : مقالات فيها مصدر و 3000 بايت تصنيف`
2. `تصنيف : مقالات زادهوم داريجابوت تصنيف : بلايص مسكونين ف إقليم برشيد ، جهة د ّ ار لبيضا`
3. `ن ّ اس اللي خدامين ف د ّ ولة : 4 , 4 % إقتصاد نسبة ن ّ`

**Context Size 4:**

1. `تصنيف : دوار ف لمغريب تصنيف : دوار ف لمغريب تصنيف : دوار ف لمغريب تصنيف : دوار ف`
2. `نسبة ن ّ اس ن ّ شيطين ( ل ّ ي يقدرو يخدمو ) : 50 , 2 %`
3. `. مصادر تصنيف : عوام د تقويم لميلادي تصنيف : مقالات زادهوم داريجابوت تصنيف : عوام 380 قبل لميلاد`


### Key Findings

- **Best Predictability:** Context-4 with 96.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (454,694 contexts)
- **Recommendation:** Context-3 or Context-4 for text generation

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/12_zipf_law.png)

![Top Words](visualizations/14_top20_words.png)

![Coverage Curve](visualizations/15_vocab_coverage.png)

### Statistics

| Metric | Value |
|--------|-------|
| Vocabulary Size | 81,712 |
| Total Tokens | 2,308,873 |
| Mean Frequency | 28.26 |
| Median Frequency | 4 |
| Frequency Std Dev | 559.90 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ف | 84,463 |
| 2 | د | 69,201 |
| 3 | و | 61,463 |
| 4 | تصنيف | 37,231 |
| 5 | ل | 34,076 |
| 6 | ديال | 32,761 |
| 7 | من | 29,612 |
| 8 | على | 19,717 |
| 9 | لي | 18,627 |
| 10 | ب | 18,189 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | بيتسي | 2 |
| 2 | وصانعي | 2 |
| 3 | وأهميتها | 2 |
| 4 | بورديو | 2 |
| 5 | بلومر | 2 |
| 6 | مقترحة | 2 |
| 7 | anchor | 2 |
| 8 | الرسميةاللي | 2 |
| 9 | بعصبة | 2 |
| 10 | ماڭي | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0380 |
| R² (Goodness of Fit) | 0.999162 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.3% |
| Top 1,000 | 63.8% |
| Top 5,000 | 78.6% |
| Top 10,000 | 84.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9992 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.3% of corpus
- **Long Tail:** 71,712 words needed for remaining 15.2% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/16_embedding_isotropy.png)

![Similarity Matrix](visualizations/18_embedding_similarity.png)

![t-SNE Words](visualizations/20_tsne_words.png)

![t-SNE Sentences](visualizations/21_tsne_sentences.png)

### Model Comparison

| Model | Vocab Size | Dimension | Avg Norm | Std Norm | Isotropy |
|-------|------------|-----------|----------|----------|----------|
| **mono_32d** | 37,528 | 32 | 4.010 | 1.183 | 0.8264 🏆 |
| **mono_64d** | 37,528 | 64 | 4.579 | 1.040 | 0.8183 |
| **mono_128d** | 37,528 | 128 | 5.112 | 0.875 | 0.7212 |
| **embeddings_enhanced** | 0 | 0 | 0.000 | 0.000 | 0.0000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8264 (more uniform distribution)
- **Dimension Trade-off:** Higher dimensions capture more semantics but reduce isotropy
- **Vocabulary Coverage:** All models cover 37,528 words
- **Recommendation:** 100d for balanced semantic capture and efficiency

---
## 6. Summary & Recommendations

![Performance Dashboard](visualizations/24_performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **32k BPE** | Best compression (3.68x) with low UNK rate |
| N-gram | **5-gram** | Lowest perplexity (486) |
| Markov | **Context-4** | Highest predictability (96.3%) |
| 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 |
|---|---------------|-------------|
| 01 | Tokenizer Compression | Compression ratios by vocabulary size |
| 02 | Tokenizer Fertility | Average token length by vocabulary |
| 03 | Tokenizer OOV | Unknown token rates |
| 04 | Tokenizer Tokens | Total tokens by vocabulary |
| 05 | N-gram Perplexity | Perplexity by n-gram size |
| 06 | N-gram Entropy | Entropy by n-gram size |
| 07 | N-gram Coverage | Top pattern coverage |
| 08 | N-gram Unique | Unique n-gram counts |
| 09 | Markov Entropy | Entropy by context size |
| 10 | Markov Branching | Branching factor by context |
| 11 | Markov Contexts | Unique context counts |
| 12 | Zipf's Law | Frequency-rank distribution with fit |
| 13 | Vocab Frequency | Word frequency distribution |
| 14 | Top 20 Words | Most frequent words |
| 15 | Vocab Coverage | Cumulative coverage curve |
| 16 | Embedding Isotropy | Vector space uniformity |
| 17 | Embedding Norms | Vector magnitude distribution |
| 18 | Similarity Matrix | Word similarity heatmap |
| 19 | Nearest Neighbors | Similar words for key terms |
| 20 | t-SNE Words | 2D word embedding visualization |
| 21 | t-SNE Sentences | 2D sentence embedding visualization |
| 22 | Position Encoding | Encoding method comparison |
| 23 | Model Sizes | Storage requirements |
| 24 | Dashboard | Comprehensive performance overview |

---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2025-12-27 03:37:35*