README.md

---
language: haw
language_name: Hawaiian
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: 3.473
  - name: best_isotropy
    type: isotropy
    value: 0.6902
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Hawaiian** 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** | 3.272x | 3.28 | 0.0523% | 86,081 |
| **16k** | 3.363x | 3.37 | 0.0537% | 83,741 |
| **32k** | 3.442x | 3.45 | 0.0550% | 81,827 |
| **64k** | 3.473x 🏆 | 3.49 | 0.0555% | 81,083 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `He aupuni kiwikā ‘o , i ka panalā‘au o Salamanca, ma Castille a Leon, ma Sepania...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 16k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 32k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 64k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |

**Sample 2:** `He aupuni kiwikā ‘o , i ka panalā‘au o Salamanca, ma Castille a Leon, ma Sepania...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 16k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 32k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 64k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |

**Sample 3:** `He aupuni kiwikā ‘o , i ka panalā‘au o Burgos, ma Castille a Leon, ma Sepania. o...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 16k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 32k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |
| 64k | `▁he ▁aupuni ▁kiwikā ▁‘ o ▁, ▁i ▁ka ▁panalā ‘ ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 3.473x compression
- **Lowest UNK Rate:** 8k with 0.0523% 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 | 1,927 | 10.91 | 8,889 | 35.3% | 69.2% |
| **2-gram** | Subword | 172 🏆 | 7.43 | 2,081 | 78.7% | 99.4% |
| **3-gram** | Word | 4,988 | 12.28 | 16,613 | 22.9% | 52.1% |
| **3-gram** | Subword | 1,130 | 10.14 | 13,854 | 42.3% | 82.6% |
| **4-gram** | Word | 9,312 | 13.18 | 27,880 | 17.9% | 41.4% |
| **4-gram** | Subword | 4,664 | 12.19 | 56,149 | 24.2% | 60.9% |
| **5-gram** | Word | 7,445 | 12.86 | 20,542 | 19.1% | 42.5% |
| **5-gram** | Subword | 11,187 | 13.45 | 104,114 | 16.0% | 46.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i ka` | 7,715 |
| 2 | `a me` | 4,500 |
| 3 | `o ka` | 3,392 |
| 4 | `i nā` | 3,235 |
| 5 | `ma ka` | 2,812 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i ka makahiki` | 1,458 |
| 2 | `a me ka` | 1,387 |
| 3 | `he aupuni kiwikā` | 1,246 |
| 4 | `castille a leon` | 1,214 |
| 5 | `aupuni kiwikā o` | 1,117 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `he aupuni kiwikā o` | 1,115 |
| 2 | `castille a leon ma` | 1,107 |
| 3 | `ma castille a leon` | 1,107 |
| 4 | `a leon ma sepania` | 1,106 |
| 5 | `ka panalā au o` | 1,087 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ma castille a leon ma` | 1,107 |
| 2 | `castille a leon ma sepania` | 1,106 |
| 3 | `i ka panalā au o` | 1,058 |
| 4 | `he aupuni kiwikā o i` | 973 |
| 5 | `a leon ma sepania o` | 953 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 144,590 |
| 2 | `_ k` | 78,727 |
| 3 | `k a` | 68,606 |
| 4 | `i _` | 64,388 |
| 5 | `_ m` | 61,725 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a` | 40,157 |
| 2 | `k a _` | 35,837 |
| 3 | `_ m a` | 34,601 |
| 4 | `a _ m` | 27,428 |
| 5 | `n a _` | 26,431 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a _` | 28,598 |
| 2 | `a n a _` | 15,773 |
| 3 | `a _ m a` | 14,949 |
| 4 | `_ m a _` | 14,806 |
| 5 | `_ i _ k` | 13,220 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _ k a _` | 10,231 |
| 2 | `_ h o ʻ o` | 9,268 |
| 3 | `_ k a _ h` | 8,914 |
| 4 | `_ i _ k a` | 8,275 |
| 5 | `_ m e a _` | 7,759 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 172
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~47% 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 | 0.7250 | 1.653 | 4.38 | 29,186 | 27.5% |
| **1** | Subword | 0.9483 | 1.930 | 6.15 | 996 | 5.2% |
| **2** | Word | 0.3100 | 1.240 | 1.82 | 127,141 | 69.0% |
| **2** | Subword | 0.8333 | 1.782 | 4.77 | 6,120 | 16.7% |
| **3** | Word | 0.1613 | 1.118 | 1.32 | 230,368 | 83.9% |
| **3** | Subword | 0.7682 | 1.703 | 3.53 | 29,158 | 23.2% |
| **4** | Word | 0.0847 🏆 | 1.060 | 1.14 | 302,875 | 91.5% |
| **4** | Subword | 0.5617 | 1.476 | 2.33 | 102,840 | 43.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ka poʻe a me anna ma pukalani mea uamaiʻakomi wāʻkalama ka sīuakalāmanāʻmō ka rell no kā`
2. `i ka makahiki he aupuni kiwikā o kona mau hana ʻana ma kahi e komo mua`
3. `o nā kūlana makauhale ʻāpana ka iʻa ua hoʻonohonoho ʻo ia i ka hakakā inā kīwaʻma`

