---
language: to
language_name: Tongan
language_family: austronesian_polynesian
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-austronesian_polynesian
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 3.497
  - name: best_isotropy
    type: isotropy
    value: 0.1197
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tongan** 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** | 3.249x | 3.26 | 0.0193% | 181,040 |
| **16k** | 3.400x | 3.41 | 0.0202% | 173,006 |
| **32k** | 3.497x 🏆 | 3.50 | 0.0208% | 168,209 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `*E.W. Gifford, Tongan myths and tales, Bernice Pauahi Bishop museum bulletin 8,`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁* e . w . ▁gifford , ▁tongan ▁myths ▁and ... (+10 more)` | 20 |
| 16k | `▁* e . w . ▁gifford , ▁tongan ▁myths ▁and ... (+10 more)` | 20 |
| 32k | `▁* e . w . ▁gifford , ▁tongan ▁myths ▁and ... (+10 more)` | 20 |

**Sample 2:** `Ko Pulukalia ko ha fonua ia ʻi ʻEulope. ʻi ʻEulope`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ko ▁puluka lia ▁ko ▁ha ▁fonua ▁ia ▁ʻ i ▁ʻ ... (+6 more)` | 16 |
| 16k | `▁ko ▁pulukalia ▁ko ▁ha ▁fonua ▁ia ▁ʻ i ▁ʻ eulope ... (+5 more)` | 15 |
| 32k | `▁ko ▁pulukalia ▁ko ▁ha ▁fonua ▁ia ▁ʻ i ▁ʻ eulope ... (+5 more)` | 15 |

**Sample 3:** `*E. Wood-Ellem, Queen Sālote of Tonga, Auckland university press,`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁* e . ▁wood - ellem , ▁queen ▁sālote ▁of ... (+6 more)` | 16 |
| 16k | `▁* e . ▁wood - ellem , ▁queen ▁sālote ▁of ... (+6 more)` | 16 |
| 32k | `▁* e . ▁wood - ellem , ▁queen ▁sālote ▁of ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 32k achieves 3.497x compression
- **Lowest UNK Rate:** 8k with 0.0193% 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 | 948 | 9.89 | 3,349 | 42.1% | 79.1% |
| **2-gram** | Subword | 208 🏆 | 7.70 | 1,246 | 74.3% | 99.8% |
| **3-gram** | Word | 2,018 | 10.98 | 5,257 | 30.2% | 67.0% |
| **3-gram** | Subword | 1,378 | 10.43 | 7,944 | 35.9% | 79.6% |
| **4-gram** | Word | 2,947 | 11.53 | 8,403 | 28.6% | 57.9% |
| **4-gram** | Subword | 5,492 | 12.42 | 31,079 | 20.2% | 53.5% |
| **5-gram** | Word | 1,994 | 10.96 | 5,965 | 34.1% | 63.8% |
| **5-gram** | Subword | 12,282 | 13.58 | 57,462 | 14.5% | 40.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ko e` | 4,790 |
| 2 | `ʻi he` | 2,011 |
| 3 | `ʻo e` | 1,405 |
| 4 | `ʻa e` | 1,335 |
| 5 | `mo e` | 1,134 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ʻi he ngaahi` | 431 |
| 2 | `ko e fuʻu` | 383 |
| 3 | `e fuʻu ʻakau` | 375 |
| 4 | `hingoa ʻi he` | 341 |
| 5 | `he ngaahi lea` | 336 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ko e fuʻu ʻakau` | 365 |
| 2 | `ʻi he ngaahi lea` | 335 |
| 3 | `he ngaahi lea kehe` | 331 |
| 4 | `hingoa ʻi he ngaahi` | 328 |
| 5 | `vaʻa fekumi ngoue vainī` | 309 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ʻi he ngaahi lea kehe` | 331 |
| 2 | `hingoa ʻi he ngaahi lea` | 328 |
| 3 | `hokohoko ngaahi ʻakau vaʻa fekumi` | 309 |
| 4 | `ngaahi ʻakau vaʻa fekumi ngoue` | 309 |
| 5 | `ʻakau vaʻa fekumi ngoue vainī` | 309 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 28,242 |
| 2 | `a _` | 24,953 |
| 3 | `i _` | 22,182 |
| 4 | `o _` | 19,549 |
| 5 | `_ ʻ` | 19,509 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ e _` | 9,332 |
| 2 | `n g a` | 8,789 |
| 3 | `k o _` | 7,921 |
| 4 | `h e _` | 7,566 |
| 5 | `o _ e` | 7,505 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o _ e _` | 7,450 |
| 2 | `_ k o _` | 5,828 |
| 3 | `k o _ e` | 4,823 |
| 4 | `_ h e _` | 4,523 |
| 5 | `_ ʻ i _` | 3,803 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k o _ e _` | 4,799 |
| 2 | `_ k o _ e` | 4,059 |
| 3 | `i _ h e _` | 3,520 |
| 4 | `_ f a k a` | 3,147 |
| 5 | `ʻ o k u _` | 2,999 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 208
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~41% 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 | 0.7580 | 1.691 | 4.11 | 15,572 | 24.2% |
| **1** | Subword | 0.8923 | 1.856 | 6.74 | 432 | 10.8% |
| **2** | Word | 0.2407 | 1.182 | 1.56 | 63,563 | 75.9% |
| **2** | Subword | 0.9268 | 1.901 | 5.18 | 2,905 | 7.3% |
| **3** | Word | 0.1088 | 1.078 | 1.20 | 98,178 | 89.1% |
| **3** | Subword | 0.7964 | 1.737 | 3.51 | 15,009 | 20.4% |
| **4** | Word | 0.0474 🏆 | 1.033 | 1.07 | 116,582 | 95.3% |
| **4** | Subword | 0.5667 | 1.481 | 2.28 | 52,648 | 43.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `e limufonua ko e ʻakau kālava maʻa e ongo foha ʻo tonga land acts v l`
2. `ko e vahe hihifo ʻo e meʻa kelekele mo e matalaʻiʻakau kula kuusi ko e lotu`
3. `he ngaahi lau ʻoku mamaha ʻa ha alaufuli pea ʻoku ui foki ko e pī pea`

