---
language: km
language_name: Khmer
language_family: austroasiatic_khmer
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_khmer
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 4.889
  - name: best_isotropy
    type: isotropy
    value: 0.8701
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Khmer** 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** | 3.556x | 3.54 | 0.1756% | 741,877 |
| **16k** | 4.063x | 4.05 | 0.2006% | 649,413 |
| **32k** | 4.511x | 4.49 | 0.2228% | 584,909 |
| **64k** | 4.889x 🏆 | 4.87 | 0.2415% | 539,636 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `សាវតារ ភូមិតាបឹបនេះយើងពុំបានជ្រាបច្បាស់ទេ ។ តែយើងបានដឹងថាក្នុងភូមិនេះមានទួលកប់ខ្...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁សាវ តារ ▁ភូមិ ត ាប ឹប នេះ យើង ពុំ បាន ... (+24 more)` | 34 |
| 16k | `▁សាវ តារ ▁ភូមិ តាប ឹប នេះ យើង ពុំ បាន ជ្រាប ... (+21 more)` | 31 |
| 32k | `▁សាវ តារ ▁ភូមិ តាប ឹប នេះ យើង ពុំបាន ជ្រាប ច្បាស់ ... (+17 more)` | 27 |
| 64k | `▁សាវតារ ▁ភូមិ តាប ឹប នេះយើង ពុំបាន ជ្រាប ច្បាស់ទេ ▁។ ▁តែ ... (+13 more)` | 23 |

**Sample 2:** `៖ ឃុំស៊ុង ឃុំមានជ័យ ឃុំសំឡូត ឃុំកំពង់ល្ពៅ ឃុំអូរសំរិល ឃុំតាតោក ឃុំតាសាញ សូមមើលផង...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁៖ ▁ឃុំ ស៊ ុង ▁ឃុំ មានជ័យ ▁ឃុំ សំ ឡ ូត ... (+18 more)` | 28 |
| 16k | `▁៖ ▁ឃុំ ស៊ ុង ▁ឃុំមានជ័យ ▁ឃុំ សំឡូត ▁ឃុំកំពង់ ល ្ពៅ ... (+13 more)` | 23 |
| 32k | `▁៖ ▁ឃុំ ស៊ុង ▁ឃុំមានជ័យ ▁ឃុំ សំឡូត ▁ឃុំកំពង់ ល្ពៅ ▁ឃុំអូរ សំរ ... (+10 more)` | 20 |
| 64k | `▁៖ ▁ឃុំ ស៊ុង ▁ឃុំមានជ័យ ▁ឃុំ សំឡូត ▁ឃុំកំពង់ល្ពៅ ▁ឃុំអូរ សំរិល ▁ឃុំ ... (+7 more)` | 17 |

