---
language: za
language_name: Zhuang
language_family: taikadai_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-taikadai_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: 3.419
  - name: best_isotropy
    type: isotropy
    value: 0.1745
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Zhuang** 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** | 2.806x | 2.81 | 0.4774% | 128,613 |
| **16k** | 3.128x | 3.14 | 0.5321% | 115,393 |
| **32k** | 3.419x 🏆 | 3.43 | 0.5815% | 105,580 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Bingh Conghhozhau（Vahgun：白喉）《常见病证壮医诊疗规范》, dwg cungj bingh ndeu. Doeg Wnq bingh W...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁bingh ▁congh hozhau ( vahgun : 白 喉 )《 常见病证壮医诊疗规范 ... (+18 more)` | 28 |
| 16k | `▁bingh ▁congh hozhau ( vahgun : 白 喉 )《 常见病证壮医诊疗规范 ... (+18 more)` | 28 |
| 32k | `▁bingh ▁conghhozhau ( vahgun : 白喉 )《 常见病证壮医诊疗规范 》, ▁dwg ... (+16 more)` | 26 |

**Sample 2:** `Mali dwg aen guekgya youq Feihcouh, soujduh dwg Bamako. Feihcouh`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mal i ▁dwg ▁aen ▁guekgya ▁youq ▁feihcouh , ▁soujduh ▁dwg ... (+6 more)` | 16 |
| 16k | `▁mali ▁dwg ▁aen ▁guekgya ▁youq ▁feihcouh , ▁soujduh ▁dwg ▁bamak ... (+3 more)` | 13 |
| 32k | `▁mali ▁dwg ▁aen ▁guekgya ▁youq ▁feihcouh , ▁soujduh ▁dwg ▁bamako ... (+2 more)` | 12 |

**Sample 3:** `Niger dwg aen guekgya youq Feihcouh, soujduh dwg Niamey. Feihcouh`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁niger ▁dwg ▁aen ▁guekgya ▁youq ▁feihcouh , ▁soujduh ▁dwg ▁ni ... (+4 more)` | 14 |
| 16k | `▁niger ▁dwg ▁aen ▁guekgya ▁youq ▁feihcouh , ▁soujduh ▁dwg ▁niamey ... (+2 more)` | 12 |
| 32k | `▁niger ▁dwg ▁aen ▁guekgya ▁youq ▁feihcouh , ▁soujduh ▁dwg ▁niamey ... (+2 more)` | 12 |


### Key Findings

- **Best Compression:** 32k achieves 3.419x compression
- **Lowest UNK Rate:** 8k with 0.4774% 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 | 1,324 | 10.37 | 2,862 | 33.4% | 75.3% |
| **2-gram** | Subword | 292 🏆 | 8.19 | 2,421 | 66.8% | 98.4% |
| **3-gram** | Word | 1,603 | 10.65 | 3,591 | 31.8% | 70.2% |
| **3-gram** | Subword | 1,849 | 10.85 | 11,233 | 31.0% | 74.9% |
| **4-gram** | Word | 3,210 | 11.65 | 7,510 | 26.0% | 54.9% |
| **4-gram** | Subword | 7,224 | 12.82 | 38,214 | 16.4% | 49.0% |
| **5-gram** | Word | 2,596 | 11.34 | 5,995 | 28.0% | 58.6% |
| **5-gram** | Subword | 16,250 | 13.99 | 64,425 | 10.8% | 35.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dwg aen` | 951 |
| 2 | `doeg wnq` | 505 |
| 3 | `yinzminz gunghozgoz` | 489 |
| 4 | `cunghvaz yinzminz` | 409 |
| 5 | `dwg cungj` | 393 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `cunghvaz yinzminz gunghozgoz` | 409 |
| 2 | `vwnzyen doiqciuq baihrog` | 260 |
| 3 | `doiqciuq baihrog lienzcanh` | 259 |
| 4 | `saehgienh doekfag dai` | 204 |
| 5 | `doekfag dai nyied` | 203 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `vwnzyen doiqciuq baihrog lienzcanh` | 259 |
| 2 | `dwg aen swhyienzsoq beij` | 198 |
| 3 | `youq ligmoq ndeu bi` | 192 |
| 4 | `ligmoq ndeu bi neix` | 192 |
| 5 | `𬆗 ngoenzciet 節日 𭥓節` | 192 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dai 去世 𬆗 ngoenzciet 節日` | 192 |
| 2 | `去世 𬆗 ngoenzciet 節日 𭥓節` | 192 |
| 3 | `youq ligmoq ndeu bi neix` | 192 |
| 4 | `ligmoq ndeu bi neix daj` | 192 |
| 5 | `doekfag 出生 𬻨𰅞 dai 去世` | 191 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g` | 30,692 |
| 2 | `e n` | 25,550 |
| 3 | `a e` | 19,708 |
| 4 | `_ d` | 17,651 |
| 5 | `z _` | 17,038 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n g` | 8,544 |
| 2 | `n g h` | 8,287 |
| 3 | `a e n` | 7,258 |
| 4 | `_ d a` | 6,381 |
| 5 | `i n g` | 6,244 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g h _` | 3,421 |
| 2 | `a e n _` | 3,094 |
| 3 | `d w g _` | 3,059 |
| 4 | `n g j _` | 2,964 |
| 5 | `_ d w g` | 2,805 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d w g _` | 2,772 |
| 2 | `_ a e n _` | 2,723 |
| 3 | `_ c u n g` | 2,337 |
| 4 | `_ y o u q` | 1,886 |
| 5 | `y o u q _` | 1,809 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 292
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.6137 | 1.530 | 3.36 | 23,267 | 38.6% |
| **1** | Subword | 1.1528 | 2.223 | 5.67 | 3,715 | 0.0% |
| **2** | Word | 0.1628 | 1.119 | 1.30 | 77,229 | 83.7% |
| **2** | Subword | 0.3332 | 1.260 | 2.13 | 21,044 | 66.7% |
| **3** | Word | 0.0535 | 1.038 | 1.09 | 99,423 | 94.6% |
| **3** | Subword | 0.3942 | 1.314 | 2.14 | 44,681 | 60.6% |
| **4** | Word | 0.0282 🏆 | 1.020 | 1.04 | 106,492 | 97.2% |
| **4** | Subword | 0.3653 | 1.288 | 1.80 | 95,273 | 63.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `dwg aen yenzgiucunghsinh ciusou caeuq cwngfuj doeg wnq gij nei swenj hwnjdaeuj lo hoeng dingzlai seu...`
2. `aen fap hingzcwng bumwnz caeuq dajciengj gij guenjleix gaicawx daehyinh gij swhliu nangqdaengz cwzyi...`
3. `youq imdb ngaeuzgyae daigoz caivi nienz caeuq baugau bonjdieg caeuq gwzming dihgaeuq miz 5 aen fap`

