README.md

---
language: vo
language_name: Volapük
language_family: constructed_auxlang
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-constructed_auxlang
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: 3.916
  - name: best_isotropy
    type: isotropy
    value: 0.7749
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Volapük** 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** | 3.197x | 3.20 | 0.5032% | 180,830 |
| **16k** | 3.471x | 3.48 | 0.5464% | 166,556 |
| **32k** | 3.716x | 3.72 | 0.5850% | 155,556 |
| **64k** | 3.916x 🏆 | 3.92 | 0.6164% | 147,631 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Hjo (Svedänapük: ) binon zifil in Götaläniän Vesüdik. Hjo labon belödanis 6 203 ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁h jo ▁( svedänapük : ▁) ▁binon ▁zifil ▁in ▁göt ... (+16 more)` | 26 |
| 16k | `▁h jo ▁( svedänapük : ▁) ▁binon ▁zifil ▁in ▁götaläniän ... (+14 more)` | 24 |
| 32k | `▁h jo ▁( svedänapük : ▁) ▁binon ▁zifil ▁in ▁götaläniän ... (+14 more)` | 24 |
| 64k | `▁hjo ▁( svedänapük : ▁) ▁binon ▁zifil ▁in ▁götaläniän ▁vesüdik ... (+12 more)` | 22 |

**Sample 2:** `Hiel Ishmael Larry "Ish" Smith yulul 5, Charlotte) binom bäsetaglöpädan Lamerikä...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁hiel ▁is h ma el ▁larry ▁" ish " ▁smith ... (+12 more)` | 22 |
| 16k | `▁hiel ▁is h ma el ▁larry ▁" ish " ▁smith ... (+12 more)` | 22 |
| 32k | `▁hiel ▁ish ma el ▁larry ▁" ish " ▁smith ▁yulul ... (+11 more)` | 21 |
| 64k | `▁hiel ▁ish ma el ▁larry ▁" ish " ▁smith ▁yulul ... (+11 more)` | 21 |

**Sample 3:** `Dabinons: Włodzimierz Nowak (* hidramatan Polänik. Włodzimierz Nowak (* higasedi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁dabinons : ▁włodzimierz ▁nowak ▁(* ▁hidramatan ▁polänik . ▁włodzimierz ▁nowak ... (+7 more)` | 17 |
| 16k | `▁dabinons : ▁włodzimierz ▁nowak ▁(* ▁hidramatan ▁polänik . ▁włodzimierz ▁nowak ... (+6 more)` | 16 |
| 32k | `▁dabinons : ▁włodzimierz ▁nowak ▁(* ▁hidramatan ▁polänik . ▁włodzimierz ▁nowak ... (+6 more)` | 16 |
| 64k | `▁dabinons : ▁włodzimierz ▁nowak ▁(* ▁hidramatan ▁polänik . ▁włodzimierz ▁nowak ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 64k achieves 3.916x compression
- **Lowest UNK Rate:** 8k with 0.5032% 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 | 3,125 | 11.61 | 37,618 | 29.8% | 66.2% |
| **2-gram** | Subword | 347 🏆 | 8.44 | 4,542 | 59.6% | 99.0% |
| **3-gram** | Word | 7,395 | 12.85 | 80,785 | 22.5% | 54.1% |
| **3-gram** | Subword | 2,243 | 11.13 | 32,775 | 27.3% | 72.0% |
| **4-gram** | Word | 16,716 | 14.03 | 164,670 | 20.7% | 43.5% |
| **4-gram** | Subword | 7,575 | 12.89 | 160,036 | 18.5% | 53.4% |
| **5-gram** | Word | 20,422 | 14.32 | 152,322 | 20.8% | 39.9% |
| **5-gram** | Subword | 15,916 | 13.96 | 420,224 | 14.7% | 46.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `zif in` | 23,665 |
| 2 | `yüms plödik` | 20,232 |
| 3 | `pö el` | 19,080 |
| 4 | `in linglänapük` | 18,675 |
| 5 | `äbinon mö` | 17,793 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `binon zif in` | 14,995 |
| 2 | `n e lunetü` | 11,419 |
| 3 | `65 u plu` | 10,594 |
| 4 | `u plu 65` | 10,594 |
| 5 | `äbinon mö us` | 10,519 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `65 u plu 65` | 10,594 |
| 2 | `yüms plödik pö el` | 9,488 |
| 3 | `18 u läs 18` | 7,047 |
| 4 | `bäldotü lifayels 18 u` | 7,044 |
| 5 | `in linglänapük pö el` | 6,055 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pö el imdb in linglänapük` | 3,910 |
| 2 | `lödanef timü pöpinumam yela mens` | 3,571 |
| 3 | `ma el u s census` | 3,565 |
| 4 | `el u s census bureau` | 3,565 |
| 5 | `s census bureau pöpinumamabür lamerikänik` | 3,565 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 464,689 |
| 2 | `i n` | 404,578 |
| 3 | `s _` | 337,545 |
| 4 | `_ l` | 283,077 |
| 5 | `a n` | 277,466 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i n _` | 179,997 |
| 2 | `_ i n` | 147,153 |
| 3 | `b i n` | 130,072 |
| 4 | `i n o` | 118,929 |
| 5 | `n s _` | 112,426 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ i n _` | 143,998 |
| 2 | `b i n o` | 114,754 |
| 3 | `ä n i k` | 86,347 |
| 4 | `i n o n` | 80,373 |
| 5 | `ä b i n` | 61,595 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `b i n o n` | 80,174 |
| 2 | `_ ä b i n` | 61,576 |
| 3 | `i n o n _` | 55,167 |
| 4 | `ä b i n o` | 50,901 |
| 5 | `_ b i n o` | 46,130 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 347
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~46% 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 | 0.8517 | 1.805 | 4.90 | 117,661 | 14.8% |
| **1** | Subword | 0.8843 | 1.846 | 6.38 | 1,924 | 11.6% |
| **2** | Word | 0.2726 | 1.208 | 1.74 | 575,135 | 72.7% |
| **2** | Subword | 0.8560 | 1.810 | 5.21 | 12,269 | 14.4% |
| **3** | Word | 0.1218 | 1.088 | 1.32 | 997,030 | 87.8% |
| **3** | Subword | 0.7807 | 1.718 | 4.00 | 63,875 | 21.9% |
| **4** | Word | 0.0717 🏆 | 1.051 | 1.19 | 1,309,197 | 92.8% |
| **4** | Subword | 0.6693 | 1.590 | 2.90 | 255,568 | 33.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `in tallinn äbinom spotavabistiran suomiyänik yüms plödik pö el biographical directory of canada in d...`
2. `e blägans 27 4 s konlets far out life a b dönu päpübon ün as wally`
3. `ün ün el firstcycling in vesüda siyop fed ela são paulo in komot berkshire in deutänapük`

