---
language: ss
language_name: Swati
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: 5.616
  - name: best_isotropy
    type: isotropy
    value: 0.6744
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Swati** 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** | 4.045x | 4.05 | 0.4074% | 268,766 |
| **16k** | 4.553x | 4.56 | 0.4586% | 238,783 |
| **32k** | 5.026x | 5.03 | 0.5062% | 216,332 |
| **64k** | 5.616x 🏆 | 5.62 | 0.5656% | 193,596 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Kusoka yinchubo lesusa sikhumba sesibeletho esitfweni sangasese semuntfu sangans...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kuso ka ▁yin chubo ▁le susa ▁sikhumba ▁sesi bele tho ... (+11 more)` | 21 |
| 16k | `▁kuso ka ▁yin chubo ▁le susa ▁sikhumba ▁sesi beletho ▁esitfweni ... (+7 more)` | 17 |
| 32k | `▁kusoka ▁yinchubo ▁le susa ▁sikhumba ▁sesi beletho ▁esitfweni ▁sangasese ▁semuntfu ... (+3 more)` | 13 |
| 64k | `▁kusoka ▁yinchubo ▁lesusa ▁sikhumba ▁sesibeletho ▁esitfweni ▁sangasese ▁semuntfu ▁sangansense .` | 10 |

**Sample 2:** `7 Bhimbídvwane. Lilanga 7 enyangeni yeBhimbídvwane.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 7 ▁bhimbídvwane . ▁lilanga ▁ 7 ▁enyangeni ▁yebhimbídvwane .` | 10 |
| 16k | `▁ 7 ▁bhimbídvwane . ▁lilanga ▁ 7 ▁enyangeni ▁yebhimbídvwane .` | 10 |
| 32k | `▁ 7 ▁bhimbídvwane . ▁lilanga ▁ 7 ▁enyangeni ▁yebhimbídvwane .` | 10 |
| 64k | `▁ 7 ▁bhimbídvwane . ▁lilanga ▁ 7 ▁enyangeni ▁yebhimbídvwane .` | 10 |

**Sample 3:** `Wonkhe emalanga enyangeni emnyakeni. |- Kúfúna . Kúbópha The History Channel iwe...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wonkhe ▁emalanga ▁enyangeni ▁emnyakeni . ▁| - ▁kúfúna ▁. ▁kúbópha ... (+14 more)` | 24 |
| 16k | `▁wonkhe ▁emalanga ▁enyangeni ▁emnyakeni . ▁| - ▁kúfúna ▁. ▁kúbópha ... (+12 more)` | 22 |
| 32k | `▁wonkhe ▁emalanga ▁enyangeni ▁emnyakeni . ▁| - ▁kúfúna ▁. ▁kúbópha ... (+12 more)` | 22 |
| 64k | `▁wonkhe ▁emalanga ▁enyangeni ▁emnyakeni . ▁|- ▁kúfúna ▁. ▁kúbópha ▁the ... (+10 more)` | 20 |


