---
language: pwn
language_name: Paiwan
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: 4.197
  - name: best_isotropy
    type: isotropy
    value: 0.2318
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Paiwan** 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** | 3.662x | 3.66 | 0.7466% | 241,760 |
| **16k** | 3.933x | 3.94 | 0.8020% | 225,069 |
| **32k** | 4.197x 🏆 | 4.20 | 0.8558% | 210,910 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `aicu a qalici (陰莖) kinacavacavan nua uqaljai, tua sinipukelang nua naqemati tu u...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁aicu ▁a ▁qali ci ▁( 陰 莖 ) ▁kinacavacavan ▁nua ... (+11 more)` | 21 |
| 16k | `▁aicu ▁a ▁qalici ▁( 陰 莖 ) ▁kinacavacavan ▁nua ▁uqaljai ... (+10 more)` | 20 |
| 32k | `▁aicu ▁a ▁qalici ▁( 陰 莖 ) ▁kinacavacavan ▁nua ▁uqaljai ... (+8 more)` | 18 |

**Sample 2:** `kivecik(紋身) aicu a titjen a payuan kivecik a vavayan a pitalima. 排灣族來義鄉傳統手紋`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kivecik ( 紋 身 ) ▁aicu ▁a ▁titjen ▁a ▁payuan ... (+16 more)` | 26 |
| 16k | `▁kivecik ( 紋 身 ) ▁aicu ▁a ▁titjen ▁a ▁payuan ... (+10 more)` | 20 |
| 32k | `▁kivecik ( 紋身 ) ▁aicu ▁a ▁titjen ▁a ▁payuan ▁kivecik ... (+6 more)` | 16 |

**Sample 3:** `Pucevuljan(煙起的地方) avan tiribi dorama i taiwan. inalang tua tiribi na kacalisian....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pucev uljan ( 煙 起 的 地方 ) ▁avan ▁tiribi ... (+26 more)` | 36 |
| 16k | `▁pucevuljan ( 煙起的地方 ) ▁avan ▁tiribi ▁dorama ▁i ▁taiwan . ... (+18 more)` | 28 |
| 32k | `▁pucevuljan ( 煙起的地方 ) ▁avan ▁tiribi ▁dorama ▁i ▁taiwan . ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 32k achieves 4.197x compression
- **Lowest UNK Rate:** 8k with 0.7466% 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 | 1,599 | 10.64 | 3,476 | 30.6% | 70.4% |
| **2-gram** | Subword | 175 🏆 | 7.45 | 2,439 | 79.5% | 98.6% |
| **3-gram** | Word | 2,724 | 11.41 | 4,579 | 19.2% | 57.3% |
| **3-gram** | Subword | 1,042 | 10.03 | 9,633 | 41.2% | 85.4% |
| **4-gram** | Word | 4,987 | 12.28 | 7,623 | 13.9% | 41.7% |
| **4-gram** | Subword | 4,257 | 12.06 | 30,586 | 22.0% | 60.0% |
| **5-gram** | Word | 3,658 | 11.84 | 5,388 | 15.3% | 44.9% |
| **5-gram** | Subword | 10,340 | 13.34 | 49,675 | 13.3% | 42.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `aicu a` | 1,188 |
| 2 | `a cavilj` | 821 |
| 3 | `a caucau` | 748 |
| 4 | `a a` | 732 |
| 5 | `ka a` | 570 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a a a` | 530 |
| 2 | `ka a cavilj` | 413 |
| 3 | `palidring a djalan` | 222 |
| 4 | `a djalan na` | 167 |
| 5 | `a palidring a` | 164 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a a a a` | 514 |
| 2 | `a palidring a djalan` | 164 |
| 3 | `palidring a djalan na` | 143 |
| 4 | `a djalan na taiwan` | 63 |
| 5 | `gaku na kukumin a` | 62 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a a a a a` | 500 |
| 2 | `a palidring a djalan na` | 130 |
| 3 | `palidring a djalan na taiwan` | 62 |
| 4 | `venecikan na takakudan a umaq` | 41 |
| 5 | `a venecikan na takakudan a` | 39 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 54,084 |
| 2 | `a n` | 30,246 |
| 3 | `_ a` | 28,919 |
| 4 | `n _` | 16,909 |
| 5 | `k a` | 16,220 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a _` | 22,599 |
| 2 | `a n _` | 14,379 |
| 3 | `_ k a` | 8,495 |
| 4 | `u a _` | 8,199 |
| 5 | `a _ k` | 6,913 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ a _` | 4,611 |
| 2 | `n _ a _` | 4,406 |
| 3 | `a n _ a` | 4,391 |
| 4 | `u _ a _` | 3,968 |
| 5 | `a n g a` | 3,863 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n _ a _` | 3,756 |
| 2 | `_ t u a _` | 2,908 |
| 3 | `_ a _ c a` | 2,118 |
| 4 | `k a t a _` | 2,100 |
| 5 | `_ n u a _` | 1,928 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 175
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~43% 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 | 0.4964 | 1.411 | 3.23 | 22,120 | 50.4% |
| **1** | Subword | 1.2269 | 2.341 | 6.30 | 2,701 | 0.0% |
| **2** | Word | 0.2355 | 1.177 | 1.53 | 71,169 | 76.5% |
| **2** | Subword | 0.4160 | 1.334 | 2.32 | 17,020 | 58.4% |
| **3** | Word | 0.0941 | 1.067 | 1.15 | 108,439 | 90.6% |
| **3** | Subword | 0.3831 | 1.304 | 2.05 | 39,422 | 61.7% |
| **4** | Word | 0.0376 🏆 | 1.026 | 1.05 | 124,759 | 96.2% |
| **4** | Subword | 0.3237 | 1.252 | 1.72 | 80,954 | 67.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a tja sini pakigaljuanga tua zusi yuli citing a cavilj a tja sicavu tua qinaljan sa`
2. `i marekacemecemel i vudai izua a 源氏物語 ka a puday ljaceng tua mareka caucau pukeljang a`
3. `tua cawtun a cavilj sigac masansika drusapuluq sa pitju a cengkung a qemungcuy maqati a tja`