**Sample 3:** `ម៉ៃឃើលអាចសំដៅលើ៖ ម៉ៃឃើល ហ្វារ៉ាដេយ ម៉ៃឃើល ចាកសាន់ ម៉ៃឃើល វីកឃឺវី`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ម៉ ៃ ឃ ើល អាច សំដៅលើ ៖ ▁ម៉ ៃ ឃ ... (+22 more)` | 32 |
| 16k | `▁ម៉ៃឃើល អាច សំដៅលើ៖ ▁ម៉ៃឃើល ▁ហ ្វារ ៉ា ដ េយ ▁ម៉ៃឃើល ... (+8 more)` | 18 |
| 32k | `▁ម៉ៃឃើល អាចសំដៅលើ៖ ▁ម៉ៃឃើល ▁ហ្វារ ៉ា ដេយ ▁ម៉ៃឃើល ▁ចាក សាន់ ▁ម៉ៃឃើល ... (+4 more)` | 14 |
| 64k | `▁ម៉ៃឃើល អាចសំដៅលើ៖ ▁ម៉ៃឃើល ▁ហ្វារ៉ាដេយ ▁ម៉ៃឃើល ▁ចាក សាន់ ▁ម៉ៃឃើល ▁វីក ឃឺ ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 64k achieves 4.889x compression
- **Lowest UNK Rate:** 8k with 0.1756% 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 | 29,102 | 14.83 | 72,055 | 8.9% | 24.7% |
| **2-gram** | Subword | 5,212 🏆 | 12.35 | 88,256 | 22.4% | 57.4% |
| **3-gram** | Word | 53,084 | 15.70 | 103,452 | 6.4% | 17.4% |
| **3-gram** | Subword | 51,695 | 15.66 | 499,965 | 8.2% | 24.3% |
| **4-gram** | Word | 118,314 | 16.85 | 213,260 | 4.3% | 12.7% |
| **4-gram** | Subword | 260,843 | 17.99 | 1,609,249 | 4.4% | 12.4% |
| **5-gram** | Word | 100,822 | 16.62 | 180,877 | 4.2% | 13.0% |
| **5-gram** | Subword | 609,986 | 19.22 | 2,327,771 | 3.0% | 8.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `example example` | 21,905 |
| 2 | `of the` | 4,908 |
| 3 | `ត្រូវ បាន` | 3,687 |
| 4 | `នៅ ក្នុង` | 3,249 |
| 5 | `ព្រះ អង្គ` | 2,574 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `example example example` | 10,790 |
| 2 | `villageភូមិ villageភូមិ villageភូមិ` | 1,612 |
| 3 | `ត្រូវ បាន គេ` | 1,169 |
| 4 | `៤៩៣ ប្រ ក` | 995 |
| 5 | `សាសនា ព្រះពុទ្ធសាសនា វត្ត` | 640 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `example example example example` | 1,615 |
| 2 | `villageភូមិ villageភូមិ villageភូមិ villageភូមិ` | 1,380 |
| 3 | `អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា វត្ត` | 558 |
| 4 | `បឋមសិក្សា អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា` | 536 |
| 5 | `អប់រំ បឋមសិក្សា អនុវិទ្យាល័យ សាសនា` | 535 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ` | 1,151 |
| 2 | `អប់រំ បឋមសិក្សា អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា` | 535 |
| 3 | `បឋមសិក្សា អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា វត្ត` | 528 |
| 4 | `e លិច w ត្បូង s` | 455 |
| 5 | `n កើត e លិច w` | 454 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `។ _` | 199,513 |
| 2 | `បា ន` | 145,143 |
| 3 | `ង _` | 128,650 |
| 4 | `កា រ` | 123,593 |
| 5 | `e _` | 121,925 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ និ ង` | 83,168 |
| 2 | `_ ។ _` | 67,258 |
| 3 | `រ ប ស់` | 64,716 |
| 4 | `_ ដែ ល` | 42,564 |
| 5 | `_ t h` | 39,828 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `m p l e` | 34,032 |
| 2 | `p l e _` | 33,694 |
| 3 | `_ e x a` | 33,362 |
| 4 | `a m p l` | 33,310 |
| 5 | `e x a m` | 33,310 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ e x a m` | 33,301 |
| 2 | `a m p l e` | 33,292 |
| 3 | `e x a m p` | 33,273 |
| 4 | `x a m p l` | 33,273 |
| 5 | `m p l e _` | 33,105 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 5,212
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~8% 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 | 0.2782 | 1.213 | 2.41 | 859,644 | 72.2% |
| **1** | Subword | 1.0301 | 2.042 | 17.81 | 14,759 | 0.0% |
| **2** | Word | 0.1500 | 1.110 | 1.34 | 2,064,587 | 85.0% |
| **2** | Subword | 0.6645 | 1.585 | 5.47 | 262,778 | 33.5% |
| **3** | Word | 0.0584 | 1.041 | 1.09 | 2,764,478 | 94.2% |
| **3** | Subword | 0.4625 | 1.378 | 2.82 | 1,436,052 | 53.8% |
| **4** | Word | 0.0205 🏆 | 1.014 | 1.03 | 3,007,497 | 98.0% |
| **4** | Subword | 0.3127 | 1.242 | 1.86 | 4,049,871 | 68.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `និង ឡាវ ព្រះឧបជ្ឈាហ៍ ទេពវង្ស សម្តេច ព្រះអភិសិរីសុគន្ធាមហាសង្ឃរាជាធិបតី សម្តេចព្រះមហាសង្ឃរាជ បួរ គ្រី...`
2. `example example example example ៧ លោកស្រី គាត់ បាន សម្រាប់ និកាយ ហ្សេន តានត្រិក និងដែនដីបរិសុទ្ធ ដែន...`
3. `the united states union premier league cup នេះក៏ជាការប្រកួតផ្លូវការណ៍ក្រោមការគ្រប់គ្រងរបស់ cambodian...`

