---
language: wuu
language_name: Wu Chinese
language_family: sinitic_other
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-sinitic_other
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: 2.139
  - name: best_isotropy
    type: isotropy
    value: 0.6410
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

# Wu Chinese - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Wu Chinese** 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 |
|------------|-------------|---------------|----------|--------------|
| **16k** | 1.645x | 1.65 | 0.0470% | 189,167 |
| **32k** | 1.914x | 1.92 | 0.0547% | 162,652 |
| **64k** | 2.139x 🏆 | 2.15 | 0.0612% | 145,478 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `感觉系统（英语：sensory system）是神经系统中处理感觉信息个一部分。感觉系统包括感受器、神经通路搭子大脑中搭感觉知觉有关个部分。`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 16k | `▁ 感 觉 系统 ( 英语 : s ens ory ... (+35 more)` | 45 |
| 32k | `▁ 感觉 系统 ( 英语 : s ens ory ▁system ... (+28 more)` | 38 |
| 64k | `▁ 感觉 系统 ( 英语 : sens ory ▁system ) ... (+25 more)` | 35 |

**Sample 2:** `大事记 明代宗为了筹募经费而开始贩卖度牒，直到明末，导致僧尼剧增，寺院林立。 德里苏丹国赛义德王朝锡林德总督巴赫鲁尔·洛迪佔据了德里，赛义德王朝被洛迪王朝取代。...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 16k | `▁大事记 ▁明 代 宗 为了 筹 募 经 费 而 ... (+63 more)` | 73 |
| 32k | `▁大事记 ▁明代 宗 为了 筹 募 经 费 而 开始 ... (+52 more)` | 62 |
| 64k | `▁大事记 ▁明代 宗 为了 筹 募 经费 而 开始 贩卖 ... (+46 more)` | 56 |

**Sample 3:** `吉兰丹州（）是马来西亚拉西马北部个一個州，首府為哥打峇鲁。該州北接泰国，东北为南中国海，西接霹雳州，南临彭亨州，东南为登嘉樓州。吉兰丹国号为Darul Naim...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 16k | `▁吉 兰 丹 州 () 是 马来西亚 拉 西 马 ... (+59 more)` | 69 |
| 32k | `▁吉 兰 丹 州 () 是马来西亚 拉西 马 北部 个一個 ... (+51 more)` | 61 |
| 64k | `▁吉 兰 丹州 () 是马来西亚 拉西 马 北部 个一個 州 ... (+45 more)` | 55 |


### Key Findings

- **Best Compression:** 64k achieves 2.139x compression
- **Lowest UNK Rate:** 16k with 0.0470% 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 | 1,616 🏆 | 10.66 | 2,926 | 27.3% | 67.5% |
| **2-gram** | Subword | 7,919 | 12.95 | 59,139 | 22.8% | 51.4% |
| **3-gram** | Word | 2,273 | 11.15 | 3,242 | 19.6% | 59.2% |
| **3-gram** | Subword | 27,775 | 14.76 | 121,509 | 9.3% | 30.8% |
| **4-gram** | Word | 5,014 | 12.29 | 6,809 | 13.7% | 37.6% |
| **4-gram** | Subword | 81,103 | 16.31 | 233,152 | 5.5% | 16.3% |
| **5-gram** | Word | 3,786 | 11.89 | 5,117 | 16.4% | 41.5% |
| **5-gram** | Subword | 104,659 | 16.68 | 225,092 | 4.4% | 13.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `出生 逝世` | 1,249 |
| 2 | `of the` | 596 |
| 3 | `2 2` | 359 |
| 4 | `大事记 中国` | 331 |
| 5 | `1 1` | 266 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `2 2 2` | 234 |
| 2 | `1 1 1` | 152 |
| 3 | `作词 作曲 编曲` | 84 |
| 4 | `原唱 作词 作曲` | 82 |
| 5 | `演唱曲目 原唱 作词` | 82 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `2 2 2 2` | 180 |
| 2 | `1 1 1 1` | 114 |
| 3 | `演唱曲目 原唱 作词 作曲` | 82 |
| 4 | `原唱 作词 作曲 编曲` | 82 |
| 5 | `作词 作曲 编曲 排名` | 73 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `2 2 2 2 2` | 146 |
| 2 | `1 1 1 1 1` | 93 |
| 3 | `演唱曲目 原唱 作词 作曲 编曲` | 82 |
| 4 | `原唱 作词 作曲 编曲 排名` | 73 |
| 5 | `地区 邮政编码 地区 邮政编码 地区` | 54 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `。 _` | 20,314 |
| 2 | `e _` | 14,212 |
| 3 | `a n` | 13,204 |
| 4 | `i n` | 10,947 |
| 5 | `n _` | 10,755 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t h e` | 3,901 |
| 2 | `_ t h` | 3,488 |
| 3 | `_ — _` | 3,447 |
| 4 | `_ o f` | 3,437 |
| 5 | `_ - _` | 3,310 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ o f _` | 3,134 |
| 2 | `t h e _` | 3,085 |
| 3 | `_ t h e` | 2,842 |
| 4 | `— _ — _` | 2,489 |
| 5 | `_ — _ —` | 2,487 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t h e _` | 2,564 |
| 2 | `_ — _ — _` | 2,487 |
| 3 | `— _ — _ —` | 1,986 |
| 4 | `a t i o n` | 1,684 |
| 5 | `。 _ 出 生 _` | 1,567 |


