---
language: ceb
language_name: Cebuano
language_family: austronesian_philippine_central
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_philippine_central
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: 4.059
  - name: best_isotropy
    type: isotropy
    value: 0.7670
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-07
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Cebuano** 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** | 3.174x | 3.18 | 0.3878% | 267,679 |
| **16k** | 3.550x | 3.55 | 0.4338% | 239,262 |
| **32k** | 3.813x | 3.82 | 0.4660% | 222,758 |
| **64k** | 4.059x 🏆 | 4.06 | 0.4960% | 209,290 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Kahenera sa mga kaka ang Cteniza. Ang Cteniza sakop sa kabanay nga Ctenizidae. A...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kahenera ▁sa ▁mga ▁kaka ▁ang ▁cten iza . ▁ang ▁cten ... (+23 more)` | 33 |
| 16k | `▁kahenera ▁sa ▁mga ▁kaka ▁ang ▁cten iza . ▁ang ▁cten ... (+22 more)` | 32 |
| 32k | `▁kahenera ▁sa ▁mga ▁kaka ▁ang ▁cten iza . ▁ang ▁cten ... (+21 more)` | 31 |
| 64k | `▁kahenera ▁sa ▁mga ▁kaka ▁ang ▁cten iza . ▁ang ▁cten ... (+21 more)` | 31 |

**Sample 2:** `Ang Jizō-saki ngalan niining mga mosunod: Heyograpiya Hapon Shakaga Hana, punta,...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ang ▁j iz ō - s aki ▁ngalan ▁ni in ... (+47 more)` | 57 |
| 16k | `▁ang ▁j iz ō - s aki ▁ngalan ▁ni ining ... (+36 more)` | 46 |
| 32k | `▁ang ▁j iz ō - s aki ▁ngalan ▁niining ▁mga ... (+32 more)` | 42 |
| 64k | `▁ang ▁j iz ō - s aki ▁ngalan ▁niining ▁mga ... (+32 more)` | 42 |

**Sample 3:** `Ang (MCMLXXXIII) mao ang usa ka tuig sa kalendaryong Gregoryano. Ang maoy usa ka...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ang ▁( m c m l xx x iii ) ... (+32 more)` | 42 |
| 16k | `▁ang ▁( m c m l xx x iii ) ... (+28 more)` | 38 |
| 32k | `▁ang ▁( m c m l xxx iii ) ▁mao ... (+24 more)` | 34 |
| 64k | `▁ang ▁( mc m l xxx iii ) ▁mao ▁ang ... (+22 more)` | 32 |


### Key Findings

- **Best Compression:** 64k achieves 4.059x compression
- **Lowest UNK Rate:** 8k with 0.3878% 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 | 3,171 | 11.63 | 3,446,236 | 37.4% | 76.3% |
| **2-gram** | Subword | 218 🏆 | 7.77 | 33,604 | 70.8% | 99.5% |
| **3-gram** | Word | 6,839 | 12.74 | 7,766,658 | 32.6% | 69.1% |
| **3-gram** | Subword | 1,277 | 10.32 | 196,868 | 35.6% | 83.3% |
| **4-gram** | Word | 13,177 | 13.69 | 16,952,568 | 31.0% | 62.8% |
| **4-gram** | Subword | 3,898 | 11.93 | 1,019,139 | 22.5% | 67.3% |
| **5-gram** | Word | 19,115 | 14.22 | 18,655,008 | 30.0% | 58.4% |
| **5-gram** | Subword | 7,890 | 12.95 | 3,628,728 | 16.7% | 59.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sa nasod` | 7,048,649 |
| 2 | `km sa` | 6,204,569 |
| 3 | `palibot sa` | 5,653,512 |
| 4 | `ang mga` | 5,645,464 |
| 5 | `mga gi` | 5,576,920 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mga gi basihan` | 5,576,915 |
| 2 | `ang mga gi` | 5,576,913 |
| 3 | `gi basihan niini` | 5,576,912 |
| 4 | `geonames org cc` | 3,664,283 |
| 5 | `org cc by` | 3,664,283 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ang mga gi basihan` | 5,576,913 |
| 2 | `mga gi basihan niini` | 5,576,912 |
| 3 | `geonames org cc by` | 3,664,283 |
| 4 | `org cc by post` | 3,664,270 |
| 5 | `cc by post updated` | 3,664,269 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ang mga gi basihan niini` | 5,576,912 |
| 2 | `geonames org cc by post` | 3,664,270 |
| 3 | `org cc by post updated` | 3,664,269 |
| 4 | `cc by post updated database` | 3,664,234 |
| 5 | `post updated database download sa` | 3,664,233 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 176,572,408 |
| 2 | `a n` | 170,636,786 |
| 3 | `n g` | 127,660,424 |
| 4 | `s a` | 126,044,028 |
| 5 | `_ s` | 125,029,167 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s a` | 104,157,280 |
| 2 | `s a _` | 95,124,588 |
| 3 | `a n g` | 80,898,551 |
| 4 | `n g _` | 79,824,327 |
| 5 | `_ a n` | 50,392,535 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s a _` | 94,060,964 |
| 2 | `a n g _` | 70,289,894 |
| 3 | `_ a n g` | 46,728,827 |
| 4 | `_ n g a` | 28,593,356 |
| 5 | `n g a _` | 26,245,654 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a n g _` | 46,539,851 |
| 2 | `_ n g a _` | 26,090,887 |
| 3 | `n _ s a _` | 24,592,104 |
| 4 | `. _ a n g` | 21,317,144 |
| 5 | `a n g _ k` | 20,331,305 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 218
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~60% 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 | 1.4579 | 2.747 | 8.46 | 2,622,358 | 0.0% |
| **1** | Subword | 1.5846 | 2.999 | 12.23 | 10,636 | 0.0% |
| **2** | Word | 0.5081 | 1.422 | 2.51 | 21,964,306 | 49.2% |
| **2** | Subword | 0.6448 | 1.564 | 3.57 | 129,845 | 35.5% |
| **3** | Word | 0.2262 | 1.170 | 1.63 | 54,790,128 | 77.4% |
| **3** | Subword | 0.6034 | 1.519 | 3.47 | 463,245 | 39.7% |
| **4** | Word | 0.0992 🏆 | 1.071 | 1.32 | 89,104,487 | 90.1% |
| **4** | Subword | 0.6107 | 1.527 | 3.20 | 1,608,648 | 38.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `sa lintjønnåsen bungtod mikkelhaugen ang poluostrov zuyeva sa amihanan sidlakan dagat kahaboga ang k...`
2. `ang kinainitan nga matang nga sama niini turkey hill sa british columbia river ang kinahabogang dapi...`
3. `nga sama niini villabuena del atlántico sur peru nga ugahon ang kinabasaan nga bulan hunyo sa`