**Context Size 2:**

1. `example example example ៣ example example ២៧ example example ១១ example example ៧ example example ex...`
2. `of the mahayana idea that such an attack scenario dynamically shall make use of both the dmt`
3. `ត្រូវ បាន អភិវឌ្ឍន សម្រាប់ kde 3 បាន ការ តែង តាំង ជា អភិបាល នៃ តំបន់អុីវាណូ ហ្វ្រែនគីវស៍ ក្នុង នាម`

**Context Size 3:**

1. `example example example ៤១ example example example ៦ example example example ១២ example example exam...`
2. `villageភូមិ villageភូមិ villageភូមិ villageភូមិ village ព្រំប្រទល់នៃ ទិសខាងកើត e ខាងត្បូង s ខាងលិច w...`
3. `ត្រូវ បាន គេ ធ្វើ តេស្ដ នៅ ក្នុង ថ្នាក់ b និង c គឺជារង្វាស់នៃជ្រុងនៃ ត្រីកោណ ដែលមាន ក្រលាផ្ទៃ f និង ...`

**Context Size 4:**

1. `example example example example ៣ ស្រី ៨ example example example ៣៣ example example example ៩ exampl...`
2. `villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ villageភូមិ village ព្រំប្រទ...`
3. `អនុវិទ្យាល័យ សាសនា ព្រះពុទ្ធសាសនា វត្ត ផ្សារ រមណីដ្ឋាន ឯកសារពិគ្រោះ គណកម្មការជាតិរៀបចំការបោះឆ្នោត ខេ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_plovon_(ហៅថានេះ​សេចក្តី`
2. `​ច្បាប់​ជាជន៍ជា​គួរលាវបាទទួ`
3. `ង​ថា_មាគរ_ck_និងសែន​`

**Context Size 2:**

1. `។_rel.2_សង្ខិត្តំ។]_(_s`
2. `បាន​លទ្ធផលស្គាល់ច្បាស់លាស់_។_ស`
3. `ង_ត្រឡប់​យកមន្រ្តីខុទ្ទកាល័យ_និ`

**Context Size 3:**

1. `_និង_កម្រិត។_ផ្លូវថូម៉ាស"_(r`
2. `_។_នាម៉ឺន​ពិធី​មាំ​ថែមទៀតផង`
3. `របស់វីតាមីន_atter_leve`

