---
language: lb
language_name: Luxembourgish
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: 4.804
  - name: best_isotropy
    type: isotropy
    value: 0.8333
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Luxembourgish** 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** | 3.853x | 3.85 | 0.0904% | 659,416 |
| **16k** | 4.222x | 4.22 | 0.0990% | 601,768 |
| **32k** | 4.537x | 4.54 | 0.1064% | 560,028 |
| **64k** | 4.804x 🏆 | 4.81 | 0.1127% | 528,875 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Reclinghem ass eng franséisch Gemeng am Kanton Fruges am Departement Pas-de-Cala...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁re cl ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ... (+20 more)` | 30 |
| 16k | `▁re cl ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ... (+20 more)` | 30 |
| 32k | `▁re cl inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ... (+18 more)` | 28 |
| 64k | `▁re cl inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ... (+18 more)` | 28 |

**Sample 2:** `Bomy ass eng franséisch Gemeng am Kanton Fruges am Departement Pas-de-Calais. am...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁b om y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fru ... (+19 more)` | 29 |
| 16k | `▁bom y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fru ges ... (+18 more)` | 28 |
| 32k | `▁bom y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ▁am ... (+17 more)` | 27 |
| 64k | `▁bom y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ▁am ... (+17 more)` | 27 |

**Sample 3:** `Ruminghem ass eng franséisch Gemeng am Departement Pas-de-Calais an der Regioun ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁rum ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas ... (+21 more)` | 31 |
| 16k | `▁rum ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas ... (+19 more)` | 29 |
| 32k | `▁rum inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas - ... (+18 more)` | 28 |
| 64k | `▁rum inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas - ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 4.804x compression
- **Lowest UNK Rate:** 8k with 0.0904% 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 | 62,562 | 15.93 | 314,805 | 10.7% | 24.2% |
| **2-gram** | Subword | 318 🏆 | 8.31 | 7,549 | 63.0% | 98.9% |
| **3-gram** | Word | 192,148 | 17.55 | 547,285 | 5.0% | 13.5% |
| **3-gram** | Subword | 2,850 | 11.48 | 64,806 | 23.1% | 66.6% |
| **4-gram** | Word | 356,085 | 18.44 | 876,356 | 4.3% | 11.3% |
| **4-gram** | Subword | 16,948 | 14.05 | 383,042 | 12.4% | 36.3% |
| **5-gram** | Word | 281,035 | 18.10 | 647,259 | 4.7% | 12.1% |
| **5-gram** | Subword | 67,612 | 16.04 | 1,248,329 | 8.3% | 23.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `vun der` | 83,364 |
| 2 | `an der` | 70,319 |
| 3 | `um spaweck` | 36,982 |
| 4 | `vun de` | 26,136 |
| 5 | `ass eng` | 25,638 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `an der regioun` | 10,968 |
| 2 | `ass eng franséisch` | 8,527 |
| 3 | `franséisch administrativ andeelung` | 5,357 |
| 4 | `administrativ andeelung am` | 5,155 |
| 5 | `gemeng am departement` | 5,056 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `franséisch administrativ andeelung am` | 5,149 |
| 2 | `administrativ andeelung am arrondissement` | 4,760 |
| 3 | `ass eng franséisch gemeng` | 4,208 |
| 4 | `ëm wat geet et` | 4,198 |
| 5 | `wat geet et am` | 4,109 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `franséisch administrativ andeelung am arrondissement` | 4,759 |
| 2 | `ëm wat geet et am` | 4,109 |
| 3 | `wat geet et am film` | 4,060 |
| 4 | `ass eng franséisch gemeng am` | 3,394 |
| 5 | `eng franséisch gemeng am departement` | 3,212 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e r` | 2,283,425 |
| 2 | `e n` | 1,750,568 |
| 3 | `n _` | 1,684,884 |
| 4 | `_ d` | 1,610,037 |
| 5 | `e _` | 1,476,507 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e r _` | 951,492 |
| 2 | `_ d e` | 876,571 |
| 3 | `e n _` | 679,558 |
| 4 | `s c h` | 638,025 |
| 5 | `n _ d` | 455,328 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _ d e` | 312,530 |
| 2 | `d e r _` | 303,229 |
| 3 | `_ a n _` | 280,443 |
| 4 | `_ d e _` | 275,944 |
| 5 | `_ d e r` | 254,059 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e r _` | 250,063 |
| 2 | `_ v u n _` | 204,878 |
| 3 | `n _ d e r` | 163,335 |
| 4 | `_ v u m _` | 162,050 |
| 5 | `_ a n _ d` | 155,413 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 318
- **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 | 0.9491 | 1.931 | 7.90 | 521,387 | 5.1% |
| **1** | Subword | 0.9460 | 1.927 | 6.76 | 3,270 | 5.4% |
| **2** | Word | 0.3309 | 1.258 | 1.98 | 4,108,190 | 66.9% |
| **2** | Subword | 0.8550 | 1.809 | 5.87 | 22,062 | 14.5% |
| **3** | Word | 0.1377 | 1.100 | 1.27 | 8,097,151 | 86.2% |
| **3** | Subword | 0.8305 | 1.778 | 4.76 | 129,396 | 17.0% |
| **4** | Word | 0.0569 🏆 | 1.040 | 1.09 | 10,254,064 | 94.3% |
| **4** | Subword | 0.7479 | 1.679 | 3.58 | 615,656 | 25.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de la résistance boîte vun der haiteger perspektiv am juni huet zur trounfollgerin akzeptabel d shir...`
2. `an technik gebuer den oflaf vum walter hill haaptacteuren nathalie reuter lëtzebuergesch grammaire d...`
3. `der iau offiziell nom brittesche science 2 etapp 50 m den traité vu montpellier am arrondissement`

