README.md

---
language: gl
language_name: Galician
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: 4.855
  - name: best_isotropy
    type: isotropy
    value: 0.8055
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-13
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Galician** 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** | 3.858x | 3.86 | 0.0578% | 2,440,248 |
| **16k** | 4.272x | 4.27 | 0.0640% | 2,203,809 |
| **32k** | 4.611x | 4.61 | 0.0691% | 2,041,816 |
| **64k** | 4.855x 🏆 | 4.86 | 0.0728% | 1,939,285 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Galería de imaxes do río Lima, en Portugal. Véxase tamén de imaxes de Galicia`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁galería ▁de ▁imaxes ▁do ▁río ▁li ma , ▁en ▁portugal ... (+7 more)` | 17 |
| 16k | `▁galería ▁de ▁imaxes ▁do ▁río ▁lima , ▁en ▁portugal . ... (+6 more)` | 16 |
| 32k | `▁galería ▁de ▁imaxes ▁do ▁río ▁lima , ▁en ▁portugal . ... (+6 more)` | 16 |
| 64k | `▁galería ▁de ▁imaxes ▁do ▁río ▁lima , ▁en ▁portugal . ... (+6 more)` | 16 |

**Sample 2:** `Como topónimo Gurgueiro pode referirse a: En Galiza Gurgueiro, parroquia do conc...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁como ▁topónimo ▁g ur gueiro ▁pode ▁referirse ▁a : ▁en ... (+22 more)` | 32 |
| 16k | `▁como ▁topónimo ▁gur gueiro ▁pode ▁referirse ▁a : ▁en ▁galiza ... (+17 more)` | 27 |
| 32k | `▁como ▁topónimo ▁gur gueiro ▁pode ▁referirse ▁a : ▁en ▁galiza ... (+17 more)` | 27 |
| 64k | `▁como ▁topónimo ▁gur gueiro ▁pode ▁referirse ▁a : ▁en ▁galiza ... (+17 more)` | 27 |

**Sample 3:** `Acontecementos Os escitas fanse co poder en Media (até -625). Nacementos Mortes ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁acontecementos ▁os ▁es ci tas ▁f anse ▁co ▁poder ▁en ... (+32 more)` | 42 |
| 16k | `▁acontecementos ▁os ▁es ci tas ▁f anse ▁co ▁poder ▁en ... (+30 more)` | 40 |
| 32k | `▁acontecementos ▁os ▁esci tas ▁fanse ▁co ▁poder ▁en ▁media ▁( ... (+28 more)` | 38 |
| 64k | `▁acontecementos ▁os ▁escitas ▁fanse ▁co ▁poder ▁en ▁media ▁( até ... (+27 more)` | 37 |


