---
language: vi
language_name: Vietnamese
language_family: austroasiatic_vietic
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-austroasiatic_vietic
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: 3.900
  - name: best_isotropy
    type: isotropy
    value: 0.8322
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-18
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Vietnamese** 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** | 3.647x | 3.65 | 0.1376% | 4,322,437 |
| **16k** | 3.775x | 3.77 | 0.1424% | 4,176,769 |
| **32k** | 3.851x | 3.85 | 0.1453% | 4,093,428 |
| **64k** | 3.900x 🏆 | 3.90 | 0.1471% | 4,042,743 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Siphona scutellata là một loài ruồi trong họ Tachinidae. Chú thích Liên kết ngoà...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁si ph ona ▁sc ut ell ata ▁là ▁một ▁loài ... (+12 more)` | 22 |
| 16k | `▁si ph ona ▁scut ellata ▁là ▁một ▁loài ▁ruồi ▁trong ... (+9 more)` | 19 |
| 32k | `▁si ph ona ▁scut ellata ▁là ▁một ▁loài ▁ruồi ▁trong ... (+9 more)` | 19 |
| 64k | `▁siph ona ▁scutellata ▁là ▁một ▁loài ▁ruồi ▁trong ▁họ ▁tach ... (+7 more)` | 17 |

**Sample 2:** `Kocaali là một xã thuộc huyện Ergani, tỉnh Diyarbakır, Thổ Nhĩ Kỳ. Dân số thời đ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁k oc a ali ▁là ▁một ▁xã ▁thuộc ▁huyện ▁er ... (+31 more)` | 41 |
| 16k | `▁k oca ali ▁là ▁một ▁xã ▁thuộc ▁huyện ▁er g ... (+29 more)` | 39 |
| 32k | `▁k oca ali ▁là ▁một ▁xã ▁thuộc ▁huyện ▁er g ... (+28 more)` | 38 |
| 64k | `▁k oca ali ▁là ▁một ▁xã ▁thuộc ▁huyện ▁erg ani ... (+24 more)` | 34 |

**Sample 3:** `Glipidiomorpha riesei là một loài bọ cánh cứng trong họ Mordellidae. Loài này đư...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gl ip idi omorpha ▁r ies ei ▁là ▁một ▁loài ... (+24 more)` | 34 |
| 16k | `▁gl ip idi omorpha ▁r ies ei ▁là ▁một ▁loài ... (+24 more)` | 34 |
| 32k | `▁gl ip idi omorpha ▁ries ei ▁là ▁một ▁loài ▁bọ ... (+21 more)` | 31 |
| 64k | `▁gl ip idi omorpha ▁riesei ▁là ▁một ▁loài ▁bọ ▁cánh ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 64k achieves 3.900x compression
- **Lowest UNK Rate:** 8k with 0.1376% 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 | 106,320 | 16.70 | 2,695,824 | 10.1% | 25.1% |
| **2-gram** | Subword | 409 🏆 | 8.67 | 93,876 | 59.2% | 96.0% |
| **3-gram** | Word | 890,077 | 19.76 | 9,913,320 | 6.8% | 13.5% |
| **3-gram** | Subword | 2,984 | 11.54 | 411,919 | 25.5% | 66.3% |
| **4-gram** | Word | 2,796,979 | 21.42 | 22,248,727 | 6.3% | 11.5% |
| **4-gram** | Subword | 16,513 | 14.01 | 1,959,172 | 13.3% | 41.5% |
| **5-gram** | Word | 2,571,700 | 21.29 | 19,242,355 | 7.4% | 13.5% |
| **5-gram** | Subword | 69,615 | 16.09 | 6,377,982 | 8.7% | 27.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `là một` | 1,495,225 |
| 2 | `chú thích` | 852,707 |
| 3 | `tham khảo` | 804,096 |
| 4 | `một loài` | 728,551 |
| 5 | `trong họ` | 711,111 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `là một loài` | 722,924 |
| 2 | `liên kết ngoài` | 620,713 |
| 3 | `loài này được` | 453,066 |
| 4 | `chú thích liên` | 440,159 |
| 5 | `thích liên kết` | 440,150 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `chú thích liên kết` | 440,133 |
| 2 | `thích liên kết ngoài` | 439,810 |
| 3 | `được mô tả năm` | 384,043 |
| 4 | `chú thích tham khảo` | 365,017 |
| 5 | `vật được mô tả` | 363,438 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `chú thích liên kết ngoài` | 439,801 |
| 2 | `vật được mô tả năm` | 363,377 |
| 3 | `tả khoa học đầu tiên` | 335,608 |
| 4 | `khoa học đầu tiên năm` | 309,398 |
| 5 | `đầu tiên năm chú thích` | 263,309 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t` | 44,618,705 |
| 2 | `n g` | 36,466,380 |
| 3 | `_ c` | 30,008,094 |
| 4 | `n _` | 29,116,380 |
| 5 | `g _` | 27,402,011 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g _` | 27,209,259 |
| 2 | `_ t h` | 17,092,068 |
| 3 | `_ t r` | 10,431,331 |
| 4 | `_ c h` | 9,946,202 |
| 5 | `n h _` | 9,905,520 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g _ t` | 4,408,233 |
| 2 | `_ v à _` | 3,874,748 |
| 3 | `_ l à _` | 3,858,257 |
| 4 | `c ủ a _` | 3,768,746 |
| 5 | `_ c ủ a` | 3,768,226 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c ủ a _` | 3,765,562 |
| 2 | `_ đ ư ợ c` | 3,314,830 |
| 3 | `đ ư ợ c _` | 3,299,257 |
| 4 | `_ m ộ t _` | 3,246,287 |
| 5 | `_ n ă m _` | 3,101,391 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 409
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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 | 0.7563 | 1.689 | 9.23 | 2,640,968 | 24.4% |
| **1** | Subword | 1.2157 | 2.323 | 15.79 | 34,963 | 0.0% |
| **2** | Word | 0.4386 | 1.355 | 3.10 | 24,350,395 | 56.1% |
| **2** | Subword | 0.5203 | 1.434 | 3.02 | 551,811 | 48.0% |
| **3** | Word | 0.2736 | 1.209 | 1.81 | 75,436,653 | 72.6% |
| **3** | Subword | 0.4089 | 1.328 | 2.69 | 1,667,382 | 59.1% |
| **4** | Word | 0.1518 🏆 | 1.111 | 1.33 | 136,713,102 | 84.8% |
| **4** | Subword | 0.4863 | 1.401 | 2.89 | 4,478,768 | 51.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `là tổng thống như đường sắt bắc iwate grulla morioka thống shad striper rượt đuổi theo`
2. `và lavrov đã đi hết các xơ cứng trong hiệp hòa thảo loài khác biệt hiệu`
3. `của mình mang tên đàn đạo đền một mạng nicaragua 3 năm vật hoang mạc thiên`