**Context Size 4:**

1. `mple_៥០_និងប្រទេសអូស្រ្ដាលី_កេន`
2. `ple_example_example`
3. `_example_example_ex`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (4,049,871 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 | 168,571 |
| Total Tokens | 2,917,143 |
| Mean Frequency | 17.31 |
| Median Frequency | 3 |
| Frequency Std Dev | 265.83 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | និង | 40,023 |
| 2 | example | 33,205 |
| 3 | the | 28,680 |
| 4 | ជា | 28,379 |
| 5 | បាន | 26,100 |
| 6 | មាន | 21,881 |
| 7 | of | 20,677 |
| 8 | ដែល | 18,961 |
| 9 | នៅ | 18,044 |
| 10 | ក្នុង | 16,838 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | កេលីម៉ាន់តាន់ | 2 |
| 2 | สทิงพระ | 2 |
| 3 | ទេសបាលតំបន់ | 2 |
| 4 | វត្តច័ន្ទ | 2 |
| 5 | និងការអភិវឌ្ឍខ្លួនឯង | 2 |
| 6 | milliontimes | 2 |
| 7 | អក្សរចិនបុរាណ | 2 |
| 8 | នៅលើផ្ទៃខាងក្រោយងងឹត | 2 |
| 9 | វគ្គជម្រុះជុំទី៣ | 2 |
| 10 | wagnalls | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0175 |
| R² (Goodness of Fit) | 0.996035 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 27.0% |
| Top 1,000 | 51.0% |
| Top 5,000 | 68.7% |
| Top 10,000 | 75.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9960 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 27.0% of corpus
- **Long Tail:** 158,571 words needed for remaining 24.4% 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 | 0.8684 | 0.3333 | N/A | N/A |
| **mono_64d** | 64 | 0.8701 🏆 | 0.2501 | N/A | N/A |
| **mono_128d** | 128 | 0.7385 | 0.2098 | N/A | N/A |
| **aligned_32d** | 32 | 0.8684 | 0.3316 | 0.0940 | 0.3400 |
| **aligned_64d** | 64 | 0.8701 | 0.2521 | 0.1220 | 0.4760 |
| **aligned_128d** | 128 | 0.7385 | 0.2166 | 0.2480 | 0.6260 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.8701 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2656. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 24.8% 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 | **0.614** | 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 |
|--------|----------|
| `-ស` | សឧត្តរំ, ស្វាហ៊ីលី, សម្បកក្រៅរុំ |
| `-ប` | បានដល់ការទាយគតិរបស់ព្រះសិទ្ធត្ថរាជកុមារ, បឋមជ្ឈានតោ, ប្រាសាទបាក់បែកនៅខាងក្រោយនៃវត្តស្រីមឿងនៅវាំងចន្ទន៍ភាគកណ្ដាល |
| `-ក` | ក្រាំងចិន, ក្រមាខ្មែរ, ក្នុងកាលខាងក្រោយ |
| `-អ` | អង្គុយក្នុងទីសមគួរហើយ, អេអូនីសេ, អូរាំងអាស្លី |
| `-ន` | និងបន្លែ, នៃម៉ាស់សរុបនៃប្រព័ន្ធព្រះអាទិត្យ, និងបរិវារមួយក្រុមបានភៀសទៅជ្រកកោនក្នុងប្រទេសសៀមជាមួយព្រះ |
| `-ម` | មានប្រាសាទ, ម្យ៉ាងទៀតសោត, មានឱកាស |
| `-s` | supra, sharia, signals |
| `-រ` | រមែងសញ្ជប់សញ្ជឹង, រណ្តៅតូច, របស់ព្រះពុទ្ធមួយភាគដែរ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ង` | រមែងសញ្ជប់សញ្ជឹង, ត្បូងពណ៌បៃតង, ដើម្បីនឹង |
| `-យ` | អង្គុយក្នុងទីសមគួរហើយ, ធ្វើឱ្យជាស្ថានទីរីករាយ, គ្មានមន្ទីរពេទ្យ |
| `-ន` | ក្រាំងចិន, យោន, គឺមិនមាន |
| `-រ` | បានដល់ការទាយគតិរបស់ព្រះសិទ្ធត្ថរាជកុមារ, ក្រមាខ្មែរ, របស់ព្រះពុទ្ធមួយភាគដែរ |
| `-ត` | គឺមិនមាននិមិត្ត, ម្យ៉ាងទៀតសោត, និងរារាំងការពង្រីកខ្លួនរបស់ចិនបន្តទៅទៀត |
| `-ក` | នៃតំបន់ប្រាសាទសំបូរព្រៃគុក, ក្នុងសំដីរបស់អ្នក, និងចក |
| `-ម` | ទៅកាន់មនុស្សទាំងអស់ក្នុងសង្គម, ដូចជាកោះត្រល់ជាដើម, ទឹកនោមផ្អែម |
| `-s` | nicolas, thoughts, characters |

