---
language: btm
language_name: Batak Mandailing
language_family: austronesian_batak
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_batak
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: 5.210
  - name: best_isotropy
    type: isotropy
    value: 0.4518
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

# Batak Mandailing - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Batak Mandailing** 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** | 4.164x | 4.17 | 0.0881% | 216,736 |
| **16k** | 4.609x | 4.61 | 0.0975% | 195,810 |
| **32k** | 5.005x | 5.01 | 0.1059% | 180,321 |
| **64k** | 5.210x 🏆 | 5.22 | 0.1103% | 173,224 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Kumpulan Setia ima sala sada huta na adong i kecamatan Huta Bargot, kabupaten Ma...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kumpulan ▁set ia ▁ima ▁sala ▁sada ▁huta ▁na ▁adong ▁i ... (+14 more)` | 24 |
| 16k | `▁kumpulan ▁setia ▁ima ▁sala ▁sada ▁huta ▁na ▁adong ▁i ▁kecamatan ... (+13 more)` | 23 |
| 32k | `▁kumpulan ▁setia ▁ima ▁sala ▁sada ▁huta ▁na ▁adong ▁i ▁kecamatan ... (+13 more)` | 23 |
| 64k | `▁kumpulan ▁setia ▁ima ▁sala ▁sada ▁huta ▁na ▁adong ▁i ▁kecamatan ... (+13 more)` | 23 |

**Sample 2:** `Muara Soma ima sala sada huta na ading i kecamatan Batang Natal, kabupaten Manda...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁muara ▁so ma ▁ima ▁sala ▁sada ▁huta ▁na ▁ading ▁i ... (+14 more)` | 24 |
| 16k | `▁muara ▁soma ▁ima ▁sala ▁sada ▁huta ▁na ▁ading ▁i ▁kecamatan ... (+13 more)` | 23 |
| 32k | `▁muara ▁soma ▁ima ▁sala ▁sada ▁huta ▁na ▁ading ▁i ▁kecamatan ... (+13 more)` | 23 |
| 64k | `▁muara ▁soma ▁ima ▁sala ▁sada ▁huta ▁na ▁ading ▁i ▁kecamatan ... (+13 more)` | 23 |

**Sample 3:** `24 Januari ima ari pa-24 i kalender Gregorian dohot 361 ari (sanga 362 ari i tao...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 2 4 ▁januari ▁ima ▁ari ▁pa - 2 4 ... (+24 more)` | 34 |
| 16k | `▁ 2 4 ▁januari ▁ima ▁ari ▁pa - 2 4 ... (+24 more)` | 34 |
| 32k | `▁ 2 4 ▁januari ▁ima ▁ari ▁pa - 2 4 ... (+24 more)` | 34 |
| 64k | `▁ 2 4 ▁januari ▁ima ▁ari ▁pa - 2 4 ... (+24 more)` | 34 |


