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README.md

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+---
+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*

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models/word_markov/wuu_markov_ctx1_word_metadata.json

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