---
language: xh
language_name: Xhosa
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: 4.929
  - name: best_isotropy
    type: isotropy
    value: 0.8914
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Xhosa** 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** | 3.679x | 3.68 | 0.2207% | 429,593 |
| **16k** | 4.111x | 4.11 | 0.2466% | 384,442 |
| **32k** | 4.548x | 4.55 | 0.2728% | 347,524 |
| **64k** | 4.929x 🏆 | 4.93 | 0.2956% | 320,656 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `I-Orta Nova (kude kube ebizwa ngokuba yi-Orta) ngumasipala wase-Italiya onabemi ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁i - or ta ▁nova ▁( kude ▁kube ▁ebizwa ▁ngokuba ... (+16 more)` | 26 |
| 16k | `▁i - or ta ▁nova ▁( kude ▁kube ▁ebizwa ▁ngokuba ... (+15 more)` | 25 |
| 32k | `▁i - orta ▁nova ▁( kude ▁kube ▁ebizwa ▁ngokuba ▁yi ... (+13 more)` | 23 |
| 64k | `▁i - orta ▁nova ▁( kude ▁kube ▁ebizwa ▁ngokuba ▁yi ... (+13 more)` | 23 |

**Sample 2:** `Icawa yindawo yokuhlanganisana yamaKristu, nokuba angamaKatolika, amaOthodoki ok...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁icawa ▁yindawo ▁yoku hlang ani sana ▁yama kristu , ▁nokuba ... (+13 more)` | 23 |
| 16k | `▁icawa ▁yindawo ▁yoku hlangani sana ▁yama kristu , ▁nokuba ▁angama ... (+11 more)` | 21 |
| 32k | `▁icawa ▁yindawo ▁yoku hlanganisana ▁yamakristu , ▁nokuba ▁angama katolika , ... (+5 more)` | 15 |
| 64k | `▁icawa ▁yindawo ▁yoku hlanganisana ▁yamakristu , ▁nokuba ▁angama katolika , ... (+3 more)` | 13 |

**Sample 3:** `IDaouche yilali kunye nendawo yasemaphandleni eNiger. Ukusukela ibinabemi Iimbek...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ida o u che ▁yilali ▁kunye ▁nendawo ▁yasemaphandleni ▁eniger . ... (+6 more)` | 16 |
| 16k | `▁ida o u che ▁yilali ▁kunye ▁nendawo ▁yasemaphandleni ▁eniger . ... (+4 more)` | 14 |
| 32k | `▁ida ouche ▁yilali ▁kunye ▁nendawo ▁yasemaphandleni ▁eniger . ▁ukusukela ▁ibinabemi ... (+2 more)` | 12 |
| 64k | `▁idaouche ▁yilali ▁kunye ▁nendawo ▁yasemaphandleni ▁eniger . ▁ukusukela ▁ibinabemi ▁iimbekiselo ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 64k achieves 4.929x compression
- **Lowest UNK Rate:** 8k with 0.2207% 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 | 3,253 | 11.67 | 5,073 | 16.6% | 52.9% |
| **2-gram** | Subword | 259 🏆 | 8.02 | 2,144 | 68.4% | 99.5% |
| **3-gram** | Word | 3,451 | 11.75 | 5,094 | 16.6% | 50.4% |
| **3-gram** | Subword | 2,203 | 11.11 | 15,967 | 24.4% | 72.7% |
| **4-gram** | Word | 9,133 | 13.16 | 12,576 | 11.1% | 29.3% |
| **4-gram** | Subword | 12,328 | 13.59 | 78,348 | 10.9% | 38.3% |
| **5-gram** | Word | 7,660 | 12.90 | 10,427 | 12.5% | 30.1% |
| **5-gram** | Subword | 39,954 | 15.29 | 185,127 | 6.4% | 23.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kunye ne` | 613 |
| 2 | `emzantsi afrika` | 405 |
| 3 | `of the` | 341 |
| 4 | `ngokuba yi` | 328 |
| 5 | `emva koko` | 192 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `iimbekiselo amakhonkco angaphandle` | 97 |
| 2 | `c eyona nyanga` | 78 |
| 3 | `cc by post` | 76 |
| 4 | `org cc by` | 76 |
| 5 | `sa geonames org` | 76 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sa geonames org cc` | 76 |
| 2 | `org cc by post` | 76 |
| 3 | `geonames org cc by` | 76 |
| 4 | `updated database download sa` | 76 |
| 5 | `post updated database download` | 76 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sa geonames org cc by` | 76 |
| 2 | `org cc by post updated` | 76 |
| 3 | `cc by post updated database` | 76 |
| 4 | `by post updated database download` | 76 |
| 5 | `post updated database download sa` | 76 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 100,386 |
| 2 | `e _` | 62,380 |
| 3 | `a n` | 57,095 |
| 4 | `o _` | 53,048 |
| 5 | `n g` | 49,243 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a _` | 21,271 |
| 2 | `_ n g` | 19,972 |
| 3 | `_ k w` | 17,850 |
| 4 | `_ k u` | 17,761 |
| 5 | `a _ k` | 15,793 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n y e _` | 11,326 |
| 2 | `e l a _` | 8,721 |
| 3 | `_ u k u` | 8,570 |
| 4 | `a _ n g` | 8,421 |
| 5 | `_ n g o` | 8,259 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k u b a _` | 5,628 |
| 2 | `u n y e _` | 5,544 |
| 3 | `k u n y e` | 5,475 |
| 4 | `n y e _ n` | 5,432 |
| 5 | `_ k u n y` | 5,381 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 259
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.6070 | 1.523 | 3.17 | 104,417 | 39.3% |
| **1** | Subword | 1.1180 | 2.171 | 9.35 | 521 | 0.0% |
| **2** | Word | 0.1066 | 1.077 | 1.18 | 329,356 | 89.3% |
| **2** | Subword | 1.0676 | 2.096 | 6.29 | 4,869 | 0.0% |
| **3** | Word | 0.0246 | 1.017 | 1.03 | 387,463 | 97.5% |
| **3** | Subword | 0.9182 | 1.890 | 4.35 | 30,613 | 8.2% |
| **4** | Word | 0.0088 🏆 | 1.006 | 1.01 | 398,295 | 99.1% |
| **4** | Subword | 0.7004 | 1.625 | 2.83 | 133,109 | 30.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i multibit ye analog computer ngomzila wefowuni kuquka i eccentric kwaye iza wamkele ukristu bc nang...`
2. `kunye newololo music education act isikolo samagriqua phesheya kwenciba nakumaxesha angaphambili kun...`
3. `kwaye inomsebenzi wokutyumba oosompempe ukuba bamthabathe ngokwegqwirha elikhwela esinga ejongise ng...`