**Context Size 2:**

1. `sa nasod ang klima bugnaw nga ugahon ang kasarangang giiniton c ang kasarangang pag ulan milimetro m...`
2. `km sa amihanan kasadpan sa washington d c metros ibabaw sa dagat kahaboga ang nahimutangan sa mållok`
3. `palibot sa desa caringin administratibo nga balangay ang kudumbuwa sa geonames org cc by post update...`

**Context Size 3:**

1. `mga gi basihan niini jessup guymer in austrobaileya 7 15 govaerts r ed for a full list of`
2. `ang mga gi basihan niini kūh e tīr sa rehiyon palibot sa parksville knob hapit nalukop sa kaumahan`
3. `gi basihan niini nhamiraze sa geonames org cc by post updated database download sa pahang suba sa ma...`

**Context Size 4:**

1. `ang mga gi basihan niini austdalen sa geonames org cc by post updated database download sa suba sa i...`
2. `mga gi basihan niini cañada del mundo sa dominikanhong republika nahimutang ni sa sentro nga bahin s...`
3. `geonames org cc by post updated database download sa bungtod sa northern estado sa sudan sa sudan ng...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_nahinababaes_pi`
2. `a_mga_nl._sangan`
3. `nga_mibluagingal`

**Context Size 2:**

1. `a_amasmyctomihapr`
2. `andsby)];_p.m._an`
3. `ngaloado_nga_gel.`

**Context Size 3:**

1. `_sa_hayop_sa_tro._`
2. `sa_orrell_(cc-by)]`
3. `ang_sourgoin_tom_n`

**Context Size 4:**

1. `_sa_nasod,_km_sa_[_`
2. `ang_patag_tuig._kin`
3. `_ang_kinabarat_aaku`


### Key Findings

- **Best Predictability:** Context-4 (word) with 90.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,608,648 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 | 2,197,636 |
| Total Tokens | 770,818,249 |
| Mean Frequency | 350.75 |
| Median Frequency | 6 |
| Frequency Std Dev | 78759.96 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | sa | 95,123,802 |
| 2 | ang | 48,189,862 |
| 3 | nga | 26,091,942 |
| 4 | ug | 11,614,833 |
| 5 | mga | 11,196,843 |
| 6 | c | 9,761,410 |
| 7 | ni | 8,490,669 |
| 8 | niini | 7,626,074 |
| 9 | palibot | 7,306,530 |
| 10 | nasod | 7,071,533 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kaliforńijo | 2 |
| 2 | kaliforniya | 2 |
| 3 | کیلیفورنیا | 2 |
| 4 | couzzens | 2 |
| 5 | hellgrammite | 2 |
| 6 | powena | 2 |
| 7 | californië | 2 |
| 8 | mcgarva | 2 |
| 9 | fightertown | 2 |
| 10 | ferril | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.4288 |
| R² (Goodness of Fit) | 0.993579 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 63.2% |
| Top 1,000 | 88.4% |
| Top 5,000 | 93.1% |
| Top 10,000 | 94.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9936 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 63.2% of corpus
- **Long Tail:** 2,187,636 words needed for remaining 5.6% 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 | 0.7670 🏆 | 0.3194 | N/A | N/A |
| **mono_64d** | 64 | 0.7432 | 0.2748 | N/A | N/A |
| **mono_128d** | 128 | 0.6660 | 0.2423 | N/A | N/A |
| **aligned_32d** | 32 | 0.7670 | 0.3286 | 0.1020 | 0.4400 |
| **aligned_64d** | 64 | 0.7432 | 0.2716 | 0.2480 | 0.6140 |
| **aligned_128d** | 128 | 0.6660 | 0.2452 | 0.3300 | 0.7240 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7670 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2803. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 33.0% 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 | **-0.024** | 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` | mazanderanica, magnesita, magnhildmyra |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | susumwa, pucanaylla, mazanderanica |
