---
language: szy
language_name: Sakizaya
language_family: austronesian_formosan
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_formosan
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: 3.882
  - name: best_isotropy
    type: isotropy
    value: 0.7206
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sakizaya** 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** | 3.383x | 3.39 | 0.1851% | 601,273 |
| **16k** | 3.613x | 3.61 | 0.1977% | 563,108 |
| **32k** | 3.789x | 3.79 | 0.2073% | 536,850 |
| **64k** | 3.882x 🏆 | 3.88 | 0.2124% | 524,017 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `(kamu nu hulam：照顧) diput tu babalaki. 照顧老人。 malalitin tu ihekalay atu zumaay a n...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁( kamu ▁nu ▁hulam : 照 顧 ) ▁d iput ... (+16 more)` | 26 |
| 16k | `▁( kamu ▁nu ▁hulam : 照顧 ) ▁d iput ▁tu ... (+14 more)` | 24 |
| 32k | `▁( kamu ▁nu ▁hulam : 照顧 ) ▁diput ▁tu ▁babalaki ... (+12 more)` | 22 |
| 64k | `▁( kamu ▁nu ▁hulam : 照顧 ) ▁diput ▁tu ▁babalaki ... (+11 more)` | 21 |

**Sample 2:** `(kasatubangan:u kamu nu Hulam:被殖民、被奴隸 pasatubangan:讓他做奴隸)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁( kas atu bangan : u ▁kamu ▁nu ▁hulam : ... (+17 more)` | 27 |
| 16k | `▁( kas atu bangan : u ▁kamu ▁nu ▁hulam : ... (+17 more)` | 27 |
| 32k | `▁( kas atu bangan : u ▁kamu ▁nu ▁hulam : ... (+16 more)` | 26 |
| 64k | `▁( kas atubangan : u ▁kamu ▁nu ▁hulam : 被 ... (+9 more)` | 19 |

**Sample 3:** `kamu nu hulam：掉下 tinaku a kamu mihetik 掉下 mihetik kaku tu kalisiw i ginko. 我去銀行提...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kamu ▁nu ▁hulam : 掉 下 ▁tinaku ▁a ▁kamu ▁mih ... (+29 more)` | 39 |
| 16k | `▁kamu ▁nu ▁hulam : 掉 下 ▁tinaku ▁a ▁kamu ▁mih ... (+26 more)` | 36 |
| 32k | `▁kamu ▁nu ▁hulam : 掉 下 ▁tinaku ▁a ▁kamu ▁mih ... (+26 more)` | 36 |
| 64k | `▁kamu ▁nu ▁hulam : 掉下 ▁tinaku ▁a ▁kamu ▁mihetik ▁ ... (+21 more)` | 31 |


### Key Findings

- **Best Compression:** 64k achieves 3.882x compression
- **Lowest UNK Rate:** 8k with 0.1851% 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 | 8,778 | 13.10 | 36,425 | 17.4% | 45.6% |
| **2-gram** | Subword | 254 🏆 | 7.99 | 27,613 | 77.3% | 95.0% |
| **3-gram** | Word | 11,965 | 13.55 | 51,761 | 13.4% | 44.7% |
| **3-gram** | Subword | 1,471 | 10.52 | 60,255 | 37.3% | 81.6% |
| **4-gram** | Word | 18,427 | 14.17 | 98,389 | 13.3% | 43.1% |
| **4-gram** | Subword | 6,740 | 12.72 | 170,144 | 17.8% | 54.2% |
| **5-gram** | Word | 13,641 | 13.74 | 78,197 | 15.0% | 47.2% |
| **5-gram** | Subword | 20,122 | 14.30 | 280,627 | 10.5% | 36.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a tademaw` | 9,781 |
| 2 | `a mihcaan` | 6,305 |
| 3 | `sa u` | 4,975 |
| 4 | `idaw ku` | 4,643 |
| 5 | `ku tademaw` | 4,369 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kamu nu hulam` | 1,808 |
| 2 | `nasulitan nasakamuan atu` | 1,789 |
| 3 | `namakayniay a nasulitan` | 1,789 |
| 4 | `a nasulitan nasakamuan` | 1,789 |
| 5 | `nasakamuan atu natinengan` | 1,757 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a nasulitan nasakamuan atu` | 1,789 |
| 2 | `namakayniay a nasulitan nasakamuan` | 1,778 |
| 3 | `nasulitan nasakamuan atu natinengan` | 1,755 |
| 4 | `atu zumaay a natinengan` | 1,673 |
| 5 | `tu ihekalay atu zumaay` | 1,466 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `namakayniay a nasulitan nasakamuan atu` | 1,778 |
| 2 | `a nasulitan nasakamuan atu natinengan` | 1,755 |
| 3 | `tu ihekalay atu zumaay a` | 1,465 |
| 4 | `malalitin tu ihekalay atu zumaay` | 1,463 |
| 5 | `ihekalay atu zumaay a natinengan` | 1,462 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u _` | 357,853 |
| 2 | `a n` | 299,562 |
| 3 | `a _` | 290,493 |
| 4 | `a y` | 241,409 |
| 5 | `_ a` | 215,000 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a y _` | 143,914 |
| 2 | `_ a _` | 137,006 |
| 3 | `a n _` | 126,871 |
| 4 | `t u _` | 101,083 |
| 5 | `_ s a` | 100,121 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n u _` | 84,566 |
| 2 | `_ t u _` | 65,522 |
| 3 | `_ k u _` | 59,832 |
| 4 | `a y _ a` | 54,817 |
| 5 | `y _ a _` | 47,865 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a y _ a _` | 47,058 |
| 2 | `_ a t u _` | 22,206 |
| 3 | `t a d e m` | 21,403 |
| 4 | `a d e m a` | 21,335 |
| 5 | `d e m a w` | 21,328 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 254
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~36% 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 | 0.4793 | 1.394 | 3.89 | 158,896 | 52.1% |
| **1** | Subword | 2.1979 | 4.588 | 29.06 | 6,068 | 0.0% |
| **2** | Word | 0.2677 | 1.204 | 1.80 | 616,064 | 73.2% |
| **2** | Subword | 0.5459 | 1.460 | 2.59 | 176,243 | 45.4% |
| **3** | Word | 0.1031 | 1.074 | 1.20 | 1,105,652 | 89.7% |
| **3** | Subword | 0.2326 | 1.175 | 1.58 | 456,451 | 76.7% |
| **4** | Word | 0.0342 🏆 | 1.024 | 1.06 | 1,321,192 | 96.6% |
| **4** | Subword | 0.1897 | 1.141 | 1.47 | 718,822 | 81.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a kamu nu sakizaya 940 sejek 9 位由執政黨與反對黨分別任命之參議員組成 任期五年 每五年舉行一次普選 malawi sa cacay ademiad mapatay im...`
2. `nu u miliyaway a cidekay 南島語族 saan ya a kawaw panay有專屬的工作`
3. `tu 報刊會涼 u siwkay nu sakizaya 鄒族 cou uici itan 卑南 triyatriyaran 阿美 bu a sapaluma`

