---
language: eu
language_name: Basque
language_family: basque
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-basque
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: 4.507
  - name: best_isotropy
    type: isotropy
    value: 0.6711
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-12
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Basque** 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** | 3.579x | 3.58 | 0.0525% | 2,041,670 |
| **16k** | 3.957x | 3.96 | 0.0580% | 1,846,361 |
| **32k** | 4.270x | 4.27 | 0.0626% | 1,711,199 |
| **64k** | 4.507x 🏆 | 4.51 | 0.0661% | 1,621,038 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `, , Galesko udalerri bat da, Monmouthshire konderrian. Kanpo estekak konderriko ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁, ▁, ▁galesko ▁udalerri ▁bat ▁da , ▁mon mo uth ... (+7 more)` | 17 |
| 16k | `▁, ▁, ▁galesko ▁udalerri ▁bat ▁da , ▁mon mouth shire ... (+6 more)` | 16 |
| 32k | `▁, ▁, ▁galesko ▁udalerri ▁bat ▁da , ▁monmouthshire ▁konderrian . ... (+4 more)` | 14 |
| 64k | `▁, ▁, ▁galesko ▁udalerri ▁bat ▁da , ▁monmouthshire ▁konderrian . ... (+4 more)` | 14 |

**Sample 2:** `, Mexikoko Revillagigedo uhartediako uharte bat da, Ozeano Barean. uhartedia`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁, ▁mexikoko ▁re vill ag ig edo ▁uharte d iako ... (+10 more)` | 20 |
| 16k | `▁, ▁mexikoko ▁re vill ag ig edo ▁uharted iako ▁uharte ... (+9 more)` | 19 |
| 32k | `▁, ▁mexikoko ▁re vill ag ig edo ▁uharted iako ▁uharte ... (+7 more)` | 17 |
| 64k | `▁, ▁mexikoko ▁re vill ag ig edo ▁uharted iako ▁uharte ... (+7 more)` | 17 |

**Sample 3:** `{{mineral infotaula | kategoria silikato mineralak|silikato]]`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ {{ min eral ▁inf ota ula ▁| ▁kategoria ▁silikato ... (+7 more)` | 17 |
| 16k | `▁ {{ min eral ▁inf ota ula ▁| ▁kategoria ▁silikato ... (+6 more)` | 16 |
| 32k | `▁ {{ mineral ▁infotaula ▁| ▁kategoria ▁silikato ▁mineralak | s ... (+3 more)` | 13 |
| 64k | `▁ {{ mineral ▁infotaula ▁| ▁kategoria ▁silikato ▁mineralak | s ... (+2 more)` | 12 |


### Key Findings

- **Best Compression:** 64k achieves 4.507x compression
- **Lowest UNK Rate:** 8k with 0.0525% 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 | 101,400 | 16.63 | 1,518,553 | 10.5% | 31.4% |
| **2-gram** | Subword | 226 🏆 | 7.82 | 17,699 | 72.3% | 99.5% |
| **3-gram** | Word | 128,394 | 16.97 | 2,211,893 | 10.6% | 32.1% |
| **3-gram** | Subword | 1,909 | 10.90 | 132,832 | 27.9% | 76.3% |
| **4-gram** | Word | 179,917 | 17.46 | 3,667,160 | 11.5% | 30.7% |
| **4-gram** | Subword | 10,807 | 13.40 | 755,000 | 12.9% | 43.1% |
| **5-gram** | Word | 134,161 | 17.03 | 2,865,762 | 13.8% | 31.9% |
| **5-gram** | Subword | 41,735 | 15.35 | 2,680,749 | 7.6% | 27.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kanpo estekak` | 411,094 |
| 2 | `izan zen` | 219,794 |
| 3 | `bat da` | 194,039 |
| 4 | `ziren eta` | 172,147 |
| 5 | `enpresak ziren` | 157,767 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `erreferentziak kanpo estekak` | 152,739 |
| 2 | `erreferentziak ikus gainera` | 78,821 |
| 3 | `ziren horien artean` | 67,157 |
| 4 | `gertuen dauden herriak` | 66,904 |
| 5 | `bakarrik bizi ziren` | 64,949 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dauden herriak erakusten ditu` | 33,543 |
| 2 | `honek gertuen dauden herriak` | 33,541 |
| 3 | `france par comune frantziako` | 33,541 |
| 4 | `par comune frantziako udalerri` | 33,541 |
| 5 | `diagrama honek gertuen dauden` | 33,540 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `france par comune frantziako udalerri` | 33,541 |
| 2 | `diagrama honek gertuen dauden herriak` | 33,540 |
| 3 | `honek gertuen dauden herriak erakusten` | 33,540 |
| 4 | `gertuen dauden herriak erakusten ditu` | 33,540 |
| 5 | `emploi et population active et` | 33,539 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n` | 16,166,768 |
| 2 | `a _` | 14,488,655 |
| 3 | `n _` | 14,293,162 |
| 4 | `_ e` | 11,880,846 |
| 5 | `a r` | 11,450,376 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n _` | 8,377,081 |
| 2 | `k o _` | 5,400,285 |
| 3 | `e t a` | 5,000,482 |
| 4 | `r e n` | 4,339,867 |
| 5 | `a k _` | 4,189,214 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e t a _` | 3,251,221 |
| 2 | `_ e t a` | 3,085,028 |
| 3 | `r e n _` | 2,969,339 |
| 4 | `a k o _` | 2,216,397 |
| 5 | `a r e n` | 2,019,670 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ e t a _` | 2,973,733 |
| 2 | `a r e n _` | 1,944,215 |
| 3 | `_ z i r e` | 942,772 |
| 4 | `z i r e n` | 928,644 |
| 5 | `t z e n _` | 881,836 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 226
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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 | 0.9814 | 1.974 | 11.89 | 2,034,056 | 1.9% |
| **1** | Subword | 1.0508 | 2.072 | 6.91 | 11,299 | 0.0% |
| **2** | Word | 0.3086 | 1.238 | 1.95 | 24,154,380 | 69.1% |
| **2** | Subword | 0.6282 | 1.546 | 4.22 | 78,093 | 37.2% |
| **3** | Word | 0.1002 | 1.072 | 1.21 | 46,969,150 | 90.0% |
| **3** | Subword | 0.6997 | 1.624 | 4.08 | 329,201 | 30.0% |
| **4** | Word | 0.0366 🏆 | 1.026 | 1.07 | 56,781,994 | 96.3% |
| **4** | Subword | 0.6958 | 1.620 | 3.58 | 1,344,420 | 30.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `eta 20 emakume aktoreak mikel jondoni joanes leizarraga izendatu zuten azpian 99 lanean hasi zen urt...`
2. `da horretan zangozako merindadean sartu zen 2 lizeo teknologiko asko horietako bi pertsona bakoitzek...`
3. `zen bertako zuzendaritzarekin doktoretza osatu zuen rayuela eleberri hauek erdialdeko asian dub duba...`