### Key Findings

- **Best Perplexity:** 2-gram (word) with 1,616
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~13% 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 | 0.2252 | 1.169 | 1.67 | 213,385 | 77.5% |
| **1** | Subword | 1.9391 | 3.835 | 30.25 | 12,723 | 0.0% |
| **2** | Word | 0.0575 | 1.041 | 1.10 | 342,915 | 94.2% |
| **2** | Subword | 0.5697 | 1.484 | 2.77 | 384,552 | 43.0% |
| **3** | Word | 0.0189 | 1.013 | 1.03 | 360,203 | 98.1% |
| **3** | Subword | 0.2223 | 1.167 | 1.47 | 1,063,474 | 77.8% |
| **4** | Word | 0.0074 🏆 | 1.005 | 1.01 | 353,710 | 99.3% |
| **4** | Subword | 0.1256 | 1.091 | 1.23 | 1,559,569 | 87.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `of depression 个经济衰退开始 伊拉世界范围内造成了巨大创伤 导致普遍个失业搭贫困 富兰克林 皮尔斯franklin 民主党 乔治 唐宁搭唐宁街个典故 分类 microsoft windo...`
2. `the honourable privy 分类 作家 評論員 朱立熙 前華視副總 與劉文正同班 鄭啟明 中華民國風工程學會理事長 曾任國立海洋大學河海工程系副教授 淡大土木工程系副教授 教授 杜秉明 ...`
3. `英语 new jersey 是美国新泽西州个最大高等学府 是一所公立研究型大学 渠个主校区垃拉佛罗里达州个首府 塔拉哈西 英语 the interpreter all the world cup 法語...`

**Context Size 2:**

1. `出生 逝世 伊莎贝拉一世 西班牙卡斯蒂利亚女王 4年 0 06 0 39 0 24 3 38 0 206 58 64`
2. `of the population converted into years of amor en los tiempos del cólera 英文 love in all`
3. `2 2 2 2 6 美國永久居民 1 4 4 4 4 5 百萬人 23 4 97 百萬人`

**Context Size 3:**

1. `2 2 2 1 4 6 5 6 3 3 4 2 3 3 3 3 3 3`
2. `1 1 1 1 1 2 2 3 windows macos gpl 主页 arcadeflex 0 36 13 多种街机系统 java`
3. `作词 作曲 编曲 排名 互投 1 李克勤 李维嘉 谢谢你的爱 刘德华 林秋离 熊美玲 johnny yim 5 7 haya乐团 张大大`

**Context Size 4:**

1. `2 2 2 2 赛艇 17px fisa 4 5 6 4 4 8 8 苏诗丁 5 3 6 5`
2. `1 1 1 1 2 3 1 1 5 2 6 3 4 2 1 1 1 1 1`
3. `演唱曲目 原唱 作词 作曲 编曲 排名 互投 1 赵 传 李 锐 大地 beyond 刘卓辉 黄家驹 terence teo 7`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_仙子因为北京车获胜拉该地形成美`
2. `atha）_l_00_22_-关`
3. `e_-_425_skherorl`

