---
language: ext
language_name: Extremaduran
language_family: romance_iberian
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-romance_iberian
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: 4.372
  - name: best_isotropy
    type: isotropy
    value: 0.9067
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Extremaduran** 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** | 3.478x | 3.48 | 0.0648% | 600,441 |
| **16k** | 3.822x | 3.82 | 0.0712% | 546,380 |
| **32k** | 4.135x | 4.14 | 0.0770% | 505,062 |
| **64k** | 4.372x 🏆 | 4.38 | 0.0814% | 477,614 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `El 30 diziembri es el dia 364 del añu del calandáriu gregorianu i el 365º enos a...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁el ▁ 3 0 ▁diziembri ▁es ▁el ▁dia ▁ 3 ... (+29 more)` | 39 |
| 16k | `▁el ▁ 3 0 ▁diziembri ▁es ▁el ▁dia ▁ 3 ... (+29 more)` | 39 |
| 32k | `▁el ▁ 3 0 ▁diziembri ▁es ▁el ▁dia ▁ 3 ... (+29 more)` | 39 |
| 64k | `▁el ▁ 3 0 ▁diziembri ▁es ▁el ▁dia ▁ 3 ... (+27 more)` | 37 |

**Sample 2:** `El 19 hebreru es el 50º dia del añu en el calandáriu gregorianu. Quean 315 dias ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁el ▁ 1 9 ▁hebreru ▁es ▁el ▁ 5 0 ... (+29 more)` | 39 |
| 16k | `▁el ▁ 1 9 ▁hebreru ▁es ▁el ▁ 5 0 ... (+29 more)` | 39 |
| 32k | `▁el ▁ 1 9 ▁hebreru ▁es ▁el ▁ 5 0 ... (+29 more)` | 39 |
| 64k | `▁el ▁ 1 9 ▁hebreru ▁es ▁el ▁ 5 0 ... (+29 more)` | 39 |

**Sample 3:** `Tacuarembó es una ciá d'Uruguai, assitiá al norti el país. Tien 54.755 abitantis...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ta cua re mb ó ▁es ▁una ▁ciá ▁d ' ... (+19 more)` | 29 |
| 16k | `▁ta cua re mb ó ▁es ▁una ▁ciá ▁d ' ... (+19 more)` | 29 |
| 32k | `▁ta cuarembó ▁es ▁una ▁ciá ▁d ' uruguai , ▁assitiá ... (+15 more)` | 25 |
| 64k | `▁tacuarembó ▁es ▁una ▁ciá ▁d ' uruguai , ▁assitiá ▁al ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 4.372x compression
- **Lowest UNK Rate:** 8k with 0.0648% 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 | 11,318 | 13.47 | 27,182 | 14.2% | 35.6% |
| **2-gram** | Subword | 262 🏆 | 8.03 | 4,275 | 70.0% | 98.7% |
| **3-gram** | Word | 17,299 | 14.08 | 27,961 | 9.0% | 25.0% |
| **3-gram** | Subword | 2,200 | 11.10 | 28,489 | 27.6% | 72.5% |
| **4-gram** | Word | 27,085 | 14.73 | 37,870 | 7.0% | 17.6% |
| **4-gram** | Subword | 12,567 | 13.62 | 126,878 | 13.2% | 39.2% |
| **5-gram** | Word | 16,506 | 14.01 | 22,378 | 8.8% | 20.4% |
| **5-gram** | Subword | 45,178 | 15.46 | 294,061 | 6.9% | 23.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la` | 4,212 |
| 2 | `la su` | 2,706 |
| 3 | `i el` | 2,284 |
| 4 | `i la` | 2,035 |
| 5 | `el su` | 1,935 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `atijus p ahuera` | 683 |
| 2 | `cita web url` | 449 |
| 3 | `enos añus bisiestus` | 365 |
| 4 | `calandáriu gregorianu i` | 319 |
| 5 | `del añu del` | 310 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `calandáriu gregorianu i el` | 306 |
| 2 | `añu del calandáriu gregorianu` | 306 |
| 3 | `del añu del calandáriu` | 306 |
| 4 | `enos añus bisiestus quean` | 302 |
| 5 | `el añu del añu` | 300 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `del añu del calandáriu gregorianu` | 306 |
| 2 | `del calandáriu gregorianu i el` | 275 |
| 3 | `añu del calandáriu gregorianu i` | 275 |
| 4 | `dias pa acabbal el añu` | 175 |
| 5 | `pa acabbal el añu del` | 170 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 194,258 |
| 2 | `s _` | 163,216 |
| 3 | `_ d` | 139,278 |
| 4 | `_ e` | 133,047 |
| 5 | `e n` | 117,755 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 102,922 |
| 2 | `e l _` | 62,266 |
| 3 | `d e _` | 58,067 |
| 4 | `l a _` | 52,414 |
| 5 | `_ l a` | 44,697 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 56,922 |
| 2 | `_ l a _` | 32,672 |
| 3 | `_ e l _` | 30,073 |
| 4 | `_ d e l` | 29,370 |
| 5 | `_ e n _` | 21,212 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e l _` | 15,677 |
| 2 | `_ q u e _` | 13,393 |
| 3 | `c i ó n _` | 11,996 |
| 4 | `_ l o s _` | 11,355 |
| 5 | `s _ d e _` | 11,280 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 262
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.8380 | 1.788 | 5.16 | 122,307 | 16.2% |
| **1** | Subword | 0.9966 | 1.995 | 7.81 | 1,527 | 0.3% |
| **2** | Word | 0.2568 | 1.195 | 1.57 | 629,256 | 74.3% |
| **2** | Subword | 0.9335 | 1.910 | 5.25 | 11,916 | 6.7% |
| **3** | Word | 0.0752 | 1.054 | 1.12 | 988,570 | 92.5% |
| **3** | Subword | 0.7665 | 1.701 | 3.73 | 62,498 | 23.3% |
| **4** | Word | 0.0222 🏆 | 1.016 | 1.03 | 1,102,038 | 97.8% |
| **4** | Subword | 0.6113 | 1.528 | 2.66 | 233,063 | 38.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de cuerpu en hormigón d estus territorius án desenvolviu estu está en esti con una vos`
2. `la industria petrolera del passagi l obra de llamau boreal quandu ay buelta toma el tonel`
3. `el su labol envestigaora que debi alas enormis murus i ailá que en conxuntu e koval`

