README.md

---
language: mi
language_name: Māori
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: 3.987
  - name: best_isotropy
    type: isotropy
    value: 0.5498
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Māori** 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** | 3.637x | 3.64 | 0.0513% | 150,109 |
| **16k** | 3.798x | 3.81 | 0.0536% | 143,743 |
| **32k** | 3.931x | 3.94 | 0.0554% | 138,904 |
| **64k** | 3.987x 🏆 | 3.99 | 0.0562% | 136,949 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ko Tūnihia (reo Ārapi: الجمهورية التونسية, al-Jumhūrīyah at-Tūnisīyah) he whenua...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ko ▁tū nihia ▁( reo ▁ārapi : ▁ال ج م ... (+45 more)` | 55 |
| 16k | `▁ko ▁tūnihia ▁( reo ▁ārapi : ▁ال ج مهورية ▁ال ... (+39 more)` | 49 |
| 32k | `▁ko ▁tūnihia ▁( reo ▁ārapi : ▁الجمهورية ▁التونسية , ▁al ... (+27 more)` | 37 |
| 64k | `▁ko ▁tūnihia ▁( reo ▁ārapi : ▁الجمهورية ▁التونسية , ▁al ... (+27 more)` | 37 |

**Sample 2:** `Ko Kōkiri Ahitereiria Ataahua () te waiata a whenua mo Ahitereiria.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ko ▁kōkiri ▁ahitereiria ▁ata ahua ▁() ▁te ▁waiata ▁a ▁whenua ... (+3 more)` | 13 |
| 16k | `▁ko ▁kōkiri ▁ahitereiria ▁ataahua ▁() ▁te ▁waiata ▁a ▁whenua ▁mo ... (+2 more)` | 12 |
| 32k | `▁ko ▁kōkiri ▁ahitereiria ▁ataahua ▁() ▁te ▁waiata ▁a ▁whenua ▁mo ... (+2 more)` | 12 |
| 64k | `▁ko ▁kōkiri ▁ahitereiria ▁ataahua ▁() ▁te ▁waiata ▁a ▁whenua ▁mo ... (+2 more)` | 12 |

**Sample 3:** `Ko Kiri Te Kanawa he kaiwaiata rongonui nō Aotearoa.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ko ▁kiri ▁te ▁kana wa ▁he ▁kaiwaiata ▁rongonui ▁nō ▁aotearoa ... (+1 more)` | 11 |
| 16k | `▁ko ▁kiri ▁te ▁kanawa ▁he ▁kaiwaiata ▁rongonui ▁nō ▁aotearoa .` | 10 |
| 32k | `▁ko ▁kiri ▁te ▁kanawa ▁he ▁kaiwaiata ▁rongonui ▁nō ▁aotearoa .` | 10 |
| 64k | `▁ko ▁kiri ▁te ▁kanawa ▁he ▁kaiwaiata ▁rongonui ▁nō ▁aotearoa .` | 10 |


