README.md

---
language: frp
language_name: Arpitan
language_family: romance_galloitalic
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-romance_galloitalic
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 4.432
  - name: best_isotropy
    type: isotropy
    value: 0.8533
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Arpitan** 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** | 3.752x | 3.76 | 0.1908% | 159,349 |
| **16k** | 4.028x | 4.03 | 0.2048% | 148,425 |
| **32k** | 4.260x | 4.27 | 0.2166% | 140,346 |
| **64k** | 4.432x 🏆 | 4.44 | 0.2254% | 134,893 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `David Charvet (Liyon, 15 de mê est un actor francês d'origina arpetana. Charvet,...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁david ▁char vet ▁( liyon , ▁ 1 5 ▁de ... (+18 more)` | 28 |
| 16k | `▁david ▁charvet ▁( liyon , ▁ 1 5 ▁de ▁mê ... (+15 more)` | 25 |
| 32k | `▁david ▁charvet ▁( liyon , ▁ 1 5 ▁de ▁mê ... (+15 more)` | 25 |
| 64k | `▁david ▁charvet ▁( liyon , ▁ 1 5 ▁de ▁mê ... (+15 more)` | 25 |

**Sample 2:** `Cort-Mayor, tot-pariér Cort-Màyœr (Croméyeui en vâldoten), est na comena de la V...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cort - mayor , ▁tot - pariér ▁cort - m ... (+28 more)` | 38 |
| 16k | `▁cort - mayor , ▁tot - pariér ▁cort - m ... (+27 more)` | 37 |
| 32k | `▁cort - mayor , ▁tot - pariér ▁cort - m ... (+26 more)` | 36 |
| 64k | `▁cort - mayor , ▁tot - pariér ▁cort - màyœr ... (+21 more)` | 31 |

**Sample 3:** `Antê est na comena de la Vâl d’Aoûta. de la Vâl d’Aoûta`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ant ê ▁est ▁na ▁comena ▁de ▁la ▁vâl ▁d ’ ... (+8 more)` | 18 |
| 16k | `▁ant ê ▁est ▁na ▁comena ▁de ▁la ▁vâl ▁d ’ ... (+8 more)` | 18 |
| 32k | `▁antê ▁est ▁na ▁comena ▁de ▁la ▁vâl ▁d ’ aoûta ... (+7 more)` | 17 |
| 64k | `▁antê ▁est ▁na ▁comena ▁de ▁la ▁vâl ▁d ’ aoûta ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.432x compression
- **Lowest UNK Rate:** 8k with 0.1908% 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 | 3,875 | 11.92 | 12,862 | 22.5% | 56.7% |
| **2-gram** | Subword | 300 🏆 | 8.23 | 2,633 | 63.9% | 99.1% |
| **3-gram** | Word | 7,576 | 12.89 | 21,319 | 15.1% | 45.6% |
| **3-gram** | Subword | 2,356 | 11.20 | 19,570 | 26.8% | 69.6% |
| **4-gram** | Word | 12,950 | 13.66 | 38,195 | 12.2% | 39.0% |
| **4-gram** | Subword | 10,867 | 13.41 | 86,875 | 14.5% | 41.7% |
| **5-gram** | Word | 10,775 | 13.40 | 31,168 | 12.8% | 41.5% |
| **5-gram** | Subword | 28,788 | 14.81 | 185,811 | 9.5% | 30.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la` | 7,927 |
| 2 | `de l` | 4,843 |
| 3 | `en francês` | 2,035 |
| 4 | `est un` | 1,537 |
| 5 | `est na` | 1,506 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `notes et rèferences` | 921 |
| 2 | `lims de defôr` | 887 |
| 3 | `et rèferences notes` | 838 |
| 4 | `que sè trôve` | 823 |
| 5 | `du calendriér grègorien` | 787 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `notes et rèferences notes` | 838 |
| 2 | `que sè trôve dens` | 676 |
| 3 | `sè trôve dens lo` | 616 |
| 4 | `règ ion ôvèrgne rôno` | 598 |
| 5 | `trôve dens lo dèpartament` | 594 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `que sè trôve dens lo` | 610 |
| 2 | `sè trôve dens lo dèpartament` | 594 |
| 3 | `règ ion ôvèrgne rôno ârpes` | 583 |
| 4 | `en règ ion ôvèrgne rôno` | 573 |
| 5 | `trôve dens lo dèpartament de` | 541 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d` | 93,461 |
| 2 | `e _` | 89,908 |
| 3 | `s _` | 81,969 |
| 4 | `a _` | 81,049 |
| 5 | `_ l` | 70,807 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 53,565 |
| 2 | `d e _` | 42,218 |
| 3 | `e s _` | 30,241 |
| 4 | `l a _` | 24,855 |
| 5 | `_ l a` | 20,309 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 40,630 |
| 2 | `_ l a _` | 18,775 |
| 3 | `d e _ l` | 16,081 |
| 4 | `_ e t _` | 16,050 |
| 5 | `_ d u _` | 12,274 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _ l` | 15,995 |
| 2 | `_ e s t _` | 8,935 |
| 3 | `e _ l a _` | 8,731 |
| 4 | `d e _ l a` | 7,987 |
| 5 | `a _ d e _` | 7,692 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 300
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.6833 | 1.606 | 3.88 | 60,657 | 31.7% |
| **1** | Subword | 1.0805 | 2.115 | 8.29 | 778 | 0.0% |
| **2** | Word | 0.2270 | 1.170 | 1.54 | 234,074 | 77.3% |
| **2** | Subword | 0.9698 | 1.959 | 5.76 | 6,449 | 3.0% |
| **3** | Word | 0.0984 | 1.071 | 1.18 | 358,473 | 90.2% |
| **3** | Subword | 0.8264 | 1.773 | 3.96 | 37,109 | 17.4% |
| **4** | Word | 0.0495 🏆 | 1.035 | 1.08 | 419,570 | 95.1% |
| **4** | Subword | 0.6064 | 1.522 | 2.56 | 146,964 | 39.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de la ples èpatâs dens lo seto de les alemagnes ôtriche contre pendent sa m m`
2. `la ferveur d or de l en règ ionalisto de l endrêt vocabulèro rèferences notes et`
3. `et dictionnaire français liyon nèssences giuseppe mariano egaña universidad de vôd dês lo seto patoi...`

