---
language: tay
language_name: Atayal
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: 3.937
  - name: best_isotropy
    type: isotropy
    value: 0.6811
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Atayal** 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** | 3.548x | 3.55 | 0.2003% | 384,001 |
| **16k** | 3.734x | 3.74 | 0.2108% | 364,864 |
| **32k** | 3.856x | 3.86 | 0.2176% | 353,338 |
| **64k** | 3.937x 🏆 | 3.94 | 0.2222% | 346,059 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Will Arnett kawas tay ryax sa tay 4 nqu tay 5, Will Arnett, squliq na Bunge’. ci...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁will ▁arn ett ▁kawas ▁tay ▁ryax ▁sa ▁tay ▁ 4 ... (+24 more)` | 34 |
| 16k | `▁will ▁arn ett ▁kawas ▁tay ▁ryax ▁sa ▁tay ▁ 4 ... (+24 more)` | 34 |
| 32k | `▁will ▁arnett ▁kawas ▁tay ▁ryax ▁sa ▁tay ▁ 4 ▁nqu ... (+22 more)` | 32 |
| 64k | `▁will ▁arnett ▁kawas ▁tay ▁ryax ▁sa ▁tay ▁ 4 ▁nqu ... (+22 more)` | 32 |

**Sample 2:** `cingay balay llamu/kinkyalan nya phpah. hoqay su' abaw na phpah qasa lwah. iyat ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cingay ▁balay ▁llamu / k ink yalan ▁nya ▁phpah . ... (+18 more)` | 28 |
| 16k | `▁cingay ▁balay ▁llamu / k ink yalan ▁nya ▁phpah . ... (+16 more)` | 26 |
| 32k | `▁cingay ▁balay ▁llamu / kinkyalan ▁nya ▁phpah . ▁hoqay ▁su ... (+12 more)` | 22 |
| 64k | `▁cingay ▁balay ▁llamu / kinkyalan ▁nya ▁phpah . ▁hoqay ▁su ... (+12 more)` | 22 |

**Sample 3:** `ksxun (被敬重) Mrhuw Yumimg ka ksxun nha mita kwara maki qalang sami. (由命耆老在我們部落很受人...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ks xun ▁( 被 敬 重 ) ▁mrhuw ▁yu mi ... (+26 more)` | 36 |
| 16k | `▁ks xun ▁( 被 敬重 ) ▁mrhuw ▁yu mim g ... (+23 more)` | 33 |
| 32k | `▁ksxun ▁( 被敬重 ) ▁mrhuw ▁yumimg ▁ka ▁ksxun ▁nha ▁mita ... (+10 more)` | 20 |
| 64k | `▁ksxun ▁( 被敬重 ) ▁mrhuw ▁yumimg ▁ka ▁ksxun ▁nha ▁mita ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 64k achieves 3.937x compression
- **Lowest UNK Rate:** 8k with 0.2003% 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 | 3,184 | 11.64 | 13,869 | 25.5% | 63.6% |
| **2-gram** | Subword | 260 🏆 | 8.02 | 5,715 | 71.6% | 98.1% |
| **3-gram** | Word | 4,214 | 12.04 | 22,311 | 25.5% | 60.8% |
| **3-gram** | Subword | 1,646 | 10.68 | 21,057 | 33.3% | 78.1% |
| **4-gram** | Word | 9,656 | 13.24 | 54,321 | 21.7% | 50.4% |
| **4-gram** | Subword | 6,466 | 12.66 | 75,451 | 18.1% | 52.9% |
| **5-gram** | Word | 9,511 | 13.22 | 50,500 | 22.2% | 50.1% |
| **5-gram** | Subword | 15,348 | 13.91 | 137,181 | 11.7% | 39.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hya ga` | 6,473 |
| 2 | `s uli` | 2,840 |
| 3 | `gyencumin ga` | 2,299 |
| 4 | `uli tayan` | 2,183 |
| 5 | `pqwasan biru` | 1,860 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s uli tayan` | 2,182 |
| 2 | `pinspngan gyencumin ga` | 1,473 |
| 3 | `kwara s uli` | 1,448 |
| 4 | `hi ku kwara` | 1,445 |
| 5 | `ku kwara s` | 1,445 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hi ku kwara s` | 1,445 |
| 2 | `ku kwara s uli` | 1,445 |
| 3 | `kwara s uli tayan` | 1,445 |
| 4 | `sa knita sa brbiru` | 1,401 |
| 5 | `cinkhulan sa knita sa` | 1,401 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ku kwara s uli tayan` | 1,445 |
| 2 | `hi ku kwara s uli` | 1,445 |
| 3 | `cinkhulan sa knita sa brbiru` | 1,401 |
| 4 | `sa knita sa brbiru lists` | 882 |
| 5 | `knita sa brbiru lists of` | 882 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 122,942 |
| 2 | `a n` | 88,116 |
| 3 | `y a` | 79,076 |
| 4 | `_ n` | 70,851 |
| 5 | `g a` | 62,384 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n _` | 44,559 |
| 2 | `_ n a` | 40,951 |
| 3 | `n a _` | 34,903 |
| 4 | `n g _` | 30,103 |
| 5 | `_ g a` | 29,840 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a _` | 32,577 |
| 2 | `_ g a _` | 21,648 |
| 3 | `_ t a y` | 16,975 |
| 4 | `t a y _` | 12,076 |
| 5 | `a n g _` | 11,989 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t a y _` | 10,709 |
| 2 | `k a w a s` | 8,363 |
| 3 | `_ k a w a` | 7,754 |
| 4 | `a w a s _` | 7,042 |
| 5 | `y a ’ _ g` | 6,882 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 260
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~40% 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 | 0.6602 | 1.580 | 4.61 | 39,339 | 34.0% |
| **1** | Subword | 1.7512 | 3.366 | 12.08 | 3,139 | 0.0% |
| **2** | Word | 0.2844 | 1.218 | 1.71 | 181,030 | 71.6% |
| **2** | Subword | 0.4330 | 1.350 | 2.34 | 37,911 | 56.7% |
| **3** | Word | 0.1014 | 1.073 | 1.19 | 308,446 | 89.9% |
| **3** | Subword | 0.3425 | 1.268 | 2.04 | 88,638 | 65.8% |
| **4** | Word | 0.0422 🏆 | 1.030 | 1.08 | 365,569 | 95.8% |
| **4** | Subword | 0.3240 | 1.252 | 1.82 | 180,359 | 67.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `na spyang maki yow na linhuyan gyencumin ga 68 buwan 292 buwan nya kwara s uli`
2. `ga 107 kg banggo na holi na sbunaw wal mhuqil sraral mbuwah nuway ay hya ga`
3. `sa bleqaw ta mlahang sali buwan nya skwan biru laqi cinkhulan sa zik na qalang myan`