**Context Size 2:**

1. `de la riba côa un falar fronteirizu una horma nominal hue l primel monarca del reinu condau`
2. `la su orientación sessual i sūtra ilu frasi corta considerau comu unu los puebrus essesti tamien un`
3. `i el lengua ga áfrica ga gasta ɛ ɛ ŋ ŋ i ɔ a final parabra pol`

**Context Size 3:**

1. `atijus p ahuera ficha nel coe ficha ena página dela bwf premius i conteus en tournamentsoftware com ...`
2. `cita web url shuts down aaa video game studio in deal with oxenfree creator night school netflix anu...`
3. `enos añus bisiestus del añu`

**Context Size 4:**

1. `calandáriu gregorianu i el 277º enos añus bisiestus quean 178 dias pa acabal el añu 323 enos añus bi...`
2. `añu del calandáriu gregorianu i el 185º enos añus bisiestus quean 195 dias pa acabbal el añu del añu`
3. `del añu del calandáriu gregorianu i el número 65 enos añus bisiestus quean 21 dias pa acabal el añu`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_el_herd'el_dá_l`
2. `ancu_lona_el_dis`
3. `erese_ru.612_fim`

**Context Size 2:**

1. `a_gratas_espiel_d`
2. `s_ano_quandificit`
3. `_del_hundu_(lempo`

**Context Size 3:**

1. `_de_purtal,_las_i_`
2. `el_arreyesu_poemad`
3. `de_vicenti._produc`

**Context Size 4:**

1. `_de_di_a_norti_sust`
2. `_la_parti,_ena_cuya`
3. `_el_italis_se_bulga`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (233,063 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 | 53,238 |
| Total Tokens | 1,122,429 |
| Mean Frequency | 21.08 |
| Median Frequency | 4 |
| Frequency Std Dev | 409.27 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 57,224 |
| 2 | la | 33,854 |
| 3 | el | 32,235 |
| 4 | i | 30,275 |
| 5 | en | 22,556 |
| 6 | del | 15,918 |
| 7 | a | 13,852 |
| 8 | que | 13,806 |
| 9 | d | 13,408 |
| 10 | los | 11,612 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | travíes | 2 |
| 2 | ricibun | 2 |
| 3 | consoliol | 2 |
| 4 | estituçionis | 2 |
| 5 | euricu | 2 |
| 6 | galiçia | 2 |
| 7 | clodovéu | 2 |
| 8 | teudis | 2 |
| 9 | rodricu | 2 |
| 10 | hurr | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9657 |
| R² (Goodness of Fit) | 0.997877 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.8% |
| Top 1,000 | 61.7% |
| Top 5,000 | 78.3% |
| Top 10,000 | 85.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9979 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.8% of corpus
- **Long Tail:** 43,238 words needed for remaining 14.6% 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 | 0.9067 | 0.3131 | N/A | N/A |
| **mono_64d** | 64 | 0.8780 | 0.2309 | N/A | N/A |
| **mono_128d** | 128 | 0.6213 | 0.1891 | N/A | N/A |
| **aligned_32d** | 32 | 0.9067 🏆 | 0.3079 | 0.0780 | 0.3100 |
| **aligned_64d** | 64 | 0.8780 | 0.2304 | 0.1160 | 0.4240 |
| **aligned_128d** | 128 | 0.6213 | 0.1848 | 0.1560 | 0.5260 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.9067 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2427. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 15.6% 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 | **-0.122** | 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 |
|--------|----------|
| `-co` | colar, conseherus, corujas |
| `-re` | restauración, reprehentación, rectangular |
