---
language: ms
language_name: Malay
language_family: austronesian_malay
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-austronesian_malay
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: 5.467
  - name: best_isotropy
    type: isotropy
    value: 0.7590
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Malay** 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** | 4.396x | 4.40 | 0.0792% | 1,649,775 |
| **16k** | 4.887x | 4.89 | 0.0880% | 1,484,029 |
| **32k** | 5.238x | 5.24 | 0.0943% | 1,384,577 |
| **64k** | 5.467x 🏆 | 5.47 | 0.0985% | 1,326,382 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Patavan merupakan sebuah kawasan yang terletak di Iran. Rujukan di Kaunti Sowme'...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁p ata van ▁merupakan ▁sebuah ▁kawasan ▁yang ▁terletak ▁di ▁iran ... (+10 more)` | 20 |
| 16k | `▁p ata van ▁merupakan ▁sebuah ▁kawasan ▁yang ▁terletak ▁di ▁iran ... (+9 more)` | 19 |
| 32k | `▁p ata van ▁merupakan ▁sebuah ▁kawasan ▁yang ▁terletak ▁di ▁iran ... (+8 more)` | 18 |
| 64k | `▁pata van ▁merupakan ▁sebuah ▁kawasan ▁yang ▁terletak ▁di ▁iran . ... (+7 more)` | 17 |

**Sample 2:** `Elikesik, Alanya merupakan sebuah kawasan yang terletak di Turki. Lihat juga Dae...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁e lik es ik , ▁al anya ▁merupakan ▁sebuah ▁kawasan ... (+13 more)` | 23 |
| 16k | `▁e lik es ik , ▁al anya ▁merupakan ▁sebuah ▁kawasan ... (+13 more)` | 23 |
| 32k | `▁e lik esik , ▁al anya ▁merupakan ▁sebuah ▁kawasan ▁yang ... (+12 more)` | 22 |
| 64k | `▁e lik esik , ▁alanya ▁merupakan ▁sebuah ▁kawasan ▁yang ▁terletak ... (+11 more)` | 21 |

**Sample 3:** `Mélagues ialah komun di jabatan di Aveyron selatan Perancis. Lihat juga Komun di...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁m é lagu es ▁ialah ▁komun ▁di ▁jabatan ▁di ▁av ... (+17 more)` | 27 |
| 16k | `▁mé lagu es ▁ialah ▁komun ▁di ▁jabatan ▁di ▁aveyron ▁selatan ... (+11 more)` | 21 |
| 32k | `▁mé lagu es ▁ialah ▁komun ▁di ▁jabatan ▁di ▁aveyron ▁selatan ... (+11 more)` | 21 |
| 64k | `▁mé lagu es ▁ialah ▁komun ▁di ▁jabatan ▁di ▁aveyron ▁selatan ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 5.467x compression
- **Lowest UNK Rate:** 8k with 0.0792% 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 | 154,800 | 17.24 | 1,398,741 | 9.5% | 21.6% |
| **2-gram** | Subword | 230 🏆 | 7.85 | 34,956 | 72.4% | 99.3% |
| **3-gram** | Word | 325,387 | 18.31 | 2,569,328 | 10.9% | 21.5% |
| **3-gram** | Subword | 1,970 | 10.94 | 177,272 | 30.0% | 74.6% |
| **4-gram** | Word | 377,074 | 18.52 | 3,858,678 | 13.0% | 24.9% |
| **4-gram** | Subword | 11,507 | 13.49 | 899,517 | 15.2% | 43.5% |
| **5-gram** | Word | 161,998 | 17.31 | 2,522,183 | 16.9% | 31.6% |
| **5-gram** | Subword | 45,772 | 15.48 | 2,934,104 | 9.2% | 28.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pada tahun` | 182,854 |
| 2 | `merupakan sebuah` | 180,992 |
| 3 | `terletak di` | 177,681 |
| 4 | `yang terletak` | 164,205 |
| 5 | `pautan luar` | 142,071 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `yang terletak di` | 145,449 |
| 2 | `rujukan pautan luar` | 85,486 |
| 3 | `komun di jabatan` | 62,009 |
| 4 | `ini juga merupakan` | 48,368 |
| 5 | `merupakan sebuah kawasan` | 47,805 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kayu yang telah ditebang` | 47,171 |
| 2 | `pada batang kayu hidup` | 47,170 |
| 3 | `kayu dan dapat menyebabkan` | 47,170 |
| 4 | `hidup atau kayu yang` | 47,158 |
| 5 | `atau kayu yang telah` | 47,158 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pada batang kayu hidup atau` | 47,158 |
| 2 | `kayu hidup atau kayu yang` | 47,158 |
| 3 | `hidup atau kayu yang telah` | 47,158 |
| 4 | `atau kayu yang telah ditebang` | 47,158 |
| 5 | `batang kayu hidup atau kayu` | 47,158 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n` | 20,347,605 |
| 2 | `n _` | 12,967,523 |
| 3 | `a _` | 9,650,615 |
| 4 | `n g` | 8,591,886 |
| 5 | `e r` | 8,563,362 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n _` | 10,591,409 |
| 2 | `a n g` | 4,452,343 |
| 3 | `n g _` | 3,798,949 |
| 4 | `_ m e` | 3,721,748 |
| 5 | `_ d a` | 3,505,831 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k a n _` | 2,911,587 |
| 2 | `a n g _` | 2,824,382 |
| 3 | `_ m e n` | 1,732,841 |
| 4 | `d a n _` | 1,723,759 |
| 5 | `_ d a n` | 1,689,159 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a n _` | 1,659,387 |
| 2 | `y a n g _` | 1,558,610 |
| 3 | `_ y a n g` | 1,536,001 |
| 4 | `p a d a _` | 1,174,037 |
| 5 | `n g a n _` | 1,075,874 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 230
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.8903 | 1.854 | 12.05 | 1,355,695 | 11.0% |
| **1** | Subword | 1.3613 | 2.569 | 10.50 | 18,334 | 0.0% |
| **2** | Word | 0.4107 | 1.329 | 2.43 | 16,287,373 | 58.9% |
| **2** | Subword | 0.5296 | 1.444 | 3.13 | 192,441 | 47.0% |
| **3** | Word | 0.1577 | 1.116 | 1.33 | 39,552,428 | 84.2% |
| **3** | Subword | 0.5062 | 1.420 | 3.06 | 602,656 | 49.4% |
| **4** | Word | 0.0565 🏆 | 1.040 | 1.09 | 52,397,468 | 94.4% |
| **4** | Subword | 0.5777 | 1.492 | 3.09 | 1,842,490 | 42.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `dan berukuran kecil jepun pautan luar pesisir permaisuri imperial jepun dia juga berkhidmat di pulau...`
2. `di sini pada perlawanan 213 kampung rujukan pautan luar the kebar district south park hyo song`
3. `yang paling muda bahagian barat daya perancis lihat juga komun di rantau ini mempunyai ketahanan sel...`