**Context Size 2:**

1. `dwg aen hawsingz youq baihnamz yacouh soujduh de dwg youq yiengh lizsij cingzgvang lawz cungj mbouj ...`
2. `doeg wnq haijnanz vwnzyen doxgven lienhciep baihrog meijgoz dakota`
3. `cunghvaz yinzminz gunghozgoz de hix dwg aen vuengzciuz cunghgoz dungjci daj 960 nienz ciq nienz`

**Context Size 3:**

1. `cunghvaz yinzminz gunghozgoz 115 中华人民共和国公共图书馆法 aen fap duzsuhgvanj caezyungh cunghvaz yinzminz gungh...`
2. `vwnzyen doiqciuq baihrog lienzcanh 港珠澳大桥管理局官網 香港政府 港珠澳大橋香港段網頁 澳門政府 港珠澳大橋交通資訊`
3. `saehgienh doekfag dai nyied`

**Context Size 4:**

1. `dwg aen swhyienzsoq beij gouj cib gouj nyaeq`
2. `ligmoq ndeu bi neix daj singhgiz roek codaeuz saehgienh 事件 doekfag 出生 𬻨𰅞 dai 去世 𬆗 ngoenzciet 節日 𭥓節`
3. `去世 𬆗 ngoenzciet 節日 𭥓節 1 roxnaeuz 2 nyied cieng lienhciep baihrog`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_daeramionq_gmbi`
2. `ngveu_caenggh_do`
3. `elou_cinyizhadwg`