### 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 |
|------|----------|------------------|----------|
| `ight` | 2.39x | 50 contexts | fight, night, sight |
| `tion` | 2.28x | 46 contexts | option, nation, lotion |
| `ment` | 2.30x | 39 contexts | cement, moment, mental |
| `atio` | 2.39x | 33 contexts | ratio, nation, horatio |
| `nter` | 2.15x | 37 contexts | enter, inter, winter |
| `inte` | 2.29x | 29 contexts | intel, inter, winter |
| `stor` | 2.31x | 27 contexts | story, jstor, storm |
| `ctio` | 2.40x | 23 contexts | action, section, actions |
| `illa` | 2.19x | 27 contexts | illam, villa, silla |
| `ubli` | 2.35x | 19 contexts | dublin, public, publié |
| `pres` | 2.24x | 22 contexts | press, ypres, presse |
| `iver` | 2.18x | 22 contexts | liver, river, waiver |

### 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 |
|--------|--------|-----------|----------|
| `-ប` | `-ន` | 50 words | បណ្តាញសាកលវិទ្យាល័យអាស៊ាន, បង្ហាញខ្លួន |
| `-ក` | `-ង` | 49 words | ការប្រើដំណរក្នុង, ក្រាំងខ្លុង |
| `-ប` | `-យ` | 46 words | បានត្រាស់សេចក្តីនេះរួចហើយ, បន្សាយ |
| `-ន` | `-យ` | 44 words | និងសម្តែងដោយ, និងបានយសសក្ដិគ្រប់សព្វណាស់ទៅហើយ |
| `-ក` | `-យ` | 40 words | កម្លាំងថយ, ក៏ពោលពាក្យ |
| `-ក` | `-ន` | 39 words | កៈទឿន, ការឈ្លានពានរបស់ជប៉ុន |
| `-ន` | `-ង` | 38 words | និងចៅប្រមាញ់វិងស៊ុង, និងនៅសងខាង |
| `-ន` | `-រ` | 37 words | និងវិចិត្រសិល្បៈខេត្តព្រះវិហារ, នាយសមុទ្រ |
| `-ស` | `-ន` | 36 words | សីលជាស្ពាន, សារពត័មាន |
| `-ស` | `-រ` | 35 words | សុពាហុត្ថេរ, សភិយត្ថេរ |

### 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 |
|------|-----------------|------------|------|
| abdagases | **`abdaga-s-es`** | 7.5 | `s` |
| នៅពីក្រោយខ្នង | **`នៅពីក្រោយខ្-ន-ង`** | 7.5 | `ន` |
| tlaxcaltecas | **`tlaxcalteca-s`** | 4.5 | `tlaxcalteca` |
| instrumental | **`instrument-al`** | 4.5 | `instrument` |
| អន្តរជាតិ | **`អ-ន-្តរជាតិ`** | 4.5 | `្តរជាតិ` |
| អបដិក្កូលេ | **`អ-បដិក្កូលេ`** | 4.5 | `បដិក្កូលេ` |
| scholarships | **`scholarship-s`** | 4.5 | `scholarship` |
| ស្រមោចហែរ | **`ស្រមោចហែ-រ`** | 4.5 | `ស្រមោចហែ` |
| replacements | **`replacement-s`** | 4.5 | `replacement` |
| ពួកសត្វតែងមាន | **`ព-ួកសត្វតែងមា-ន`** | 3.0 | `ួកសត្វតែងមា` |
| grancrest | **`grancr-es-t`** | 3.0 | `grancr` |
| ប្រទាញសងខាង | **`ប្រទាញសងខា-ង`** | 1.5 | `ប្រទាញសងខា` |
| ក្នុងថ្ងៃនេះបាន | **`ក្នុងថ្ងៃនេះបា-ន`** | 1.5 | `ក្នុងថ្ងៃនេះបា` |
| vidyādhara | **`vidyādhar-a`** | 1.5 | `vidyādhar` |
| ក្រុមហាម៉ាស់ | **`ក-្រុមហាម៉ាស់`** | 1.5 | `្រុមហាម៉ាស់` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Khmer 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 (4.89x) |
| N-gram | **2-gram** | Lowest perplexity (5,212) |
| Markov | **Context-4** | Highest predictability (98.0%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-10 08:23:26*