---
language: kab
language_name: Kabyle
language_family: berber
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-berber
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: 3.787
  - name: best_isotropy
    type: isotropy
    value: 0.8059
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kabyle** 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** | 3.109x | 3.11 | 0.1037% | 513,076 |
| **16k** | 3.378x | 3.38 | 0.1127% | 472,257 |
| **32k** | 3.612x | 3.62 | 0.1205% | 441,659 |
| **64k** | 3.787x 🏆 | 3.79 | 0.1263% | 421,278 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ho Chi Minh City — Tamanaɣt n tmurt n Dong Nam Bo, Vietnam. Tettwassen s isem n ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ho ▁chi ▁min h ▁city ▁— ▁tamanaɣt ▁n ▁tmurt ▁n ... (+18 more)` | 28 |
| 16k | `▁ho ▁chi ▁minh ▁city ▁— ▁tamanaɣt ▁n ▁tmurt ▁n ▁d ... (+17 more)` | 27 |
| 32k | `▁ho ▁chi ▁minh ▁city ▁— ▁tamanaɣt ▁n ▁tmurt ▁n ▁dong ... (+14 more)` | 24 |
| 64k | `▁ho ▁chi ▁minh ▁city ▁— ▁tamanaɣt ▁n ▁tmurt ▁n ▁dong ... (+13 more)` | 23 |

**Sample 2:** `Montargis d tamdint n Fransa. D tamaneɣt n agezdu (département) n Loiret. Zedɣen...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mont arg is ▁d ▁tamdint ▁n ▁fransa . ▁d ▁tamaneɣt ... (+18 more)` | 28 |
| 16k | `▁mont arg is ▁d ▁tamdint ▁n ▁fransa . ▁d ▁tamaneɣt ... (+17 more)` | 27 |
| 32k | `▁mont argis ▁d ▁tamdint ▁n ▁fransa . ▁d ▁tamaneɣt ▁n ... (+15 more)` | 25 |
| 64k | `▁mont argis ▁d ▁tamdint ▁n ▁fransa . ▁d ▁tamaneɣt ▁n ... (+15 more)` | 25 |

**Sample 3:** `Oregon d yiwen seg Yiwunak Yeddukklen. Tajumma-nnes 255.026 km2. Zedɣen-t 2.241....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁or eg on ▁d ▁yiwen ▁seg ▁yiwunak ▁yeddukklen . ▁tajumma ... (+36 more)` | 46 |
| 16k | `▁or eg on ▁d ▁yiwen ▁seg ▁yiwunak ▁yeddukklen . ▁tajumma ... (+36 more)` | 46 |
| 32k | `▁oregon ▁d ▁yiwen ▁seg ▁yiwunak ▁yeddukklen . ▁tajumma - nnes ... (+34 more)` | 44 |
| 64k | `▁oregon ▁d ▁yiwen ▁seg ▁yiwunak ▁yeddukklen . ▁tajumma - nnes ... (+34 more)` | 44 |


### Key Findings

- **Best Compression:** 64k achieves 3.787x compression
- **Lowest UNK Rate:** 8k with 0.1037% 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 | 7,571 | 12.89 | 19,430 | 16.5% | 43.3% |
| **2-gram** | Subword | 303 🏆 | 8.25 | 3,654 | 66.0% | 98.4% |
| **3-gram** | Word | 11,108 | 13.44 | 22,206 | 13.3% | 34.1% |
| **3-gram** | Subword | 2,694 | 11.40 | 25,828 | 26.3% | 66.9% |
| **4-gram** | Word | 19,522 | 14.25 | 32,796 | 10.1% | 25.2% |
| **4-gram** | Subword | 15,004 | 13.87 | 120,516 | 12.4% | 38.1% |
| **5-gram** | Word | 11,855 | 13.53 | 19,714 | 12.9% | 29.9% |
| **5-gram** | Subword | 48,269 | 15.56 | 267,598 | 7.1% | 23.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i d` | 3,560 |
| 2 | `kra n` | 1,303 |
| 3 | `tmurt n` | 1,292 |
| 4 | `yiwet n` | 1,270 |
| 5 | `twilayt n` | 1,230 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n twilayt n` | 1,040 |
| 2 | `deg useggas n` | 826 |
| 3 | `isem is s` | 557 |
| 4 | `is nniḍen s` | 543 |
| 5 | `ismawen is nniḍen` | 542 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ismawen is nniḍen s` | 542 |
| 2 | `taɣiwant n twilayt n` | 284 |
| 3 | `is nniḍen s teqbaylit` | 272 |
| 4 | `isem is s latinit` | 272 |
| 5 | `isem is s tefransist` | 272 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ismawen is nniḍen s teqbaylit` | 272 |
| 2 | `ismawen is nniḍen s tmaziɣt` | 270 |
| 3 | `ismawen isem is s latinit` | 264 |
| 4 | `d taɣiwant n twilayt n` | 263 |
| 5 | `is nniḍen s tmaziɣt isseqdac` | 254 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 184,557 |
| 2 | `_ t` | 121,740 |
| 3 | `e n` | 95,979 |
| 4 | `_ a` | 93,884 |
| 5 | `_ n` | 91,808 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n _` | 77,599 |
| 2 | `e n _` | 58,304 |
| 3 | `_ t a` | 38,861 |
| 4 | `_ d _` | 35,833 |
| 5 | `n _ t` | 32,724 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n _ t` | 23,561 |
| 2 | `_ d e g` | 22,211 |
| 3 | `d e g _` | 21,956 |
| 4 | `t _ n _` | 18,573 |
| 5 | `n _ n _` | 13,088 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e g _` | 21,039 |
| 2 | `_ n _ y i` | 7,349 |
| 3 | `d e g _ t` | 6,497 |
| 4 | `t _ n _ t` | 6,453 |
| 5 | `e n _ n _` | 6,375 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 303
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.6846 | 1.607 | 4.33 | 96,821 | 31.5% |
| **1** | Subword | 1.1181 | 2.171 | 8.37 | 1,137 | 0.0% |
| **2** | Word | 0.2442 | 1.184 | 1.61 | 417,535 | 75.6% |
| **2** | Subword | 0.9627 | 1.949 | 5.62 | 9,513 | 3.7% |
| **3** | Word | 0.0844 | 1.060 | 1.15 | 667,894 | 91.6% |
| **3** | Subword | 0.8237 | 1.770 | 4.02 | 53,433 | 17.6% |
| **4** | Word | 0.0286 🏆 | 1.020 | 1.04 | 763,067 | 97.1% |
| **4** | Subword | 0.6223 | 1.539 | 2.65 | 214,801 | 37.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `n tewsit a u ad snernin tamusni iǧaḥ dayen aɛyiɣ baṛka yi ddunit akken ad kecment`
2. `d yifrax seld tama akaɣeḍ ssenṭaḍen t yettwalin dakk n medden semman askasi ɣef leḥsab n`
3. `deg ddaw yifassen yessedras yessenqas seg teftist n yimɣan yeǧǧuǧǧugen taẓrigt tamezwarut i lmend n ...`

