---
language: nr
language_name: South Ndebele
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: 6.115
  - name: best_isotropy
    type: isotropy
    value: 0.4750
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# South Ndebele - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **South Ndebele** 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** | 4.500x | 4.50 | 0.2494% | 232,512 |
| **16k** | 5.097x | 5.10 | 0.2826% | 205,268 |
| **32k** | 5.669x | 5.67 | 0.3143% | 184,546 |
| **64k** | 6.115x 🏆 | 6.12 | 0.3390% | 171,093 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `UJoe Sibanyoni ungusomarhwebo no mphathi omkhulu matekisi, ohlala eKwaggafontein...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁u jo e ▁si ban yoni ▁ungu soma rhwebo ▁no ... (+13 more)` | 23 |
| 16k | `▁u joe ▁si ban yoni ▁ungu somarhwebo ▁no ▁mphathi ▁omkhulu ... (+9 more)` | 19 |
| 32k | `▁ujoe ▁sibanyoni ▁ungu somarhwebo ▁no ▁mphathi ▁omkhulu ▁matekisi , ▁ohlala ... (+3 more)` | 13 |
| 64k | `▁ujoe ▁sibanyoni ▁ungusomarhwebo ▁no ▁mphathi ▁omkhulu ▁matekisi , ▁ohlala ▁ekwaggafontein ... (+2 more)` | 12 |

**Sample 2:** `UJabu Mahlangu obuye aziwe ngo Jabu Pule wayengumdlai wecembe lebhola i Kaizer C...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁u ja bu ▁mahlangu ▁obu ye ▁azi we ▁ngo ▁ja ... (+21 more)` | 31 |
| 16k | `▁uja bu ▁mahlangu ▁obu ye ▁aziwe ▁ngo ▁ja bu ▁pu ... (+17 more)` | 27 |
| 32k | `▁uja bu ▁mahlangu ▁obu ye ▁aziwe ▁ngo ▁jabu ▁pu le ... (+11 more)` | 21 |
| 64k | `▁ujabu ▁mahlangu ▁obuye ▁aziwe ▁ngo ▁jabu ▁pule ▁wayengumdlai ▁wecembe ▁lebhola ... (+7 more)` | 17 |

**Sample 3:** `iSiyabuswa yilokishi lakwaNdebele, eSewula Afrika.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁isi yabuswa ▁yi lokishi ▁la kwandebele , ▁esewula ▁afrika .` | 10 |
| 16k | `▁isi yabuswa ▁yilokishi ▁la kwandebele , ▁esewula ▁afrika .` | 9 |
| 32k | `▁isiyabuswa ▁yilokishi ▁la kwandebele , ▁esewula ▁afrika .` | 8 |
| 64k | `▁isiyabuswa ▁yilokishi ▁lakwandebele , ▁esewula ▁afrika .` | 7 |


### Key Findings

- **Best Compression:** 64k achieves 6.115x compression
- **Lowest UNK Rate:** 8k with 0.2494% 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 | 887 | 9.79 | 1,218 | 30.9% | 91.1% |
| **2-gram** | Subword | 215 🏆 | 7.75 | 1,135 | 73.9% | 99.9% |
| **3-gram** | Word | 874 | 9.77 | 1,068 | 26.9% | 95.6% |
| **3-gram** | Subword | 1,524 | 10.57 | 8,047 | 29.1% | 80.7% |
| **4-gram** | Word | 3,504 | 11.77 | 3,737 | 8.1% | 34.6% |
| **4-gram** | Subword | 6,910 | 12.75 | 33,324 | 13.8% | 47.8% |
| **5-gram** | Word | 3,016 | 11.56 | 3,094 | 6.8% | 37.0% |
| **5-gram** | Subword | 18,833 | 14.20 | 66,076 | 8.5% | 30.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `esewula afrika` | 202 |
| 2 | `south africa` | 125 |
| 3 | `wesewula afrika` | 101 |
| 4 | `kanye ne` | 98 |
| 5 | `of the` | 90 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `retrieved from retrieved` | 50 |
| 2 | `from retrieved on` | 49 |
| 3 | `ku ifunyenwe ngomhlaka` | 48 |
| 4 | `of south africa` | 41 |
| 5 | `in south africa` | 36 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `retrieved from retrieved on` | 44 |
| 2 | `litholakala ku lifunyenwe ngomhlaka` | 33 |
| 3 | `litholakala ku ifunyenwe ngomhlaka` | 27 |
| 4 | `eenhlokwaneni ezilandelako sizokutjheja bonyana` | 16 |
| 5 | `itholakala ku ifunyenwe ngomhlaka` | 16 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ku ifunyenwe ngomhlaka 24 kunobayeni` | 12 |
| 2 | `litholakala ku ifunyenwe ngomhlaka 24` | 12 |
| 3 | `u s department of energy` | 10 |
| 4 | `litholakala ku lifunyenwe ngomhlaka 19` | 8 |
| 5 | `website retrieved from retrieved on` | 8 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 34,916 |
| 2 | `a n` | 21,629 |
| 3 | `n g` | 17,440 |
| 4 | `l a` | 16,021 |
| 5 | `i _` | 15,755 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n a _` | 7,746 |
| 2 | `l a _` | 6,995 |
| 3 | `_ n g` | 6,159 |
| 4 | `n g a` | 5,962 |
| 5 | `a _ n` | 5,787 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n a _` | 4,951 |
| 2 | `_ u k u` | 3,681 |
| 3 | `a n g a` | 2,726 |
| 4 | `a _ n g` | 2,689 |
| 5 | `e n i _` | 2,674 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ u k u` | 1,464 |
| 2 | `a b a n t` | 1,460 |
| 3 | `l a n g a` | 1,382 |
| 4 | `k h u l u` | 1,293 |
| 5 | `_ n g o k` | 1,293 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 215
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.5928 | 1.508 | 2.90 | 34,363 | 40.7% |
| **1** | Subword | 1.2345 | 2.353 | 11.18 | 185 | 0.0% |
| **2** | Word | 0.1023 | 1.073 | 1.16 | 99,105 | 89.8% |
| **2** | Subword | 1.3055 | 2.472 | 7.07 | 2,065 | 0.0% |
| **3** | Word | 0.0231 | 1.016 | 1.03 | 114,483 | 97.7% |
| **3** | Subword | 0.9022 | 1.869 | 3.87 | 14,600 | 9.8% |
| **4** | Word | 0.0074 🏆 | 1.005 | 1.01 | 117,392 | 99.3% |
| **4** | Subword | 0.5974 | 1.513 | 2.39 | 56,446 | 40.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `begodu yamenyezelwa njengezakhamuzi zabantu zinikela amathuba alinganako nofana anganasithunzi bese ...`
2. `i cape ne oukwanyama iinkomba zephasi namhlanje abentwana abanengi bakhethe ukufudukela emadorobheni...`
3. `bona unepilo begodu inemingcele yelwandle asekuthomeni kwelwandle lapho akhethwa khona nesiqhema sez...`

