---
language: li
language_name: Limburgish
language_family: germanic_west_continental
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-germanic_west_continental
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: 4.334
  - name: best_isotropy
    type: isotropy
    value: 0.8428
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Limburgish** 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** | 3.459x | 3.46 | 0.1960% | 1,011,080 |
| **16k** | 3.797x | 3.80 | 0.2151% | 921,278 |
| **32k** | 4.092x | 4.09 | 0.2319% | 854,737 |
| **64k** | 4.334x 🏆 | 4.34 | 0.2456% | 807,087 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Andréia Assis Horta (Juiz de Fora, 27 juli is 'n Braziliaanse actrice. luuj geba...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁andré ia ▁ass is ▁h ort a ▁( j u ... (+25 more)` | 35 |
| 16k | `▁andré ia ▁ass is ▁h ort a ▁( j u ... (+25 more)` | 35 |
| 32k | `▁andré ia ▁ass is ▁hort a ▁( ju iz ▁de ... (+23 more)` | 33 |
| 64k | `▁andré ia ▁ass is ▁horta ▁( ju iz ▁de ▁fora ... (+21 more)` | 31 |

**Sample 2:** `'ne Artiest kan zieë: 'ne keunstenaer 'ne vieëarts`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁' ne ▁art ie st ▁kan ▁zieë : ▁' ne ... (+9 more)` | 19 |
| 16k | `▁' ne ▁art ie st ▁kan ▁zieë : ▁' ne ... (+7 more)` | 17 |
| 32k | `▁' ne ▁artie st ▁kan ▁zieë : ▁' ne ▁keunstenaer ... (+4 more)` | 14 |
| 64k | `▁' ne ▁artiest ▁kan ▁zieë : ▁' ne ▁keunstenaer ▁' ... (+3 more)` | 13 |

**Sample 3:** `Sarthe kan verwieze nao: Sarthe, e departement in Frankriek; Sarthe (reveer), 'n...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁s art he ▁kan ▁verwieze ▁nao : ▁s art he ... (+18 more)` | 28 |
| 16k | `▁sart he ▁kan ▁verwieze ▁nao : ▁sart he , ▁e ... (+15 more)` | 25 |
| 32k | `▁sart he ▁kan ▁verwieze ▁nao : ▁sart he , ▁e ... (+15 more)` | 25 |
| 64k | `▁sarthe ▁kan ▁verwieze ▁nao : ▁sarthe , ▁e ▁departement ▁in ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.334x compression
- **Lowest UNK Rate:** 8k with 0.1960% 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 | 25,519 | 14.64 | 104,821 | 14.0% | 30.4% |
| **2-gram** | Subword | 290 🏆 | 8.18 | 5,406 | 65.9% | 99.0% |
| **3-gram** | Word | 57,452 | 15.81 | 140,834 | 5.2% | 20.7% |
| **3-gram** | Subword | 2,584 | 11.34 | 41,526 | 25.6% | 68.5% |
| **4-gram** | Word | 92,727 | 16.50 | 222,778 | 5.0% | 19.9% |
| **4-gram** | Subword | 15,721 | 13.94 | 237,337 | 12.2% | 36.4% |
| **5-gram** | Word | 56,199 | 15.78 | 150,129 | 7.1% | 25.7% |
| **5-gram** | Subword | 63,875 | 15.96 | 706,039 | 7.2% | 21.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `in de` | 30,200 |
| 2 | `in t` | 21,536 |
| 3 | `van de` | 18,942 |
| 4 | `vaan de` | 18,520 |
| 5 | `d n` | 16,860 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `in d n` | 3,329 |
| 2 | `vaan d n` | 1,343 |
| 3 | `sjtörf op laeftied` | 1,213 |
| 4 | `d n twintigsten` | 1,212 |
| 5 | `in nederlands limburg` | 1,211 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `d n twintigsten iew` | 1,191 |
| 2 | `in d n twintigsten` | 1,188 |
| 3 | `gebaore in d n` | 922 |
| 4 | `n gemeinte in de` | 660 |
| 5 | `gesjtorve in d n` | 648 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `in d n twintigsten iew` | 1,185 |
| 2 | `gebaore in d n twintigsten` | 849 |
| 3 | `iew gesjtorve in d n` | 552 |
| 4 | `is n gemeinte in de` | 512 |
| 5 | `luuj gebaore in d n` | 473 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 1,069,069 |
| 2 | `n _` | 685,730 |
| 3 | `e r` | 585,416 |
| 4 | `d e` | 557,458 |
| 5 | `_ d` | 524,469 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `d e _` | 338,019 |
| 2 | `_ d e` | 319,388 |
| 3 | `e n _` | 204,043 |
| 4 | `a n _` | 186,738 |
| 5 | `_ i n` | 184,570 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 262,977 |
| 2 | `_ i n _` | 141,695 |
| 3 | `_ ' t _` | 137,201 |
| 4 | `_ e n _` | 110,552 |
| 5 | `n _ d e` | 97,695 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _ d e _` | 87,044 |
| 2 | `_ v a n _` | 83,372 |
| 3 | `_ v a a n` | 69,215 |
| 4 | `v a a n _` | 67,924 |
| 5 | `n _ ' t _` | 47,099 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 290
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.8891 | 1.852 | 6.68 | 294,084 | 11.1% |
| **1** | Subword | 0.8968 | 1.862 | 7.36 | 2,040 | 10.3% |
| **2** | Word | 0.2863 | 1.219 | 1.77 | 1,959,482 | 71.4% |
| **2** | Subword | 0.9152 | 1.886 | 5.69 | 15,015 | 8.5% |
| **3** | Word | 0.1004 | 1.072 | 1.18 | 3,453,211 | 90.0% |
| **3** | Subword | 0.8160 | 1.761 | 4.49 | 85,340 | 18.4% |
| **4** | Word | 0.0334 🏆 | 1.023 | 1.05 | 4,063,251 | 96.7% |
| **4** | Subword | 0.7481 | 1.680 | 3.35 | 382,984 | 25.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de wereld de vlaot det de groete maot vaan boebij de regio abruzze en zouteveen heraldrywiki`
2. `in de wetensjap en fugas biamonti 592 680 2 biej casteldelfino frankriek liegk t polletiek erkènning`
3. `t arrondissemint wat te speule de vikinge geleid de wienterasse en evangelis 94 5 351 gebäörtenisse`