### Key Findings

- **Best Compression:** 64k achieves 4.855x compression
- **Lowest UNK Rate:** 8k with 0.0578% 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 | 177,694 | 17.44 | 1,599,435 | 7.3% | 19.3% |
| **2-gram** | Subword | 245 🏆 | 7.94 | 20,270 | 70.9% | 99.1% |
| **3-gram** | Word | 807,045 | 19.62 | 3,552,102 | 4.3% | 10.2% |
| **3-gram** | Subword | 2,104 | 11.04 | 147,394 | 28.3% | 74.1% |
| **4-gram** | Word | 1,759,879 | 20.75 | 5,677,444 | 3.4% | 7.5% |
| **4-gram** | Subword | 12,759 | 13.64 | 835,381 | 12.6% | 40.0% |
| **5-gram** | Word | 1,252,252 | 20.26 | 3,696,764 | 3.5% | 8.1% |
| **5-gram** | Subword | 56,114 | 15.78 | 2,862,824 | 6.8% | 23.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a súa` | 166,299 |
| 2 | `véxase tamén` | 147,020 |
| 3 | `e a` | 141,357 |
| 4 | `que se` | 140,843 |
| 5 | `o seu` | 139,408 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `notas véxase tamén` | 95,486 |
| 2 | `lugar da parroquia` | 82,962 |
| 3 | `da parroquia de` | 77,119 |
| 4 | `véxase tamén outros` | 57,984 |
| 5 | `tamén outros artigos` | 57,948 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `lugar da parroquia de` | 74,902 |
| 2 | `véxase tamén outros artigos` | 57,933 |
| 3 | `véxase tamén ligazóns externas` | 46,507 |
| 4 | `lugares e parroquias lugares` | 41,059 |
| 5 | `notas véxase tamén outros` | 37,978 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `notas véxase tamén outros artigos` | 37,947 |
| 2 | `é un lugar da parroquia` | 36,571 |
| 3 | `lugares e parroquias lugares de` | 36,422 |
| 4 | `un lugar da parroquia de` | 32,976 |
| 5 | `notas véxase tamén ligazóns externas` | 27,554 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 15,175,729 |
| 2 | `a _` | 14,798,960 |
| 3 | `o _` | 13,352,930 |
| 4 | `_ d` | 12,106,131 |
| 5 | `s _` | 11,921,693 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 6,968,387 |
| 2 | `d e _` | 6,412,643 |
| 3 | `o s _` | 4,111,887 |
| 4 | `_ c o` | 3,620,668 |
| 5 | `a s _` | 3,409,570 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 5,450,285 |
| 2 | `_ e n _` | 1,570,834 |
| 3 | `c i ó n` | 1,543,944 |
| 4 | `o _ d e` | 1,530,833 |
| 5 | `_ q u e` | 1,455,346 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ q u e _` | 1,344,486 |
| 2 | `o _ d e _` | 1,307,199 |
| 3 | `s _ d e _` | 1,120,819 |
| 4 | `c i ó n _` | 1,079,093 |
| 5 | `a _ d e _` | 1,051,617 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 245
- **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 | 1.0271 | 2.038 | 12.90 | 1,350,064 | 0.0% |
| **1** | Subword | 1.1629 | 2.239 | 7.96 | 10,661 | 0.0% |
| **2** | Word | 0.4319 | 1.349 | 2.66 | 17,398,522 | 56.8% |
| **2** | Subword | 0.6671 | 1.588 | 4.32 | 84,803 | 33.3% |
| **3** | Word | 0.1909 | 1.142 | 1.44 | 46,200,692 | 80.9% |
| **3** | Subword | 0.6991 | 1.624 | 4.08 | 366,443 | 30.1% |
| **4** | Word | 0.0765 🏆 | 1.054 | 1.14 | 66,305,200 | 92.4% |
| **4** | Subword | 0.6839 | 1.606 | 3.51 | 1,494,151 | 31.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de outubro josé manuel fernández novoa médico e impulsou a altura inerme ante o en polo`
2. `a mellor de sabedoría pervivindo algúns atribúenlle a proa cafè món e coli estas características ori...`
3. `e a cal será desmontado en hábitats de vanuatu nacionais e os tempos rexistrados participación a`

**Context Size 2:**

1. `a súa orixe no mercado invernal o manchester united fc do racing club de ferrol onde antigamente`
2. `véxase tamén outros artigos dólar internacional é unha substancia derivada da norma xurídica ditada ...`
3. `e a segunda guerra mundial voou por primeira vez a vida dedicándose a promover abertamente a bandeir...`

**Context Size 3:**

1. `notas véxase tamén bibliografía bradbury mark becoming somaliland james currey isbn michael schoiswo...`
2. `lugar da parroquia de nantón no concello de fisterra san paio de carreira monte da cidá é un`
3. `da parroquia de augas santas no concello de lugo san amaro lugar da parroquia de cobres no concello`

**Context Size 4:**

1. `lugar da parroquia de san pedro de antealtares da mesma cidade compostela dise que compuxo esta pía ...`
2. `véxase tamén outros artigos lugares de nigrán de nigrán de fútbol do cd lalín do algeciras cf do ad`
3. `véxase tamén ligazóns externas de en lingua francesa de francia da arte do alemán ao francés da univ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_gon_axianto_fab`
2. `abre_po_douraba_`
3. `elá_s_121_dola_d`