**Context Size 2:**

1. `ko e motuʻa feituʻu ʻi he talatupuʻa ʻo ʻahoʻeitu ʻi he taimi ni koeʻuhi ʻenau hiki ki`
2. `ʻi he ngaahi lea kehe ʻara lea fakakuki kalabuci damu lea fakafisi pūrau lea fakatahisi hutu he`
3. `ʻo e lea heliaki ko e matapā ʻeni tokua naʻe ʻomi ki tongá ni ʻi tongá ni`

**Context Size 3:**

1. `ʻi he ngaahi lea kehe tōmāti lea fakakuki lea fakatahisi ʻōhiʻa ma ka nahele lea fakahauaiʻi s pimpi...`
2. `ko e fuʻu ʻakau lahi ia ʻoku tupu ofi ki he haʻamonga ʻa maui pupunga fetuʻu ko e`
3. `e fuʻu ʻakau siʻi ia mei he ʻatamai ʻo māmani ʻa ia ʻoku hoko ai ʻa e ngaahi`

**Context Size 4:**

1. `ko e fuʻu ʻakau lahi ia mo e ngaahi ngeʻesi ʻelilivao ʻoku ui ko e nati foki ʻoku kulokula`
2. `ʻi he ngaahi lea kehe mākeke lea fakahauaiʻi masitati kapisi lea fakahaʻamoa kāpati lea fakakuki pīn...`
3. `he ngaahi lea kehe toua lea fakaniuē malina lea fakahaʻamoa rōpiāni piāni lea fakakuki tataku hokoho...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_nofo_pue,_kae_b`
2. `au,_hi_ngaʻau_i_`
3. `ita_hi_ctowo_ʻot`