**Context Size 2:**

1. `vun der gemeng miersch e läit um zesammenfluss vun der zäit wou en zanterhier all kéier fréizäiteg`
2. `an der atmosphär ionosphär magnetosphär plasmasphär no physiko cheemesche prozesser ozonosphär respe...`
3. `um spaweck chris s 33 35 artikel aus der circonscriptioun vun de ponts et chaussées zu lëtzebuerg`

**Context Size 3:**

1. `an der regioun bretagne bei der kantonalreform vun gouf de kanton gegrënnt gemengen am kanton bellev...`
2. `ass eng franséisch harfspillerin mat néng joer hat an eng ofsécherungze vill e groussen deel vun de ...`
3. `franséisch administrativ andeelung am arrondissement thonon les bains ouest war bis mäerz eng fransé...`

**Context Size 4:**

1. `franséisch administrativ andeelung am arrondissement bayonne am arrondissement bayonne op der via po...`
2. `administrativ andeelung am arrondissement toulon am departement var an der regioun provence alpes cô...`
3. `ass eng franséisch gemeng an de vogesen an der regioun grand est d gemeng val de meuse ass duerch`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_den_(kitesinge_`
2. `enit_wäerengi_lë`
3. `nodun_1_che_hen:`

**Context Size 2:**

1. `errevo,_opgebsäit`
2. `en_ster_den._joen`
3. `n_ofeng_mist_um_(`

**Context Size 3:**

1. `er_war_bruce_filme`
2. `_de_mobizent_gi_ma`
3. `en_1_ster_-_repren`

**Context Size 4:**

1. `n_den_eng_belschaft`
2. `der_revolumbahnen_d`
3. `_an_der_a_pilger_im`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (615,656 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 | 248,214 |
| Total Tokens | 13,192,531 |
| Mean Frequency | 53.15 |
| Median Frequency | 4 |
| Frequency Std Dev | 1571.96 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 305,799 |
| 2 | an | 283,342 |
| 3 | der | 250,632 |
| 4 | d | 249,992 |
| 5 | vun | 205,518 |
| 6 | a | 182,029 |
| 7 | vum | 162,657 |
| 8 | den | 146,511 |
| 9 | am | 141,289 |
| 10 | ass | 127,097 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | enquêteprozedur | 2 |
| 2 | notifikatioun | 2 |
| 3 | jauferbësch | 2 |
| 4 | jauf | 2 |
| 5 | sabigotho | 2 |
| 6 | proprietärintern | 2 |
| 7 | lëtzebuergfir | 2 |
| 8 | multicentrisch | 2 |
| 9 | urbanem | 2 |
| 10 | neytiri | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0100 |
| R² (Goodness of Fit) | 0.999149 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 37.9% |
| Top 1,000 | 60.1% |
| Top 5,000 | 75.1% |
| Top 10,000 | 81.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9991 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 37.9% of corpus
- **Long Tail:** 238,214 words needed for remaining 18.5% 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 | 0.8333 🏆 | 0.3443 | N/A | N/A |
| **mono_64d** | 64 | 0.8177 | 0.2743 | N/A | N/A |
| **mono_128d** | 128 | 0.7923 | 0.2124 | N/A | N/A |
| **aligned_32d** | 32 | 0.8333 | 0.3472 | 0.1420 | 0.4680 |
| **aligned_64d** | 64 | 0.8177 | 0.2730 | 0.2800 | 0.6120 |
| **aligned_128d** | 128 | 0.7923 | 0.2086 | 0.3360 | 0.7540 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8333 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2766. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 33.6% 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 | **-0.481** | 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` | saviez, storeria, semoy |
| `-a` | autrichienne, antiker, augh |
| `-b` | baleareschen, bongaert, braunsberger |
| `-ma` | markéieren, maserati, marsas |
| `-m` | markéieren, methodologescher, montlauzun |
| `-p` | puren, premièren, prange |
| `-d` | diestro, dumcke, dinas |
| `-c` | chrétienne, cazilhac, carvifolia |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | markéieren, zommen, guzman |
| `-en` | markéieren, zommen, baleareschen |
| `-e` | chrétienne, hennie, dumcke |
| `-er` | methodologescher, antiker, gruppementer |
| `-r` | methodologescher, antiker, gruppementer |
| `-t` | bongaert, renfort, individualitéit |
| `-s` | fraissines, oenomaus, fourons |
| `-g` | verëffentlechung, udeng, combining |

