---
language: bbc
language_name: Batak Toba
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: 3.662
  - name: best_isotropy
    type: isotropy
    value: 0.8133
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Batak Toba** 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** | 3.300x | 3.30 | 0.2266% | 1,666,856 |
| **16k** | 3.529x | 3.53 | 0.2423% | 1,558,753 |
| **32k** | 3.662x 🏆 | 3.66 | 0.2515% | 1,502,009 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Janji i ma sada huta (desa) na adong di Kecamatan Siempat Nempu Hilir, Kabupaten...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁janji ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+16 more)` | 26 |
| 16k | `▁janji ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+16 more)` | 26 |
| 32k | `▁janji ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+16 more)` | 26 |

**Sample 2:** `Siboras i ma sada huta (desa) na adong di Kecamatan Silima Pungga Pungga, Kabupa...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sib oras ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ... (+16 more)` | 26 |
| 16k | `▁siboras ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+15 more)` | 25 |
| 32k | `▁siboras ▁i ▁ma ▁sada ▁huta ▁( desa ) ▁na ▁adong ... (+15 more)` | 25 |

**Sample 3:** `Sukorejo i ma sada huta na adong di Kecamatan Ulujami, Kabupaten Pemalang, Propi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁suk orejo ▁i ▁ma ▁sada ▁huta ▁na ▁adong ▁di ▁kecamatan ... (+11 more)` | 21 |
| 16k | `▁sukorejo ▁i ▁ma ▁sada ▁huta ▁na ▁adong ▁di ▁kecamatan ▁ulujami ... (+10 more)` | 20 |
| 32k | `▁sukorejo ▁i ▁ma ▁sada ▁huta ▁na ▁adong ▁di ▁kecamatan ▁ulujami ... (+10 more)` | 20 |


### Key Findings

- **Best Compression:** 32k achieves 3.662x compression
- **Lowest UNK Rate:** 8k with 0.2266% 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 | 8,503 | 13.05 | 26,404 | 17.5% | 42.9% |
| **2-gram** | Subword | 185 🏆 | 7.53 | 3,447 | 77.7% | 99.2% |
| **3-gram** | Word | 22,449 | 14.45 | 43,137 | 8.4% | 25.3% |
| **3-gram** | Subword | 1,216 | 10.25 | 18,046 | 38.1% | 83.2% |
| **4-gram** | Word | 44,360 | 15.44 | 67,584 | 5.9% | 16.2% |
| **4-gram** | Subword | 5,587 | 12.45 | 70,061 | 19.7% | 54.7% |
| **5-gram** | Word | 29,774 | 14.86 | 42,910 | 7.1% | 18.6% |
| **5-gram** | Subword | 17,403 | 14.09 | 153,430 | 12.1% | 36.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `angka na` | 4,424 |
| 2 | `dung i` | 4,327 |
| 3 | `ni si` | 4,060 |
| 4 | `i ma` | 3,682 |
| 5 | `ni jahowa` | 2,892 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `anak ni si` | 1,613 |
| 2 | `i ma sada` | 784 |
| 3 | `na adong di` | 741 |
| 4 | `dung i ninna` | 735 |
| 5 | `hata ni jahowa` | 703 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `on do hata ni` | 423 |
| 2 | `i ma sada huta` | 417 |
| 3 | `songon on do hata` | 408 |
| 4 | `na adong di kecamatan` | 353 |
| 5 | `angka anak ni si` | 336 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `songon on do hata ni` | 406 |
| 2 | `on do hata ni jahowa` | 250 |
| 3 | `i ma sada huta na` | 215 |
| 4 | `desa na adong di kecamatan` | 191 |
| 5 | `km jala godang ni ruasna` | 175 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 206,965 |
| 2 | `a n` | 205,323 |
| 3 | `n g` | 154,062 |
| 4 | `i _` | 142,882 |
| 5 | `n a` | 122,548 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n g` | 81,918 |
| 2 | `_ m a` | 76,355 |
| 3 | `n a _` | 58,981 |
| 4 | `_ n a` | 53,557 |
| 5 | `a n _` | 51,287 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n i _` | 34,904 |
| 2 | `_ n a _` | 33,621 |
| 3 | `_ d i _` | 25,919 |
| 4 | `a n g k` | 24,948 |
| 5 | `_ m a _` | 23,827 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n g k a` | 19,235 |
| 2 | `_ a n g k` | 17,946 |
| 3 | `n g k a _` | 17,765 |
| 4 | `_ j a l a` | 14,671 |
| 5 | `j a l a _` | 14,594 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 185
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~37% 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 | 0.9199 | 1.892 | 6.44 | 50,491 | 8.0% |
| **1** | Subword | 0.9288 | 1.904 | 7.09 | 1,431 | 7.1% |
| **2** | Word | 0.3746 | 1.296 | 2.02 | 324,952 | 62.5% |
| **2** | Subword | 0.7034 | 1.628 | 4.04 | 10,144 | 29.7% |
| **3** | Word | 0.1537 | 1.112 | 1.28 | 656,964 | 84.6% |
| **3** | Subword | 0.6472 | 1.566 | 3.17 | 40,950 | 35.3% |
| **4** | Word | 0.0591 🏆 | 1.042 | 1.09 | 838,369 | 94.1% |
| **4** | Subword | 0.5206 | 1.435 | 2.40 | 129,601 | 47.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ni tano naung leleng on marupaya maningkathon kesadaran masarakat na pauli pintu ni si hannas dohot`
2. `na talup do angka naposongku alai anggo raoanna nang jahudi tubu ni halak batak di tongatongamu`
3. `i si arni anak ni harangan na mengatur istimewa dok gumodang sian saluhut na nidabuna i`