**Context Size 2:**

1. `i d yuran dyujin layirs d 81 tinfaliyin tivaṭikaniyin ffɣent d aṭas n tamerrit deg tagzirt a`
2. `kra n wakud ma yella idles afr ensis yeǧhed yeffeɣ i tlisa n snat n tamiwin a`
3. `tmurt n rusya aseggas n dɣa gan d arraw n yakuf di tsut tis 7 aẓaṛ nsen`

**Context Size 3:**

1. `n twilayt n wehran zedɣen tt 6 800 n yimezdaɣen n batnet`
2. `deg useggas n yettwaḥsab azal n 2 600 000 n yimezdaɣen di singapur gar asen 60 d imaliziyen`
3. `isem is s tefransist genêt pas de nom spécifique genista tricuspidatatazeggart n weɣyulgenêt pas de ...`

**Context Size 4:**

1. `ismawen is nniḍen s teqbaylit ismawen is nniḍen s tmaziɣt isseqdac tiwelhiwin imeɣlalen n tizzegzut`
2. `taɣiwant n twilayt n tmenɣest zedɣen tt 28 022 n yimezdaɣen tamdint a d tin aydeg d zgant tmura`
3. `isem is s tefransist genêt purgatif ulac isem is s tefṛansist ismawen is nniḍen s teqbaylit ismawen ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_zir_wayalluntaw`
2. `ami_a_4_d_t_ad_m`
3. `etinan_1_an_awek`