**Context Size 2:**

1. `。_澳大利」〔glonoël_f_`
2. `e_'comande_handri`
3. `an_rw-hyd_gires_v`

**Context Size 3:**

1. `the_flee_y_特色词汇_我—`
2. `_theffide）是由两条有得公共`
3. `_—_—_3.30%_參加高中社區服`

**Context Size 4:**

1. `_of_the_nakara_ou_k`
2. `the_boy_adley,_clau`
3. `_the_warraglypha》（日`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,559,569 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 | 32,292 |
| Total Tokens | 241,506 |
| Mean Frequency | 7.48 |
| Median Frequency | 3 |
| Frequency Std Dev | 50.87 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | of | 3,198 |
| 2 | the | 3,043 |
| 3 | 英语 | 2,743 |
| 4 | 分类 | 2,491 |
| 5 | 2 | 2,396 |
| 6 | 1 | 2,018 |
| 7 | 大事记 | 1,930 |
| 8 | 出生 | 1,790 |
| 9 | 逝世 | 1,772 |
| 10 | 3 | 1,615 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 衢化公司电石厂 | 2 |
| 2 | 浙江大成 | 2 |
| 3 | 温州佳运 | 2 |
| 4 | 队数 | 2 |
| 5 | 绍兴塔牌 | 2 |
| 6 | 舟山舟峰 | 2 |
| 7 | 台州王野 | 2 |
| 8 | 义乌土木建设 | 2 |
| 9 | 杭州天业电子 | 2 |
| 10 | 天业电子 | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8530 |
| R² (Goodness of Fit) | 0.995865 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.0% |
| Top 1,000 | 46.3% |
| Top 5,000 | 67.8% |
| Top 10,000 | 78.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9959 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.0% of corpus
- **Long Tail:** 22,292 words needed for remaining 21.7% 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 | 0.6410 | 0.3758 | N/A | N/A |
| **mono_64d** | 64 | 0.2896 | 0.3654 | N/A | N/A |
| **mono_128d** | 128 | 0.0637 | 0.3638 | N/A | N/A |
| **aligned_32d** | 32 | 0.6410 🏆 | 0.3750 | 0.0500 | 0.2840 |
| **aligned_64d** | 64 | 0.2896 | 0.3749 | 0.0680 | 0.3380 |
| **aligned_128d** | 128 | 0.0637 | 0.3655 | 0.0820 | 0.3460 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6410 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3701. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.2% 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 | **2.111** | 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 |
|--------|----------|
| `-s` | saidu, sakigake, scientists |
| `-m` | mas, musume, missionary |
| `-a` | apparatus, at, angel |
| `-c` | christi, christensen, cotillard |
| `-b` | barnes, brassica, bushou |
| `-p` | plutocracy, parti, parent |
| `-t` | towns, translated, tellabs |
| `-d` | duels, dieu, diadem |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | barnes, rigs, enemies |
| `-e` | verte, sakigake, musume |
| `-n` | watson, christensen, wigan |
| `-a` | brassica, barbara, patricia |
| `-on` | watson, baron, anderson |
| `-r` | soccer, ratzinger, isomer |
| `-y` | plutocracy, way, missionary |
| `-t` | parent, at, hurt |

### 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 |
|------|----------|------------------|----------|
| `族自治州` | 2.45x | 13 contexts | 甘南藏族自治州, 海南藏族自治州, 甘孜藏族自治州 |
| `atio` | 1.98x | 18 contexts | ratio, oratio, ratios |
| `tion` | 1.91x | 17 contexts | motion, action, nation |
| `我是歌手` | 2.43x | 7 contexts | 我是歌手第八季, 我是歌手第四季, 我是歌手第三季 |
| `是歌手第` | 2.43x | 7 contexts | 我是歌手第八季, 我是歌手第四季, 我是歌手第三季 |

### 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` | `-s` | 29 words | points, primates |
| `-c` | `-s` | 29 words | chinois, comptes |
| `-s` | `-s` | 25 words | shakespeares, seuss |
| `-c` | `-n` | 25 words | chuushin, callaghan |
| `-c` | `-e` | 24 words | course, complete |
| `-m` | `-s` | 23 words | maximus, meiers |
| `-a` | `-n` | 23 words | asunción, anderson |
| `-a` | `-s` | 23 words | antilles, arts |
| `-p` | `-n` | 23 words | ponn, prachachon |
| `-s` | `-e` | 21 words | serie, soreyuke |

### 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 |
|------|-----------------|------------|------|
| 玛理诺marino | **`玛理诺mar-in-o`** | 7.5 | `in` |
| submitted | **`submit-t-ed`** | 7.5 | `t` |
| australasia | **`australa-s-ia`** | 7.5 | `s` |
| gilbertese | **`gilbert-es-e`** | 6.0 | `gilbert` |
| interests | **`inter-es-ts`** | 6.0 | `inter` |
| alchemists | **`alchemist-s`** | 4.5 | `alchemist` |
| nobunagas | **`nobunaga-s`** | 4.5 | `nobunaga` |
| christian | **`christi-an`** | 4.5 | `christi` |
| wikipedias | **`wikipedia-s`** | 4.5 | `wikipedia` |
| governments | **`government-s`** | 4.5 | `government` |
| productions | **`production-s`** | 4.5 | `production` |
| entertainmentna | **`entertainment-na`** | 4.5 | `entertainment` |
| childrens | **`children-s`** | 4.5 | `children` |
| publishers | **`publisher-s`** | 4.5 | `publisher` |
| assessment | **`a-s-sessment`** | 4.5 | `sessment` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Wu Chinese 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 (2.14x) |
| N-gram | **2-gram** | Lowest perplexity (1,616) |
| Markov | **Context-4** | Highest predictability (99.3%) |
| 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 04:47:13*