**Context Size 2:**

1. `zif in tat north carolina binof kanitan lindäna seänuänik pm ün zäladels 2`
2. `yüms plödik calan resodatoped szalánta google maps in macarän sürfat ela simaxis binon mö 19 89 km`
3. `pö el internet broadway database in linglänapük pö el imdb in linglänapük pö el tnb in rumänapük`

**Context Size 3:**

1. `binon zif in komot scotts bluff in tat nebraska in lamerikän nüns taledavik riverside topon videtü 3...`
2. `n e lunetü 9 43 l sürfat ela terzigno binon mö 23 18 km loria labon belödanis 8`
3. `65 u plu 65 ädabinons zänedo pösods 2 29 a lomanef e pösods 2 95 a famül demü`

**Context Size 4:**

1. `65 u plu 65 ädabinons zänedo pösods 2 87 a famül demü bäldot 19 2 lödanas ela weirton älabons`
2. `yüms plödik pö el olympedia in linglänapük pö el filmportal de in deutänapük ün deutänik deutänik de...`
3. `18 u läs 18 in lödöp älödölis 71 3 äbinons matans äkobolödöl 8 7 pädugons fa vom nen himatan`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_l_ülu_ü_ik,_yen`
2. `nonamü_erarnob:_`
3. `a_he_läleauls_0,`