**Context Size 2:**

1. `angka na di ginjang ni angka ompunami umbahen manjadi angka i tu ahu do jahowa molo ahu`
2. `dung i ro di salelenglelengna psalmen 94 94 1 ale anaha sai parateatehon hamu panariason ni bibirhon`
3. `ni si jakkob anak ni si rehabeam di jerusalem 7 17 dua lombu lima birubiru tunggal sada`

**Context Size 3:**

1. `anak ni si aron hahanasida i marhalado di joro ni jahowa tungkan jolo ni rimberimbe i 40 27`
2. `i ma sada nagara na maringanan di lobu panjang`
3. `na adong di halak batak toba tombur tarbahen sian sibuk ni manuk na dibumbui`

**Context Size 4:**

1. `on do hata ni tuhan jahowa nunga pola hupatoltol tanganku maruari ingkon lehononku do i tu ompumuna ...`
2. `i ma sada huta na adong di kecamatan silima pungga pungga kabupaten dairi propinsi sumatera utara in...`
3. `songon on do hata ni tuhan jahowa hape so tutu jahowa mandok 22 29 ia situan na torop isi`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_man_i_sa_nina_s`
2. `amai_palalaseu_n`
3. `ndi_ᯔ_no_pa_de_d`

**Context Size 2:**

1. `a_lamar_na._jalut`
2. `ani_ni_ahit_bando`
3. `ng_dongkop_hot_ad`

**Context Size 3:**

1. `angitlawa_rajai,_d`
2. `_marhalahite_hite_`
3. `na_sapangku_imbolo`

**Context Size 4:**

1. `_ni_jahowa_hamu_ang`
2. `_na_marsaro_mameuth`
3. `_di_jeremia_7_novem`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (129,601 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 | 24,923 |
| Total Tokens | 971,594 |
| Mean Frequency | 38.98 |
| Median Frequency | 4 |
| Frequency Std Dev | 557.86 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ni | 34,971 |
| 2 | na | 33,958 |
| 3 | i | 32,913 |
| 4 | ma | 26,658 |
| 5 | di | 25,940 |
| 6 | tu | 20,429 |
| 7 | do | 19,116 |
| 8 | angka | 17,411 |
| 9 | jala | 14,584 |
| 10 | dohot | 13,515 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ᯇᯔᯒᯪᯉ᯲ᯖ | 2 |
| 2 | kayo | 2 |
| 3 | uttar | 2 |
| 4 | ltr | 2 |
| 5 | font | 2 |
| 6 | ebrima | 2 |
| 7 | border | 2 |
| 8 | cellpadding | 2 |
| 9 | td | 2 |
| 10 | align | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1806 |
| R² (Goodness of Fit) | 0.997033 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 53.7% |
| Top 1,000 | 78.5% |
| Top 5,000 | 91.4% |
| Top 10,000 | 95.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9970 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 53.7% of corpus
- **Long Tail:** 14,923 words needed for remaining 4.3% 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 | 0.8133 | 0.3464 | N/A | N/A |
| **mono_64d** | 64 | 0.7715 | 0.2725 | N/A | N/A |
| **mono_128d** | 128 | 0.4709 | 0.2523 | N/A | N/A |
| **aligned_32d** | 32 | 0.8133 🏆 | 0.3386 | 0.0140 | 0.1240 |
| **aligned_64d** | 64 | 0.7715 | 0.2780 | 0.0560 | 0.2460 |
| **aligned_128d** | 128 | 0.4709 | 0.2525 | 0.1340 | 0.3160 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8133 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2900. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 13.4% 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 | **-0.493** | 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 |
|--------|----------|
| `-ma` | mangain, manuhati, mamingkiri |
| `-pa` | pangir, pahosing, parsonduk |
| `-di` | disiorhon, didege, diri |
| `-man` | mangain, manuhati, mangkasiholi |
| `-mar` | marilah, marhabanhaban, marnioli |
| `-ha` | hapistaranmuna, harajaon, hanna |
| `-par` | parsonduk, partalianta, parnidaan |
| `-si` | sitorus, sitalutuk, sinimpan |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | disiorhon, mangain, getasan |
| `-a` | acara, opatsa, hapistaranmuna |
| `-on` | disiorhon, harajaon, mandaon |
| `-an` | getasan, nangkohan, bulanan |
| `-na` | hapistaranmuna, etonganna, utamana |
| `-hon` | disiorhon, hinungkuphon, ditoishon |
| `-ng` | humosing, pahosing, taretong |
| `-nna` | etonganna, hanna, salpuanna |