| `-es` | escurtol, escapal, escarchaura |
| `-ca` | cabras, callao, castellterçol |
| `-de` | despertal, decumenta, deputá |
| `-pr` | preparación, prasençuela, prostíbulus |
| `-en` | entegrás, entiais, entleert |
| `-con` | conseherus, condis, conservaban |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | entegrás, conseherus, entiais |
| `-a` | samogitia, wera, bela |
| `-u` | niesporu, floru, hurídicu |
| `-us` | conseherus, pasaus, sublevaus |
| `-as` | corujas, arqueolóhicas, cabras |
| `-is` | entiais, llavis, edificionis |
| `-ia` | samogitia, bizkaia, sacudia |
| `-al` | ordinal, despertal, ñial |

### 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 |
|------|----------|------------------|----------|
| `cion` | 2.12x | 91 contexts | acion, nacion, ficion |
| `ioni` | 2.52x | 39 contexts | ionis, ionia, ioniza |
| `onis` | 2.37x | 46 contexts | çonis, zonis, ionis |
| `ació` | 2.44x | 41 contexts | nació, ación, nación |
| `acio` | 2.12x | 61 contexts | lacio, dacio, acion |
| `ción` | 2.25x | 47 contexts | oción, ación, nación |
| `enci` | 1.81x | 107 contexts | encia, venci, venciu |
| `ient` | 1.81x | 106 contexts | cient, cientu, mienta |
| `enta` | 1.69x | 145 contexts | lenta, menta, renta |
| `entu` | 1.98x | 69 contexts | centu, ventu, lentu |
| `trem` | 2.43x | 28 contexts | tremar, tremal, extrem |
| `ment` | 1.79x | 92 contexts | mentá, mentó, mente |

### 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 |
|--------|--------|-----------|----------|
| `-co` | `-s` | 88 words | concursantes, construcionis |
| `-ca` | `-s` | 75 words | cataratas, carrozas |
| `-co` | `-u` | 74 words | coronaeru, coyu |
| `-es` | `-s` | 73 words | escocesas, esploraoris |
| `-pr` | `-s` | 70 words | proucias, protects |
| `-co` | `-a` | 68 words | contemporaña, copia |
| `-re` | `-s` | 56 words | records, restus |
| `-de` | `-s` | 56 words | denominaciones, deáletus |
| `-es` | `-a` | 52 words | estatua, escultora |
| `-re` | `-u` | 48 words | restaurau, recuentu |

### 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 |
|------|-----------------|------------|------|
| presseguíu | **`pr-es-seguíu`** | 6.0 | `seguíu` |
| nutrientis | **`nutrient-is`** | 4.5 | `nutrient` |
| familiaris | **`familiar-is`** | 4.5 | `familiar` |
| espubricáu | **`es-pubricáu`** | 4.5 | `pubricáu` |
| reproución | **`re-pr-ouci-ón`** | 4.5 | `ouci` |
| mencionaus | **`menciona-us`** | 4.5 | `menciona` |
| atividáis | **`atividá-is`** | 4.5 | `atividá` |
| reconversión | **`re-con-vers-ión`** | 4.5 | `vers` |
| reconociblis | **`re-con-ocibl-is`** | 4.5 | `ocibl` |
| favorecius | **`favoreci-us`** | 4.5 | `favoreci` |
| reapertura | **`re-apertura`** | 4.5 | `apertura` |
| puebracionis | **`puebracion-is`** | 4.5 | `puebracion` |
| recitandu | **`re-citandu`** | 4.5 | `citandu` |
| propuesta | **`pr-opuesta`** | 4.5 | `opuesta` |
| espubricandu | **`es-pubricandu`** | 4.5 | `pubricandu` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Extremaduran 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 (4.37x) |
| N-gram | **2-gram** | Lowest perplexity (262) |
| Markov | **Context-4** | Highest predictability (97.8%) |
| 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: 2026-01-04 14:52:09*