### Key Findings

- **Best Compression:** 64k achieves 3.987x compression
- **Lowest UNK Rate:** 8k with 0.0513% 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 | 705 | 9.46 | 6,245 | 49.9% | 87.5% |
| **2-gram** | Subword | 171 🏆 | 7.42 | 2,075 | 79.6% | 99.6% |
| **3-gram** | Word | 1,013 | 9.98 | 9,926 | 41.4% | 85.1% |
| **3-gram** | Subword | 945 | 9.88 | 12,961 | 39.4% | 88.7% |
| **4-gram** | Word | 1,172 | 10.19 | 16,021 | 40.6% | 83.8% |
| **4-gram** | Subword | 2,943 | 11.52 | 50,169 | 24.5% | 71.2% |
| **5-gram** | Word | 1,030 | 10.01 | 12,463 | 41.9% | 86.0% |
| **5-gram** | Subword | 5,494 | 12.42 | 88,213 | 18.8% | 62.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o te` | 12,376 |
| 2 | `ko te` | 7,593 |
| 3 | `i te` | 7,520 |
| 4 | `ki te` | 6,736 |
| 5 | `takiwā o` | 5,380 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `toitū te whenua` | 4,800 |
| 2 | `kite i te` | 3,310 |
| 3 | `he mea kite` | 3,304 |
| 4 | `mea kite i` | 3,304 |
| 5 | `new zealand he` | 3,271 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mea kite i te` | 3,304 |
| 2 | `he mea kite i` | 3,304 |
| 3 | `zealand he mea kite` | 3,271 |
| 4 | `new zealand he mea` | 3,271 |
| 5 | `toitū te whenua land` | 3,270 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `he mea kite i te` | 3,304 |
| 2 | `zealand he mea kite i` | 3,271 |
| 3 | `new zealand he mea kite` | 3,271 |
| 4 | `toitū te whenua land information` | 3,270 |
| 5 | `land information new zealand he` | 3,270 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t` | 130,423 |
| 2 | `e _` | 120,072 |
| 3 | `i _` | 95,061 |
| 4 | `a _` | 80,419 |
| 5 | `t e` | 80,353 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t e _` | 67,768 |
| 2 | `_ t e` | 62,829 |
| 3 | `_ o _` | 33,303 |
| 4 | `i _ t` | 32,362 |
| 5 | `e _ t` | 32,097 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t e _` | 61,846 |
| 2 | `i _ t e` | 21,978 |
| 3 | `o _ t e` | 20,819 |
| 4 | `t e _ t` | 18,461 |
| 5 | `_ h e _` | 17,269 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _ t e _` | 21,833 |
| 2 | `o _ t e _` | 20,672 |
| 3 | `_ t e _ t` | 17,983 |
| 4 | `t e _ t a` | 12,754 |
| 5 | `_ o _ t e` | 12,383 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 171
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~62% 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 | 0.6767 | 1.598 | 3.84 | 28,167 | 32.3% |
| **1** | Subword | 0.9035 | 1.871 | 6.22 | 1,068 | 9.6% |
| **2** | Word | 0.2309 | 1.174 | 1.56 | 107,287 | 76.9% |
| **2** | Subword | 0.7978 | 1.738 | 4.37 | 6,632 | 20.2% |
| **3** | Word | 0.1002 | 1.072 | 1.19 | 166,148 | 90.0% |
| **3** | Subword | 0.7225 | 1.650 | 3.30 | 28,939 | 27.7% |
| **4** | Word | 0.0444 🏆 | 1.031 | 1.08 | 195,678 | 95.6% |
| **4** | Subword | 0.5194 | 1.433 | 2.19 | 95,255 | 48.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `te haina here turi te ope hōia ka puta ai ki toitū te kaihautū whenua he`
2. `o te he rite tēnei mō te takiwā ēnei whare matā pākawa pungatara s g ghost`
3. `ko ngā rā tonu te reo pākehā kaihautū whenua e ai ki ā nuku whiringa ā`

**Context Size 2:**

1. `o te awa garonne ko bordeaux reo wīwī bordeaux bɔʁdo reo occitan vairas te tāone nui tirohia`
2. `ko te he tau o te wai pounamu ko ōtepoti te tāone matua o aotearoa brainyhistory 999`
3. `i te reo pākehā he wāhi nohoia e te tangata engari kāore anō kia tae te nui`

**Context Size 3:**

1. `toitū te whenua he nohanga he locality rānei ki te reo pākehā he wāhi nohoia e te tangata`
2. `kite i te o waitaha`
3. `he mea kite i te o waikato en list of sgt frog characters garuru platoon ja ガルル小隊 プルル看護長`

**Context Size 4:**

1. `he mea kite i te o te moana a toi he takiwā o aotearoa kei te ika a māui`
2. `mea kite i te o te whanga nui a tara smith s p history and traditions of the maoris`
3. `new zealand he mea kite i te o te tai poutini kei te uru o te wai pounamu ko`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_hanohonuhiai_tu`
2. `a_he_ke_i_bo_the`
3. `i_in_mat,_o_a_ia`