**Context Size 2:**

1. `de la rèpublica francêsa entre lo v continu et le r roulâ at étâ remplaciê per le`
2. `de l alsace iwar werlen matthias grünert èd italica raetica gallica studia linguarum litterarum arti...`
3. `en francês est na comena francêsa et arpetana de banye èthendiu per piérro duplê lo jouventua calço`

**Context Size 3:**

1. `notes et rèferences notes vocabulèro rèferences de l en de l en de tant qu en môrts roxelane`
2. `et rèferences notes rèferences de la savouè francês de l isera les doux dèrriérs kilomètros ont uvèr...`
3. `lims de defôr âjo de france`

**Context Size 4:**

1. `notes et rèferences notes rèferences de la savouè d avâl arpetan de sports d hivèrn du musê dôfenen ...`
2. `que sè trôve dens lo dèpartament de la lêre en règ ion ôvèrgne rôno ârpes los habitents du velâjo`
3. `sè trôve dens lo dèpartament de la lêre en règ ion borgogne franche comtât los habitents du velâjo s...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_dir_dust_di,_t,`
2. `et_ubolesatre_p.`
3. `at._élyâyarçanâl`

**Context Size 2:**

1. `_des_de_de_39-64_`
2. `e_nonqu’es_procal`
3. `s_véls_devartiérs`

**Context Size 3:**

1. `_de_du_chârmetllar`
2. `de_loirenciacionâr`
3. `es_ont_de_la_vencr`

**Context Size 4:**

1. `_de_la_barmacopo_de`
2. `_la_vela_des_vocabu`
3. `de_la_bourk_»_adv_d`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (146,964 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 | 25,646 |
| Total Tokens | 594,200 |
| Mean Frequency | 23.17 |
| Median Frequency | 3 |
| Frequency Std Dev | 373.02 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 41,301 |
| 2 | la | 20,109 |
| 3 | et | 16,321 |
| 4 | en | 13,958 |
| 5 | lo | 13,046 |
| 6 | du | 12,396 |
| 7 | l | 11,637 |
| 8 | est | 9,993 |
| 9 | d | 9,696 |
| 10 | a | 6,854 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | gewesen | 2 |
| 2 | müh | 2 |
| 3 | professors | 2 |
| 4 | seiant | 2 |
| 5 | hoch | 2 |
| 6 | sich | 2 |
| 7 | too | 2 |
| 8 | pereat | 2 |
| 9 | pèreisset | 2 |
| 10 | rêpond | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1126 |
| R² (Goodness of Fit) | 0.996613 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 48.2% |
| Top 1,000 | 74.5% |
| Top 5,000 | 88.1% |
| Top 10,000 | 93.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9966 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 48.2% of corpus
- **Long Tail:** 15,646 words needed for remaining 6.7% 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 | 0.8533 | 0.3620 | N/A | N/A |
| **mono_64d** | 64 | 0.7080 | 0.3125 | N/A | N/A |
| **mono_128d** | 128 | 0.2790 | 0.2979 | N/A | N/A |
| **aligned_32d** | 32 | 0.8533 🏆 | 0.3573 | 0.0340 | 0.2060 |
| **aligned_64d** | 64 | 0.7080 | 0.3022 | 0.0800 | 0.2980 |
| **aligned_128d** | 128 | 0.2790 | 0.2962 | 0.1260 | 0.4020 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8533 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3213. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 12.6% 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 | **0.381** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-co` | cornèlye, columbân, compto |
| `-ch` | chouèséssont, chesalles, chasper |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | besièrs, mans, chesalles |
| `-es` | chesalles, romanes, sassenajouèses |
| `-on` | frutificacion, enstitucion, différenciation |
| `-nt` | chouèséssont, variant, fassévont |
| `-ns` | mans, dragons, pontesans |

