Moroccan Arabic — Full Ablation Study & Research Report
Detailed evaluation of all model variants trained on Moroccan Arabic Wikipedia data by Wikilangs.
📋 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
Analysis and Evaluation
- 1. Tokenizer Evaluation
- 2. N-gram Model Evaluation
- 3. Markov Chain Evaluation
- 4. Vocabulary Analysis
- 5. Word Embeddings Evaluation
- 6. Morphological Analysis (Experimental)
- 7. Summary & Recommendations
- Metrics Glossary
- Visualizations Index
1. Tokenizer Evaluation
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
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
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:
ف ايكنان نقص ب سباب غتيال لماليك لأمازيغي ؤ ولّا على المنطق والبحث كان حتا زلزالو نسبة نّاس اللي سبق ليهوم مصادر ربحو جايزة أحسن 10 سنين موراها تولّا لحكم الداتيد لميداليات ف إقليم لحوز جهة مراكش آسفي ف المغرب من بعد باللي كان نتر خيالي
Context Size 2:
واصلة ل 3 ف لعقد ديال عوام كيوافق ف تّقويم لهيجري ؤ ف تّقويم لڭريڭوري بدا نهارنسبة د الشوماج واصلة ل 6 6 044 0 290 يوكطوتانية هيدروجين 7 7 و لخصوبة لكاملةف لمغريب هاد دّوار كينتامي ل مشيخة أيت قضني لي كتضم 9 د دّواور لعاداد د سّكان
Context Size 3:
ف نسبة د التسكويل واصلة ل 90 8 و نسبة د لأمية واصلة ل 50 33 لخدمة ففيها مصدر و بايت على حساب النوع د لحنش التشلال التنفوسي فشلان لكبدة لكوما و bites a dو نسبة د الشوماج واصلة ل 18 4 و لموعدّال د لعمر عند الجواج اللولاني هوّ 23 87
Context Size 4:
نسبة نّاس اللي خدامين في لقطاع لخاص 39 1 مصادر الرباط سلا القنيطرة قروية ف إقليم لخميسات مسكونين فنّاس اللي خدامين ف لپريڤي 57 1 مصادر الرباط سلا القنيطرة قروية ف إقليم سيدي إيفني جهة ݣلميم وادعلى 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:
_أو_جة_م_-اسبش_دالاف_ف،_عية_لحدالعة_ل_وعبر،_اليب
Context Size 2:
الجديات)._عنصاد_ا_لخمسيوسيحطولا_صرة_ديال_لهي_بزرقة_
Context Size 3:
_اللي_خمائيات_ديال_ف_لجمهورية_الطابلات_(گاع_ل_من_مابين
Context Size 4:
_ديال_المرسى_ديال_اديالهوم_مصادر_فيهم_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
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
5.1 Cross-Lingual Alignment
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
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
- Compare within model families: Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
- Consider trade-offs: Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
- Context matters: Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
- Corpus influence: All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
- 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 |
Generated by Wikilangs Pipeline · 2026-03-02 12:03:50



















