README.md

---
language: lfn
language_name: Lingua Franca Nova
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: 4.137
  - name: best_isotropy
    type: isotropy
    value: 0.8761
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Lingua Franca Nova - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lingua Franca Nova** 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** | 3.632x | 3.63 | 0.1705% | 715,630 |
| **16k** | 3.867x | 3.87 | 0.1815% | 672,083 |
| **32k** | 4.035x | 4.04 | 0.1894% | 644,133 |
| **64k** | 4.137x 🏆 | 4.14 | 0.1942% | 628,275 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `+Indiana 125px 125px 250px Indiana es un stato de la Statos Unida de America. La...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁+ in dian a ▁ 1 2 5 px ▁ ... (+36 more)` | 46 |
| 16k | `▁+ indian a ▁ 1 2 5 px ▁ 1 ... (+35 more)` | 45 |
| 32k | `▁+ indian a ▁ 1 2 5 px ▁ 1 ... (+33 more)` | 43 |
| 64k | `▁+ indian a ▁ 1 2 5 px ▁ 1 ... (+32 more)` | 42 |

**Sample 2:** `La du Libros de Cronicas es libros de la Biblia cual parteni a la Atesta Vea. de...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁la ▁du ▁libros ▁de ▁cron icas ▁es ▁libros ▁de ▁la ... (+11 more)` | 21 |
| 16k | `▁la ▁du ▁libros ▁de ▁cron icas ▁es ▁libros ▁de ▁la ... (+11 more)` | 21 |
| 32k | `▁la ▁du ▁libros ▁de ▁cronicas ▁es ▁libros ▁de ▁la ▁biblia ... (+10 more)` | 20 |
| 64k | `▁la ▁du ▁libros ▁de ▁cronicas ▁es ▁libros ▁de ▁la ▁biblia ... (+10 more)` | 20 |

**Sample 3:** `Ester es un libro de la Biblia cual parteni a la Biblia Ivri. de la Biblia`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ester ▁es ▁un ▁libro ▁de ▁la ▁biblia ▁cual ▁parteni ▁a ... (+7 more)` | 17 |
| 16k | `▁ester ▁es ▁un ▁libro ▁de ▁la ▁biblia ▁cual ▁parteni ▁a ... (+7 more)` | 17 |
| 32k | `▁ester ▁es ▁un ▁libro ▁de ▁la ▁biblia ▁cual ▁parteni ▁a ... (+7 more)` | 17 |
| 64k | `▁ester ▁es ▁un ▁libro ▁de ▁la ▁biblia ▁cual ▁parteni ▁a ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.137x compression
- **Lowest UNK Rate:** 8k with 0.1705% 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 | 9,018 | 13.14 | 39,100 | 20.8% | 41.9% |
| **2-gram** | Subword | 184 🏆 | 7.52 | 4,504 | 78.1% | 99.2% |
| **3-gram** | Word | 28,531 | 14.80 | 59,892 | 7.7% | 24.0% |
| **3-gram** | Subword | 1,347 | 10.40 | 26,118 | 36.1% | 82.0% |
| **4-gram** | Word | 52,858 | 15.69 | 80,781 | 4.4% | 15.1% |
| **4-gram** | Subword | 6,904 | 12.75 | 115,589 | 18.7% | 50.0% |
| **5-gram** | Word | 32,358 | 14.98 | 41,656 | 4.7% | 15.2% |
| **5-gram** | Subword | 23,385 | 14.51 | 259,986 | 11.5% | 32.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la` | 28,704 |
| 2 | `en la` | 14,199 |
| 3 | `ia es` | 14,034 |
| 4 | `a la` | 7,928 |
| 5 | `es un` | 7,174 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ia es un` | 1,623 |
| 2 | `ia es la` | 1,386 |
| 3 | `la plu de` | 1,047 |
| 4 | `un de la` | 1,033 |
| 5 | `lo ia es` | 1,002 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `es un de la` | 454 |
| 2 | `la fini de la` | 361 |
| 3 | `la comensa de la` | 321 |
| 4 | `un parte de la` | 286 |
| 5 | `de la statos unida` | 264 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `la statos unida de america` | 238 |
| 2 | `de la statos unida de` | 218 |
| 3 | `a la fini de la` | 136 |
| 4 | `es un parte de la` | 123 |
| 5 | `la cuantia de abitores en` | 122 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 471,297 |
| 2 | `e _` | 281,415 |
| 3 | `_ e` | 201,402 |
| 4 | `l a` | 187,457 |
| 5 | `_ l` | 186,995 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a _` | 151,686 |
| 2 | `_ l a` | 143,115 |
| 3 | `_ d e` | 121,132 |
| 4 | `d e _` | 115,749 |
| 5 | `e s _` | 89,194 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l a _` | 137,110 |
| 2 | `_ d e _` | 99,945 |
| 3 | `_ e s _` | 49,053 |
| 4 | `e _ l a` | 46,379 |
| 5 | `a _ d e` | 42,477 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _ l a _` | 45,228 |
| 2 | `a _ d e _` | 34,291 |
| 3 | `_ d e _ l` | 32,166 |
| 4 | `d e _ l a` | 30,190 |
| 5 | `a _ l a _` | 21,486 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 184
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~33% 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 | 0.8109 | 1.754 | 5.92 | 93,298 | 18.9% |
| **1** | Subword | 0.7726 | 1.708 | 5.36 | 3,230 | 22.7% |
| **2** | Word | 0.3547 | 1.279 | 2.00 | 550,845 | 64.5% |
| **2** | Subword | 0.7165 | 1.643 | 4.03 | 17,307 | 28.3% |
| **3** | Word | 0.1481 | 1.108 | 1.29 | 1,098,963 | 85.2% |
| **3** | Subword | 0.6583 | 1.578 | 3.30 | 69,645 | 34.2% |
| **4** | Word | 0.0537 🏆 | 1.038 | 1.08 | 1,408,038 | 94.6% |
| **4** | Subword | 0.5740 | 1.489 | 2.54 | 229,441 | 42.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `la corpo cual abitua par la cursos ombrin l ma nun la popla ante insamel den`
2. `de la barcon skíðblaðnir cual dona o 53 5 dirk baltzly stoic joy fi at osteraic`
3. `es disputada on ia es debatada en problemes jeneral a la reali reformas de new hampshire`