| `-s` | heteraxinoides, gastroglottis, supersentiens |
| `-en` | sveinebakken, elgemyrdalen, føytongjen |
| `-is` | gastroglottis, nooksackensis, naraiensis |
| `-us` | pseudogymnostreptus, rearedpiaractus, supremus |
| `-ia` | omphalomia, eugomontia, leucospilaria |
| `-la` | pucanaylla, diltilla, bulbulla |
| `-na` | thunbergiana, jajina, coolarrikinna |

### 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 |
|------|----------|------------------|----------|
| `lson` | 2.69x | 160 contexts | olson, alson, elson |
| `ahim` | 2.83x | 95 contexts | kahim, rahim, tahim |
| `eona` | 2.74x | 87 contexts | teona, meona, leona |
| `ngto` | 2.54x | 108 contexts | hangto, singto, langto |
| `ugna` | 2.37x | 146 contexts | yugna, pugna, ugnat |
| `ogue` | 2.44x | 115 contexts | bogue, logue, gogue |
| `etro` | 2.08x | 203 contexts | netro, uetro, etrou |
| `ands` | 2.06x | 206 contexts | sands, wands, pands |
| `abaw` | 2.19x | 74 contexts | mabaw, labaw, tabaw |
| `ecie` | 2.61x | 34 contexts | decie, pecies, specie |
| `ated` | 2.52x | 37 contexts | dated, rated, hated |
| `atag` | 1.65x | 256 contexts | atagn, datag, atago |

### 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 |
|--------|--------|-----------|----------|
| `-ma` | `-a` | 56 words | matarrala, mahmudiya |
| `-ma` | `-s` | 25 words | macrostrobilus, macroconus |
| `-ma` | `-na` | 13 words | magiana, manvoumouna |
| `-ma` | `-us` | 9 words | macrostrobilus, macroconus |
| `-ma` | `-la` | 8 words | matarrala, macunolla |
| `-ma` | `-is` | 7 words | mallecensis, marizópolis |
| `-ma` | `-ia` | 4 words | maligia, mariahuslia |
| `-ma` | `-ra` | 3 words | mautotara, macrochiera |
| `-ma` | `-en` | 3 words | maben, maureen |
| `-ma` | `-es` | 2 words | macroscelides, mashes |

### 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 |
|------|-----------------|------------|------|
| whittieriana | **`whittier-ia-na`** | 6.0 | `whittier` |
| darwiniana | **`darwin-ia-na`** | 6.0 | `darwin` |
| huicumera | **`huicume-ra`** | 4.5 | `huicume` |
| javorkana | **`javorka-na`** | 4.5 | `javorka` |
| olavsbekken | **`olavsbekk-en`** | 4.5 | `olavsbekk` |
| campelles | **`campell-es`** | 4.5 | `campell` |
| apolinaria | **`apolinar-ia`** | 4.5 | `apolinar` |
| steyskalia | **`steyskal-ia`** | 4.5 | `steyskal` |
| liniholmen | **`liniholm-en`** | 4.5 | `liniholm` |
| finngrunden | **`finngrund-en`** | 4.5 | `finngrund` |
| maaprobahan | **`ma-aprobahan`** | 4.5 | `aprobahan` |
| macrostylospora | **`ma-crostylospo-ra`** | 3.0 | `crostylospo` |
| saharolana | **`saharo-la-na`** | 3.0 | `saharo` |
| maxwellensis | **`ma-xwellens-is`** | 3.0 | `xwellens` |
| mappianthus | **`ma-ppianth-us`** | 3.0 | `ppianth` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Cebuano 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 (4.06x) |
| N-gram | **2-gram** | Lowest perplexity (218) |
| Markov | **Context-4** | Highest predictability (90.1%) |
| 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: 2026-01-07 20:10:38*