**Context Size 2:**

1. `_tionei._torahing`
2. `e_whi_whitū_tāorm`
3. `i_aotu_whe_wi_he_`

**Context Size 3:**

1. `te_paenga_o_ngā_pu`
2. `_te_“matahi_i_ki_a`
3. `_o_tāone_tāone_noh`

**Context Size 4:**

1. `_te_reo_huru_whirin`
2. `i_te_ai_i_te_tokera`
3. `o_te_papaki_te_rohe`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (95,255 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 | 11,670 |
| Total Tokens | 572,993 |
| Mean Frequency | 49.10 |
| Median Frequency | 3 |
| Frequency Std Dev | 801.57 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | te | 64,133 |
| 2 | o | 34,097 |
| 3 | ko | 21,829 |
| 4 | he | 18,921 |
| 5 | i | 16,028 |
| 6 | ki | 12,979 |
| 7 | ngā | 9,360 |
| 8 | e | 9,113 |
| 9 | whenua | 8,565 |
| 10 | a | 8,027 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kaitono | 2 |
| 2 | dansk | 2 |
| 3 | ˈtænˀsk | 2 |
| 4 | tenemākareo | 2 |
| 5 | pākehāhej | 2 |
| 6 | fra | 2 |
| 7 | joāeyeshvad | 2 |
| 8 | hedder | 2 |
| 9 | lycopersicum | 2 |
| 10 | tomato | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2239 |
| R² (Goodness of Fit) | 0.987898 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 72.0% |
| Top 1,000 | 91.2% |
| Top 5,000 | 97.1% |
| Top 10,000 | 99.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9879 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 72.0% of corpus
- **Long Tail:** 1,670 words needed for remaining 0.6% 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 | 0.5498 🏆 | 0.3626 | N/A | N/A |
| **mono_64d** | 64 | 0.1805 | 0.3661 | N/A | N/A |
| **mono_128d** | 128 | 0.0211 | 0.3761 | N/A | N/A |
| **aligned_32d** | 32 | 0.5498 | 0.3657 | 0.0260 | 0.1840 |
| **aligned_64d** | 64 | 0.1805 | 0.3550 | 0.0380 | 0.2240 |
| **aligned_128d** | 128 | 0.0211 | 0.3770 | 0.0480 | 0.2580 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.5498 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3671. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.8% 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 | **0.386** | 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` | tupono, taputapuatea, taraire |
| `-p` | pupuhi, pekanga, patukirikiri |
| `-m` | microsoft, momona, metcalf |
| `-k` | kāreti, kairangahau, kakabai |
| `-ma` | mashhad, marge, manukorihi |
| `-h` | honiara, homai, hūtāne |
| `-a` | arapohue, ano, ahiahi |
| `-ta` | taputapuatea, taraire, taradale |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | honiara, pekanga, complexa |
| `-i` | homai, pupuhi, kāreti |
| `-e` | shore, hūtāne, arapohue |
| `-ia` | whakatakotohia, whakatuwheratia, incisapaesia |
| `-s` | reunionnais, carpodetus, press |
| `-ga` | pekanga, pānuitanga, patunga |
| `-n` | levin, susan, princeton |
| `-o` | werokoko, ano, tupono |

### 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 |
|------|----------|------------------|----------|
| `inga` | 1.83x | 42 contexts | hinga, ringa, huinga |
| `angi` | 1.91x | 28 contexts | rangi, tangi, angitū |
| `whak` | 1.96x | 25 contexts | whaka, whakia, whakaū |
| `rang` | 1.56x | 58 contexts | range, rangi, ranga |
| `hang` | 1.83x | 28 contexts | hangā, hanga, hangai |
| `akat` | 2.00x | 20 contexts | akatea, whakatō, whakatū |
| `enga` | 1.71x | 34 contexts | henga, renga, awenga |
| `onga` | 1.84x | 24 contexts | longa, ponga, tonga |
| `aita` | 1.70x | 19 contexts | taita, vaita, whaita |
| `taut` | 1.78x | 14 contexts | tautau, tautoro, tautuhi |
| `ngat` | 1.50x | 19 contexts | ngati, ngata, ngatea |
| `whan` | 1.81x | 9 contexts | whano, whanga, whanau |

### 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 |
|--------|--------|-----------|----------|
| `-t` | `-a` | 203 words | temuka, tākaka |
| `-p` | `-a` | 187 words | pūhonoiika, parawhenua |
| `-k` | `-a` | 158 words | kopinga, kētia |
| `-m` | `-a` | 123 words | maramara, mandiraja |
| `-h` | `-a` | 122 words | hōhipera, henga |
| `-t` | `-i` | 117 words | tāpoi, tuatini |
| `-r` | `-a` | 109 words | rubra, robusta |
| `-a` | `-a` | 93 words | ahumoana, akarana |
| `-k` | `-i` | 89 words | kuki, koheriki |
| `-m` | `-i` | 83 words | moanaui, mangaiti |

### 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 |
|------|-----------------|------------|------|
| waikāretu | **`wa-i-kāretu`** | 7.5 | `kāretu` |
| matapouri | **`ma-ta-pouri`** | 7.5 | `pouri` |
| whakaratohia | **`whakarato-hi-a`** | 7.5 | `hi` |
| tamarangi | **`ta-ma-rangi`** | 7.5 | `rangi` |
| ngātokowaru | **`ngātokow-a-ru`** | 7.5 | `a` |
| whakatūnga | **`whakatū-ng-a`** | 7.5 | `ng` |
| huasolanum | **`hu-a-solanum`** | 7.5 | `solanum` |
| ulaanbaatar | **`ulaanbaat-a-r`** | 7.5 | `a` |
| joāeyeshvad | **`joāeyeshv-a-d`** | 7.5 | `a` |
| kaipūtaiao | **`ka-i-pūtaiao`** | 7.5 | `pūtaiao` |
| korerotia | **`korero-ti-a`** | 7.5 | `ti` |
| azərbaycan | **`azərbayc-a-n`** | 7.5 | `a` |
| tohatohahia | **`tohatoha-hi-a`** | 7.5 | `hi` |
| rokohanga | **`ro-ko-hanga`** | 7.5 | `hanga` |
| taharangi | **`ta-ha-rangi`** | 7.5 | `rangi` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Māori 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 (3.99x) |
| N-gram | **2-gram** | Lowest perplexity (171) |
| Markov | **Context-4** | Highest predictability (95.6%) |
| 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 11:44:01*