---
language: zu
language_name: Zulu
language_family: bantu_southern
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-bantu_southern
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: 5.059
  - name: best_isotropy
    type: isotropy
    value: 0.7797
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Zulu** 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** | 3.796x | 3.80 | 0.4092% | 301,785 |
| **16k** | 4.244x | 4.25 | 0.4575% | 269,929 |
| **32k** | 4.672x | 4.68 | 0.5037% | 245,198 |
| **64k** | 5.059x 🏆 | 5.06 | 0.5454% | 226,437 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `I-Ouled Ahmed Timmi ngumasipala futhi yidolobha elikwisifundazwe se Adrar, e-Alj...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁i - ouled ▁ah med ▁ti m mi ▁ngumasipala ▁futhi ... (+15 more)` | 25 |
| 16k | `▁i - ouled ▁ahmed ▁ti m mi ▁ngumasipala ▁futhi ▁yidolobha ... (+14 more)` | 24 |
| 32k | `▁i - ouled ▁ahmed ▁ti mmi ▁ngumasipala ▁futhi ▁yidolobha ▁eli ... (+13 more)` | 23 |
| 64k | `▁i - ouled ▁ahmed ▁ti mmi ▁ngumasipala ▁futhi ▁yidolobha ▁eli ... (+13 more)` | 23 |

**Sample 2:** `I-Umm Bel yidolobha elikwisifundazwe se South Kordofan, eSudan. Imithombo ase Su...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁i - um m ▁bel ▁yidolobha ▁eli kwisifundazwe ▁se ▁south ... (+7 more)` | 17 |
| 16k | `▁i - um m ▁bel ▁yidolobha ▁eli kwisifundazwe ▁se ▁south ... (+7 more)` | 17 |
| 32k | `▁i - umm ▁bel ▁yidolobha ▁eli kwisifundazwe ▁se ▁south ▁kordofan ... (+6 more)` | 16 |
| 64k | `▁i - umm ▁bel ▁yidolobha ▁eli kwisifundazwe ▁se ▁south ▁kordofan ... (+6 more)` | 16 |

**Sample 3:** `ISousse yisifundazwe sase Thuniziya. Imithombo zase Thuniziya`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁iso us se ▁yisifundazwe ▁sase ▁thuniziya . ▁imithombo ▁zase ▁thuniziya` | 10 |
| 16k | `▁isousse ▁yisifundazwe ▁sase ▁thuniziya . ▁imithombo ▁zase ▁thuniziya` | 8 |
| 32k | `▁isousse ▁yisifundazwe ▁sase ▁thuniziya . ▁imithombo ▁zase ▁thuniziya` | 8 |
| 64k | `▁isousse ▁yisifundazwe ▁sase ▁thuniziya . ▁imithombo ▁zase ▁thuniziya` | 8 |


### Key Findings

- **Best Compression:** 64k achieves 5.059x compression
- **Lowest UNK Rate:** 8k with 0.4092% 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 | 3,031 | 11.57 | 11,107 | 29.9% | 59.1% |
| **2-gram** | Subword | 252 🏆 | 7.97 | 2,750 | 69.7% | 99.6% |
| **3-gram** | Word | 2,282 | 11.16 | 10,014 | 34.2% | 65.5% |
| **3-gram** | Subword | 2,028 | 10.99 | 20,811 | 25.8% | 75.4% |
| **4-gram** | Word | 7,169 | 12.81 | 29,569 | 24.8% | 48.3% |
| **4-gram** | Subword | 10,632 | 13.38 | 107,674 | 12.5% | 42.2% |
| **5-gram** | Word | 6,986 | 12.77 | 25,819 | 24.3% | 47.4% |
| **5-gram** | Subword | 33,821 | 15.05 | 270,035 | 8.3% | 27.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kwesifundazwe se` | 3,204 |
| 2 | `imithombo ase` | 3,075 |
| 3 | `imithombo zase` | 2,993 |
| 4 | `kulandwe ngo` | 2,897 |
| 5 | `esingaphansi kwesifundazwe` | 2,436 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `esingaphansi kwesifundazwe se` | 2,436 |
| 2 | `yisifunda esingaphansi kwesifundazwe` | 2,424 |
| 3 | `yidolobha elikwisifundazwe se` | 1,989 |
| 4 | `kulandwe ngo zibandlela` | 1,191 |
| 5 | `e aljeriya imithombo` | 1,073 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `yisifunda esingaphansi kwesifundazwe se` | 2,424 |
| 2 | `futhi yidolobha elikwisifundazwe se` | 865 |
| 3 | `ngumasipala futhi yidolobha elikwisifundazwe` | 778 |
| 4 | `ethiopia shapefiles ethiopias administrative` | 755 |
| 5 | `shapefiles ethiopias administrative woredas` | 755 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ngumasipala futhi yidolobha elikwisifundazwe se` | 778 |
| 2 | `org kulandwe ngo masingana 4` | 755 |
| 3 | `shapefiles ethiopias administrative woredas africaopendata` | 755 |
| 4 | `africaopendata org kulandwe ngo masingana` | 755 |
| 5 | `woredas africaopendata org kulandwe ngo` | 755 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 204,965 |
| 2 | `e _` | 133,326 |
| 3 | `n g` | 129,678 |
| 4 | `a n` | 126,471 |
| 5 | `i _` | 119,226 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a _` | 40,639 |
| 2 | `_ n g` | 40,201 |
| 3 | `n g a` | 38,052 |
| 4 | `t h i` | 34,873 |
| 5 | `o k u` | 33,998 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t h i _` | 27,064 |
| 2 | `_ u k u` | 22,270 |
| 3 | `_ n g o` | 19,184 |
| 4 | `u t h i` | 17,337 |
| 5 | `e l a _` | 17,028 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u t h i _` | 16,069 |
| 2 | `i f u n d` | 12,578 |
| 3 | `f u n d a` | 12,506 |
| 4 | `s i f u n` | 11,468 |
| 5 | `t h o m b` | 9,287 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 252
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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 | 0.6996 | 1.624 | 3.77 | 162,102 | 30.0% |
| **1** | Subword | 0.9455 | 1.926 | 7.47 | 974 | 5.4% |
| **2** | Word | 0.1187 | 1.086 | 1.21 | 608,961 | 88.1% |
| **2** | Subword | 0.9300 | 1.905 | 5.59 | 7,271 | 7.0% |
| **3** | Word | 0.0263 | 1.018 | 1.04 | 733,914 | 97.4% |
| **3** | Subword | 0.8812 | 1.842 | 4.36 | 40,628 | 11.9% |
| **4** | Word | 0.0098 🏆 | 1.007 | 1.01 | 758,379 | 99.0% |
| **4** | Subword | 0.7127 | 1.639 | 2.95 | 176,908 | 28.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i motha owazalwa umgadli kusukela futhi yidolobha elikwisifundazwe se bizerte north kivu ekhongo bra...`
2. `futhi abantu abaningi ngokukhipha amasoka awo abizwa i psl onamagoli aphakeme ngonyaka imithombo kap...`
3. `imithombo zase khongo kinshasa administrative woredas africaopendata org kulandwe ngo masingana 4 fb...`

