---
language: co
language_name: Corsican
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: 4.216
  - name: best_isotropy
    type: isotropy
    value: 0.8262
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Corsican** 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** | 3.429x | 3.43 | 0.0264% | 363,461 |
| **16k** | 3.706x | 3.71 | 0.0285% | 336,335 |
| **32k** | 3.986x | 3.99 | 0.0307% | 312,675 |
| **64k** | 4.216x 🏆 | 4.22 | 0.0325% | 295,625 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ophrys splendida hè una pianta chì face partita di a famiglia di l'orchidaceae. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ophrys ▁sp len di da ▁hè ▁una ▁pianta ▁chì ▁face ... (+13 more)` | 23 |
| 16k | `▁ophrys ▁splen di da ▁hè ▁una ▁pianta ▁chì ▁face ▁partita ... (+12 more)` | 22 |
| 32k | `▁ophrys ▁splendi da ▁hè ▁una ▁pianta ▁chì ▁face ▁partita ▁di ... (+11 more)` | 21 |
| 64k | `▁ophrys ▁splendida ▁hè ▁una ▁pianta ▁chì ▁face ▁partita ▁di ▁a ... (+10 more)` | 20 |

**Sample 2:** `U Mucale hè una cumuna di u dipartimentu di a Corsica suprana. Geografia Storia ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁u ▁mu cale ▁hè ▁una ▁cumuna ▁di ▁u ▁dipartimentu ▁di ... (+14 more)` | 24 |
| 16k | `▁u ▁mu cale ▁hè ▁una ▁cumuna ▁di ▁u ▁dipartimentu ▁di ... (+14 more)` | 24 |
| 32k | `▁u ▁mucale ▁hè ▁una ▁cumuna ▁di ▁u ▁dipartimentu ▁di ▁a ... (+13 more)` | 23 |
| 64k | `▁u ▁mucale ▁hè ▁una ▁cumuna ▁di ▁u ▁dipartimentu ▁di ▁a ... (+13 more)` | 23 |

**Sample 3:** `L'Emilia è Romagna hè una regione taliana. taliana`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁l ' e mi lia ▁è ▁roma gna ▁hè ▁una ... (+4 more)` | 14 |
| 16k | `▁l ' emi lia ▁è ▁roma gna ▁hè ▁una ▁regione ... (+3 more)` | 13 |
| 32k | `▁l ' emi lia ▁è ▁romagna ▁hè ▁una ▁regione ▁taliana ... (+2 more)` | 12 |
| 64k | `▁l ' emilia ▁è ▁romagna ▁hè ▁una ▁regione ▁taliana . ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 64k achieves 4.216x compression
- **Lowest UNK Rate:** 8k with 0.0264% 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 | 9,217 | 13.17 | 49,361 | 22.0% | 44.8% |
| **2-gram** | Subword | 220 🏆 | 7.78 | 3,170 | 71.3% | 99.6% |
| **3-gram** | Word | 24,245 | 14.57 | 83,032 | 11.2% | 30.7% |
| **3-gram** | Subword | 1,698 | 10.73 | 22,203 | 28.4% | 77.7% |
| **4-gram** | Word | 41,699 | 15.35 | 137,212 | 9.3% | 25.7% |
| **4-gram** | Subword | 9,000 | 13.14 | 106,299 | 13.9% | 42.6% |
| **5-gram** | Word | 36,326 | 15.15 | 111,629 | 9.3% | 26.7% |
| **5-gram** | Subword | 31,819 | 14.96 | 280,787 | 8.5% | 26.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `di u` | 18,692 |
| 2 | `di a` | 18,500 |
| 3 | `di l` | 13,231 |
| 4 | `di i` | 10,603 |
| 5 | `à u` | 9,233 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a famiglia di` | 4,349 |
| 2 | `hè una spezia` | 3,359 |
| 3 | `di a famiglia` | 2,699 |
| 4 | `hè una pianta` | 2,612 |
| 5 | `una spezia di` | 2,290 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `di a famiglia di` | 2,629 |
| 2 | `a famiglia di i` | 2,171 |
| 3 | `hè una spezia di` | 2,064 |
| 4 | `annantu à wikimedia commons` | 1,945 |
| 5 | `à wikimedia commons di` | 1,924 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `annantu à wikimedia commons di` | 1,924 |
| 2 | `à wikimedia commons di corsica` | 1,923 |
| 3 | `appartinendu à a famiglia di` | 1,506 |
| 4 | `flora corsica 2 ed edisud` | 1,421 |
| 5 | `d gamisans j flora corsica` | 1,419 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _` | 432,205 |
| 2 | `a _` | 403,888 |
| 3 | `u _` | 315,849 |
| 4 | `_ d` | 246,098 |
| 5 | `d i` | 216,563 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i` | 172,754 |
| 2 | `d i _` | 151,658 |
| 3 | `_ i n` | 82,722 |
| 4 | `_ u _` | 81,534 |
| 5 | `_ a _` | 73,027 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i _` | 143,050 |
| 2 | `_ i n _` | 57,478 |
| 3 | `a _ d i` | 45,041 |
| 4 | `_ h è _` | 45,025 |
| 5 | `i _ d i` | 35,043 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ d i _` | 37,617 |
| 2 | `i _ d i _` | 29,786 |
| 3 | `u _ d i _` | 28,746 |
| 4 | `e _ d i _` | 24,400 |
| 5 | `i o n e _` | 21,123 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 220
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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 | 0.8927 | 1.857 | 5.58 | 123,322 | 10.7% |
| **1** | Subword | 0.8627 | 1.818 | 6.97 | 1,238 | 13.7% |
| **2** | Word | 0.3106 | 1.240 | 1.80 | 686,898 | 68.9% |
| **2** | Subword | 0.9133 | 1.883 | 5.37 | 8,617 | 8.7% |
| **3** | Word | 0.1339 | 1.097 | 1.25 | 1,233,325 | 86.6% |
| **3** | Subword | 0.7817 | 1.719 | 3.96 | 46,221 | 21.8% |
| **4** | Word | 0.0623 🏆 | 1.044 | 1.10 | 1,539,570 | 93.8% |
| **4** | Subword | 0.6452 | 1.564 | 2.90 | 182,986 | 35.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `di tuda hè una spezia hè un missale rumanu mandatu pè a prutezzione di l isula`
2. `u calendariu gregorianu evenimenti nascite morte celebrazione feste i primi cristiani è l euru e zon...`
3. `a bellula chì faci cantà senza scoddhi e pratuline i bagni di 25 aprile di nettaru`