**Context Size 2:**

1. `esewula afrika idorojaneli litholakala ngemva kwamakhilomitha ama 53 esewula yedorobha i middleburg ...`
2. `south africa studia historiae ecclesiasticae 48 1 pp 30 55 ilimi lisetjenziswa ngokufanako kodwana i...`
3. `wesewula afrika kanye ne ciskei ngomrhayili may nokho aba khona amalungiselelo enziwako kodwana ukut...`

**Context Size 3:**

1. `retrieved from retrieved on umtjhagalo wabomma umnqopho omkhulu wombuso webandlululo bekukuhlukanisa...`
2. `from retrieved on indlela iintjhijilwezi ezingararululwa ngayo urhulumende kufuze wandise amahlelo w...`
3. `ku ifunyenwe ngomhlaka 24 kunobayeni ihlathulule ilimi njengehlelo elihlelekileko lezokuthintana lel...`

**Context Size 4:**

1. `retrieved from retrieved on ekulumenakhe ayethula ngesikhathi athumba unongorwana uthi lokhu kungikh...`
2. `litholakala ku lifunyenwe ngomhlaka 7 kutjhirhweni ikhotho le ukuze iragele phambili nokulalelwa kwe...`
3. `litholakala ku ifunyenwe ngomhlaka 24 kunobayeni ngokufanako umtjhini nanyana isithuthi esisebenzisa...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `ani_si_nizisi_et`
2. `_okundema_athizi`
3. `ekweko_dii_u_a-_`