### 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 |
|------|----------|------------------|----------|
| `ranc` | 1.61x | 40 contexts | franc, rancé, drance |
| `cion` | 1.68x | 33 contexts | accion, nocion, nacion |
| `etan` | 2.23x | 12 contexts | gaetano, arpetan, erpetan |
| `anta` | 1.82x | 22 contexts | santa, antan, tanta |
| `peta` | 2.23x | 11 contexts | petar, arpetan, erpetan |
| `acio` | 1.82x | 20 contexts | nacion, lacion, stacion |
| `avou` | 1.81x | 17 contexts | avoué, avouë, avouì |
| `uiss` | 2.18x | 10 contexts | buisse, suisso, suisse |
| `isto` | 1.53x | 26 contexts | visto, istos, cristo |
| `iant` | 1.75x | 16 contexts | diant, aviant, étiant |
| `rpet` | 2.23x | 8 contexts | arpetan, arpette, erpetan |
| `omen` | 1.56x | 19 contexts | women, romen, comenê |

### 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 |
|--------|--------|-----------|----------|
| `-co` | `-s` | 69 words | concèpcions, conches |
| `-ch` | `-s` | 40 words | chexbres, chevâls |
| `-co` | `-es` | 26 words | conches, comenes |
| `-co` | `-on` | 22 words | comparèson, coalicion |
| `-co` | `-nt` | 19 words | confondont, corent |
| `-ch` | `-es` | 18 words | chexbres, chasèles |
| `-co` | `-ns` | 13 words | concèpcions, cotens |
| `-ch` | `-on` | 10 words | chambllon, chillon |
| `-ch` | `-nt` | 5 words | chavonont, chantont |
| `-ch` | `-ns` | 4 words | chens, chaneins |

### 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 |
|------|-----------------|------------|------|
| trentines | **`trentin-es`** | 4.5 | `trentin` |
| neuchâteloises | **`neuchâtelois-es`** | 4.5 | `neuchâtelois` |
| reprèsentent | **`reprèsente-nt`** | 4.5 | `reprèsente` |
| vôdouèses | **`vôdouès-es`** | 4.5 | `vôdouès` |
| dèssèrtes | **`dèssèrt-es`** | 4.5 | `dèssèrt` |
| grenoblouèses | **`grenoblouès-es`** | 4.5 | `grenoblouès` |
| véselyinouèses | **`véselyinouès-es`** | 4.5 | `véselyinouès` |
| appellent | **`appelle-nt`** | 4.5 | `appelle` |
| charentes | **`ch-arent-es`** | 3.0 | `arent` |
| conclusion | **`co-nclusi-on`** | 3.0 | `nclusi` |
| comparèsons | **`co-mparèso-ns`** | 3.0 | `mparèso` |
| siuventes | **`siuve-nt-es`** | 3.0 | `siuve` |
| compèticions | **`co-mpèticio-ns`** | 3.0 | `mpèticio` |
| châtenêècrivont | **`ch-âtenêècrivo-nt`** | 3.0 | `âtenêècrivo` |
| communities | **`co-mmuniti-es`** | 3.0 | `mmuniti` |

### 6.6 Linguistic Interpretation

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

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.43x) |
| N-gram | **2-gram** | Lowest perplexity (300) |
| Markov | **Context-4** | Highest predictability (95.1%) |
| 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: 2026-01-04 14:50:14*