**Context Size 2:**

1. `n_ualekcemniyezme`
2. `_tmaztionittes-te`
3. `en_walt_yel_amen_`

**Context Size 3:**

1. `_n_n_wassnes_clin,`
2. `en_deg_160_n_macaf`
3. `_tasuqi,_neɣ_s_asw`

**Context Size 4:**

1. `_n_taggar_n_lignett`
2. `_deg_zik_(aqqaṛen_n`
3. `deg_unit_i_d-yeqqam`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (214,801 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 | 38,216 |
| Total Tokens | 801,998 |
| Mean Frequency | 20.99 |
| Median Frequency | 3 |
| Frequency Std Dev | 517.14 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | n | 78,490 |
| 2 | d | 50,398 |
| 3 | deg | 22,375 |
| 4 | s | 15,955 |
| 5 | i | 14,664 |
| 6 | ad | 9,209 |
| 7 | is | 7,643 |
| 8 | di | 6,332 |
| 9 | seg | 5,286 |
| 10 | a | 5,100 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | eskil | 2 |
| 2 | tatinawit | 2 |
| 3 | tahelinistit | 2 |
| 4 | tigrigiyin | 2 |
| 5 | yimensiyen | 2 |
| 6 | tychy | 2 |
| 7 | abarṭinun | 2 |
| 8 | parthenos | 2 |
| 9 | nḥerrem | 2 |
| 10 | ubani | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0302 |
| R² (Goodness of Fit) | 0.997642 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 44.1% |
| Top 1,000 | 66.9% |
| Top 5,000 | 82.8% |
| Top 10,000 | 89.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9976 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 44.1% of corpus
- **Long Tail:** 28,216 words needed for remaining 10.9% 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 | 0.8059 🏆 | 0.3140 | N/A | N/A |
| **mono_64d** | 64 | 0.5286 | 0.2866 | N/A | N/A |
| **mono_128d** | 128 | 0.1321 | 0.2758 | N/A | N/A |
| **aligned_32d** | 32 | 0.8059 | 0.3266 | 0.0200 | 0.2100 |
| **aligned_64d** | 64 | 0.5286 | 0.2915 | 0.0480 | 0.2920 |
| **aligned_128d** | 128 | 0.1321 | 0.2848 | 0.0780 | 0.3160 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8059 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2965. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 7.8% 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 | **0.266** | 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 |
|--------|----------|
| `-t` | timesrifgin, tribulus, teqbilt |
| `-a` | anmezray, abruri, achieving |
| `-ta` | taɣerdemmuct, tagi, tanefrant |
| `-i` | idris, inigan, imuhaɣ |
| `-ti` | timesrifgin, timenzimawen, tilellit |
| `-te` | teqbilt, teẓẓun, texḍa |
| `-u` | umdafar, uzawag, udfel |
| `-ye` | yebbwi, yeksan, yewala |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | timesrifgin, yeksan, ḥulfun |
| `-en` | yikatalanen, ttɛeddayen, yḍemɛen |
| `-t` | ssekrent, teqbilt, taɣerdemmuct |
| `-s` | tribulus, idris, wegnes |
| `-a` | daïra, susṭara, waqila |
| `-in` | timesrifgin, tebɣin, tiznasin |
| `-e` | odense, brise, gustave |
| `-r` | umdafar, muɣrar, neuer |

### 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 |
|------|----------|------------------|----------|
| `etta` | 1.75x | 102 contexts | setta, netta, tettaf |
| `ttwa` | 1.80x | 70 contexts | ittwa, attwaɣ, uttwaɣ |
| `aren` | 1.82x | 48 contexts | raren, qaren, karen |
| `anen` | 1.98x | 31 contexts | ranen, banen, ibanen |
| `elli` | 1.42x | 95 contexts | nelli, zelli, belli |
| `tame` | 1.90x | 28 contexts | tameṭ, tamet, tamelt |
| `egga` | 1.46x | 79 contexts | yegga, tegga, teggar |
| `mazi` | 1.79x | 27 contexts | mazis, amazi, maziɣ |
| `ettw` | 2.07x | 15 contexts | yettwaɣ, tettwaɣ, yettweg |
| `segg` | 1.76x | 23 contexts | usegg, aseggi, seggas |
| `zdaɣ` | 2.02x | 13 contexts | imzdaɣ, tezdaɣ, yezdaɣ |
| `ezda` | 1.53x | 31 contexts | tezdaɣ, yezdaɣ, wezdam |

### 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 |
|--------|--------|-----------|----------|
| `-t` | `-t` | 744 words | tamattant, tḥandast |
| `-i` | `-n` | 510 words | iɣiren, izegriren |
| `-i` | `-en` | 474 words | iɣiren, izegriren |
| `-t` | `-n` | 441 words | tedqiqin, tibankiwin |
| `-t` | `-in` | 347 words | tedqiqin, tibankiwin |
| `-y` | `-n` | 170 words | yinmezrayen, yimdebbṛen |
| `-ye` | `-n` | 164 words | yemxallafen, yettwakten |
| `-y` | `-en` | 151 words | yinmezrayen, yimdebbṛen |
| `-ye` | `-en` | 132 words | yemxallafen, yettwakten |
| `-t` | `-a` | 127 words | tsuda, takma |

### 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 |
|------|-----------------|------------|------|
| populations | **`populatio-n-s`** | 7.5 | `n` |
| americanus | **`america-n-us`** | 7.5 | `n` |
| ttɛawanen | **`ttɛawa-n-en`** | 7.5 | `n` |
| yinyutrunen | **`yinyutru-n-en`** | 7.5 | `n` |
| tkebbanin | **`tkebba-n-in`** | 7.5 | `n` |
| conclusions | **`conclusio-n-s`** | 7.5 | `n` |
| constantine | **`constanti-n-e`** | 7.5 | `n` |
| iwezlanen | **`iwezla-n-en`** | 7.5 | `n` |
| isemrasen | **`isemra-s-en`** | 7.5 | `s` |
| ticebḥanin | **`ticebḥ-an-in`** | 7.5 | `an` |
| uctavyanus | **`uctavya-n-us`** | 7.5 | `n` |
| iwindalen | **`iwind-al-en`** | 7.5 | `al` |
| oudjidane | **`oudjida-n-e`** | 7.5 | `n` |
| isbegsanen | **`isbegsa-n-en`** | 7.5 | `n` |
| tisinsinin | **`tisinsi-n-in`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kabyle 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 (3.79x) |
| N-gram | **2-gram** | Lowest perplexity (303) |
| Markov | **Context-4** | Highest predictability (97.1%) |
| 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: 2026-01-10 07:12:49*