**Context Size 2:**

1. `e_pertide_recació`
2. `a_mán,_e_acipobro`
3. `o_cruque_seta._e_`

**Context Size 3:**

1. `_de_direculta_desc`
2. `de_libra_súa_idena`
3. `os_aneirashi,_unha`

**Context Size 4:**

1. `_de_marticide_on_d.`
2. `_en_funciosos_ríxid`
3. `ción_regreira_da_ac`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,494,151 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 | 625,330 |
| Total Tokens | 87,603,878 |
| Mean Frequency | 140.09 |
| Median Frequency | 4 |
| Frequency Std Dev | 9798.07 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 5,468,609 |
| 2 | a | 2,599,768 |
| 3 | e | 2,303,284 |
| 4 | o | 2,069,024 |
| 5 | en | 1,636,097 |
| 6 | que | 1,373,339 |
| 7 | do | 1,309,653 |
| 8 | da | 1,272,492 |
| 9 | no | 696,789 |
| 10 | un | 677,110 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | nodulisporium | 2 |
| 2 | sylviforme | 2 |
| 3 | cladosporioides | 2 |
| 4 | ccnsc | 2 |
| 5 | bessels | 2 |
| 6 | espertina | 2 |
| 7 | esperpenta | 2 |
| 8 | faïence | 2 |
| 9 | malecoloxía | 2 |
| 10 | clappi | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0034 |
| R² (Goodness of Fit) | 0.997371 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.7% |
| Top 1,000 | 60.3% |
| Top 5,000 | 76.2% |
| Top 10,000 | 82.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9974 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.7% of corpus
- **Long Tail:** 615,330 words needed for remaining 17.4% 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 | 0.8055 | 0.3709 | N/A | N/A |
| **mono_64d** | 64 | 0.7807 | 0.2987 | N/A | N/A |
| **mono_128d** | 128 | 0.7103 | 0.2440 | N/A | N/A |
| **aligned_32d** | 32 | 0.8055 🏆 | 0.3769 | 0.4140 | 0.7540 |
| **aligned_64d** | 64 | 0.7807 | 0.2912 | 0.5720 | 0.8760 |
| **aligned_128d** | 128 | 0.7103 | 0.2400 | 0.7240 | 0.9400 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8055 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3036. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 72.4% 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 | **-0.648** | 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` | avalíen, ardre, autocompracencia |
| `-s` | subxéneros, saybrook, societys |
| `-ma` | marcharían, mandiargues, malenkov |
| `-c` | comú, citizens, celestron |
| `-m` | muñozdianteira, monoamino, meszaros |
| `-p` | papovaviridae, próvaí, phani |
| `-t` | taragaza, trenque, top |
| `-b` | bharani, battuto, baninter |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | subxéneros, illiers, citizens |
| `-a` | kottila, 5ha, muñozdianteira |
| `-e` | violone, fable, papovaviridae |
| `-o` | firmamento, everxetismo, battuto |
| `-os` | subxéneros, sáibaos, avetouros |
| `-n` | avalíen, celestron, jamin |
| `-as` | xeodas, criovolcánicas, kangas |
| `-es` | lifesciences, exemplares, remontadores |

### 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 |
|------|----------|------------------|----------|
| `icas` | 1.91x | 173 contexts | icase, micas, icasa |
| `ació` | 1.77x | 148 contexts | ación, nació, lació |
| `emen` | 1.59x | 249 contexts | jemen, emene, iemen |
| `ntos` | 1.72x | 87 contexts | untos, óntos, antos |
| `atur` | 1.49x | 156 contexts | datur, ature, satur |
| `orma` | 1.34x | 257 contexts | torma, ormal, porma |
| `oqui` | 1.75x | 64 contexts | toqui, coqui, noqui |
| `ncia` | 1.45x | 152 contexts | ūncia, uncia, encia |
| `naci` | 1.62x | 84 contexts | nacif, nacin, nacio |
| `ific` | 1.33x | 192 contexts | ifici, ificar, unifica |
| `cció` | 1.70x | 55 contexts | acció, lecció, acción |
| `roqu` | 1.62x | 67 contexts | roqué, roque, croque |

### 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 |
|--------|--------|-----------|----------|
| `-c` | `-s` | 203 words | craniais, codiciadas |
| `-a` | `-s` | 175 words | angers, aeroplanos |
| `-p` | `-s` | 144 words | predis, pags |
| `-a` | `-a` | 122 words | adenda, avicennia |
| `-p` | `-a` | 121 words | penichaira, paralaia |
| `-c` | `-a` | 117 words | cabreiresa, camisasca |
| `-c` | `-o` | 105 words | canonízao, córnico |
| `-e` | `-s` | 105 words | escravos, eppes |
| `-s` | `-s` | 104 words | solsticiais, solicitamos |
| `-c` | `-e` | 101 words | citándose, creedence |

### 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 |
|------|-----------------|------------|------|
| unbekannt | **`unbekan-n-t`** | 7.5 | `n` |
| gestalten | **`gestal-te-n`** | 7.5 | `te` |
| acanthium | **`acanth-i-um`** | 7.5 | `i` |
| matjhabeng | **`matjhab-e-ng`** | 7.5 | `e` |
| manufactúraa | **`manufactúr-a-a`** | 7.5 | `a` |
| bibliorum | **`biblio-r-um`** | 7.5 | `r` |
| andersens | **`ander-se-ns`** | 7.5 | `se` |
| contrataran | **`contrata-ra-n`** | 7.5 | `ra` |
| anacharsis | **`anachar-s-is`** | 7.5 | `s` |
| aavasaksa | **`aavasak-s-a`** | 7.5 | `s` |
| endorfinas | **`endorfi-n-as`** | 7.5 | `n` |
| cuestiónanse | **`cuestión-an-se`** | 7.5 | `an` |
| albacetenses | **`albaceten-s-es`** | 7.5 | `s` |
| toplumsal | **`toplum-s-al`** | 7.5 | `s` |
| synaxarium | **`synaxar-i-um`** | 7.5 | `i` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Galician 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 (4.85x) |
| N-gram | **2-gram** | Lowest perplexity (245) |
| Markov | **Context-4** | Highest predictability (92.4%) |
| 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: 2026-01-13 08:28:57*