---
language: wa
language_name: Walloon
language_family: romance_galloitalic
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_galloitalic
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 3.891
  - name: best_isotropy
    type: isotropy
    value: 0.8697
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Walloon** 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** | 3.370x | 3.37 | 0.2270% | 337,479 |
| **16k** | 3.589x | 3.59 | 0.2418% | 316,838 |
| **32k** | 3.767x | 3.77 | 0.2537% | 301,900 |
| **64k** | 3.891x 🏆 | 3.89 | 0.2621% | 292,270 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `el minêyolodjince : Morance par djin Morance pa malåde Li morance, ça pout esse ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁el ▁minêyolodjince ▁: ▁mor ance ▁par ▁djin ▁mor ance ▁pa ... (+20 more)` | 30 |
| 16k | `▁el ▁minêyolodjince ▁: ▁morance ▁par ▁djin ▁morance ▁pa ▁malåde ▁li ... (+15 more)` | 25 |
| 32k | `▁el ▁minêyolodjince ▁: ▁morance ▁par ▁djin ▁morance ▁pa ▁malåde ▁li ... (+15 more)` | 25 |
| 64k | `▁el ▁minêyolodjince ▁: ▁morance ▁par ▁djin ▁morance ▁pa ▁malåde ▁li ... (+15 more)` | 25 |

**Sample 2:** `tcheke (lingaedje) : lingaedje del Tchekeye tcheke del banke : papî po payî`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tche ke ▁( lingaedje ) ▁: ▁lingaedje ▁del ▁tche keye ... (+9 more)` | 19 |
| 16k | `▁tcheke ▁( lingaedje ) ▁: ▁lingaedje ▁del ▁tchekeye ▁tcheke ▁del ... (+5 more)` | 15 |
| 32k | `▁tcheke ▁( lingaedje ) ▁: ▁lingaedje ▁del ▁tchekeye ▁tcheke ▁del ... (+5 more)` | 15 |
| 64k | `▁tcheke ▁( lingaedje ) ▁: ▁lingaedje ▁del ▁tchekeye ▁tcheke ▁del ... (+5 more)` | 15 |

**Sample 3:** `anêyes | anêyes | anêyes | anêyes | anêyes | | | | | | | | | Evenmints Personåli...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ... (+13 more)` | 23 |
| 16k | `▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ... (+13 more)` | 23 |
| 32k | `▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ... (+13 more)` | 23 |
| 64k | `▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ▁anêyes ▁| ... (+13 more)` | 23 |


### Key Findings

- **Best Compression:** 64k achieves 3.891x compression
- **Lowest UNK Rate:** 8k with 0.2270% 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 | 13,161 | 13.68 | 50,899 | 15.9% | 38.7% |
| **2-gram** | Subword | 287 🏆 | 8.17 | 3,898 | 66.2% | 98.9% |
| **3-gram** | Word | 27,389 | 14.74 | 75,959 | 10.3% | 28.8% |
| **3-gram** | Subword | 2,270 | 11.15 | 30,979 | 28.7% | 71.3% |
| **4-gram** | Word | 43,477 | 15.41 | 111,769 | 10.0% | 25.5% |
| **4-gram** | Subword | 11,809 | 13.53 | 153,308 | 14.8% | 41.1% |
| **5-gram** | Word | 23,357 | 14.51 | 68,834 | 14.4% | 33.1% |
| **5-gram** | Subword | 40,103 | 15.29 | 373,182 | 8.5% | 26.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c est` | 19,149 |
| 2 | `e walon` | 7,096 |
| 3 | `dins l` | 6,135 |
| 4 | `gn a` | 5,364 |
| 5 | `di l` | 5,071 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c est ene` | 4,038 |
| 2 | `c est on` | 3,474 |
| 3 | `c est l` | 2,865 |
| 4 | `i gn a` | 1,935 |
| 5 | `ciste anêye la` | 1,829 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ont vnou å monde` | 1,112 |
| 2 | `rilomés walons et waloneus` | 926 |
| 3 | `la rilomés walons et` | 919 |
| 4 | `ancyin ptit ban del` | 907 |
| 5 | `ptit ban del walonreye` | 881 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `la rilomés walons et waloneus` | 919 |
| 2 | `ancyin ptit ban del walonreye` | 876 |
| 3 | `èn ancyin ptit ban del` | 862 |
| 4 | `est èn ancyin ptit ban` | 860 |
| 5 | `c est èn ancyin ptit` | 795 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 346,952 |
| 2 | `s _` | 328,323 |
| 3 | `_ d` | 305,245 |
| 4 | `e s` | 247,267 |
| 5 | `_ l` | 199,665 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e s _` | 158,630 |
| 2 | `_ d i` | 98,745 |
| 3 | `e _ d` | 74,828 |
| 4 | `_ d e` | 71,105 |
| 5 | `s _ d` | 59,946 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l ' _` | 52,800 |
| 2 | `_ d i _` | 48,903 |
| 3 | `l e s _` | 45,518 |
| 4 | `_ d ' _` | 40,065 |
| 5 | `_ l e s` | 39,565 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e s _` | 39,370 |
| 2 | `_ d e s _` | 36,468 |
| 3 | `a e d j e` | 30,194 |
| 4 | `_ e s t _` | 28,789 |
| 5 | `w a l o n` | 26,821 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 287
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.8999 | 1.866 | 6.37 | 116,505 | 10.0% |
| **1** | Subword | 0.9760 | 1.967 | 8.18 | 1,236 | 2.4% |
| **2** | Word | 0.3359 | 1.262 | 1.91 | 738,986 | 66.4% |
| **2** | Subword | 0.9487 | 1.930 | 6.02 | 10,102 | 5.1% |
| **3** | Word | 0.1299 | 1.094 | 1.24 | 1,402,590 | 87.0% |
| **3** | Subword | 0.8319 | 1.780 | 4.29 | 60,750 | 16.8% |
| **4** | Word | 0.0508 🏆 | 1.036 | 1.08 | 1,734,432 | 94.9% |
| **4** | Subword | 0.6556 | 1.575 | 2.86 | 260,171 | 34.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `l pîce di a passé les diferincyî des floricontes thumb li holande c est ene cwårêye`
2. `a hesta li trope a sketé dji shijhele ou des viyaedjes so pås rfondeus do lussimbork`
3. `di scrire disk e l påye ki vént lére li 219inme po do calindrî grigoryin li`