**Context Size 2:**

1. `di u mare à trasporti maritimi portivechju hà ancu statu cunnisciuta sottu u nomu simonu a casata`
2. `di a spagna un statu di spiritu turmintosa da veda dinò camisgia pilonu a camisgetta di corsica`
3. `di l europa occidentale di cipru di u bacinu mediterraniu induv ella hè ghjunta in alisgiani u`

**Context Size 3:**

1. `a famiglia di l orobanchaceae si distingui da i so grandi fiori gialli è arancini à forma di`
2. `hè una spezia largamente sparta in a so aria di ripartizioni eppuri certi pupulazioni poni essa mina...`
3. `di a famiglia di i brassicaceae si caratterizeghja da u so portu cispugliosu è cumpattu aghjunghjend...`

**Context Size 4:**

1. `di a famiglia di l arecaceae ed hè largamenti apprizzatu par a so biddezza è u so simbulu astrunomic...`
2. `a famiglia di i sapindaceae discrizzioni l acer negundo hè un arburi scascianti chì pò aghjunghja un...`
3. `hè una spezia di pianta chì faci parti di a famiglia di l hirundinidae descrizzione a rundinella cas...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_diri_25_à_di_d'`
2. `iori_hà_siceisu_`
3. `adia_puvezota_fi`

