COMPREHENSIVE_RESEARCH_REPORT.md

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.

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1. Tokenizer Evaluation

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

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2. N-gram Model Evaluation

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

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3. Markov Chain Evaluation

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

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4. Vocabulary Analysis

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

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5. Word Embeddings Evaluation

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

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6. Summary & Recommendations

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

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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

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Generated by Wikilangs Models Pipeline

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