### Key Findings

- **Best Compression:** 64k achieves 5.616x compression
- **Lowest UNK Rate:** 8k with 0.4074% 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 | 1,182 | 10.21 | 1,980 | 31.2% | 76.3% |
| **2-gram** | Subword | 230 🏆 | 7.84 | 1,614 | 72.8% | 99.6% |
| **3-gram** | Word | 1,207 | 10.24 | 1,767 | 26.2% | 74.8% |
| **3-gram** | Subword | 1,732 | 10.76 | 11,292 | 28.6% | 78.3% |
| **4-gram** | Word | 4,701 | 12.20 | 5,505 | 9.8% | 31.8% |
| **4-gram** | Subword | 8,252 | 13.01 | 47,059 | 13.6% | 45.5% |
| **5-gram** | Word | 4,101 | 12.00 | 4,561 | 9.0% | 31.5% |
| **5-gram** | Subword | 22,502 | 14.46 | 93,259 | 8.5% | 29.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ningizimu afrika` | 321 |
| 2 | `kanye ne` | 310 |
| 3 | `ngemnyaka wa` | 303 |
| 4 | `eningizimu afrika` | 284 |
| 5 | `kúfúna kúbópha` | 190 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wase ningizimu afrika` | 166 |
| 2 | `likhodi le inthanethi` | 157 |
| 3 | `usd likhodi le` | 150 |
| 4 | `km2 linani bantfu` | 145 |
| 5 | `pib usd likhodi` | 140 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `usd likhodi le inthanethi` | 150 |
| 2 | `pib usd likhodi le` | 140 |
| 3 | `african national congress anc` | 34 |
| 4 | `ungusopolitiki wase ningizimu afrika` | 20 |
| 5 | `le african national congress` | 19 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pib usd likhodi le inthanethi` | 140 |
| 2 | `archived from the original on` | 17 |
| 3 | `licembu lepolitiki lase ningizimu afrika` | 16 |
| 4 | `km2 pib usd likhodi le` | 15 |
| 5 | `yetinkhundla the national physical development` | 15 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 44,148 |
| 2 | `a n` | 27,375 |
| 3 | `e _` | 27,173 |
| 4 | `i _` | 25,993 |
| 5 | `l a` | 25,619 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k u` | 10,337 |
| 2 | `_ l e` | 10,103 |
| 3 | `_ n g` | 9,569 |
| 4 | `l a _` | 9,180 |
| 5 | `a _ k` | 8,164 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t s i _` | 5,957 |
| 2 | `_ n g e` | 5,441 |
| 3 | `a _ n g` | 4,181 |
| 4 | `n y e _` | 3,934 |
| 5 | `a _ k u` | 3,702 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u t s i _` | 3,274 |
| 2 | `a n y e _` | 2,771 |
| 3 | `k a n y e` | 2,535 |
| 4 | `n y e _ n` | 2,524 |
| 5 | `_ k a n y` | 2,505 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 230
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.6025 | 1.518 | 2.92 | 48,904 | 39.7% |
| **1** | Subword | 0.9034 | 1.870 | 6.18 | 699 | 9.7% |
| **2** | Word | 0.1026 | 1.074 | 1.17 | 142,184 | 89.7% |
| **2** | Subword | 0.9440 | 1.924 | 5.27 | 4,316 | 5.6% |
| **3** | Word | 0.0243 | 1.017 | 1.03 | 165,786 | 97.6% |
| **3** | Subword | 0.8350 | 1.784 | 3.69 | 22,731 | 16.5% |
| **4** | Word | 0.0077 🏆 | 1.005 | 1.01 | 170,336 | 99.2% |
| **4** | Subword | 0.5985 | 1.514 | 2.40 | 83,771 | 40.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `kanye nanobe jana gana iriphabliki inhlokodolobha basseterre linani bantfu labadzala ngemnyaka wa li...`
2. `i central police station kanye nesikhatsi sekukhula ngekushesha kantsi yena eduardo mondlane uphuma ...`
3. `kutsi seyingenta matsandza ngekuba ngumdlali we structural anthropology 33 19 december durban yabese...`

**Context Size 2:**

1. `ningizimu afrika lelisekela ema afrika kanye nembhali wetinkondlo wase iningizimu afrika itfola inku...`
2. `kanye ne computer science tinhlelo te undergraduate kuphela ema undergraduate majors e bachelor of e...`
3. `ngemnyaka wa waphindze waba sikhulumi sesigungu savelonkhe tikhatsi letimbili letingachubeki kusukel...`

**Context Size 3:**

1. `wase ningizimu afrika umfundzisi umbhali wemafilimu kanye nemlweli wemalungelo ebantfu ushicilele im...`
2. `likhodi le inthanethi ba kúfúna kúbópha ibhosinya ne hezegovi ibhulgariya ikhuroshiya shekhi idenima...`
3. `usd likhodi le inthanethi jm kúfúna kúbópha ijamayikha iwebhusayithi jamayikha`

**Context Size 4:**

1. `usd likhodi le inthanethi fi ax kúfúna kúbópha ifini iwebhusayithi`
2. `pib usd likhodi le inthanethi si kúfúna kúbópha slovenia si your gateway to information on slovenia ...`
3. `african national congress anc iminyaka yebuncane nekufundza mantashe watalelwa e eastern cape wakhul...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_isahale_fun._nd`
2. `aba:_i_emlaku_kh`
3. `emakúne_liohoneu`