**Context Size 2:**

1. `de la zoroastristes balotxi talix curdi sude ueste la parolas franses azur la italian borghetto site...`
2. `en la norde este de gao este de portugal a sveria sude cual es reveninte a un`
3. `ia es ancora conservada en la periodo neolitica entre sirca 600 resta la sola planeta estra la`

**Context Size 3:**

1. `ia es un esperta ivri e noam ia deveni tan streta ce lo ia fende a la impero`
2. `ia es la causa de ordina e ricia cual benefia multe la sosia e la bonstate de la`
3. `la plu de la mundo antica ante ce lo ia causa alga ajuntas e cambias de curso produida`

**Context Size 4:**

1. `es un de la cuatro fundores lejendal en sua istoria ciiv on de la sites la plu grande en`
2. `la fini de la autonomia political elinica periodo roman la penisola elinica ia es perdeda cuando la ...`
3. `la comensa de la frase ma car la ojetos es clar marcada la ordina de parolas es fisada frase`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_e_en_ema_5_en_₾`
2. `adomcla_mefinte_`
3. `entes_e_der_di_c`

**Context Size 2:**

1. `a_letalosabiafist`
2. `e_ias_con_arla_se`
3. `_eten_ur,_mun_bed`

**Context Size 3:**

1. `la_clangolfo"_(mun`
2. `_la_a_poplandrogra`
3. `_de_colui_la_la_pa`

**Context Size 4:**

1. `_la_plu_coresto_des`
2. `_de_ajunta_si_la_di`
3. `_es_enviada_en_espr`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (229,441 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 | 38,182 |
| Total Tokens | 1,563,914 |
| Mean Frequency | 40.96 |
| Median Frequency | 4 |
| Frequency Std Dev | 1058.15 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | la | 140,783 |
| 2 | de | 100,756 |
| 3 | es | 49,802 |
| 4 | e | 48,843 |
| 5 | en | 41,997 |
| 6 | ia | 41,968 |
| 7 | un | 39,220 |
| 8 | a | 24,501 |
| 9 | per | 16,086 |
| 10 | sua | 12,580 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | rodrik | 2 |
| 2 | avrilo | 2 |
| 3 | filiovscaia | 2 |
| 4 | roerichisme | 2 |
| 5 | mgb | 2 |
| 6 | surjeria | 2 |
| 7 | carpentier | 2 |
| 8 | partizanscaia | 2 |
| 9 | roericism | 2 |
| 10 | roeriches | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1594 |
| R² (Goodness of Fit) | 0.991951 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 52.0% |
| Top 1,000 | 75.1% |
| Top 5,000 | 89.4% |
| Top 10,000 | 93.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9920 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 52.0% of corpus
- **Long Tail:** 28,182 words needed for remaining 6.1% 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 | 0.8761 🏆 | 0.3453 | N/A | N/A |
| **mono_64d** | 64 | 0.8354 | 0.2522 | N/A | N/A |
| **mono_128d** | 128 | 0.5702 | 0.2254 | N/A | N/A |
| **aligned_32d** | 32 | 0.8761 | 0.3560 | 0.1040 | 0.3520 |
| **aligned_64d** | 64 | 0.8354 | 0.2596 | 0.1160 | 0.3960 |
| **aligned_128d** | 128 | 0.5702 | 0.2233 | 0.1680 | 0.4720 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8761 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2770. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 16.8% 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 | **-0.537** | 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` | semanal, stelo, style |