**Context Size 2:**

1. `ngzsoux_geiz_cuz_`
2. `enh_hatitzahgingz`
3. `aenz_dengh_sawz_d`

**Context Size 3:**

1. `eng_cei._noemhyung`
2. `ngh/www.gxfs.gover`
3. `aengniengz_dawz_it`

**Context Size 4:**

1. `ngh_baenz。de_mbouj_`
2. `aen_ngawh_gvidinghc`
3. `dwg_boux_cung_hawj_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (95,273 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 | 8,300 |
| Total Tokens | 126,265 |
| Mean Frequency | 15.21 |
| Median Frequency | 3 |
| Frequency Std Dev | 76.56 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | dwg | 3,064 |
| 2 | aen | 2,774 |
| 3 | youq | 1,787 |
| 4 | gij | 1,716 |
| 5 | caeuq | 1,707 |
| 6 | de | 1,173 |
| 7 | dangj | 1,155 |
| 8 | ndeu | 1,074 |
| 9 | miz | 1,071 |
| 10 | nienz | 955 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | eb | 2 |
| 2 | domq | 2 |
| 3 | roxcaek | 2 |
| 4 | cazlix | 2 |
| 5 | yienzyaigyaj | 2 |
| 6 | ciglouz | 2 |
| 7 | gaiconh | 2 |
| 8 | siujse | 2 |
| 9 | daihdaeuz | 2 |
| 10 | ndawdeih | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0806 |
| R² (Goodness of Fit) | 0.988587 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.4% |
| Top 1,000 | 74.5% |
| Top 5,000 | 94.4% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9886 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.4% of corpus
- **Long Tail:** -1,700 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 | 0.1745 🏆 | 0.4909 | N/A | N/A |
| **mono_64d** | 64 | 0.0267 | 0.4790 | N/A | N/A |
| **mono_128d** | 128 | 0.0037 | 0.5068 | N/A | N/A |
| **aligned_32d** | 32 | 0.1745 | 0.4940 | 0.0060 | 0.0520 |
| **aligned_64d** | 64 | 0.0267 | 0.4851 | 0.0060 | 0.0760 |
| **aligned_128d** | 128 | 0.0037 | 0.4813 | 0.0080 | 0.0580 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.1745 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4895. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 0.8% 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 | **0.660** | 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` | seen, soengqfangz, seite |
| `-g` | gaemmaenh, gaenj, gisuz |
| `-c` | cawqfad, cwnggen, cingsuj |
| `-d` | duzguk, daengx, dawznduj |
| `-b` | bouxciengqfwen, bihbingz, besatzungen |
| `-da` | daengx, dawznduj, daiseiq |
| `-m` | mostly, mboengq, mittig |
| `-h` | hermann, hwng, houz |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-z` | soengqfangz, vangz, bihbingz |
| `-h` | gaemmaenh, veih, haemh |
| `-j` | gaenj, cingsuj, dawznduj |
| `-n` | hermann, seen, bouxciengqfwen |
| `-g` | hwng, öffnung, mittig |
| `-ng` | hwng, öffnung, doxceng |
| `-gh` | sihgingh, doucwngh, swhcungh |
| `-gz` | soengqfangz, vangz, bihbingz |

### 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 |
|------|----------|------------------|----------|
| `engz` | 1.59x | 48 contexts | mengz, rengz, nengz |
| `ungh` | 1.57x | 37 contexts | yungh, cungh, gungh |
| `engh` | 1.66x | 28 contexts | naengh, nyengh, yiengh |
| `oeng` | 1.53x | 37 contexts | coeng, doeng, soeng |
| `ieng` | 1.57x | 33 contexts | sieng, cieng, rieng |
| `angj` | 1.63x | 24 contexts | dangj, gangj, yangj |
| `ingz` | 1.52x | 27 contexts | lingz, cingz, hingz |
| `aeng` | 1.54x | 25 contexts | naeng, daeng, laeng |
| `angh` | 1.48x | 26 contexts | gangh, yangh, vangh |
| `ungj` | 1.68x | 15 contexts | cungj, dungj, dungjci |
| `ingh` | 1.49x | 20 contexts | cingh, lingh, dingh |
| `daen` | 1.56x | 17 contexts | daeng, ndaen, daenj |

### 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 |
|--------|--------|-----------|----------|
| `-g` | `-z` | 135 words | gisuz, gungyungz |
| `-g` | `-h` | 104 words | gaemmaenh, gveicouh |
| `-c` | `-h` | 94 words | ciemqfamh, cugciemh |
| `-c` | `-z` | 92 words | congz, cauhbaenz |
| `-d` | `-z` | 88 words | deuz, denhgoz |
| `-d` | `-h` | 87 words | doengjnyouh, diengzcah |
| `-s` | `-z` | 84 words | soengqfangz, swyenz |
| `-b` | `-z` | 81 words | bihbingz, bienliz |
| `-s` | `-h` | 81 words | saeh, sihgingh |
| `-d` | `-j` | 62 words | dawznduj, doxbeij |

### 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 |
|------|-----------------|------------|------|
| habdoengz | **`ha-b-doengz`** | 6.0 | `doengz` |
| doengzeiq | **`doengz-e-iq`** | 6.0 | `doengz` |
| kampfraumes | **`kampfraum-es`** | 4.5 | `kampfraum` |
| ausführungen | **`ausführung-en`** | 4.5 | `ausführung` |
| individuals | **`individual-s`** | 4.5 | `individual` |
| totalverluste | **`totalverlust-e`** | 4.5 | `totalverlust` |
| hergestellten | **`hergestellt-en`** | 4.5 | `hergestellt` |
| ausgerüsteten | **`ausgerüstet-en`** | 4.5 | `ausgerüstet` |
| misuhcangj | **`mi-s-uhcangj`** | 4.5 | `uhcangj` |
| cwngcigyah | **`cwngcigya-h`** | 4.5 | `cwngcigya` |
| interviews | **`interview-s`** | 4.5 | `interview` |
| eingebaute | **`eingebaut-e`** | 4.5 | `eingebaut` |
| diengingh | **`diengi-ng-h`** | 3.0 | `diengi` |
| mingzleih | **`mingzl-e-ih`** | 3.0 | `mingzl` |
| cangqmaenh | **`cangqma-en-h`** | 3.0 | `cangqma` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Zhuang 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 | **32k BPE** | Best compression (3.42x) |
| N-gram | **2-gram** | Lowest perplexity (292) |
| Markov | **Context-4** | Highest predictability (97.2%) |
| 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: 2026-01-11 05:47:48*