**Context Size 2:**

1. `i ka makahiki ua komo ʻo ia iā asta i ka dreamcast i ka makahiki ua hoʻokipa`
2. `a me zulu he haku mele nā hōʻike i hōʻiliʻili kālā no nā kumuhana eduardo mea i`
3. `o ka wai gastric mucus loaʻa paha ka ramiro menéndez nā kūmole pāʻoi waho eūmia emānahāua mai`

**Context Size 3:**

1. `i ka makahiki ma mikikana nā hāmeʻa nā hāmeʻa nui linda cardellini lindsay weir john francis daley k...`
2. `a me ka hōʻailona ʻike nui ʻia kahi i pāʻani ai i ka hoʻonui ʻana i kāna kaʻa`
3. `he aupuni kiwikā o i ka panalā au o soria ma castille a leon ma sepania o zamora`

**Context Size 4:**

1. `he aupuni kiwikā o i ka panalā au o salamanca ma castille a leon ma sepania o salamanca`
2. `ma castille a leon ma sepania o zamora`
3. `castille a leon ma sepania o león`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_hose_ma_i_hi_l_`
2. `a_kijoke_al_kuau`
3. `iānaʻomeuhelaʻia`

**Context Size 2:**

1. `a_250px_kino_mela`
2. `_kulamartona_bowe`
3. `ka_mana_ka_o_i_ma`

**Context Size 3:**

1. `_kana_o_nū_ʻo_moa_`
2. `ka_lāhelua_pard_no`
3. `_ma_a_hoʻokakou_ma`

**Context Size 4:**

1. `_ka_wā_e_kona._i_ka`
2. `ana_ma_puulena_o_ka`
3. `a_ma_kahiki_ua_hale`


### Key Findings

- **Best Predictability:** Context-4 (word) with 91.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (102,840 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 | 12,072 |
| Total Tokens | 429,287 |
| Mean Frequency | 35.56 |
| Median Frequency | 3 |
| Frequency Std Dev | 472.82 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ka | 28,808 |
| 2 | i | 21,904 |
| 3 | o | 15,069 |
| 4 | ma | 15,022 |
| 5 | nā | 12,739 |
| 6 | a | 11,420 |
| 7 | ʻo | 8,852 |
| 8 | ke | 8,793 |
| 9 | mea | 7,931 |
| 10 | me | 7,613 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | dix | 2 |
| 2 | kaiaola | 2 |
| 3 | macke | 2 |
| 4 | kunst | 2 |
| 5 | kontext | 2 |
| 6 | neubrandenburger | 2 |
| 7 | nr | 2 |
| 8 | wittenberg | 2 |
| 9 | rostock | 2 |
| 10 | ethnographic | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2265 |
| R² (Goodness of Fit) | 0.995587 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 63.7% |
| Top 1,000 | 86.4% |
| Top 5,000 | 95.9% |
| Top 10,000 | 99.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9956 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 63.7% of corpus
- **Long Tail:** 2,072 words needed for remaining 1.0% 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 | 0.6902 | 0.3929 | N/A | N/A |
| **mono_64d** | 64 | 0.3523 | 0.3703 | N/A | N/A |
| **mono_128d** | 128 | 0.1052 | 0.3418 | N/A | N/A |
| **aligned_32d** | 32 | 0.6902 🏆 | 0.3809 | 0.0260 | 0.1900 |
| **aligned_64d** | 64 | 0.3523 | 0.3634 | 0.0440 | 0.2580 |
| **aligned_128d** | 128 | 0.1052 | 0.3458 | 0.0940 | 0.3380 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6902 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3658. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 9.4% 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 | **-0.093** | 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 |
|--------|----------|
| `-ho` | hoʻouna, hokkaidō, hoʻohiki |
| `-ma` | marins, makoto, makemakika |
| `-ka` | kanu, katsutaro, karla |
| `-hoʻ` | hoʻouna, hoʻohiki, hoʻāhewa |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | niwa, lehua, metala |
| `-na` | hoʻouna, ʻohana, tobalina |
| `-ia` | poniʻia, ekalesia, huaʻia |
| `-er` | vermeer, chapter, cutter |
| `-la` | metala, hoʻōla, anakola |