**Context Size 2:**

1. `pada tahun album lagu tema dua taman negara namadgi nil desperandum dan rock im park kwang jae`
2. `merupakan sebuah sistem perakaman bunyi sehingga syarikat yang sepatutnya dia kemudian diganti naman...`
3. `terletak di daerah schmalkalden meiningen thüringen jerman perbandaran di león senarai kawasan perba...`

**Context Size 3:**

1. `yang terletak di wilayah hajdú bihar di timur hungary di hungary perbandaran di hungary hu kazár`
2. `rujukan pautan luar national portal of india bagli`
3. `komun di jabatan oise di utara perancis lihat juga komun di jabatan cantal di selatan tengah austral...`

**Context Size 4:**

1. `kayu yang telah ditebang rujukan the world of jewel beetles bellamy c l 25 aug kumbang`
2. `kayu dan dapat menyebabkan kerosakan pada batang kayu hidup atau kayu yang telah ditebang rujukan ti...`
3. `pada batang kayu hidup atau kayu yang telah ditebang rujukan the world of jewel beetles bellamy c l ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `an_il_mekuardan_`
2. `_rum_bun_an_pawa`
3. `nyarekomert_ris,`

**Context Size 2:**

1. `ang_turuparri_ton`
2. `n_merun,_85*_esik`
3. `a_bahur,_"udperja`

**Context Size 3:**

1. `an_perkan_diberkan`
2. `ang_dia_/_bum_man_`
3. `ng_timusi_mina_ada`

**Context Size 4:**

1. `kan_syed_muar_roorg`
2. `ang_ditebangsa._mel`
3. `_mengen,_arya_acara`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,842,490 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 | 605,972 |
| Total Tokens | 70,999,280 |
| Mean Frequency | 117.17 |
| Median Frequency | 4 |
| Frequency Std Dev | 4627.23 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | dan | 1,667,877 |
| 2 | di | 1,592,069 |
| 3 | yang | 1,542,694 |
| 4 | pada | 780,935 |
| 5 | dalam | 669,363 |
| 6 | dengan | 531,319 |
| 7 | ini | 520,575 |
| 8 | untuk | 476,200 |
| 9 | sebagai | 428,345 |
| 10 | dari | 375,471 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 石塘社 | 2 |
| 2 | 燕尾脊 | 2 |
| 3 | ekapadashirshasana | 2 |
| 4 | danjae | 2 |
| 5 | sinminhoe | 2 |
| 6 | 국가 | 2 |
| 7 | kukka | 2 |
| 8 | muhurtam | 2 |
| 9 | sasayan | 2 |
| 10 | norr | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1100 |
| R² (Goodness of Fit) | 0.989051 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 30.1% |
| Top 1,000 | 59.6% |
| Top 5,000 | 78.8% |
| Top 10,000 | 85.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9891 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 30.1% of corpus
- **Long Tail:** 595,972 words needed for remaining 14.8% 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 | 0.7590 🏆 | 0.3685 | N/A | N/A |
| **mono_64d** | 64 | 0.7509 | 0.3058 | N/A | N/A |
| **mono_128d** | 128 | 0.6593 | 0.3026 | N/A | N/A |
| **aligned_32d** | 32 | 0.7590 | 0.3657 | 0.4180 | 0.7660 |
| **aligned_64d** | 64 | 0.7509 | 0.3027 | 0.6580 | 0.9240 |
| **aligned_128d** | 128 | 0.6593 | 0.3113 | 0.7120 | 0.9240 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7590 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3261. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 71.2% 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 | **0.114** | 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` | shapie, skalstad, smps |