**Context Size 2:**

1. `kanpo estekak monasterioak arkitektura erromanikoa du iurreko amabirjina xii xiii orrialdeak jatorri...`
2. `izan zen 2 altzari dendak 1 altzari denda zen 1 liburu denda batean lan egiten zuen oso`
3. `bat da horn barrutian azken zentsuaren arabera hart udalerriak 823 etxebizitza zeuden 667 hektarea e...`

**Context Size 3:**

1. `erreferentziak kanpo estekak kategoria departamenduko kantonamenduak santuen lurraldea`
2. `erreferentziak ikus gainera porichthys batrachoididae kanpo estekak fishbase org arrainak golkoko ar...`
3. `ziren horien artean 39 aktiboak ziren eta 255 apartamentuak ziren 375 etxebizitza nagusietatik 310 b...`

**Context Size 4:**

1. `dauden herriak erakusten ditu batzuen distantzia eta kokapen erlatiboa erreferentziak kanpo estekak ...`
2. `par comune frantziako udalerri guztietako datu zehatzak mapa baten bitartez eskuragarri udalerriak o...`
3. `france par comune frantziako udalerri guztietako datu zehatzak mapa baten bitartez eskuragarri udale...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_dolaugetudagu-f`
2. `a_eahaianak_grel`
3. `e_mpeldo_seaskos`