| `-a` | abri, abramica, antioc |
| `-c` | confuzi, coso, compata |
| `-t` | twain, trovas, termos |
| `-p` | planos, paχa, pa |
| `-m` | monpa, multifamilial, minerva |
| `-b` | borx, beratón, boit |
| `-ma` | majo, malvole, malva |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | wierzbicka, recambia, abramica |
| `-s` | ferus, planos, trovas |
| `-e` | naturalisme, immediate, fase |
| `-es` | vestes, urales, flexes |
| `-te` | immediate, esplotante, avente |
| `-n` | twain, beratón, beeston |
| `-o` | valonsadero, stelo, niso |
| `-as` | trovas, paias, rebelas |

### 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 |
|------|----------|------------------|----------|
| `ores` | 1.99x | 75 contexts | mores, sores, tores |
| `nter` | 1.83x | 52 contexts | inter, unter, hunter |
| `tica` | 1.75x | 62 contexts | otica, atica, etica |
| `tada` | 1.87x | 47 contexts | mutada, xutada, ditada |
| `ende` | 1.63x | 71 contexts | fende, hende, sende |
| `inte` | 1.69x | 56 contexts | intel, inter, intera |
| `ensa` | 1.82x | 41 contexts | pensa, sensa, tensa |
| `stra` | 1.65x | 55 contexts | ostra, estra, lastra |
| `sada` | 1.75x | 35 contexts | sadat, usada, fusada |
| `ngua` | 2.03x | 20 contexts | lingua, língua, sangua |
| `scri` | 2.03x | 20 contexts | script, scrima, scrive |
| `ingu` | 1.78x | 29 contexts | lingu, ingux, inguin |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-c` | `-s` | 154 words | crinoides, cirgizes |
| `-c` | `-a` | 150 words | califia, cësa |
| `-a` | `-s` | 122 words | aspiradas, ayolas |
| `-p` | `-a` | 119 words | psicica, plosiva |
| `-a` | `-a` | 113 words | atharvaveda, asterida |
| `-s` | `-s` | 111 words | stranjeres, senesentes |
| `-p` | `-s` | 111 words | preparas, preocupas |
| `-s` | `-a` | 96 words | segregada, schema |
| `-m` | `-s` | 90 words | medicas, molines |
| `-p` | `-e` | 84 words | pierce, puede |

### 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 |
|------|-----------------|------------|------|
| distraente | **`distrae-n-te`** | 7.5 | `n` |
| organizante | **`organiz-an-te`** | 7.5 | `an` |
| evidently | **`evident-l-y`** | 7.5 | `l` |
| nonreconoseda | **`no-n-reconoseda`** | 7.5 | `reconoseda` |
| sustansia | **`sustan-s-ia`** | 7.5 | `s` |
| sujesteda | **`sujes-te-da`** | 7.5 | `te` |
| premuslim | **`p-re-muslim`** | 7.5 | `muslim` |
| filiovscaia | **`filiovs-ca-ia`** | 7.5 | `ca` |
| interesante | **`interes-an-te`** | 7.5 | `an` |
| permeante | **`perme-an-te`** | 7.5 | `an` |
| partianes | **`parti-an-es`** | 7.5 | `an` |
| motorwagen | **`motorwag-e-n`** | 7.5 | `e` |
| indígenas | **`indíge-n-as`** | 7.5 | `n` |
| colasante | **`colas-an-te`** | 7.5 | `an` |
| romanianes | **`romani-an-es`** | 7.5 | `an` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lingua Franca Nova 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 (4.14x) |
| N-gram | **2-gram** | Lowest perplexity (184) |
| Markov | **Context-4** | Highest predictability (94.6%) |
| 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 10:36:40*