**Context Size 2:**

1. `e_ressia_motonga_`
2. `a_kā_ku_meʻa,_por`
3. `i_loquene,_va_‘e_`

**Context Size 3:**

1. `_e_pea._ko_e_ngaah`
2. `ngaahi_aʻu._kolo_ʻ`
3. `ko_hono_puʻangua_s`

**Context Size 4:**

1. `o_e_hine_taha_micro`
2. `_ko_e_tuituitaha_ko`
3. `ko_e_taha_kā_ko_e_h`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (52,648 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 | 6,787 |
| Total Tokens | 149,227 |
| Mean Frequency | 21.99 |
| Median Frequency | 3 |
| Frequency Std Dev | 193.13 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | e | 9,737 |
| 2 | ko | 7,170 |
| 3 | he | 4,551 |
| 4 | ʻi | 3,854 |
| 5 | ʻo | 3,196 |
| 6 | ʻoku | 2,983 |
| 7 | ia | 2,271 |
| 8 | ngaahi | 2,189 |
| 9 | ʻa | 2,030 |
| 10 | mo | 1,983 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | fohi | 2 |
| 2 | tekau | 2 |
| 3 | fakapā | 2 |
| 4 | fahaʻi | 2 |
| 5 | mutumutu | 2 |
| 6 | koká | 2 |
| 7 | mahoaʻá | 2 |
| 8 | kaí | 2 |
| 9 | lauʻolungá | 2 |
| 10 | folahi | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1311 |
| R² (Goodness of Fit) | 0.992429 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 56.6% |
| Top 1,000 | 83.9% |
| Top 5,000 | 97.6% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9924 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 56.6% of corpus
- **Long Tail:** -3,213 words needed for remaining 100.0% 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 | 0.1197 🏆 | 0.5003 | N/A | N/A |
| **mono_64d** | 64 | 0.0193 | 0.5134 | N/A | N/A |
| **mono_128d** | 128 | 0.0028 | 0.4946 | N/A | N/A |
| **aligned_32d** | 32 | 0.1197 | 0.4991 | 0.0100 | 0.0900 |
| **aligned_64d** | 64 | 0.0193 | 0.5081 | 0.0140 | 0.0980 |
| **aligned_128d** | 128 | 0.0028 | 0.5043 | 0.0140 | 0.0920 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.1197 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.5033. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.4% 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 | **0.569** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-t` | translation, totokamaka, tooi |
| `-s` | seen, state, surely |
| `-m` | mole, maʻamaʻa, menemene |
| `-p` | parazoa, puna, palm |
| `-ma` | maʻamaʻa, mamata, masipā |
| `-f` | foo, fimbristylis, floribunda |
| `-l` | lafalafa, laufale, longomapu |
| `-k` | kākā, kelenatā, kakamika |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | ʻekea, floribunda, maʻamaʻa |
| `-i` | hui, tooi, tuki |
| `-e` | mole, because, menemene |
| `-u` | tatafu, longomapu, tāupoʻou |
| `-s` | fimbristylis, berenices, occidentalis |
| `-o` | foo, epikopo, sio |
| `-ia` | pilitania, ʻaositelēlia, terminalia |
| `-ga` | moʻunga, hengehenga, taunga |

### 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 |
|------|----------|------------------|----------|
| `akat` | 1.59x | 25 contexts | kakato, fakatu, fakatū |
| `onga` | 1.41x | 25 contexts | konga, tonga, nonga |
| `ngat` | 1.64x | 15 contexts | ngata, ngatú, ngatu |
| `ʻang` | 1.66x | 12 contexts | ʻanga, paʻanga, hūʻanga |
| `kata` | 1.53x | 15 contexts | katafa, fakatau, akataha |
| `kala` | 1.38x | 19 contexts | kalae, kalasi, kakala |
| `hing` | 1.53x | 13 contexts | thing, hinga, ahinga |
| `ʻaka` | 1.71x | 8 contexts | ʻakau, ʻakaú, ʻakana |
| `akah` | 1.56x | 10 contexts | fakahū, fakaha, fakahā |
| `tata` | 1.49x | 11 contexts | tatau, tatafu, tatala |
| `akal` | 1.48x | 11 contexts | kakala, fakalao, fakalau |
| `ahin` | 1.48x | 10 contexts | vahine, ahinga, mahino |

### 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 |
|--------|--------|-----------|----------|
| `-f` | `-a` | 152 words | floribunda, fukofuka |
| `-t` | `-a` | 143 words | totokamaka, taunga |
| `-f` | `-i` | 123 words | fakafefiofi, falevai |
| `-m` | `-a` | 122 words | maʻamaʻa, moʻunga |
| `-ʻ` | `-a` | 77 words | ʻekea, ʻalava |
| `-t` | `-u` | 74 words | tatafu, tāupoʻou |
| `-t` | `-i` | 70 words | tooi, tuki |
| `-p` | `-a` | 66 words | parazoa, puna |
| `-l` | `-a` | 64 words | lafalafa, laveʻimoa |
| `-k` | `-a` | 52 words | kakamika, kulukona |

### 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 |
|------|-----------------|------------|------|
| ʻafilikani | **`ʻafilik-a-ni`** | 7.5 | `a` |
| fetuʻutaki | **`fetuʻut-a-ki`** | 7.5 | `a` |
| talafoʻou | **`ta-la-foʻou`** | 7.5 | `foʻou` |
| fakataimi | **`fa-ka-taimi`** | 7.5 | `taimi` |
| fehokotaki | **`fehokot-a-ki`** | 7.5 | `a` |
| polotonga | **`po-lo-tonga`** | 7.5 | `tonga` |
| sterninae | **`sternin-a-e`** | 7.5 | `a` |
| christian | **`christi-a-n`** | 7.5 | `a` |
| lauraceae | **`laurace-a-e`** | 7.5 | `a` |
| siulolovao | **`siulolov-a-o`** | 7.5 | `a` |
| vavalangi | **`va-va-langi`** | 7.5 | `langi` |
| grossulariaceae | **`grossulariace-a-e`** | 7.5 | `a` |
| fakakakai | **`fakakak-a-i`** | 7.5 | `a` |
| matafanga | **`ma-ta-fanga`** | 7.5 | `fanga` |
| afuhaʻapai | **`afuhaʻap-a-i`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tongan 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 | **32k BPE** | Best compression (3.50x) |
| N-gram | **2-gram** | Lowest perplexity (208) |
| Markov | **Context-4** | Highest predictability (95.3%) |
| 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: 2026-01-11 01:22:47*