**Context Size 2:**

1. `là một loài hymenoptera trong họ noctuidae chú thích tham khảo bay kazakhstan không tìm thấy tại`
2. `chú thích liên kết ngoài vật được mô tả năm vật bolivia vật brasil vật colombia vật`
3. `một loài bướm đêm trong họ cửu lý hương loài boswellia trong tôn giáo nào giáo dục`

**Context Size 3:**

1. `là một loài bọ cánh cứng trong họ melandryidae loài này được werderm mô tả khoa học năm`
2. `liên kết ngoài c vật được mô tả năm es hemianemia eximia`
3. `loài này được baker labat schatz mô tả khoa học đầu tiên năm chú thích tham khảo vật`

**Context Size 4:**

1. `chú thích liên kết ngoài vật được mô tả năm vật đặc hữu đài loan đài loan thuộc nhật`
2. `vật được mô tả năm vật đặc hữu trung quốc kim lũ mai tai hùm đơn loài vật được`
3. `khoa học đầu tiên năm chú thích liên kết ngoài vật được mô tả năm đêm indonesia đêm philippines`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_lef_19_kỳ.wanhe`
2. `n_terìng_đã_phủ_`
3. `h_"_ayroarọcá_m_`

**Context Size 2:**

1. `_thuệsố_đã_vấn_vù`
2. `ng_thuộc_nhịu_đầu`
3. `_của_nh_sác_prit_`

**Context Size 3:**

1. `ng_đã_bị_bệnh_lại_`
2. `_thắng_của_hampus_`
3. `_trang_3_joon,_nhữ`

**Context Size 4:**

1. `ng_tăng_ánh_quyết_c`
2. `_và_những_có_một_cầ`
3. `_là_volume_shop,_tâ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 84.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (4,478,768 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 | 1,088,012 |
| Total Tokens | 275,589,508 |
| Mean Frequency | 253.30 |
| Median Frequency | 4 |
| Frequency Std Dev | 12931.56 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | là | 3,896,221 |
| 2 | và | 3,888,002 |
| 3 | của | 3,770,649 |
| 4 | năm | 3,541,374 |
| 5 | được | 3,324,385 |
| 6 | một | 3,283,880 |
| 7 | trong | 2,847,858 |
| 8 | có | 2,266,526 |
| 9 | các | 2,260,160 |
| 10 | người | 1,505,528 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | bíchhạnh | 2 |
| 2 | dâuliên | 2 |
| 3 | lụanguyễn | 2 |
| 4 | zeltiq | 2 |
| 5 | côtobin | 2 |
| 6 | novitskiy | 2 |
| 7 | tarelkin | 2 |
| 8 | 齋堂 | 2 |
| 9 | zhāitáng | 2 |
| 10 | chatral | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.5197 |
| R² (Goodness of Fit) | 0.977671 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 35.9% |
| Top 1,000 | 79.0% |
| Top 5,000 | 91.3% |
| Top 10,000 | 93.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9777 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 35.9% of corpus
- **Long Tail:** 1,078,012 words needed for remaining 6.4% 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 | 0.8322 | 0.4208 | N/A | N/A |
| **mono_64d** | 64 | 0.8116 | 0.3302 | N/A | N/A |
| **mono_128d** | 128 | 0.7892 | 0.2753 | N/A | N/A |
| **aligned_32d** | 32 | 0.8322 🏆 | 0.4041 | 0.4880 | 0.8640 |
| **aligned_64d** | 64 | 0.8116 | 0.3384 | 0.7280 | 0.9680 |
| **aligned_128d** | 128 | 0.7892 | 0.2727 | 0.8360 | 0.9820 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8322 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3403. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 83.6% 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 | **-0.502** | 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` | sinothomisus, sportowe, sprogøe |