**Context Size 2:**

1. `in de sovjetunie verklaort d n hamer en ne clerus oet ein beukske zitte meistal 20 zjwaegele`
2. `in t parlemint besteit oet drei verticaol ban vaan hendeg persoeneleke door de arabische minderheid ...`
3. `van de vrouw op dees vraog brink relizjie en allein t belang van limburg ein van de`

**Context Size 3:**

1. `in d n twintigsten iew gesjtorve in de zeveteenden iew gesjtorve in d n twintigsten iew oet vereinig`
2. `vaan d n hier boeveur heer sjreef achtiende iewse componiste waore ummers neet vrij meh componeerde ...`
3. `sjtörf op laeftied leeuwarder courant gerrit ybema overleden 21 jannewarie nederlandj de twiede kame...`

**Context Size 4:**

1. `in d n twintigsten iew oet portugal`
2. `gebaore in d n twintigsten iew van d n europese raod in de media dèks en eupelek euver sinds`
3. `d n twintigsten iew gesjtorve in d n twintigsten iew gesjtorve in d n twintigsten iew oet brazilië`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_er_ieg_be_alaao`
2. `em_5,6_ncachäöbe`
3. `n_ierbret_dootel`

**Context Size 2:**

1. `e_höbbejetcharaye`
2. `n_trögkeneulgbeil`
3. `ert_eënelsjaonao_`

**Context Size 3:**

1. `de_middig._daovan_`
2. `_de_wat_en_bete_ga`
3. `en_eintösse_de_weu`

**Context Size 4:**

1. `_de_ajds_strije_was`
2. `_in_de_hein-load._m`
3. `_'t_heet,_cern_liek`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (382,984 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 | 133,120 |
| Total Tokens | 4,585,134 |
| Mean Frequency | 34.44 |
| Median Frequency | 4 |
| Frequency Std Dev | 1100.63 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 268,955 |
| 2 | in | 146,252 |
| 3 | t | 144,508 |
| 4 | en | 112,120 |
| 5 | van | 84,607 |
| 6 | n | 69,026 |
| 7 | vaan | 66,896 |
| 8 | is | 51,861 |
| 9 | op | 39,534 |
| 10 | d | 32,491 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | oeswaal | 2 |
| 2 | etappenhas | 2 |
| 3 | elsner | 2 |
| 4 | denkmaal | 2 |
| 5 | iezermaat | 2 |
| 6 | projram | 2 |
| 7 | klefisch | 2 |
| 8 | vorbei | 2 |
| 9 | kozakkevesting | 2 |
| 10 | jekaterinodar | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0255 |
| R² (Goodness of Fit) | 0.998659 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 40.3% |
| Top 1,000 | 61.8% |
| Top 5,000 | 77.1% |
| Top 10,000 | 83.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9987 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 40.3% of corpus
- **Long Tail:** 123,120 words needed for remaining 16.9% 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 | 0.8428 🏆 | 0.3285 | N/A | N/A |
| **mono_64d** | 64 | 0.8228 | 0.2334 | N/A | N/A |
| **mono_128d** | 128 | 0.8039 | 0.1762 | N/A | N/A |
| **aligned_32d** | 32 | 0.8428 | 0.3299 | 0.1080 | 0.3900 |
| **aligned_64d** | 64 | 0.8228 | 0.2386 | 0.2060 | 0.5560 |
| **aligned_128d** | 128 | 0.8039 | 0.1760 | 0.3120 | 0.6440 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8428 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2471. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 31.2% 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 | **0.184** | 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 |
|--------|----------|
| `-s` | steile, sjtadssentrum, stuhlmanni |
| `-ge` | gelaegeheje, gelangentied, gedeputeerdje |
| `-a` | aonbeit, aftonbladet, alaajd |
| `-b` | blikveld, burink, begreujde |
| `-be` | begreujde, belles, beaucamps |
| `-k` | kolonos, korehalme, kaajman |
| `-m` | mermaid, monogram, meinberg |
| `-g` | grensgebede, gulliva, gelaegeheje |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | einziejige, contraroterendje, korehalme |
| `-s` | kolonos, wirkers, pretenties |
| `-n` | kaajman, hallen, gassmann |
| `-r` | taer, raor, harder |
| `-er` | taer, harder, soeker |
| `-g` | verdraag, óntwiekkeling, meinberg |
| `-d` | blikveld, mermaid, gelangentied |
| `-en` | hallen, wijnbergen, vastelaovessezoen |