**Context Size 2:**

1. `i_re_culupula_à_s`
2. `a_ufoltrupatichar`
3. `u_à_ligna_culanea`

**Context Size 3:**

1. `_di_abbrunu,_cator`
2. `di_arbaceae._nore_`
3. `_induv'eddu;_annan`

**Context Size 4:**

1. `_di_yprestitudi_à_s`
2. `_in_amba_di_l'incen`
3. `a_di_l'aurolli_di_b`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (182,986 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 | 58,569 |
| Total Tokens | 2,191,854 |
| Mean Frequency | 37.42 |
| Median Frequency | 4 |
| Frequency Std Dev | 979.31 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | di | 143,436 |
| 2 | u | 84,175 |
| 3 | a | 76,019 |
| 4 | è | 67,153 |
| 5 | in | 58,881 |
| 6 | à | 58,439 |
| 7 | l | 48,309 |
| 8 | hè | 46,050 |
| 9 | i | 45,085 |
| 10 | da | 24,609 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | hannovra | 2 |
| 2 | multifau | 2 |
| 3 | vendanges | 2 |
| 4 | voceratrice | 2 |
| 5 | paysage | 2 |
| 6 | coin | 2 |
| 7 | paysan | 2 |
| 8 | spezialità | 2 |
| 9 | alerta | 2 |
| 10 | ꦈꦠꦩ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0566 |
| R² (Goodness of Fit) | 0.997058 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 48.9% |
| Top 1,000 | 69.5% |
| Top 5,000 | 84.0% |
| Top 10,000 | 89.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9971 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 48.9% of corpus
- **Long Tail:** 48,569 words needed for remaining 10.6% 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 | 0.8262 🏆 | 0.3363 | N/A | N/A |
| **mono_64d** | 64 | 0.8192 | 0.2582 | N/A | N/A |
| **mono_128d** | 128 | 0.7654 | 0.2010 | N/A | N/A |
| **aligned_32d** | 32 | 0.8262 | 0.3340 | 0.0540 | 0.2540 |
| **aligned_64d** | 64 | 0.8192 | 0.2633 | 0.0880 | 0.3460 |
| **aligned_128d** | 128 | 0.7654 | 0.1975 | 0.1560 | 0.4960 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8262 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2651. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 15.6% 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 | **0.002** | 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 |
|--------|----------|
| `-cu` | cunfutà, cuddazioni, cuntera |
| `-ca` | castres, caprimulgus, calciu |
| `-ri` | rivede, rispettà, riurganizò |
| `-in` | ingegneri, incausà, indì |
| `-pr` | pridatori, privileghju, preferisci |
| `-di` | dinastìa, disintegra, dicennovi |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-i` | addevi, ingegneri, midianti |
| `-u` | spagnolu, belgiu, vòtu |
| `-a` | dinastìa, leucoraja, seduta |
| `-e` | rivede, uccidentale, marginale |
| `-tu` | vòtu, validatu, prisirvatu |
| `-ti` | midianti, rapprisintati, sminticati |
| `-ni` | cuddazioni, vogliini, cardini |
| `-ta` | seduta, atalanta, rota |

### 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 |
|------|----------|------------------|----------|
| `endu` | 2.14x | 73 contexts | fendu, vendu, dendu |
| `enti` | 1.81x | 118 contexts | nenti, denti, lenti |
| `igli` | 1.63x | 112 contexts | gigli, migli, cigli |
| `aghj` | 1.46x | 142 contexts | aghji, aghju, aghja |
| `glia` | 1.66x | 70 contexts | aglia, paglia, figlia |
| `azio` | 1.75x | 56 contexts | tazio, lazio, orazio |
| `zion` | 1.65x | 64 contexts | azione, nozione, lezioni |
| `ment` | 1.48x | 87 contexts | mente, menti, menta |
| `cors` | 1.80x | 33 contexts | corso, corsa, corse |
| `ific` | 1.57x | 45 contexts | pacific, unificò, unificà |
| `tura` | 1.38x | 62 contexts | datura, altura, natura |
| `sica` | 1.56x | 37 contexts | mùsica, fìsica, sicani |

### 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 |
|--------|--------|-----------|----------|
| `-cu` | `-i` | 84 words | curteghji, cubiti |
| `-cu` | `-u` | 82 words | cuntestatu, cunvertitu |
| `-ri` | `-u` | 67 words | righjistru, riguardu |
| `-cu` | `-a` | 64 words | cultelleria, cunsacra |
| `-cu` | `-e` | 62 words | cundannate, cunstruzione |
| `-in` | `-u` | 61 words | ingombru, inchietu |
| `-ca` | `-a` | 59 words | calandra, cantata |
| `-in` | `-i` | 58 words | insufficienti, intarsizioni |
| `-ca` | `-u` | 58 words | caratteru, capistranu |
| `-pr` | `-i` | 56 words | preparazioni, prisintati |

### 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 |
|------|-----------------|------------|------|
| indibulitu | **`in-di-buli-tu`** | 7.5 | `buli` |
| dirighjitu | **`di-ri-ghji-tu`** | 7.5 | `ghji` |
| dimustrati | **`di-mustra-ti`** | 6.0 | `mustra` |
| ricustruisce | **`ri-cu-struisce`** | 6.0 | `struisce` |
| ricustruite | **`ri-cu-struite`** | 6.0 | `struite` |
| saturnianu | **`saturn-ia-nu`** | 6.0 | `saturn` |
| rivoltani | **`ri-volta-ni`** | 6.0 | `volta` |
| divenendu | **`di-venendu`** | 4.5 | `venendu` |
| indicheghjanu | **`in-di-cheghja-nu`** | 4.5 | `cheghja` |
| accupavanu | **`accupava-nu`** | 4.5 | `accupava` |
| granulita | **`granuli-ta`** | 4.5 | `granuli` |
| principionu | **`pr-in-cipio-nu`** | 4.5 | `cipio` |
| attaccani | **`attacca-ni`** | 4.5 | `attacca` |
| supranatu | **`suprana-tu`** | 4.5 | `suprana` |
| asciuvatu | **`asciuva-tu`** | 4.5 | `asciuva` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Corsican 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 (4.22x) |
| N-gram | **2-gram** | Lowest perplexity (220) |
| Markov | **Context-4** | Highest predictability (93.8%) |
| 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: 2026-01-03 20:37:45*