**Context Size 2:**

1. `n_fik_hiel_44,_in`
2. `in_denbureizeb_sü`
3. `s_äsoetü_18_eatan`

**Context Size 3:**

1. `in_labons_talevila`
2. `_in_lega._de_8,1_k`
3. `binom_el_komondöta`

**Context Size 4:**

1. `_in_grand_(pemotöl_`
2. `binon_valmil_jöltum`
3. `inons_fa_rosaurus_j`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (255,568 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 | 61,202 |
| Total Tokens | 3,072,694 |
| Mean Frequency | 50.21 |
| Median Frequency | 4 |
| Frequency Std Dev | 1018.66 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | in | 173,526 |
| 2 | e | 60,678 |
| 3 | ün | 55,000 |
| 4 | mö | 43,386 |
| 5 | hiel | 37,203 |
| 6 | binon | 36,034 |
| 7 | 18 | 33,056 |
| 8 | tü | 32,923 |
| 9 | a | 28,195 |
| 10 | km | 27,461 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | birenbaum | 2 |
| 2 | pringalle | 2 |
| 3 | séranvillers | 2 |
| 4 | walford | 2 |
| 5 | gotszalk | 2 |
| 6 | halder | 2 |
| 7 | khetib | 2 |
| 8 | allroggen | 2 |
| 9 | cogeval | 2 |
| 10 | penfentenyo | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2808 |
| R² (Goodness of Fit) | 0.989525 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 53.4% |
| Top 1,000 | 83.1% |
| Top 5,000 | 91.0% |
| Top 10,000 | 93.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9895 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 53.4% of corpus
- **Long Tail:** 51,202 words needed for remaining 6.4% 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 | 0.7749 | 0.3465 | N/A | N/A |
| **mono_64d** | 64 | 0.6105 | 0.3114 | N/A | N/A |
| **mono_128d** | 128 | 0.2495 | 0.2943 | N/A | N/A |
| **aligned_32d** | 32 | 0.7749 🏆 | 0.3426 | 0.0780 | 0.3540 |
| **aligned_64d** | 64 | 0.6105 | 0.3007 | 0.1300 | 0.4620 |
| **aligned_128d** | 128 | 0.2495 | 0.2972 | 0.1540 | 0.5380 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7749 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3154. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 15.4% 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 | **-0.132** | 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` | schiertz, solaize, sandwich |
| `-b` | büchern, bottrop, buttigliera |
| `-p` | plunumi, przeworsk, puiseaux |
| `-a` | arsenic, antunes, anggun |
| `-m` | matri, mira, mergentheim |
| `-l` | logoti, laaland, lapa |
| `-ma` | matri, mancha, maierato |
| `-k` | kalka, kods, kupcewicz |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | büchern, anggun, ayşen |
| `-s` | előszállás, dykes, wars |
| `-a` | kalka, mira, izabella |
| `-e` | herserange, jeanette, ercole |
| `-o` | maierato, ngo, franceinfo |
| `-k` | frikopapük, romakatulik, przeworsk |
| `-i` | matri, romagnosi, logoti |
| `-r` | ever, singulier, scheler |

### 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 |
|------|----------|------------------|----------|
| `apük` | 2.09x | 37 contexts | tatapük, völapük, pöpapük |
| `ödik` | 2.25x | 27 contexts | vödik, pödik, mödik |
| `edik` | 1.91x | 39 contexts | gedik, tedik, fedik |
| `änik` | 1.94x | 30 contexts | länik, dänik, zänik |
| `dons` | 1.98x | 22 contexts | lödons, vedons, fidons |
| `nons` | 2.03x | 20 contexts | binons, kanons, jinons |
| `inon` | 1.71x | 29 contexts | ninon, vinon, binon |
| `dabi` | 1.74x | 27 contexts | dabin, dabija, dabini |
| `abin` | 1.59x | 32 contexts | sabin, dabin, fabin |
| `ösod` | 2.08x | 10 contexts | pösod, pösoda, pösodi |
| `pöso` | 2.08x | 9 contexts | pösod, pösoda, pösodi |
| `doti` | 1.89x | 10 contexts | dotis, dotik, mödoti |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-s` | 82 words | páginas, petradutöls |
| `-c` | `-o` | 70 words | comelico, carpineto |
| `-s` | `-n` | 70 words | saujon, sigurbjörnsson |
| `-c` | `-a` | 66 words | chea, calera |
| `-s` | `-s` | 65 words | seichamps, suemodas |
| `-m` | `-s` | 62 words | mouchamps, medeiros |
| `-c` | `-s` | 60 words | coulaines, caparrós |
| `-s` | `-a` | 59 words | shea, santana |
| `-m` | `-a` | 57 words | meda, madariaga |
| `-p` | `-n` | 57 words | poldan, petershagen |

### 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 |
|------|-----------------|------------|------|
| woodville | **`woodvi-l-le`** | 7.5 | `l` |
| childrens | **`child-re-ns`** | 7.5 | `re` |
| coleridge | **`co-le-ridge`** | 7.5 | `ridge` |
| vergessen | **`verges-s-en`** | 7.5 | `s` |
| gradignan | **`gradig-n-an`** | 7.5 | `n` |
| knesselare | **`knessel-a-re`** | 7.5 | `a` |
| jiufotang | **`jiufot-a-ng`** | 7.5 | `a` |
| latlanteana | **`latlante-a-na`** | 7.5 | `a` |
| baragiano | **`baragi-a-no`** | 7.5 | `a` |
| fotografot | **`fotograf-o-t`** | 7.5 | `o` |
| michalska | **`michal-s-ka`** | 7.5 | `s` |
| fransänans | **`fransän-an-s`** | 6.0 | `fransän` |
| padadilädon | **`pa-dadiläd-on`** | 6.0 | `dadiläd` |
| gibraltarik | **`gibraltar-ik`** | 4.5 | `gibraltar` |
| pedakipöls | **`pedakipöl-s`** | 4.5 | `pedakipöl` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Volapük 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 (3.92x) |
| N-gram | **2-gram** | Lowest perplexity (347) |
| Markov | **Context-4** | Highest predictability (92.8%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-11 03:34:47*