---
language: lij
language_name: Ligurian
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: 3.659
  - name: best_isotropy
    type: isotropy
    value: 0.8072
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ligurian** 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** | 3.021x | 3.02 | 0.0824% | 601,973 |
| **16k** | 3.271x | 3.27 | 0.0892% | 556,020 |
| **32k** | 3.488x | 3.49 | 0.0951% | 521,472 |
| **64k** | 3.659x 🏆 | 3.66 | 0.0998% | 497,043 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Togo (nomme ofiçiâ: République Togolaise) stato de l'Africa çentro oççidentâ ind...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁to go ▁( nomme ▁ofiçiâ : ▁république ▁to gola ise ... (+24 more)` | 34 |
| 16k | `▁to go ▁( nomme ▁ofiçiâ : ▁république ▁to gola ise ... (+24 more)` | 34 |
| 32k | `▁to go ▁( nomme ▁ofiçiâ : ▁république ▁to gola ise ... (+24 more)` | 34 |
| 64k | `▁togo ▁( nomme ▁ofiçiâ : ▁république ▁to golaise ) ▁stato ... (+21 more)` | 31 |

**Sample 2:** `Fæti Euröpa Àzia Àfrica América Arte Costruçión Inovaçión Nasciûi Mòrti Âtri pro...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁américa ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ... (+6 more)` | 16 |
| 16k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁américa ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ... (+6 more)` | 16 |
| 32k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁américa ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ... (+6 more)` | 16 |
| 64k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁américa ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ... (+6 more)` | 16 |

**Sample 3:** `Fæti Euröpa Àzia Àfrica Arte Costruçión Inovaçión Nasciûi Mòrti Âtri progètti 62...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ▁âtri ... (+5 more)` | 15 |
| 16k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ▁âtri ... (+5 more)` | 15 |
| 32k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ▁âtri ... (+5 more)` | 15 |
| 64k | `▁fæti ▁euröpa ▁àzia ▁àfrica ▁arte ▁costruçión ▁inovaçión ▁nasciûi ▁mòrti ▁âtri ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 3.659x compression
- **Lowest UNK Rate:** 8k with 0.0824% 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 | 8,853 | 13.11 | 49,924 | 26.3% | 45.2% |
| **2-gram** | Subword | 320 🏆 | 8.32 | 4,859 | 63.9% | 98.1% |
| **3-gram** | Word | 14,009 | 13.77 | 67,505 | 24.0% | 39.1% |
| **3-gram** | Subword | 2,727 | 11.41 | 37,721 | 26.1% | 68.2% |
| **4-gram** | Word | 20,217 | 14.30 | 101,414 | 23.3% | 36.5% |
| **4-gram** | Subword | 15,550 | 13.92 | 176,973 | 11.9% | 37.8% |
| **5-gram** | Word | 9,572 | 13.22 | 64,332 | 30.4% | 45.0% |
| **5-gram** | Subword | 56,888 | 15.80 | 437,893 | 6.7% | 23.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l` | 19,797 |
| 2 | `o l` | 18,061 |
| 3 | `l é` | 14,515 |
| 4 | `l è` | 13,540 |
| 5 | `de l` | 9,867 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l é` | 6,311 |
| 2 | `o l é` | 6,083 |
| 3 | `o l è` | 4,965 |
| 4 | `a l è` | 4,710 |
| 5 | `pòsti de interèsse` | 3,216 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `stöia pòsti de interèsse` | 3,068 |
| 2 | `fæti euröpa àzia àfrica` | 3,016 |
| 3 | `de interèsse architetûe religiôze` | 2,952 |
| 4 | `pòsti de interèsse architetûe` | 2,952 |
| 5 | `interèsse architetûe religiôze architetûe` | 2,898 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pòsti de interèsse architetûe religiôze` | 2,952 |
| 2 | `de interèsse architetûe religiôze architetûe` | 2,898 |
| 3 | `arte costruçión inovaçión nasciûi mòrti` | 2,888 |
| 4 | `stöia pòsti de interèsse architetûe` | 2,882 |
| 5 | `giögrafîa stöia pòsti de interèsse` | 2,868 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 413,980 |
| 2 | `e _` | 401,203 |
| 3 | `_ d` | 286,230 |
| 4 | `o _` | 266,322 |
| 5 | `_ c` | 191,071 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 118,475 |
| 2 | `d e _` | 110,988 |
| 3 | `_ i n` | 87,620 |
| 4 | `_ a _` | 84,437 |
| 5 | `_ l '` | 74,032 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 102,062 |
| 2 | `_ i n t` | 38,995 |
| 3 | `_ d a _` | 38,425 |
| 4 | `a _ d e` | 29,461 |
| 5 | `_ i n _` | 28,157 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ d e _` | 26,234 |
| 2 | `_ a _ l '` | 17,187 |
| 3 | `e _ d e _` | 16,809 |
| 4 | `ç i ó n _` | 16,721 |
| 5 | `_ o _ l '` | 15,543 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 320
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.8200 | 1.765 | 4.97 | 178,552 | 18.0% |
| **1** | Subword | 1.0889 | 2.127 | 9.46 | 1,196 | 0.0% |
| **2** | Word | 0.2946 | 1.227 | 1.73 | 885,169 | 70.5% |
| **2** | Subword | 1.0226 | 2.032 | 6.45 | 11,315 | 0.0% |
| **3** | Word | 0.1100 | 1.079 | 1.19 | 1,528,711 | 89.0% |
| **3** | Subword | 0.8102 | 1.753 | 4.13 | 72,907 | 19.0% |
| **4** | Word | 0.0425 🏆 | 1.030 | 1.07 | 1,822,768 | 95.7% |
| **4** | Subword | 0.6391 | 1.557 | 2.85 | 301,052 | 36.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a sùd e ço ch u ciàn nòbile do regno de mattê bernabè çigâa meliaduce cicala`
2. `de fronte orientâ lengua do segnô de conponiménti in testimunianse da o 16 sec o l`
3. `l arçipélago de vétria fraçión de ciù ò a a i 99 finale de frànsa 531`