### Key Findings

- **Best Compression:** 64k achieves 5.210x compression
- **Lowest UNK Rate:** 8k with 0.0881% 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 | 2,149 | 11.07 | 3,846 | 24.9% | 62.3% |
| **2-gram** | Subword | 193 🏆 | 7.59 | 1,424 | 75.5% | 99.7% |
| **3-gram** | Word | 1,623 | 10.66 | 2,810 | 28.2% | 64.8% |
| **3-gram** | Subword | 1,481 | 10.53 | 9,326 | 32.5% | 79.4% |
| **4-gram** | Word | 1,998 | 10.96 | 3,539 | 27.5% | 54.8% |
| **4-gram** | Subword | 7,322 | 12.84 | 39,044 | 16.0% | 47.2% |
| **5-gram** | Word | 980 | 9.94 | 1,944 | 37.4% | 71.2% |
| **5-gram** | Subword | 20,669 | 14.34 | 80,096 | 9.7% | 30.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ima sada` | 626 |
| 2 | `on pe` | 512 |
| 3 | `na adong` | 416 |
| 4 | `sian on` | 373 |
| 5 | `i taon` | 359 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `na adong i` | 265 |
| 2 | `kabupaten mandailing natal` | 178 |
| 3 | `i kalender gregorian` | 170 |
| 4 | `sumatera utara indonesia` | 160 |
| 5 | `ima ari pa` | 157 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `provinsi sumatera utara indonesia` | 133 |
| 2 | `kabupaten mandailing natal provinsi` | 130 |
| 3 | `mandailing natal provinsi sumatera` | 129 |
| 4 | `natal provinsi sumatera utara` | 129 |
| 5 | `taon kabisat i kalender` | 126 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kabupaten mandailing natal provinsi sumatera` | 129 |
| 2 | `mandailing natal provinsi sumatera utara` | 129 |
| 3 | `natal provinsi sumatera utara indonesia` | 128 |
| 4 | `taon kabisat i kalender gregorian` | 126 |
| 5 | `huta na adong i kecamatan` | 112 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n` | 41,734 |
| 2 | `a _` | 37,272 |
| 3 | `n _` | 28,447 |
| 4 | `m a` | 25,826 |
| 5 | `i _` | 25,144 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m a` | 15,579 |
| 2 | `a n _` | 13,475 |
| 3 | `_ n a` | 11,682 |
| 4 | `a n g` | 11,673 |
| 5 | `n a _` | 10,767 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a _` | 7,012 |
| 2 | `_ m a n` | 6,102 |
| 3 | `a _ m a` | 4,445 |
| 4 | `_ i m a` | 4,125 |
| 5 | `i m a _` | 4,121 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ i m a _` | 3,948 |
| 2 | `d o h o t` | 3,004 |
| 3 | `o h o t _` | 3,001 |
| 4 | `_ d o h o` | 2,997 |
| 5 | `_ d o t _` | 2,471 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 193
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~31% 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 | 0.8033 | 1.745 | 4.52 | 26,637 | 19.7% |
| **1** | Subword | 0.8859 | 1.848 | 5.46 | 845 | 11.4% |
| **2** | Word | 0.2155 | 1.161 | 1.41 | 119,766 | 78.4% |
| **2** | Subword | 0.7876 | 1.726 | 4.38 | 4,613 | 21.2% |
| **3** | Word | 0.0517 | 1.037 | 1.07 | 168,163 | 94.8% |
| **3** | Subword | 0.7693 | 1.704 | 3.51 | 20,191 | 23.1% |
| **4** | Word | 0.0122 🏆 | 1.008 | 1.02 | 179,311 | 98.8% |
| **4** | Subword | 0.5814 | 1.496 | 2.41 | 70,850 | 41.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i kota di kotu isa rupana kahanggi namar sisolkot ni eme ni awak dot mamakena pala`
2. `na mandung manjadi aliran eksistensialisme sartre ima al qur an sm 180 an sm 70 an`
3. `ima sada provinsi sumatera utara aek sasataon rodang momo tarida do anggina si baroar dibaon na`

**Context Size 2:**

1. `ima sada sunni mazhab hanafi vasilij vladimirovič bartold art by barbara brend p 130 tai ulama na`
2. `on pe mandung dewasa pakean nai gunaon pakean adat belitong tai i instrospeksi eksperimental sudena ...`
3. `na adong juo alak sunni dot 10 huruf ngolu vokal sapetona hangeul adongdope 3 konsonannai dot 1`

**Context Size 3:**

1. `na adong i ruang woktu i sakitar lubang nalomlom adong parmukoan na i dokon horizon peristiwa objek ...`
2. `kabupaten mandailing natal provinsi sumatera utara indonesia i botung adong luak parmayaman na deges...`
3. `ima ari pa 103 ari pa 104 i taon kabisat i kalender gregorian dohot 363 ari sanga 364`

**Context Size 4:**

1. `kabupaten mandailing natal provinsi sumatera utara indonesia sumberna`
2. `natal provinsi sumatera utara indonesia pula sian on panyabungan tu kecamatan on`
3. `mandailing natal provinsi sumatera utara indonesia sumberna`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `alan_a_rian_ruse`
2. `_ana_ontuon._tan`
3. `nang_akeon_asapa`