**Context Size 2:**

1. `kunye ne 8 500 bc ngexesha lestone age ukuya ekupheleni kwekhulu le 19 pos iqela pld w`
2. `of the bhacas from earliest times to doctoral dissertation university of natal after he bought a sto...`
3. `ngokuba yi alchemy nangona kunjalo waqhubeka wasebenza kuguqulo lwendumasiso lwenoveli yodidi engumz...`

**Context Size 3:**

1. `iimbekiselo amakhonkco angaphandle indawo esemthethweni ngesiphuthukezi baseroraima`
2. `c eyona nyanga ishushu ngujulayi nge c kwaye eyona ngqele kafebruwari ngo c umyinge wokuna kwemvula ...`
3. `cc by post updated database download sa ime kumasipala wasekalix kommun kunye nephondo lasenorbotten...`

**Context Size 4:**

1. `by post updated database download sa ifumaneka kwiphondo leprovincia di foggia kunye nommandla wepug...`
2. `sa geonames org cc by post updated database download sa ifumaneka kummandla wezoqoqosho weylä savo k...`
3. `cc by post updated database download sa ifumaneka kwiphondo leprovincia di verona kunye nommandla we...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ku_nazo_eay’uth`
2. `abekwhut_(yose_:`
3. `esisi_jekwabamba`