**Context Size 2:**

1. `kwesifundazwe se somali e itiyopiya imithombo ase khongo kinshasa zase khongo kinshasa zase khongo k...`
2. `imithombo ase gabhoni zase gabhoni imithombo zase aljeriya amadolobha ase khenya imithombo zase erit...`
3. `imithombo zase aljeriya ngaphansi kwezifundazwe ezitholakala kuzona census of population okwenziwa y...`

**Context Size 3:**

1. `esingaphansi kwesifundazwe se nabeul ethuniziya imithombo zase thuniziya`
2. `yisifunda esingaphansi kwesifundazwe se aïn témouchent e aljeriya imithombo zase aljeriya ase aljeri...`
3. `yidolobha elikwisifundazwe se central eyuganda lesiqhingi singaphansi kwesifunda se mukono imithombo...`

**Context Size 4:**

1. `yisifunda esingaphansi kwesifundazwe se north kivu ekhongo kinshasa administrative zones of the demo...`
2. `futhi yidolobha elikwisifundazwe se sousse ethuniziya imithombo zase thuniziya`
3. `ngumasipala futhi yidolobha elikwisifundazwe se tizi ouzou e aljeriya imithombo zase aljeriya ase al...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_-ama_nemebontid`
2. `a_mila_lople_iny`
3. `ithis_yo._kaston`