**Context Size 2:**

1. `enpon_emailerako_`
2. `a_soa_danibola_bu`
3. `n_etak),_sa_caler`

**Context Size 3:**

1. `en_batua_utz_estek`
2. `ko_eta_gazioa_bili`
3. `eta_mota_apolibre_`

**Context Size 4:**

1. `eta_badituzten_adin`
2. `_eta_liburu_da,_adi`
3. `ren_aranoaren_kondu`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,344,420 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 | 925,645 |
| Total Tokens | 82,551,722 |
| Mean Frequency | 89.18 |
| Median Frequency | 4 |
| Frequency Std Dev | 4334.93 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | eta | 3,064,757 |
| 2 | da | 1,077,465 |
| 3 | zen | 1,014,999 |
| 4 | ziren | 906,527 |
| 5 | bat | 694,872 |
| 6 | zuen | 667,830 |
| 7 | izan | 539,156 |
| 8 | zeuden | 442,816 |
| 9 | kanpo | 430,370 |
| 10 | 1 | 427,974 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | pveducation | 2 |
| 2 | chillijchi | 2 |
| 3 | gaureguneko | 2 |
| 4 | cupla | 2 |
| 5 | marwareraren | 2 |
| 6 | vaṇī | 2 |
| 7 | antarātmā | 2 |
| 8 | ले | 2 |
| 9 | ओमन | 2 |
| 10 | barbajuan | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0446 |
| R² (Goodness of Fit) | 0.993920 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 27.0% |
| Top 1,000 | 53.3% |
| Top 5,000 | 70.7% |
| Top 10,000 | 77.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9939 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 27.0% of corpus
- **Long Tail:** 915,645 words needed for remaining 22.6% 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 | 0.6711 | 0.3672 | N/A | N/A |
| **mono_64d** | 64 | 0.6503 | 0.2977 | N/A | N/A |
| **mono_128d** | 128 | 0.5876 | 0.2512 | N/A | N/A |
| **aligned_32d** | 32 | 0.6711 🏆 | 0.3650 | 0.3080 | 0.7260 |
| **aligned_64d** | 64 | 0.6503 | 0.3045 | 0.5360 | 0.8520 |
| **aligned_128d** | 128 | 0.5876 | 0.2534 | 0.6260 | 0.8780 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6711 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3065. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 62.6% 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 | **0.176** | 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 |
|--------|----------|
| `-a` | alienak, alalpardo, azhkhluttach |
| `-s` | spiritist, stateira, sakanari |
| `-ma` | maezturekin, malasiako, malaciotis |
| `-m` | miyashita, mwir, maezturekin |
| `-e` | eakoak, euskeras, enacryos |
| `-b` | birjinarenak, budavari, blechnerren |
| `-ba` | bagoiaren, balazten, banús |
| `-t` | txingorrigain, tdpm, t280 |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | ultraeskuindarrarekin, blechnerren, borbónen |
| `-en` | blechnerren, borbónen, aynen |
| `-a` | miyashita, prestatzera, haparanda |
| `-k` | eakoak, birjinarenak, paraxialetik |
| `-o` | villasecako, sakonuneetako, alalpardo |
| `-ko` | villasecako, sakonuneetako, malasiako |
| `-ak` | eakoak, birjinarenak, alienak |
| `-in` | ultraeskuindarrarekin, uzkiarekin, txingorrigain |

### 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 |
|------|----------|------------------|----------|
| `rtze` | 1.71x | 538 contexts | artze, ertze, urtze |
| `tuzt` | 2.70x | 47 contexts | tuzte, dituzt, dtuzte |
| `ikoa` | 1.67x | 501 contexts | aikoa, oikoa, pikoa |
| `eude` | 2.63x | 45 contexts | eudes, zeude, eudel |
| `oare` | 1.66x | 385 contexts | hoare, soare, joare |
| `anle` | 2.52x | 48 contexts | nanle, anleu, zhanle |
| `atut` | 1.69x | 284 contexts | matute, batuta, statut |
| `iare` | 1.49x | 539 contexts | tiare, iaren, iaret |
| `ntza` | 1.57x | 373 contexts | intza, antza, ontza |
| `rria` | 1.54x | 343 contexts | irria, erria, orria |
| `tanl` | 2.47x | 30 contexts | tanlay, stanly, bitanle |
| `ituz` | 1.75x | 106 contexts | dituz, dituzu, abituz |

### 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 |
|--------|--------|-----------|----------|
| `-a` | `-n` | 188 words | ahtren, anbiguoen |
| `-e` | `-n` | 162 words | epilepsiarekin, ensoren |
| `-a` | `-a` | 136 words | austfonna, alotropia |
| `-b` | `-n` | 121 words | bizitasunaren, bayaniren |
| `-k` | `-n` | 111 words | koltxoiaren, kiroltasunaren |
| `-s` | `-n` | 105 words | selekzioaren, solasaldien |
| `-a` | `-k` | 102 words | arrazek, artxuk |
| `-e` | `-k` | 101 words | eszenaratzeagatik, eskumikaturik |
| `-e` | `-a` | 99 words | eulychnia, elgetarra |
| `-p` | `-n` | 97 words | presidenteordetzan, pobrezian |

### 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 |
|------|-----------------|------------|------|
| domeinuan | **`domeinu-a-n`** | 7.5 | `a` |
| aritmometroa | **`aritmometr-o-a`** | 7.5 | `o` |
| maratoiean | **`maratoi-e-an`** | 7.5 | `e` |
| goenagari | **`goenag-a-ri`** | 7.5 | `a` |
| onenerako | **`onener-a-ko`** | 7.5 | `a` |
| networken | **`networ-k-en`** | 7.5 | `k` |
| yamatentomon | **`yamatentom-o-n`** | 7.5 | `o` |
| sulfurozkoa | **`sulfuroz-ko-a`** | 7.5 | `ko` |
| entzunezkoak | **`entzunez-ko-ak`** | 7.5 | `ko` |
| esparruetako | **`esparruet-a-ko`** | 7.5 | `a` |
| ezereztasuna | **`ezereztasu-n-a`** | 7.5 | `n` |
| mugagabetasuna | **`mugagabetasu-n-a`** | 7.5 | `n` |
| zutabeari | **`zutabe-a-ri`** | 7.5 | `a` |
| rouxestevae | **`rouxestev-a-e`** | 7.5 | `a` |
| karrantzara | **`karrantz-a-ra`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Basque 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 (4.51x) |
| N-gram | **2-gram** | Lowest perplexity (226) |
| Markov | **Context-4** | Highest predictability (96.3%) |
| 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: 2026-01-12 14:02:26*