**Context Size 2:**

1. `aicu a ika namakeljang saka aza tjaljanguanguaqan a zuga nu tjapacunan tucu tucu maljian anga zidai ...`
2. `a cavilj aza cenkungaw a qinaljan a caucau nua cemual nu secevung tua amis a i tjaikacedas`
3. `a caucau i guan aza na linbien 林邊 pana qapulu kemasi kuljauc pasakaledep a navalj tua taiwan`

**Context Size 3:**

1. `a a a a a a a a a a a a a a a a a a`
2. `ka a cavilj tjelu a qiljas masansivalj drusa a kuzulj sa alu taiday sa siva a cuacau 3`
3. `palidring a djalan na qakaw 23px sikamasan pitjulj a palidring a djalan na taiwan paravacan a racev ...`

**Context Size 4:**

1. `a a a a a a a a a a a a a a a a a a a`
2. `a palidring a djalan na taiwan djalan a pasaviri itua taiwan 省道 23px sikamasan 118 a palidirng a dja...`
3. `palidring a djalan na taiwan patje dahu gu kata sanwan gu 省道 23px sikamasannemelj a palidring a djal...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `alanasemekin._ke`
2. `_a_kay_avavan"pa`
3. `ngaivazua_ilâ-1,`

**Context Size 2:**

1. `a_liljeledasa_pai`
2. `an_i_nucau,_kak(區`
3. `_ayalet_of_jilicu`

**Context Size 3:**

1. `_a_drusa_kinalj_i_`
2. `an_富源森林遊樂區vuy_umin`
3. `_kata_katj張孝娘(muma`

**Context Size 4:**

1. `a_a_qiljan_niamadju`
2. `n_a_caviljan_nua_in`
3. `an_a_hada_kuara_sin`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (80,954 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 | 7,537 |
| Total Tokens | 130,405 |
| Mean Frequency | 17.30 |
| Median Frequency | 3 |
| Frequency Std Dev | 279.99 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 22,819 |
| 2 | i | 3,801 |
| 3 | tua | 2,914 |
| 4 | ta | 2,856 |
| 5 | na | 2,750 |
| 6 | sa | 2,550 |
| 7 | nua | 1,941 |
| 8 | kata | 1,767 |
| 9 | izua | 1,539 |
| 10 | aicu | 1,375 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | tuleken | 2 |
| 2 | iqecev | 2 |
| 3 | rigi | 2 |
| 4 | 新年快樂 | 2 |
| 5 | kalevay | 2 |
| 6 | ljavia | 2 |
| 7 | capelju | 2 |
| 8 | sanvaljin | 2 |
| 9 | qazavai | 2 |
| 10 | sinikamaretimalji | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0332 |
| R² (Goodness of Fit) | 0.987155 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 56.8% |
| Top 1,000 | 81.7% |
| Top 5,000 | 96.1% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9872 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 56.8% of corpus
- **Long Tail:** -2,463 words needed for remaining 100.0% coverage