### 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 |
|------|----------|------------------|----------|
| `chte` | 1.91x | 259 contexts | achte, echte, fechte |
| `tiou` | 2.50x | 52 contexts | actioun, natioun, optioun |
| `nner` | 1.82x | 209 contexts | inner, önner, anner |
| `ller` | 1.73x | 232 contexts | eller, aller, iller |
| `atio` | 2.10x | 88 contexts | natio, ratio, patio |
| `teur` | 2.17x | 71 contexts | teuro, moteur, steurs |
| `emen` | 2.10x | 82 contexts | jemen, gemen, semen |
| `erge` | 1.82x | 145 contexts | perge, uerge, verge |
| `cteu` | 2.83x | 22 contexts | acteur, vecteur, facteur |
| `nger` | 1.74x | 150 contexts | inger, anger, unger |
| `ioun` | 2.23x | 44 contexts | aioun, spioun, unioun |
| `regi` | 2.12x | 38 contexts | regis, regia, regie |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-n` | 115 words | schouluniformen, siphonen |
| `-s` | `-e` | 106 words | semide, schreckliche |
| `-s` | `-r` | 103 words | saulzoir, schmidhauser |
| `-a` | `-e` | 88 words | arbeitspapiere, aushale |
| `-s` | `-er` | 88 words | schmidhauser, stralungsdetekter |
| `-s` | `-en` | 82 words | schouluniformen, siphonen |
| `-b` | `-e` | 76 words | bewäertbare, breve |
| `-g` | `-n` | 73 words | guidesektioun, germaniséieren |
| `-p` | `-n` | 71 words | plädéieren, phalempin |
| `-c` | `-s` | 71 words | companions, crus |

### 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 |
|------|-----------------|------------|------|
| moschtgewiicht | **`moschtgewii-ch-t`** | 7.5 | `ch` |
| approcher | **`appro-ch-er`** | 7.5 | `ch` |
| sommernacht | **`sommerna-ch-t`** | 7.5 | `ch` |
| opgebauscht | **`opgebaus-ch-t`** | 7.5 | `ch` |
| haaptobjet | **`haaptobj-e-t`** | 7.5 | `e` |
| disquisitiones | **`disquisitio-n-es`** | 7.5 | `n` |
| iwwerierdesche | **`iwwerierdes-ch-e`** | 7.5 | `ch` |
| interprétations | **`interprétatio-n-s`** | 7.5 | `n` |
| bekanntlich | **`bekanntl-i-ch`** | 7.5 | `i` |
| schläicht | **`schläi-ch-t`** | 7.5 | `ch` |
| averstanen | **`aversta-n-en`** | 7.5 | `n` |
| gestatten | **`gestat-t-en`** | 7.5 | `t` |
| dokumentaresche | **`dokumentares-ch-e`** | 7.5 | `ch` |
| criticism | **`critici-s-m`** | 7.5 | `s` |
| concoules | **`concou-le-s`** | 7.5 | `le` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Luxembourgish 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 (4.80x) |
| N-gram | **2-gram** | Lowest perplexity (318) |
| Markov | **Context-4** | Highest predictability (94.3%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 11:34:33*