**Context Size 2:**

1. `an_niviusi,_hamel`
2. `a_ida_lak_nai_jun`
3. `n_sentat_dokon_ng`

**Context Size 3:**

1. `_mambaen_dohot_par`
2. `an_ibad_oktu_piga_`
3. `_nagoda_marcoundur`

**Context Size 4:**

1. `_na_ibaen_herito_la`
2. `_manjadi_i_ruar_tu_`
3. `a_marisi.dw:_menek_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (70,850 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 | 11,148 |
| Total Tokens | 176,428 |
| Mean Frequency | 15.83 |
| Median Frequency | 4 |
| Frequency Std Dev | 130.57 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 7,229 |
| 2 | na | 7,125 |
| 3 | on | 3,997 |
| 4 | ima | 3,996 |
| 5 | dohot | 2,990 |
| 6 | ni | 2,685 |
| 7 | dot | 2,484 |
| 8 | sada | 1,834 |
| 9 | tu | 1,711 |
| 10 | ma | 1,485 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | lil | 2 |
| 2 | imah | 2 |
| 3 | nasida | 2 |
| 4 | sunusi | 2 |
| 5 | nunga | 2 |
| 6 | majmu | 2 |
| 7 | fatawa | 2 |
| 8 | fiqhi | 2 |
| 9 | panjalakian | 2 |
| 10 | martoba | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0705 |
| R² (Goodness of Fit) | 0.989075 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.8% |
| Top 1,000 | 71.1% |
| Top 5,000 | 91.4% |
| Top 10,000 | 98.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9891 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.8% of corpus
- **Long Tail:** 1,148 words needed for remaining 1.3% 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 | 0.4518 🏆 | 0.4274 | N/A | N/A |
| **mono_64d** | 64 | 0.1211 | 0.4252 | N/A | N/A |
| **mono_128d** | 128 | 0.0249 | 0.4089 | N/A | N/A |
| **aligned_32d** | 32 | 0.4518 | 0.4145 | 0.0140 | 0.1240 |
| **aligned_64d** | 64 | 0.1211 | 0.4363 | 0.0200 | 0.1760 |
| **aligned_128d** | 128 | 0.0249 | 0.4097 | 0.0540 | 0.2300 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.4518 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4203. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.4% 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 | **1.311** | 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 |
|--------|----------|
| `-ma` | marmasak, mamuloi, maligina |
| `-pa` | paderi, parkumpulan, pangajaran |
| `-man` | manakik, manyorang, mangajari |
| `-mar` | marmasak, marwujud, mariner |
| `-sa` | samananjung, sati, sakral |
| `-ta` | tarpusat, takar, tajikistan |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | tubagasan, ringkasan, disusun |
| `-a` | nikola, studia, katua |
| `-an` | tubagasan, ringkasan, parkumpulan |
| `-ng` | samananjung, pedagang, kacang |
| `-on` | bandingkon, dibandingkon, pelestarion |
| `-na` | maligina, umurna, ajayaanna |
| `-ang` | pedagang, kacang, sumbayang |

### 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 |
|------|----------|------------------|----------|
| `anga` | 1.46x | 77 contexts | nanga, angan, sanga |
| `angk` | 1.47x | 58 contexts | angko, angke, angka |
| `anda` | 1.43x | 54 contexts | ganda, tanda, banda |
| `mang` | 1.59x | 31 contexts | mango, amang, lomang |
| `amba` | 1.49x | 39 contexts | hamba, tamba, sambal |
| `ngan` | 1.40x | 43 contexts | angan, lengan, sangan |
| `dang` | 1.40x | 42 contexts | udang, ndang, dangka |
| `aran` | 1.35x | 48 contexts | arana, arang, saran |
| `angg` | 1.32x | 39 contexts | anggi, anggo, nangge |
| `anja` | 1.36x | 34 contexts | hanja, banjar, anjadi |
| `ngga` | 1.37x | 30 contexts | hingga, rongga, mangga |
| `ting` | 1.34x | 32 contexts | tingo, uting, tingon |

### 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 |
|--------|--------|-----------|----------|
| `-pa` | `-n` | 307 words | panjalakan, pambaenan |
| `-pa` | `-an` | 271 words | panjalakan, pambaenan |
| `-ma` | `-n` | 241 words | mangombangkon, maximilian |
| `-ma` | `-on` | 157 words | mangombangkon, manyesuaion |
| `-ma` | `-a` | 98 words | maringana, manurutnia |
| `-ma` | `-ng` | 69 words | malang, marancang |
| `-ma` | `-an` | 61 words | maximilian, marhalangan |
| `-pa` | `-a` | 57 words | pasca, pasadana |
| `-sa` | `-a` | 40 words | samentara, sangapiga |
| `-ma` | `-ang` | 38 words | malang, marancang |

### 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 |
|------|-----------------|------------|------|
| paporangan | **`pa-pora-ng-an`** | 7.5 | `pora` |
| marpandangan | **`mar-pa-ndang-an`** | 7.5 | `ndang` |
| bagasanna | **`bagas-an-na`** | 6.0 | `bagas` |
| pasabolas | **`pa-sa-bolas`** | 6.0 | `bolas` |
| mandurung | **`man-duru-ng`** | 6.0 | `duru` |
| sasabagas | **`sa-sa-bagas`** | 6.0 | `bagas` |
| sabalikna | **`sa-balik-na`** | 6.0 | `balik` |
| marlainan | **`mar-lain-an`** | 6.0 | `lain` |
| panilaian | **`pa-nilai-an`** | 6.0 | `nilai` |
| mardongan | **`mar-dong-an`** | 6.0 | `dong` |
| margontian | **`mar-gonti-an`** | 6.0 | `gonti` |
| mandefinision | **`man-definisi-on`** | 6.0 | `definisi` |
| pemerintahan | **`pemerintah-an`** | 4.5 | `pemerintah` |
| margandak | **`mar-gandak`** | 4.5 | `gandak` |
| habitatna | **`habitat-na`** | 4.5 | `habitat` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Batak Mandailing 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 (5.21x) |
| N-gram | **2-gram** | Lowest perplexity (193) |
| Markov | **Context-4** | Highest predictability (98.8%) |
| 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: 2026-01-03 19:44:07*