### 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 |
|------|----------|------------------|----------|
| `hoʻo` | 1.78x | 25 contexts | hoʻonā, nohoʻo, hoʻokō |
| `oʻol` | 1.88x | 20 contexts | hoʻola, hoʻoleo, hoʻolei |
| `oʻok` | 1.65x | 26 contexts | hoʻokō, hoʻokū, hoʻokau |
| `oʻoh` | 1.82x | 12 contexts | hoʻohui, hoʻohou, hoʻohua |
| `oʻop` | 1.85x | 11 contexts | hoʻopā, hoʻopau, hoʻopio |
| `aʻal` | 1.64x | 12 contexts | aʻale, kaʻala, maʻalea |
| `ʻoma` | 1.90x | 8 contexts | ʻomana, hoʻomau, hoʻomalu |
| `maik` | 1.78x | 9 contexts | maiki, maika, maikai |
| `naka` | 1.58x | 12 contexts | kānaka, kanaka, tanaka |
| `akah` | 1.52x | 13 contexts | akahi, kakaha, akahai |
| `anak` | 1.41x | 15 contexts | tanakh, kanaka, kanakā |
| `oʻom` | 1.85x | 7 contexts | hoʻomau, hoʻomoe, hoʻomalu |

### 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 |
|--------|--------|-----------|----------|
| `-ho` | `-a` | 80 words | hoʻopukakadokawa, hoʻolauleʻa |
| `-ka` | `-a` | 78 words | kaopa, kakamora |
| `-ma` | `-a` | 58 words | makaʻala, mauritiusa |
| `-ka` | `-na` | 20 words | kamaʻāina, kaumokuʻāina |
| `-ho` | `-na` | 16 words | hopena, hoʻomana |
| `-ho` | `-ia` | 14 words | hontoria, hoʻohaumia |
| `-ma` | `-na` | 14 words | mawaena, mahina |
| `-ma` | `-la` | 9 words | makaʻala, matilla |
| `-ma` | `-ia` | 9 words | malaia, maikonesia |
| `-ka` | `-la` | 9 words | kapitala, karla |

### 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 |
|------|-----------------|------------|------|
| wehewehena | **`wehewehe-na`** | 4.5 | `wehewehe` |
| kuhikuhina | **`kuhikuhi-na`** | 4.5 | `kuhikuhi` |
| kikokikona | **`kikokiko-na`** | 4.5 | `kikokiko` |
| kamakakūokalani | **`ka-ma-ka-kūokalani`** | 4.5 | `kūokalani` |
| kīʻnekelana | **`kīʻneke-la-na`** | 3.0 | `kīʻneke` |
| makekonia | **`ma-kekon-ia`** | 3.0 | `kekon` |
| hoʻoukaʻia | **`hoʻ-oukaʻ-ia`** | 3.0 | `oukaʻ` |
| masedonia | **`ma-sedon-ia`** | 3.0 | `sedon` |
| hoʻoponoponoʻia | **`hoʻ-oponoponoʻ-ia`** | 3.0 | `oponoponoʻ` |
| kalekonia | **`ka-lekon-ia`** | 3.0 | `lekon` |
| kamaʻilio | **`ka-ma-ʻilio`** | 3.0 | `ʻilio` |
| karipiana | **`ka-ripia-na`** | 3.0 | `ripia` |
| suazilana | **`suazi-la-na`** | 3.0 | `suazi` |
| hoʻokaʻina | **`hoʻ-okaʻi-na`** | 3.0 | `okaʻi` |
| hoʻopilikiaʻia | **`hoʻ-opilikiaʻ-ia`** | 3.0 | `opilikiaʻ` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Hawaiian 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 (3.47x) |
| N-gram | **2-gram** | Lowest perplexity (172) |
| Markov | **Context-4** | Highest predictability (91.5%) |
| 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 02:13:39*