---
## 5. Word Embeddings Evaluation

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

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

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

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


### 5.1 Cross-Lingual Alignment

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

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


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.2318 | 0.4443 | N/A | N/A |
| **mono_64d** | 64 | 0.0360 | 0.4479 | N/A | N/A |
| **mono_128d** | 128 | 0.0037 | 0.4516 | N/A | N/A |
| **aligned_32d** | 32 | 0.2318 🏆 | 0.4503 | 0.0153 | 0.1682 |
| **aligned_64d** | 64 | 0.0360 | 0.4544 | 0.0612 | 0.2355 |
| **aligned_128d** | 128 | 0.0037 | 0.4558 | 0.0795 | 0.2630 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.2318 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4507. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.0% 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 | **0.051** | 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 |
|--------|----------|
| `-s` | serviciilor, sineqetj, sanparavac |
| `-ma` | mavananga, marekatalem, masiljid |
| `-pa` | pacual, paywanzuku, pakan |
| `-si` | sineqetj, sisupuan, sinikieces |
| `-ka` | kaku, kabalelradhane, katalemmang |
| `-t` | tjaljev, tunis, tatun |
| `-k` | kising, kaku, kusitik |
| `-ki` | kising, kipusalimaliman, kinanavun |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-an` | sisupuan, pusikingan, sinupuan |
| `-n` | amen, zunghen, sisupuan |
| `-a` | numatazuwa, mavananga, alja |
| `-ng` | kising, wearing, kicaing |
| `-u` | dukangpu, ninpu, kaku |
| `-g` | kising, wearing, kicaing |
| `-lj` | nasetevelj, sikamasantjelulj, cemqalj |
| `-j` | sineqetj, nasetevelj, sikamasantjelulj |

### 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 |
|------|----------|------------------|----------|
| `malj` | 1.43x | 24 contexts | malje, malji, limalj |
| `alan` | 1.31x | 31 contexts | alang, calan, kalan |
| `java` | 1.40x | 18 contexts | tjava, kaljava, utjavan |
| `jalj` | 1.37x | 18 contexts | udjalj, tjalju, tjalja |
| `kema` | 1.41x | 16 contexts | kemac, kemai, keman |
| `djal` | 1.41x | 16 contexts | djali, udjalj, djalin |
| `ljan` | 1.43x | 13 contexts | aljan, iljang, ljangi |
| `nalj` | 1.69x | 8 contexts | inaljan, naljavek, pinaljak |
| `tjal` | 1.37x | 12 contexts | tjala, tjalju, tjalja |
| `ayan` | 1.36x | 11 contexts | ayanga, pavayan, kavayan |
| `emas` | 1.35x | 11 contexts | cemas, remasi, kemasi |
| `cavi` | 1.51x | 8 contexts | cavij, cavilj, tucavilj |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-n` | 201 words | sisupuan, sinupuan |
| `-s` | `-an` | 182 words | sisupuan, sinupuan |
| `-ka` | `-n` | 145 words | kacilisian, kaljasangasangasan |
| `-ka` | `-an` | 138 words | kacilisian, kaljasangasangasan |
| `-k` | `-n` | 127 words | kipusalimaliman, kinanavun |
| `-t` | `-n` | 126 words | tatun, tjanusun |
| `-k` | `-an` | 117 words | kipusalimaliman, kinavecikan |
| `-t` | `-an` | 108 words | taivuan, tjaisangasangasan |
| `-p` | `-n` | 89 words | pusikingan, pinuvecikan |
| `-p` | `-an` | 82 words | pusikingan, pinuvecikan |

### 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 |
|------|-----------------|------------|------|
| sikudjaljan | **`si-ku-djaljan`** | 7.5 | `djaljan` |
| sematjaljitiv | **`se-ma-tjaljitiv`** | 7.5 | `tjaljitiv` |
| sasipavay | **`sa-si-pavay`** | 7.5 | `pavay` |
| matadrusa | **`ma-ta-drusa`** | 7.5 | `drusa` |
| kinaqipuan | **`kinaqi-pu-an`** | 7.5 | `pu` |
| ljivakung | **`ljiva-ku-ng`** | 7.5 | `ku` |
| sikamasansimuluq | **`si-ka-masansimuluq`** | 7.5 | `masansimuluq` |
| djadjaljunan | **`djadjalju-n-an`** | 7.5 | `n` |
| rinipunan | **`rinipu-n-an`** | 7.5 | `n` |
| sekacedas | **`se-ka-cedas`** | 7.5 | `cedas` |
| blubluone | **`blubluo-n-e`** | 7.5 | `n` |
| philippines | **`philippi-n-es`** | 7.5 | `n` |
| makapalingulj | **`ma-ka-palingulj`** | 7.5 | `palingulj` |
| kadjunagnan | **`kadjunag-n-an`** | 7.5 | `n` |
| mapualang | **`ma-pu-alang`** | 7.5 | `alang` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Paiwan 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 | **32k BPE** | Best compression (4.20x) |
| N-gram | **2-gram** | Lowest perplexity (175) |
| Markov | **Context-4** | Highest predictability (96.2%) |
| 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 18:13:50*