**Context Size 2:**

1. `a_manatinhla-hi_l`
2. `an_econgopetalovu`
3. `e_inkhe_bodi,_use`

**Context Size 3:**

1. `_kulwane_yemanzanu`
2. `_letiseleko_lodzaw`
3. `_ngal_stemari_nala`

**Context Size 4:**

1. `tsi_sobhuza_ii_lica`
2. `_ngekubukwentarized`
3. `a_ngapheli_licembu_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (83,771 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 | 17,583 |
| Total Tokens | 151,832 |
| Mean Frequency | 8.64 |
| Median Frequency | 3 |
| Frequency Std Dev | 38.49 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kanye | 2,506 |
| 2 | i | 1,523 |
| 3 | afrika | 1,491 |
| 4 | kutsi | 1,291 |
| 5 | futsi | 1,060 |
| 6 | bantfu | 768 |
| 7 | of | 766 |
| 8 | e | 678 |
| 9 | the | 675 |
| 10 | ne | 670 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | wetisebenti | 2 |
| 2 | pilibhit | 2 |
| 3 | ecameroon | 2 |
| 4 | swift | 2 |
| 5 | bungcweti | 2 |
| 6 | etychy | 2 |
| 7 | wideo | 2 |
| 8 | nietypowe | 2 |
| 9 | sztalugi | 2 |
| 10 | zapałek | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8828 |
| R² (Goodness of Fit) | 0.992928 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 23.6% |
| Top 1,000 | 51.9% |
| Top 5,000 | 77.7% |
| Top 10,000 | 89.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9929 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 23.6% of corpus
- **Long Tail:** 7,583 words needed for remaining 10.3% 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 | 0.6744 | 0.3263 | N/A | N/A |
| **mono_64d** | 64 | 0.1827 | 0.3247 | N/A | N/A |
| **mono_128d** | 128 | 0.0232 | 0.3346 | N/A | N/A |
| **aligned_32d** | 32 | 0.6744 🏆 | 0.3287 | 0.0180 | 0.1640 |
| **aligned_64d** | 64 | 0.1827 | 0.3261 | 0.0480 | 0.2280 |
| **aligned_128d** | 128 | 0.0232 | 0.3424 | 0.0640 | 0.2540 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6744 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3305. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 6.4% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.078** | Low formulaic 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 |
|--------|----------|
| `-l` | lichazwa, letivela, lisotja |
| `-ku` | kugcugcutela, kushona, kunetindzawo |
| `-le` | letivela, lebeyinebantfu, lenkhomo |
| `-e` | evidence, ebhayi, enkhululekweni |
| `-a` | angakaze, apple, abengusomabhizinisi |
| `-i` | indzima, ingabe, imihume |
| `-s` | sebufati, sidvudvu, sasungulwa |
| `-n` | nekudla, ngekuntjintja, ngubabe |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | lichazwa, indzima, letivela |
| `-i` | ebhayi, sebufati, abengusomabhizinisi |
| `-e` | evidence, timbece, beje |
| `-o` | lenkhomo, kwawo, letigucukako |
| `-ni` | enkhululekweni, enkhohlakalweni, elokishini |
| `-la` | letivela, nekudla, latfola |
| `-wa` | lichazwa, kwahlanganiswa, sasungulwa |
| `-le` | apple, lohluphekile, lokwehlukile |

### 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` | 1.63x | 63 contexts | ikhule, akhula, mkhulu |
| `bant` | 2.00x | 23 contexts | bantu, bantfu, abantu |
| `anga` | 1.56x | 50 contexts | wanga, banga, yanga |
| `lang` | 1.65x | 40 contexts | langu, lange, langa |
| `enti` | 1.72x | 29 contexts | senti, isenti, yentiwa |
| `hulu` | 1.66x | 32 contexts | mkhulu, sikhulu, omkhulu |
| `kuts` | 1.74x | 26 contexts | kutsi, kutse, ekutsi |
| `indz` | 1.49x | 41 contexts | lindza, indzima, indzawo |
| `etin` | 1.70x | 25 contexts | letine, letinye, letingu |
| `ndza` | 1.41x | 30 contexts | lindza, ndzawo, indzawo |
| `antf` | 1.86x | 12 contexts | bantfu, ebantfu, labantfu |
| `khat` | 1.89x | 9 contexts | khathi, ekhatsi, emakhata |

### 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 |
|--------|--------|-----------|----------|
| `-l` | `-a` | 490 words | laniketa, lelisempumalanga |
| `-n` | `-a` | 338 words | nekugcugcutela, nekukhulumisana |
| `-e` | `-i` | 334 words | ezulwini, entasi |
| `-l` | `-e` | 317 words | leyehlukahlukene, lesifishane |
| `-e` | `-ni` | 275 words | ezulwini, ebeleni |
| `-ku` | `-a` | 255 words | kucaphela, kuwina |
| `-n` | `-i` | 226 words | ngokuthi, netigidzi |
| `-l` | `-i` | 205 words | lesisemkhatsini, lasemtsetfweni |
| `-l` | `-o` | 204 words | lusendvo, libutfo |
| `-n` | `-o` | 165 words | ngekwenhlalo, ngemalengiso |

### 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 |
|------|-----------------|------------|------|
| tfolakele | **`tfolak-e-le`** | 7.5 | `e` |
| mkhuzweni | **`mkhuz-we-ni`** | 7.5 | `we` |
| abengusihlalo | **`abengusih-la-lo`** | 7.5 | `la` |
| bekadlala | **`bekad-la-la`** | 7.5 | `la` |
| nyamatane | **`nyamat-a-ne`** | 7.5 | `a` |
| itfolakala | **`itfolak-a-la`** | 7.5 | `a` |
| impalampala | **`impalamp-a-la`** | 7.5 | `a` |
| ngesicalo | **`ngesic-a-lo`** | 7.5 | `a` |
| samasipala | **`samasip-a-la`** | 7.5 | `a` |
| tinanekwane | **`tinanekw-a-ne`** | 7.5 | `a` |
| etingijimeni | **`etingijim-e-ni`** | 7.5 | `e` |
| letinkhulungwane | **`letinkhulung-wa-ne`** | 7.5 | `wa` |
| lesentasi | **`lesent-a-si`** | 7.5 | `a` |
| ekuvinjweni | **`ekuvinj-we-ni`** | 7.5 | `we` |
| labashadene | **`labashad-e-ne`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Swati 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 (5.62x) |
| N-gram | **2-gram** | Lowest perplexity (230) |
| Markov | **Context-4** | Highest predictability (99.2%) |
| 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 22:38:00*