**Context Size 2:**

1. `a tademaw silecaday a lalangawan lisin kamu atu kabanaan si kalilidan tumuk saca babalaki mililid tu...`
2. `a mihcaan u nananuman nikaidaw atu sapatakekal hamin i cung ku u pu se su wi alesen`
3. `sa u moyan putiput tina dadiw sa nasulitan ni tuku sayun nay pabalucu ay a cidekay ku`

**Context Size 3:**

1. `kamu nu hulam a pu ha ce a kakitidaan atu nu sakay kinkuay i paris 巴黎 kina i`
2. `a nasulitan nasakamuan atu natinengan lists of national basketball association sapuyu en nba u amis ...`
3. `nasulitan nasakamuan atu natinengan 參考來源 ː malaalitin tu i hekalay atu zumaay a natinengan list of c...`

**Context Size 4:**

1. `a nasulitan nasakamuan atu natinengan lists of national basketball association players alvan adams 阿...`
2. `namakayniay a nasulitan nasakamuan atu natinengan 撒奇萊雅族語詞典 原住民族委員會線上字詞典 花蓮縣政府`
3. `nasulitan nasakamuan atu natinengan 中國高等植物資料庫全庫 中國科學院微生物研究所 行政院原住民族委員會 原住民族藥用植物 花序數位典藏國家型科技計畫 應用服務分項...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `abu_mit_in._iw-b`
2. `_uzay_ng”,isasan`
3. `ude_cihcatu_a_ay`

**Context Size 2:**

1. `u_macay_a_nida_pi`
2. `anaydaw-mici_paan`
3. `a_casa_luayinipah`

**Context Size 3:**

1. `ay_izaw_nan_藝術家mis`
2. `_a_nidaw_masa_mica`
3. `an_cuduc_tu_pyria_`

**Context Size 4:**

1. `_nu_siyhu_ku_kapah_`
2. `_tu_takuwanikeliday`
3. `_ku_akuti’_nu_baluc`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (718,822 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 | 51,046 |
| Total Tokens | 1,702,988 |
| Mean Frequency | 33.36 |
| Median Frequency | 3 |
| Frequency Std Dev | 928.70 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 138,739 |
| 2 | nu | 85,232 |
| 3 | tu | 70,354 |
| 4 | ku | 61,136 |
| 5 | u | 60,011 |
| 6 | sa | 38,061 |
| 7 | i | 34,413 |
| 8 | atu | 22,437 |
| 9 | tademaw | 19,177 |
| 10 | ci | 13,592 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | lengat | 2 |
| 2 | 屋頂的裂縫 | 2 |
| 3 | pulukelin | 2 |
| 4 | kulisimas | 2 |
| 5 | pingki | 2 |
| 6 | matulakay | 2 |
| 7 | kalimicu | 2 |
| 8 | 的未來 | 2 |
| 9 | pisasapi | 2 |
| 10 | sadihkuay | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1985 |
| R² (Goodness of Fit) | 0.993933 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.3% |
| Top 1,000 | 75.3% |
| Top 5,000 | 88.1% |
| Top 10,000 | 92.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9939 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.3% of corpus
- **Long Tail:** 41,046 words needed for remaining 7.9% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.7206 | 0.3585 | N/A | N/A |
| **mono_64d** | 64 | 0.6971 | 0.2873 | N/A | N/A |
| **mono_128d** | 128 | 0.4883 | 0.2402 | N/A | N/A |
| **aligned_32d** | 32 | 0.7206 🏆 | 0.3548 | 0.0300 | 0.1480 |
| **aligned_64d** | 64 | 0.6971 | 0.2750 | 0.0520 | 0.2520 |
| **aligned_128d** | 128 | 0.4883 | 0.2443 | 0.0700 | 0.2960 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7206 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2934. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 7.0% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.310** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