### 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` | 1.61x | 127 contexts | angan, langa, sanga |
| `angk` | 1.53x | 157 contexts | angka, bangko, angkal |
| `ngka` | 1.56x | 89 contexts | angka, bungka, engkau |
| `mang` | 1.64x | 61 contexts | amang, mangan, memang |
| `ngko` | 1.70x | 42 contexts | bangko, ingkon, angkot |
| `bang` | 1.45x | 72 contexts | bange, abang, bangis |
| `ingk` | 1.48x | 60 contexts | lingka, ingkau, ingkon |
| `onga` | 1.68x | 36 contexts | tonga, longa, bongal |
| `bahe` | 1.79x | 26 contexts | bahen, dibahe, ibahen |
| `ngan` | 1.40x | 65 contexts | angan, ingan, mangan |
| `ongo` | 1.62x | 36 contexts | longo, kongo, rongom |
| `angg` | 1.31x | 78 contexts | anggi, anggo, angguk |

### 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` | 358 words | parsapataan, partingkian |
| `-ma` | `-n` | 206 words | marpadanpadan, marharajaon |
| `-pa` | `-on` | 200 words | patoltolhon, paimbarhon |
| `-pa` | `-a` | 184 words | pallawa, pasalihonsa |
| `-pa` | `-an` | 157 words | parsapataan, partingkian |
| `-di` | `-n` | 156 words | disiaphon, dilembagahon |
| `-di` | `-on` | 134 words | disiaphon, dilembagahon |
| `-ha` | `-n` | 128 words | hasundatan, hasusaan |
| `-pa` | `-na` | 119 words | parsuhatonmuna, pabalionna |
| `-ma` | `-on` | 116 words | marharajaon, mangaluhon |

### 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 |
|------|-----------------|------------|------|
| pabotohononku | **`pa-boto-hon-on-ku`** | 9.0 | `boto` |
| paradiananku | **`par-adian-an-ku`** | 7.5 | `adian` |
| sipasahaton | **`si-pa-sahat-on`** | 7.5 | `sahat` |
| marparmangsian | **`mar-par-mang-sian`** | 7.5 | `sian` |
| panailingku | **`pan-aili-ng-ku`** | 7.5 | `aili` |
| pardonganan | **`par-dong-an-an`** | 7.5 | `dong` |
| marhamuliaon | **`mar-ha-mulia-on`** | 7.5 | `mulia` |
| diparsiajari | **`di-par-si-ajari`** | 7.5 | `ajari` |
| sipaingotna | **`si-pa-ingot-na`** | 7.5 | `ingot` |
| sipatudoson | **`si-pa-tudos-on`** | 7.5 | `tudos` |
| dipangasahon | **`di-pan-gasa-hon`** | 7.5 | `gasa` |
| situtungon | **`si-tutu-ng-on`** | 7.5 | `tutu` |
| pasahaton | **`pa-sahat-on`** | 6.0 | `sahat` |
| parbungkason | **`par-bungkas-on`** | 6.0 | `bungkas` |
| dipajomba | **`di-pa-jomba`** | 6.0 | `jomba` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Batak Toba 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 | **32k BPE** | Best compression (3.66x) |
| N-gram | **2-gram** | Lowest perplexity (185) |
| Markov | **Context-4** | Highest predictability (94.1%) |
| 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 18:37:11*