| `-t` | thổvàng, trilion, tháitô |
| `-a` | amorín, aerolindigia, awardchoice |
| `-m` | minhphạm, mớimtvca, mutungi |
| `-c` | coccomelia, clacton, clatratum |
| `-b` | batmagnai, bejt, balep |
| `-k` | karepura, kỳtriệu, kronthaler |
| `-ma` | marovt, mayran, marghanna |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | sinothomisus, orestes, trochanteralis |
| `-a` | coccomelia, karepura, nuichua |
| `-e` | pilosellae, orée, sportowe |
| `-n` | oreodendron, gaggabutan, clacton |
| `-is` | trochanteralis, neoconis, mononalis |
| `-i` | batmagnai, weinmanntái, eesi |
| `-us` | sinothomisus, brimidius, eudelus |
| `-es` | orestes, pseudaspilates, wingates |

### 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 |
|------|----------|------------------|----------|
| `atio` | 2.64x | 168 contexts | tatio, natio, fatio |
| `opte` | 2.62x | 135 contexts | opted, opter, copte |
| `nter` | 2.01x | 355 contexts | enter, inter, unter |
| `trưở` | 2.86x | 60 contexts | trưởn, trưởnɡ, trưởng |
| `tướn` | 2.93x | 45 contexts | tướng, tướngm, 4tướng |
| `pter` | 2.21x | 106 contexts | ptero, opter, apter |
| `ceae` | 3.35x | 20 contexts | aceae, ficeae, biceae |
| `rưởn` | 2.86x | 32 contexts | trưởn, rưởng, trưởnɡ |
| `huyệ` | 1.59x | 353 contexts | huyệt, huyện, chuyệ |
| `nhiề` | 2.15x | 75 contexts | nhiền, nhiềy, nhiềm |
| `uyễn` | 2.16x | 59 contexts | quyễn, duyễn, nuyễn |
| `huyể` | 2.06x | 28 contexts | chuyể, huyển, thuyểt |

### 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` | `-a` | 126 words | pnmburucuya, praeangulata |
| `-p` | `-s` | 122 words | pedicellatus, polyotis |
| `-c` | `-s` | 116 words | cicindeloides, constrictiflorus |
| `-s` | `-a` | 108 words | sungka, serbica |
| `-c` | `-a` | 103 words | chensa, conardia |
| `-s` | `-s` | 103 words | sacodes, sulamitis |
| `-a` | `-s` | 99 words | ardys, airplanes |
| `-a` | `-a` | 90 words | akassa, attenuatella |
| `-m` | `-s` | 86 words | matles, moyennes |
| `-m` | `-a` | 78 words | meryta, mātaatua |

### 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 |
|------|-----------------|------------|------|
| tolarucan | **`tolaruc-a-n`** | 7.5 | `a` |
| kazusensis | **`kazusen-s-is`** | 7.5 | `s` |
| jāgarābhivamsa | **`jāgarābhivam-s-a`** | 7.5 | `s` |
| alagappapuram | **`alagappapur-a-m`** | 7.5 | `a` |
| krickenbach | **`krickenb-a-ch`** | 7.5 | `a` |
| speculaas | **`specu-la-as`** | 7.5 | `la` |
| namsskogan | **`namsskog-a-n`** | 7.5 | `a` |
| mündersbach | **`mündersb-a-ch`** | 7.5 | `a` |
| quadrisetosus | **`quadriseto-s-us`** | 7.5 | `s` |
| thắngshonan | **`thắngshon-a-n`** | 7.5 | `a` |
| atrivenata | **`atrive-na-ta`** | 7.5 | `na` |
| hochiensis | **`hochien-s-is`** | 7.5 | `s` |
| outermost | **`outermo-s-t`** | 7.5 | `s` |
| xuechengensis | **`xuechengen-s-is`** | 7.5 | `s` |
| mesypochrysa | **`mesypochry-s-a`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Vietnamese 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 | **64k BPE** | Best compression (3.90x) |
| N-gram | **2-gram** | Lowest perplexity (409) |
| Markov | **Context-4** | Highest predictability (84.8%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-18 17:40:28*