### 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 |
|------|----------|------------------|----------|
| `onde` | 2.10x | 119 contexts | zonde, sonde, konde |
| `esjt` | 2.13x | 107 contexts | gesjt, haesjt, eesjte |
| `oond` | 2.16x | 80 contexts | hoond, poond, roond |
| `nger` | 1.80x | 164 contexts | enger, ônger, anger |
| `gesj` | 1.98x | 77 contexts | gesjt, ungesj, gesjat |
| `erla` | 1.79x | 98 contexts | verlag, erlang, ierland |
| `ersj` | 1.65x | 137 contexts | bersj, iersj, versj |
| `atie` | 1.91x | 69 contexts | satie, natie, katie |
| `chte` | 1.52x | 207 contexts | achte, echte, échte |
| `fran` | 2.33x | 31 contexts | frang, frans, franc |
| `euve` | 1.95x | 57 contexts | euver, leuve, beuve |
| `rlan` | 2.03x | 42 contexts | ørland, erlang, furlan |

### 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 |
|--------|--------|-----------|----------|
| `-b` | `-e` | 169 words | bènnevalle, beriechte |
| `-s` | `-e` | 163 words | stórve, snellere |
| `-a` | `-e` | 113 words | angelsakse, abchaze |
| `-ge` | `-e` | 100 words | gehalte, gelaegeheje |
| `-m` | `-e` | 100 words | macfarlane, move |
| `-k` | `-e` | 96 words | kaapse, kasse |
| `-t` | `-e` | 84 words | tesrizzeltate, tandjheilkónde |
| `-s` | `-s` | 76 words | souvenirs, serres |
| `-s` | `-n` | 59 words | stean, sjtein |
| `-ge` | `-d` | 58 words | gevoed, gewijzigd |

### 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 |
|------|-----------------|------------|------|
| namdalseid | **`namdals-e-id`** | 7.5 | `e` |
| hóngerddoezjend | **`hóngerddoezj-e-nd`** | 7.5 | `e` |
| besjtuurslid | **`besjtuurs-l-id`** | 7.5 | `l` |
| seriemaordeneer | **`seriemaorden-e-er`** | 7.5 | `e` |
| valkenvalei | **`valkenval-e-i`** | 7.5 | `e` |
| zieësjpegel | **`zieësjpe-ge-l`** | 7.5 | `ge` |
| monumaent | **`monuma-e-nt`** | 7.5 | `e` |
| roxenisse | **`roxenis-s-e`** | 7.5 | `s` |
| weltergewiech | **`weltergewi-e-ch`** | 7.5 | `e` |
| vriendinne | **`vriendin-n-e`** | 7.5 | `n` |
| brónnegebeed | **`brónnegebe-e-d`** | 7.5 | `e` |
| poolgebeed | **`poolgebe-e-d`** | 7.5 | `e` |
| kinderleke | **`kinderl-e-ke`** | 7.5 | `e` |
| viemerret | **`viemerr-e-t`** | 7.5 | `e` |
| blokbreke | **`blokbr-e-ke`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Limburgish 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 (4.33x) |
| N-gram | **2-gram** | Lowest perplexity (290) |
| Markov | **Context-4** | Highest predictability (96.7%) |
| 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: 2026-01-10 11:01:05*