**Context Size 2:**

1. `a_isakhamo_ezisan`
2. `e_ala_yeyidingo-m`
3. `ngemhlokotabde_iz`

**Context Size 3:**

1. `la_kwisikhulu._ngo`
2. `_ngekufund_baphosh`
3. `nganiselwenkanye_n`

**Context Size 4:**

1. `thi_isixhosa_(12.1%`
2. `_ukuya_kakhulumeni_`
3. `_ngokusha_kanyise_u`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (176,908 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 | 62,862 |
| Total Tokens | 817,095 |
| Mean Frequency | 13.00 |
| Median Frequency | 3 |
| Frequency Std Dev | 110.38 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 10,301 |
| 2 | futhi | 8,577 |
| 3 | imithombo | 8,425 |
| 4 | se | 7,351 |
| 5 | kanye | 6,221 |
| 6 | noma | 5,916 |
| 7 | afrika | 5,345 |
| 8 | e | 4,772 |
| 9 | ukuthi | 4,267 |
| 10 | ngo | 4,178 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | izimboma | 2 |
| 2 | zokushulubeza | 2 |
| 3 | miniaturowej | 2 |
| 4 | sztuki | 2 |
| 5 | profesjonalnej | 2 |
| 6 | henryk | 2 |
| 7 | wideo | 2 |
| 8 | nietypowe | 2 |
| 9 | sztalugi | 2 |
| 10 | zapałek | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9199 |
| R² (Goodness of Fit) | 0.997336 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 24.1% |
| Top 1,000 | 47.6% |
| Top 5,000 | 68.0% |
| Top 10,000 | 77.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9973 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 24.1% of corpus
- **Long Tail:** 52,862 words needed for remaining 22.9% 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 | 0.7797 🏆 | 0.2970 | N/A | N/A |
| **mono_64d** | 64 | 0.7639 | 0.2268 | N/A | N/A |
| **mono_128d** | 128 | 0.3200 | 0.1959 | N/A | N/A |
| **aligned_32d** | 32 | 0.7797 | 0.2840 | 0.0420 | 0.2500 |
| **aligned_64d** | 64 | 0.7639 | 0.2098 | 0.0900 | 0.3460 |
| **aligned_128d** | 128 | 0.3200 | 0.2045 | 0.1420 | 0.4240 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7797 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2363. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 14.2% 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 | **0.743** | 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 |
|--------|----------|
| `-i` | izingcwecwe, ijaji, iron |
| `-e` | ekhokhelwayo, eziqinisekisiwe, eː |
| `-u` | uzosiza, ubadide, ukundiyaza |
| `-a` | akunakwenzeka, akhawunti, abavuthiwe |
| `-s` | sobukhulu, suite, sicela |
| `-n` | nenkonzo, nendodana, ngumholi |
| `-ku` | kuncike, kuthonywa, kuleminyaka |
| `-k` | kwizaga, komkhankaso, knuth |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | uzosiza, nendodana, ukundiyaza |
| `-i` | zamabhaluni, ijaji, ngumholi |
| `-e` | izingcwecwe, okucacisiwe, ubadide |
| `-o` | nenkonzo, bebengenawo, ekhokhelwayo |
| `-la` | indlela, awasungula, ezwela |
| `-wa` | eyayiqondiswa, ukucekelwa, ethunyelwa |
| `-ni` | zamabhaluni, zasehlathini, egciwaneni |
| `-le` | westville, usonhlalakahle, okungalungile |

### 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 |
|------|----------|------------------|----------|
| `ifun` | 2.49x | 64 contexts | ifuna, sifuna, zifuna |
| `khul` | 2.04x | 154 contexts | khula, khulu, ekhula |
| `unda` | 2.44x | 42 contexts | lunda, undab, funda |
| `ning` | 2.25x | 57 contexts | mining, iningi, eningi |
| `sifu` | 2.54x | 34 contexts | sifuna, sifunde, sifunda |
| `aban` | 1.89x | 96 contexts | abane, abangu, abanzi |
| `anga` | 1.76x | 132 contexts | tanga, banga, angar |
| `hulu` | 2.04x | 64 contexts | uhulu, khulu, okhulu |
| `itho` | 1.90x | 81 contexts | zitho, ithole, isitho |
| `apha` | 2.02x | 58 contexts | lapha, qapha, ngapha |
| `kuth` | 1.91x | 68 contexts | ukuth, kuthi, kuthe |
| `homb` | 2.12x | 42 contexts | ukhomba, ekhomba, akhomba |

### 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 |
|--------|--------|-----------|----------|
| `-u` | `-a` | 340 words | ukunikeza, ugcina |
| `-n` | `-a` | 329 words | nokujwayela, nethaba |
| `-e` | `-a` | 244 words | enakekela, ezizosetshenziswa |
| `-e` | `-i` | 241 words | ezimbizeni, emlandweni |
| `-i` | `-a` | 212 words | ichasisa, isasasa |
| `-n` | `-i` | 186 words | namashumi, nasekuthuthukiseni |
| `-e` | `-ni` | 182 words | ezimbizeni, emlandweni |
| `-e` | `-e` | 164 words | evinjelwe, ezimisele |
| `-k` | `-a` | 155 words | kukajona, kokuvulwa |
| `-a` | `-a` | 151 words | abrama, abalandelwa |

### 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 |
|------|-----------------|------------|------|
| wasejalimane | **`wasejalim-a-ne`** | 7.5 | `a` |
| continued | **`continu-e-d`** | 7.5 | `e` |
| ukufudumala | **`ukufudum-a-la`** | 7.5 | `a` |
| wayengunkosikazi | **`wayengunkosik-a-zi`** | 7.5 | `a` |
| sikhakhane | **`sikhakh-a-ne`** | 7.5 | `a` |
| ubuhlengikazi | **`ubuhlengik-a-zi`** | 7.5 | `a` |
| afghanistani | **`afghanist-a-ni`** | 7.5 | `a` |
| owayedlalela | **`owayedla-le-la`** | 7.5 | `le` |
| samasulumane | **`samasulum-a-ne`** | 7.5 | `a` |
| abancweli | **`abanc-we-li`** | 7.5 | `we` |
| kwesilandelayo | **`kwesilande-la-yo`** | 7.5 | `la` |
| abashokobezi | **`abashokob-e-zi`** | 7.5 | `e` |
| nabwatswana | **`nabwats-wa-na`** | 7.5 | `wa` |
| ukuhlabeka | **`ukuhlab-e-ka`** | 7.5 | `e` |
| nezinselele | **`nezinse-le-le`** | 7.5 | `le` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Zulu 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 (5.06x) |
| N-gram | **2-gram** | Lowest perplexity (252) |
| Markov | **Context-4** | Highest predictability (99.0%) |
| 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: 2026-01-11 06:02:31*