**Context Size 2:**

1. `a_es._kwagom_hays`
2. `e_ngozabonfer,_ic`
3. `ano_yelo_ye_ic_ek`

**Context Size 3:**

1. `la_wenziswengokwen`
2. `_ngoxa_popolophu._`
3. `_kwimi_eli_uba_uku`

**Context Size 4:**

1. `nye_la_confederano,`
2. `ela_lwaseshumi_amaq`
3. `_ukuze_sifumandeley`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (133,109 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 | 35,909 |
| Total Tokens | 362,403 |
| Mean Frequency | 10.09 |
| Median Frequency | 3 |
| Frequency Std Dev | 60.47 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 5,328 |
| 2 | kunye | 5,290 |
| 3 | kwaye | 2,522 |
| 4 | ukuba | 2,013 |
| 5 | okanye | 1,987 |
| 6 | 1 | 1,832 |
| 7 | the | 1,804 |
| 8 | of | 1,523 |
| 9 | kwi | 1,513 |
| 10 | ke | 1,364 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | okuthengiswa | 2 |
| 2 | esitalatweni | 2 |
| 3 | ezitalatweni | 2 |
| 4 | kwesitalato | 2 |
| 5 | pilibhit | 2 |
| 6 | ezifundo | 2 |
| 7 | nenkubazeko | 2 |
| 8 | yaseluthere | 2 |
| 9 | ceulji | 2 |
| 10 | kwesport | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8870 |
| R² (Goodness of Fit) | 0.995256 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.1% |
| Top 1,000 | 46.3% |
| Top 5,000 | 69.4% |
| Top 10,000 | 80.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9953 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.1% of corpus
- **Long Tail:** 25,909 words needed for remaining 19.9% 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 | 0.8914 | 0.2946 | N/A | N/A |
| **mono_64d** | 64 | 0.6652 | 0.2434 | N/A | N/A |
| **mono_128d** | 128 | 0.1559 | 0.2440 | N/A | N/A |
| **aligned_32d** | 32 | 0.8914 🏆 | 0.2952 | 0.0360 | 0.2160 |
| **aligned_64d** | 64 | 0.6652 | 0.2484 | 0.0540 | 0.2700 |
| **aligned_128d** | 128 | 0.1559 | 0.2308 | 0.0880 | 0.3480 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8914 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2594. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.8% 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 | **0.310** | 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` | inyongo, itshintshile, iimitha |
| `-e` | ehleli, elected, esebenzayo |
| `-u` | umbane, umtu, ubunkokeli |
| `-a` | abathunywa, amabanga, arlington |
| `-n` | ngowayesakuba, njengeempawu, netherland |
| `-ne` | netherland, neutron, nelungelo |
| `-s` | steatorrhea, scored, sant |
| `-ku` | kubanjelwa, kunokwenzeka, kusenziwa |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | lokubhala, ngowayesakuba, wamaza |
| `-o` | inyongo, ngenyawo, kwintetho |
| `-i` | yabancinci, ngeentombi, ehleli |
| `-e` | itshintshile, glucose, umbane |
| `-la` | lokubhala, elivuselela, bawela |
| `-wa` | kubanjelwa, abathunywa, kwaqhutywa |
| `-ni` | ekujonganeni, empumelelweni, udlamini |
| `-yo` | esebenzayo, ukwaziyo, elichaseneyo |

### 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 |
|------|----------|------------------|----------|
| `khul` | 2.03x | 88 contexts | khulu, akhule, ekhula |
| `enzi` | 2.13x | 60 contexts | menzi, enzima, enziwa |
| `heth` | 2.04x | 68 contexts | khetha, khetho, utheth |
| `aban` | 1.89x | 70 contexts | abane, abanye, abanga |
| `okub` | 1.86x | 55 contexts | okuba, nokuba, sokuba |
| `ezin` | 1.88x | 52 contexts | ezine, ezinde, ezinee |
| `ants` | 2.26x | 23 contexts | gantsa, nantso, plants |
| `andl` | 1.90x | 41 contexts | mandla, sandla, imandla |
| `ngen` | 1.58x | 82 contexts | ingene, ongena, angena |
| `ndle` | 1.83x | 41 contexts | endle, bundle, ndlebe |
| `hulu` | 1.94x | 32 contexts | khulu, akhulu, ikhulu |
| `bant` | 2.19x | 21 contexts | bantu, abantu, ubantu |

### 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 |
|--------|--------|-----------|----------|
| `-n` | `-a` | 291 words | njengomasipala, nechina |
| `-u` | `-a` | 256 words | ukuchazwa, unobhala |
| `-n` | `-o` | 226 words | nkonzo, nenkathalo |
| `-e` | `-a` | 216 words | ephesheya, entshwana |
| `-i` | `-a` | 203 words | ingenziwa, ingena |
| `-n` | `-i` | 179 words | ngamagqabi, neegesi |
| `-e` | `-o` | 171 words | ebamako, ezichaphazelekayo |
| `-i` | `-o` | 156 words | isibonelelo, ibibalihlazo |
| `-k` | `-a` | 156 words | kuyakweza, kuyafana |
| `-l` | `-a` | 153 words | lwama, litsha |

### 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 |
|------|-----------------|------------|------|
| kamkhwebane | **`kamkhweb-a-ne`** | 7.5 | `a` |
| yasentaliyane | **`yasentaliy-a-ne`** | 7.5 | `a` |
| ubungcali | **`ubungc-a-li`** | 7.5 | `a` |
| kwiitshaneli | **`kw-i-itshaneli`** | 7.5 | `itshaneli` |
| nesijamani | **`nesijam-a-ni`** | 7.5 | `a` |
| ezingabamelwane | **`ezingabamelw-a-ne`** | 7.5 | `a` |
| uyavakala | **`uyavak-a-la`** | 7.5 | `a` |
| abafikayo | **`abafik-a-yo`** | 7.5 | `a` |
| nokudodobala | **`nokudodob-a-la`** | 7.5 | `a` |
| kwisigwebo | **`kwisig-we-bo`** | 7.5 | `we` |
| ezimfutshane | **`ezimfutsh-a-ne`** | 7.5 | `a` |
| uzbekistan | **`uzbekist-a-n`** | 7.5 | `a` |
| kwiinkulungwane | **`kwiinkulungw-a-ne`** | 7.5 | `a` |
| sebastian | **`sebasti-a-n`** | 7.5 | `a` |
| ovuthuzayo | **`ovuthuz-a-yo`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Xhosa 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 (4.93x) |
| N-gram | **2-gram** | Lowest perplexity (259) |
| Markov | **Context-4** | Highest predictability (99.1%) |
| 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: 2026-01-11 04:59:25*