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

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-ma` | masakiketay, mabunal, mata目 |
| `-ka` | kadiceman, kasikawaw, kaniket |
| `-pa` | pabelien, pakalaliw, pacukeday |
| `-sa` | saicelangan, sakatu, sakaudipan |
| `-mi` | mipelu, mipuputay, mingaayay |
| `-a` | ak, amuawaw, anuyaan |
| `-s` | saicelangan, sʉhlʉnganʉ, sakatu |
| `-m` | mipelu, muoli, masakiketay |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | pabelien, saicelangan, anuyaan |
| `-an` | saicelangan, anuyaan, kadiceman |
| `-ay` | umahicaay, masakiketay, mipuputay |
| `-y` | umahicaay, masakiketay, mipuputay |
| `-a` | yaciyana, yita, esperança |
| `-ng` | pisasing, ninaimelang, inng |
| `-g` | pisasing, ninaimelang, inng |
| `-u` | mipelu, sakatu, swu |

### 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 |
|------|----------|------------------|----------|
| `ulit` | 1.96x | 76 contexts | sulit, kulit, asulit |
| `atin` | 1.96x | 71 contexts | latin, yatin, matin |
| `inen` | 1.96x | 69 contexts | yinen, bineng, tineng |
| `tade` | 2.10x | 42 contexts | tadek, taden, tadem |
| `dema` | 2.08x | 40 contexts | demaw, demad, demak |
| `emia` | 2.16x | 34 contexts | emiad, demia, demiad |
| `awan` | 1.69x | 92 contexts | tawan, dawan, awang |
| `tine` | 2.29x | 27 contexts | tineng, atineng, utineng |
| `demi` | 2.21x | 29 contexts | demia, demied, kudemi |
| `hcaa` | 2.19x | 28 contexts | ihcaan, mihcaa, mhcaan |
| `anan` | 1.56x | 108 contexts | canan, nanan, panan |
| `anat` | 2.28x | 18 contexts | canata, kanatl, kanata |

### 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 |
|--------|--------|-----------|----------|
| `-ma` | `-y` | 218 words | mapasimaay, mapatidengay |
| `-ma` | `-ay` | 211 words | mapasimaay, mapatidengay |
| `-ka` | `-n` | 148 words | kasaupuan, kalalulan |
| `-ka` | `-an` | 141 words | kasaupuan, kalalulan |
| `-sa` | `-n` | 122 words | sakalihalayan, sakayduhan |
| `-mi` | `-y` | 120 words | mitatibay, micacuy |
| `-mi` | `-ay` | 116 words | mitatibay, mibelinay |
| `-pa` | `-n` | 114 words | pazen, pasilisian |
| `-sa` | `-an` | 93 words | sakalihalayan, sakayduhan |
| `-sa` | `-y` | 72 words | sapisahemay, sakasiidaay |

### 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 |
|------|-----------------|------------|------|
| nikuwanay | **`nikuw-an-ay`** | 7.5 | `an` |
| asasemaan | **`asase-ma-an`** | 7.5 | `ma` |
| maytebanay | **`mayteb-an-ay`** | 7.5 | `an` |
| sakaputun | **`sakapu-tu-n`** | 7.5 | `tu` |
| sapaiyuwan | **`sapaiyu-w-an`** | 7.5 | `w` |
| kasasudang | **`kasasu-da-ng`** | 7.5 | `da` |
| binacadana | **`binacad-an-a`** | 7.5 | `an` |
| nipikisaan | **`nipikis-a-an`** | 7.5 | `a` |
| lalaliyunan | **`lalaliyu-n-an`** | 7.5 | `n` |
| tadatabaki | **`ta-da-tabaki`** | 7.5 | `tabaki` |
| namakaadih | **`na-ma-kaadih`** | 7.5 | `kaadih` |
| amasasetul | **`a-ma-sasetul`** | 7.5 | `sasetul` |
| mamamelawan | **`ma-ma-melawan`** | 7.5 | `melawan` |
| tadaadidi | **`ta-da-adidi`** | 7.5 | `adidi` |
| malalawlaw | **`malalaw-l-aw`** | 7.5 | `l` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Sakizaya 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 (3.88x) |
| N-gram | **2-gram** | Lowest perplexity (254) |
| Markov | **Context-4** | Highest predictability (96.6%) |
| 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: 2026-01-11 00:15:31*