**Context Size 2:**

1. `c est adon k ele s î ont dmoré dins les codjowaedjes et des sårts miertchamp rond`
2. `e walon eplaideye di jean collette rééditer c est vos k on lyi cåze dins l esplicant`
3. `dins l esplicant motî do tchestea rnåd mora l an 150 di filozofeye des loumires ou set`

**Context Size 3:**

1. `c est ene plaece sol fagne walone metans pol trouflaedje a stî foirt sibaré pal guere di la`
2. `c est on lingaedje do sud ess do nidjeria gn a eto des tchampions microscopikes les emacralêyès cawe...`
3. `c est l eshonna di totes les dujhances et des ovraedjes d ene metowe maladeye on djåzrè puvite`

**Context Size 4:**

1. `ont vnou å monde ciste anêye la ont morou ciste anêye la rilomés walons et waloneus arthur trigaux ô...`
2. `rilomés walons et waloneus ôtès djins fiesses nåcionåles ey eternåcionåles vey eto 27 di djanvî 28 d...`
3. `la rilomés walons et waloneus rené magritte ôtès djins fiesses nåcionåles ey eternåcionåles vey eto ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_doumwic'_ma_par`
2. `estoke,_lel'_da_`
3. `s_a_e_aericr,_ix`

**Context Size 2:**

1. `e_es_moxhamarou_d`
2. `s_ni_recis_re,_in`
3. `_di_li_zen_yu_cro`

**Context Size 3:**

1. `es_osse_bassé_pass`
2. `_di_shuvan_da_måvl`
3. `e_des_espal_ricnox`

**Context Size 4:**

1. `_l'_radio_pårteye_(`
2. `_di_fevrî-mont._met`
3. `les_tchaeffner:_min`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (260,171 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 | 52,390 |
| Total Tokens | 2,080,878 |
| Mean Frequency | 39.72 |
| Median Frequency | 4 |
| Frequency Std Dev | 699.28 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | l | 60,706 |
| 2 | a | 49,899 |
| 3 | di | 49,556 |
| 4 | d | 44,591 |
| 5 | li | 41,896 |
| 6 | les | 40,671 |
| 7 | des | 36,781 |
| 8 | on | 34,019 |
| 9 | e | 30,971 |
| 10 | est | 29,225 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | strivay | 2 |
| 2 | valkeneer | 2 |
| 3 | kotsifakos | 2 |
| 4 | cogolati | 2 |
| 5 | coprezide | 2 |
| 6 | lecocq | 2 |
| 7 | siclimboigne | 2 |
| 8 | pozzo | 2 |
| 9 | samourayes | 2 |
| 10 | diplomats | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1436 |
| R² (Goodness of Fit) | 0.997501 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 48.1% |
| Top 1,000 | 72.7% |
| Top 5,000 | 86.8% |
| Top 10,000 | 91.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9975 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 48.1% of corpus
- **Long Tail:** 42,390 words needed for remaining 8.4% 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 | 0.8697 🏆 | 0.3451 | N/A | N/A |
| **mono_64d** | 64 | 0.8678 | 0.2695 | N/A | N/A |
| **mono_128d** | 128 | 0.7751 | 0.1978 | N/A | N/A |
| **aligned_32d** | 32 | 0.8697 | 0.3408 | 0.0460 | 0.2260 |
| **aligned_64d** | 64 | 0.8678 | 0.2653 | 0.0800 | 0.3180 |
| **aligned_128d** | 128 | 0.7751 | 0.1961 | 0.1180 | 0.4000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8697 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2691. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 11.8% 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 | **0.268** | High formulaic/idiomatic 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 |