**Context Size 2:**

1. `a_kos_moyo_elalan`
2. `anyenya_wisinika_`
3. `ngemvunengokubo_k`

**Context Size 3:**

1. `na_ball_stransvaal`
2. `la_ephatho_-_ecamo`
3. `_ngokwana_begaza_e`

**Context Size 4:**

1. `ana_adlalo_yase_emq`
2. `_ukuze_umvuzo_yesay`
3. `anga,_esele_isifo_s`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (56,446 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 | 12,308 |
| Total Tokens | 101,917 |
| Mean Frequency | 8.28 |
| Median Frequency | 3 |
| Frequency Std Dev | 31.87 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | begodu | 1,170 |
| 2 | i | 1,079 |
| 3 | bona | 1,057 |
| 4 | u | 804 |
| 5 | afrika | 717 |
| 6 | abantu | 666 |
| 7 | of | 666 |
| 8 | nanyana | 584 |
| 9 | kanye | 582 |
| 10 | and | 563 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | isiqundo | 2 |
| 2 | nkabinde | 2 |
| 3 | wamajuda | 2 |
| 4 | polotiki | 2 |
| 5 | progressive | 2 |
| 6 | lunga | 2 |
| 7 | ngokwehlukana | 2 |
| 8 | enjalo | 2 |
| 9 | affairs | 2 |
| 10 | isithunywa | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8997 |
| R² (Goodness of Fit) | 0.988207 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.9% |
| Top 1,000 | 55.8% |
| Top 5,000 | 83.1% |
| Top 10,000 | 95.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9882 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.9% of corpus
- **Long Tail:** 2,308 words needed for remaining 4.5% 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 | 0.4750 | 0.3518 | N/A | N/A |
| **mono_64d** | 64 | 0.1080 | 0.3618 | N/A | N/A |
| **mono_128d** | 128 | 0.0129 | 0.3564 | N/A | N/A |
| **aligned_32d** | 32 | 0.4750 🏆 | 0.3688 | 0.0020 | 0.1080 |
| **aligned_64d** | 64 | 0.1080 | 0.3760 | 0.0120 | 0.1800 |
| **aligned_128d** | 128 | 0.0129 | 0.3745 | 0.0280 | 0.2020 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.4750 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3649. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 2.8% 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 | **0.224** | 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 |
|--------|----------|
| `-e` | ezidla, ekufanele, ezincane |
| `-i` | iinhluthu, improving, isuka |
| `-a` | awukhulumi, abalimunyileko, about |
| `-u` | ukutlhaga, ukusela, ukugula |
| `-n` | nelutjha, nangokuthi, ngokudluleleko |
| `-ku` | kuzokuba, kunobayeni, kukhukhulamungu |
| `-s` | sociology, sihlukaniswa, sekhukhune |
| `-b` | bekuyindawo, buhlungu, bekuliyunithi |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | wambuza, nelutjha, sihlukaniswa |
| `-i` | awukhulumi, nangokuthi, bekuliyunithi |
| `-o` | ngokudluleleko, bekuyindawo, abalimunyileko |
| `-e` | maqhawe, sekhukhune, ekufanele |
| `-la` | ezidla, wokuthola, ukusela |
| `-ni` | ekwabelaneni, kunobayeni, emasikweni |
| `-wa` | sihlukaniswa, abawa, elidluliselwa |
| `-ko` | ngokudluleleko, abalimunyileko, ezisetjenziswako |

### 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 |
|------|----------|------------------|----------|
| `lang` | 1.86x | 45 contexts | langa, lange, ilanga |
| `khul` | 1.58x | 60 contexts | khula, khulu, khuli |
| `benz` | 1.96x | 25 contexts | benze, benza, ebenza |
| `enzi` | 1.77x | 32 contexts | enzima, enziwe, zenziwa |
| `aban` | 1.63x | 40 contexts | abane, abanga, abantu |
| `kuth` | 1.50x | 46 contexts | kuthi, ukuthi, nokuth |
| `anga` | 1.51x | 39 contexts | langa, abanga, angabi |
| `hulu` | 1.65x | 24 contexts | khulu, mkhulu, omkhulu |
| `antu` | 2.05x | 11 contexts | bantu, abantu, ubantu |
| `hlan` | 1.70x | 19 contexts | hlanu, mhlana, bahlanu |
| `nyan` | 1.48x | 29 contexts | nyanga, mnyango, bonyana |
| `hath` | 1.33x | 43 contexts | thathu, uthatha, athathe |

### 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` | 450 words | umulwana, ukufiphala |
| `-n` | `-a` | 404 words | ngokufana, ngokusebenzisana |
| `-e` | `-i` | 344 words | emathuthumbeni, emapholiseni |
| `-e` | `-ni` | 305 words | emathuthumbeni, emapholiseni |
| `-n` | `-o` | 254 words | nobunjalo, nekghono |
| `-n` | `-i` | 214 words | nobudisi, namalori |
| `-a` | `-a` | 203 words | abelana, akhambisana |
| `-i` | `-o` | 200 words | iziko, iinqunto |
| `-e` | `-a` | 198 words | eziphila, eziphikisana |
| `-i` | `-a` | 187 words | ithelerina, inamandla |

### 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 |
|------|-----------------|------------|------|
| batholakala | **`batholak-a-la`** | 7.5 | `a` |
| nakazithweleko | **`nakazithwe-le-ko`** | 7.5 | `le` |
| nakafundisako | **`nakafundis-a-ko`** | 7.5 | `a` |
| ebantwini | **`ebantw-i-ni`** | 7.5 | `i` |
| abanelwazi | **`abanel-wa-zi`** | 7.5 | `wa` |
| lokuhlobana | **`lokuhlob-a-na`** | 7.5 | `a` |
| zahlukana | **`zahluk-a-na`** | 7.5 | `a` |
| ezizumako | **`ezizum-a-ko`** | 7.5 | `a` |
| emahlubini | **`emahlub-i-ni`** | 7.5 | `i` |
| ubuntazana | **`ubuntaz-a-na`** | 7.5 | `a` |
| elakhiweko | **`elakhiw-e-ko`** | 7.5 | `e` |
| lobulondolwazi | **`lobulondol-wa-zi`** | 7.5 | `wa` |
| emkhandlwini | **`emkhandlw-i-ni`** | 7.5 | `i` |
| ikohlakalo | **`ikohlak-a-lo`** | 7.5 | `a` |
| okhanyisako | **`okhanyis-a-ko`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language South Ndebele shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (6.11x) |
| N-gram | **2-gram** | Lowest perplexity (215) |
| Markov | **Context-4** | Highest predictability (99.3%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| 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 16:03:31*