**Context Size 2:**

1. `hya ga nakahama go kwara sali buwan nya ga cingay bes nya jeraldine 杰拉爾丁 musa chicago mlahang`
2. `s uli 2 maki qu ngasal bziran ngasal psatu tegami ru pqniqan iyu rhzyal kki an tay`
3. `gyencumin ga 10 kyan ku 175 hi binah ga yat kahun sku pinspngan gyencumin ga 88 kyan`

**Context Size 3:**

1. `s uli tayan s uli tayan pinspngan gyencumin ga 3 kyan ku 15 hi nya pinspung na linhuyan`
2. `pinspngan gyencumin ga 84 kyan ku 227 hi binah ga yat kahun sku pinspngan gyencumin ga 32 kyan`
3. `kwara s uli tayan pinspngan gyencumin ga 88 kyan ku 830 hi binah ga yat kahun sku pinspngan`

**Context Size 4:**

1. `ku kwara s uli tayan s uli tayan pinspngan gyencumin ga 70 kyan ku 1 961 hi nya pinspung`
2. `hi ku kwara s uli tayan s uli tayan pinspngan gyencumin ga 67 kyan ku 191 hi binah ga`
3. `kwara s uli tayan s uli tayan pinspngan gyencumin ga 72 kyan ku 154 hi binah ga yat kahun`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ta’uyu’ul_roket`
2. `alppcinokup’,_s_`
3. `n、ci’_micirun_’u`

**Context Size 2:**

1. `a_si_qqmuchaw_psi`
2. `an_sa_shingiqutu_`
3. `yan._qwas_natjan_`

**Context Size 3:**

1. `an_ga,_syo._rhzyal`
2. `_nah_na_ga_pinliw_`
3. `na_pqwas,_ru_mimal`

**Context Size 4:**

1. `_na_te_ru_beinango,`
2. `_ga_bqanux_balay_te`
3. `_tay_9_byacing_sazi`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (180,359 contexts)
- **Recommendation:** Context-3 or Context-4 for text generation

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/zipf_law.png)

![Top Words](visualizations/top20_words.png)

![Coverage Curve](visualizations/vocab_coverage.png)