|--------|----------|
| `-s` | sorpwès, soucant, schalon |
| `-a` | ashît, aschoûter, arivéve |
| `-c` | chanchesse, crac, coûte |
| `-r` | rékem, ritape, rahoucants |
| `-d` | dvuzlêyès, djilet, djoyes |
| `-b` | begnons, branmint, borins |
| `-p` | pattepårti, popes, preyale |
| `-m` | marker, manuels, montes |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | frîmårtinisse, chanchesse, oyåve |
| `-s` | begnons, sorpwès, åmônes |
| `-es` | åmônes, popes, goidjes |
| `-t` | ashît, soucant, veyant |
| `-ye` | marveye, veskeveye, eveye |
| `-je` | kischoyaedje, laudje, redjårbaedje |
| `-nt` | soucant, veyant, branmint |
| `-n` | schalon, tramwegen, ploumtion |

### 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 |
|------|----------|------------------|----------|
| `aedj` | 2.24x | 178 contexts | aedje, saedje, taedje |
| `tche` | 1.88x | 250 contexts | tcheû, tchet, tcheu |
| `êyes` | 2.10x | 64 contexts | fêyes, idêyes, atêyes |
| `sses` | 1.86x | 93 contexts | asses, åsses, esses |
| `edje` | 2.22x | 38 contexts | nedje, aedje, wedje |
| `djes` | 2.01x | 38 contexts | ådjes, tidjes, vèdjes |
| `ants` | 1.95x | 35 contexts | wants, pzants, tnants |
| `rijh` | 1.68x | 55 contexts | prijhî, grijhe, prijhe |
| `fran` | 1.95x | 31 contexts | frane, franz, frank |
| `ranc` | 1.69x | 46 contexts | rance, franc, franci |
| `scri` | 2.10x | 18 contexts | scrit, scrip, scris |
| `teut` | 2.28x | 14 contexts | steut, eteut, asteut |

### 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` | `-e` | 184 words | capitole, crustinnisse |
| `-r` | `-e` | 183 words | riwaitaedje, rifômrece |
| `-c` | `-s` | 170 words | curieus, crouwès |
| `-s` | `-e` | 160 words | sicoreye, soucråde |
| `-a` | `-e` | 146 words | ahèsse, ake |
| `-p` | `-e` | 143 words | poelvoorde, poytreye |
| `-d` | `-e` | 141 words | dialectologique, divizêye |
| `-t` | `-e` | 131 words | turke, tontelange |
| `-p` | `-s` | 130 words | purdans, potches |
| `-s` | `-s` | 127 words | stitchîs, såvadjes |

### 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 |
|------|-----------------|------------|------|
| tchampionatn | **`tchampiona-t-n`** | 7.5 | `t` |
| cråxhoulet | **`cråxhoul-e-t`** | 7.5 | `e` |
| coirsulet | **`coirsul-e-t`** | 7.5 | `e` |
| bouxhreye | **`bouxhr-e-ye`** | 7.5 | `e` |
| pharmacien | **`pharmaci-e-n`** | 7.5 | `e` |
| forijhots | **`forijho-t-s`** | 7.5 | `t` |
| sloveneye | **`sloven-e-ye`** | 7.5 | `e` |
| fiziolodjeye | **`fiziolodj-e-ye`** | 7.5 | `e` |
| diswaibeye | **`diswaib-e-ye`** | 7.5 | `e` |
| omeyopateye | **`omeyopat-e-ye`** | 7.5 | `e` |
| påjhûlisté | **`påjhûli-s-té`** | 7.5 | `s` |
| tchimisse | **`tchimi-s-se`** | 7.5 | `s` |
| djouwreut | **`djouw-re-ut`** | 7.5 | `re` |
| ôrtografeye | **`ôrtograf-e-ye`** | 7.5 | `e` |
| plantisse | **`planti-s-se`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Walloon shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (3.89x) |
| N-gram | **2-gram** | Lowest perplexity (287) |
| Markov | **Context-4** | Highest predictability (94.9%) |
| 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: 2026-01-11 03:47:03*