| `-a` | a602, altomare, ablan |
| `-ma` | maunoury, mascheix, marzian |
| `-k` | kimbirila, krasnopolye, khairune |
| `-m` | metropolitans, mpumnosemerahtimbalan, mesoamerican |
| `-p` | patronnya, piscatori, pagalungan |
| `-b` | badoglio, bougaâ, baturuyuk |
| `-t` | tabuk, thomalla, terlelap |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | rundengan, nyongbyon, ablan |
| `-a` | thomalla, gombaknya, patronnya |
| `-s` | metropolitans, smps, cynops |
| `-an` | rundengan, ablan, pagalungan |
| `-e` | altomare, shapie, stadsgemeente |
| `-i` | piscatori, pipaltari, molinari |
| `-ya` | gombaknya, patronnya, prosidurnya |
| `-r` | toner, headmaster, wijsmuller |

### 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 |
|------|----------|------------------|----------|
| `angk` | 2.06x | 551 contexts | angku, angky, angka |
| `ngka` | 2.08x | 409 contexts | ingka, engka, ongka |
| `ingg` | 2.12x | 247 contexts | ningg, tingg, ingga |
| `ukan` | 2.12x | 227 contexts | gukan, pukan, bukan |
| `embe` | 1.99x | 165 contexts | membe, bembe, embed |
| `rkan` | 2.25x | 90 contexts | erkan, orkan, arkan |
| `memb` | 2.34x | 73 contexts | membe, memba, member |
| `enja` | 1.99x | 152 contexts | penja, senja, kenja |
| `meny` | 2.36x | 63 contexts | ameny, menya, menye |
| `ebag` | 2.54x | 42 contexts | sebag, kebagu, sebagi |
| `mber` | 1.76x | 217 contexts | imber, amber, umber |
| `ndar` | 1.71x | 238 contexts | ndara, indar, undar |

### 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` | `-n` | 126 words | perkaitan, penyelerasan |
| `-k` | `-n` | 108 words | kalinin, kaputihan |
| `-p` | `-an` | 100 words | perkaitan, penyelerasan |
| `-p` | `-a` | 100 words | polyandra, pencuba |
| `-s` | `-a` | 90 words | sayura, sametha |
| `-m` | `-n` | 87 words | mininggalkan, mazan |
| `-k` | `-an` | 80 words | kaputihan, kiniéran |
| `-s` | `-n` | 78 words | suthan, satarazwan |
| `-s` | `-s` | 78 words | sponsors, suvalmas |
| `-a` | `-a` | 66 words | ammochloa, avaa |

### 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 |
|------|-----------------|------------|------|
| qinghuang | **`qinghu-a-ng`** | 7.5 | `a` |
| tordehumos | **`tordehum-o-s`** | 7.5 | `o` |
| pulangnya | **`pulang-n-ya`** | 7.5 | `n` |
| dialirkan | **`dialir-k-an`** | 7.5 | `k` |
| penggertak | **`pengger-ta-k`** | 7.5 | `ta` |
| christiansted | **`christians-t-ed`** | 7.5 | `t` |
| epikurean | **`epikur-e-an`** | 7.5 | `e` |
| unitedpathum | **`unitedpat-h-um`** | 7.5 | `h` |
| chandrasena | **`chandrase-n-a`** | 7.5 | `n` |
| panggungnya | **`panggung-n-ya`** | 7.5 | `n` |
| sanskritnya | **`sanskrit-n-ya`** | 7.5 | `n` |
| bibliografinya | **`bibliografi-n-ya`** | 7.5 | `n` |
| kondiadou | **`kondiad-o-u`** | 7.5 | `o` |
| azmatkhan | **`azmatk-h-an`** | 7.5 | `h` |
| karakteristiknya | **`karakteristik-n-ya`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Malay 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 (5.47x) |
| N-gram | **2-gram** | Lowest perplexity (230) |
| Markov | **Context-4** | Highest predictability (94.4%) |
| 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 19:01:46*