### Statistics

| Metric | Value |
|--------|-------|
| Vocabulary Size | 17,362 |
| Total Tokens | 611,143 |
| Mean Frequency | 35.20 |
| Median Frequency | 4 |
| Frequency Std Dev | 414.96 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | na | 32,851 |
| 2 | ga | 27,245 |
| 3 | sa | 11,539 |
| 4 | tay | 10,733 |
| 5 | nya | 8,397 |
| 6 | qu | 8,173 |
| 7 | kawas | 8,159 |
| 8 | ru | 7,855 |
| 9 | hya | 7,019 |
| 10 | maki | 6,131 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | nyut | 2 |
| 2 | qnsun | 2 |
| 3 | mtlu | 2 |
| 4 | sayat | 2 |
| 5 | 泰雅族女用名 | 2 |
| 6 | rimuy是女子名 | 2 |
| 7 | 有思念之意 | 2 |
| 8 | 也有愉悅的情境 | 2 |
| 9 | 父母命名子女 | 2 |
| 10 | 期望快樂成長 | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2513 |
| R² (Goodness of Fit) | 0.994822 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 51.8% |
| Top 1,000 | 82.8% |
| Top 5,000 | 93.8% |
| Top 10,000 | 97.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9948 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 51.8% of corpus
- **Long Tail:** 7,362 words needed for remaining 2.6% 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 | 0.6811 🏆 | 0.3844 | N/A | N/A |
| **mono_64d** | 64 | 0.4048 | 0.3600 | N/A | N/A |
| **mono_128d** | 128 | 0.0450 | 0.3581 | N/A | N/A |
| **aligned_32d** | 32 | 0.6811 | 0.3751 | 0.0160 | 0.1520 |
| **aligned_64d** | 64 | 0.4048 | 0.3639 | 0.0340 | 0.1780 |
| **aligned_128d** | 128 | 0.0450 | 0.3422 | 0.0440 | 0.2260 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6811 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3639. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.4% 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 | **0.257** | 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 |
|--------|----------|
| `-m` | mktayax, msurux, mbubu |
| `-s` | sirasit, syaw, smbes |
| `-p` | plbit, portugueselinpgan, punu |
| `-k` | kangcyo, kan, kapang |
| `-t` | tluhung, tommy, tpuyan |
| `-b` | blin, brenner, buhari |
| `-a` | anli, aki, anteng |
| `-h` | harin, haru, huwa |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | kan, rengan, blin |
| `-an` | kan, rengan, cinkhulan |
| `-g` | tluhung, kapang, uwang |
| `-ng` | tluhung, kapang, uwang |
| `-a` | kora, rwa, benfica |
| `-y` | yabay, yngiy, tommy |
| `-s` | keizarmezs, smbes, hakaparis |
| `-i` | anli, aki, naui |

### 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 |
|------|----------|------------------|----------|
| `ngan` | 1.58x | 66 contexts | pngan, tngan, hngan |
| `zyuw` | 1.80x | 25 contexts | izyuw, zyuwa, pzyuwi |
| `qala` | 1.85x | 22 contexts | qalan, qalax, qqala |
| `inga` | 1.42x | 42 contexts | ingat, singa, kinga |
| `unga` | 1.58x | 26 contexts | yunga, ungat, lunga |
| `yuwa` | 1.47x | 33 contexts | yuwaw, zyuwa, yuwan |
| `ngas` | 1.96x | 13 contexts | langas, ngasan, sangas |
| `gasa` | 1.96x | 11 contexts | mgasa, ngasan, ngasal |
| `quli` | 1.48x | 24 contexts | squli, qulih, quliq |
| `uliq` | 1.57x | 19 contexts | tuliq, culiq, quliq |
| `inah` | 1.56x | 19 contexts | qinah, binah, mbinah |
| `rgya` | 1.90x | 9 contexts | rgyas, rgyax, rrgyax |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-n` | 163 words | ppspun, pinsqihan |
| `-p` | `-an` | 124 words | pinsqihan, pinbuyan |
| `-k` | `-n` | 97 words | kinyopan, kinsasan |
| `-k` | `-an` | 77 words | kinyopan, kinsasan |
| `-s` | `-n` | 65 words | sweden, snyogun |
| `-m` | `-g` | 52 words | mklahang, mahing |
| `-m` | `-ng` | 50 words | mklahang, mahing |
| `-c` | `-n` | 46 words | cmyan, ciyan |
| `-t` | `-n` | 43 words | timberwolvesginlgan, thyayun |
| `-k` | `-g` | 43 words | klhangang, khokung |

### 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 |
|------|-----------------|------------|------|
| pinthwiru | **`p-in-thwiru`** | 7.5 | `thwiru` |
| mshayhway | **`mshayh-w-ay`** | 7.5 | `w` |
| matabalay | **`ma-ta-balay`** | 7.5 | `balay` |
| msinqutux | **`ms-in-qutux`** | 7.5 | `qutux` |
| kincingay | **`ki-n-cingay`** | 7.5 | `cingay` |
| mananigay | **`manani-g-ay`** | 7.5 | `g` |
| pincyawgan | **`pincyaw-g-an`** | 7.5 | `g` |
| allenryax | **`allenr-y-ax`** | 7.5 | `y` |
| cyangcinko | **`cyangci-n-ko`** | 7.5 | `n` |
| cinbawnan | **`cinbaw-n-an`** | 7.5 | `n` |
| kinsraral | **`ki-n-sraral`** | 7.5 | `sraral` |
| sincikusya | **`sinciku-s-ya`** | 7.5 | `s` |
| pinqzywan | **`pinqzy-w-an`** | 7.5 | `w` |
| skbalayun | **`s-kbalay-un`** | 6.0 | `kbalay` |
| kakawasan | **`ka-kawas-an`** | 6.0 | `kawas` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Atayal 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 (3.94x) |
| N-gram | **2-gram** | Lowest perplexity (260) |
| Markov | **Context-4** | Highest predictability (95.8%) |
| 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 00:23:22*