**Context Size 2:**

1. `a l à in nómme fâso ò in sce téia gàlata musêo do mâ neigro comme goernao`
2. `o l impediva che i pelêujanti pelleuiante o sûnnòu da pelleuia seggian di cacciueì da oxelletti e`
3. `l é scrîta j e a e a elaborâ a ricostruçión de pröto léngoe chi léngoe dravìdiche`

**Context Size 3:**

1. `a l é conpréiza fra o triónfo de idêe rivoluçionâie coscì cómme o sécolo dòppo inta marìnn a`
2. `o l é ascì n importante çentro commerçiâ edûcatïo e coltûà a l è na sitò a mêza`
3. `o l è stæto fondoö o 28 dexembre stöia âtri progètti do gruppo italico giulia`

**Context Size 4:**

1. `stöia pòsti de interèsse architetûe religiôze architetûe civîli economîa coltûa manifestaçioîn fèste...`
2. `fæti euröpa àzia àfrica arte costruçión inovaçión nasciûi mòrti 036`
3. `pòsti de interèsse architetûe religiôze architetûe civîli economîa coltûa manifestaçioîn fèste e fêe...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_deno_sspenco_me`
2. `ao_dantel'umié_c`
3. `i_àu_e_ve_an_'as`

**Context Size 2:**

1. `a_gioîn_òcenovita`
2. `e_vìttormâ_sciü_i`
3. `_da_e_d'o_viancio`

**Context Size 3:**

1. `_de_cian_cuntròllo`
2. `de_de_paruz)_o_pre`
3. `_in_livia_àzia_tòc`

**Context Size 4:**

1. `_de_"reusa_dellese_`
2. `_interèsse_arche_in`
3. `_da_manicu,_nun_int`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (301,052 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 | 80,296 |
| Total Tokens | 2,142,871 |
| Mean Frequency | 26.69 |
| Median Frequency | 4 |
| Frequency Std Dev | 840.07 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 140,267 |
| 2 | de | 102,749 |
| 3 | l | 78,988 |
| 4 | o | 78,535 |
| 5 | e | 69,403 |
| 6 | da | 49,709 |
| 7 | in | 31,558 |
| 8 | i | 27,140 |
| 9 | u | 26,568 |
| 10 | do | 24,863 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | bashkitë | 2 |
| 2 | savais | 2 |
| 3 | attends | 2 |
| 4 | humaine | 2 |
| 5 | conne | 2 |
| 6 | promesses | 2 |
| 7 | naufrages | 2 |
| 8 | belsen | 2 |
| 9 | margòt | 2 |
| 10 | antisemìtiche | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9823 |
| R² (Goodness of Fit) | 0.998916 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.7% |
| Top 1,000 | 66.4% |
| Top 5,000 | 79.5% |
| Top 10,000 | 85.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9989 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.7% of corpus
- **Long Tail:** 70,296 words needed for remaining 14.8% 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 | 0.8072 🏆 | 0.3095 | N/A | N/A |
| **mono_64d** | 64 | 0.7236 | 0.2526 | N/A | N/A |
| **mono_128d** | 128 | 0.3751 | 0.2268 | N/A | N/A |
| **aligned_32d** | 32 | 0.8072 | 0.3052 | 0.0180 | 0.1580 |
| **aligned_64d** | 64 | 0.7236 | 0.2558 | 0.0520 | 0.2720 |
| **aligned_128d** | 128 | 0.3751 | 0.2313 | 0.1120 | 0.4000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8072 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2635. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 11.2% 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 | **0.908** | 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 |
|--------|----------|
| `-s` | spontaneamente, sciûto, sanctum |
| `-a` | archiòlogo, apatico, alverniate |
| `-c` | cavour, cuštřuia, cessiun |
| `-p` | partensa, pianeti, pecchi |
| `-m` | müàggia, meòçia, maschî |
| `-ca` | cavour, caden, caratterizzæ |
| `-d` | devota, dorso, dicitur |
| `-b` | belinda, borzonasca, berga |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | inmensa, oryza, devota |
| `-o` | dorso, archiòlogo, grano |
| `-e` | ànche, tutâle, spontaneamente |
| `-i` | olandéixi, novelli, pianeti |
| `-n` | gabìnn, finsen, trœuvan |
| `-u` | scrìtu, rilasciòu, scumpartìu |
| `-te` | spontaneamente, alverniate, frequénte |
| `-ia` | müàggia, cuštřuia, guardia |

### 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 |
|------|----------|------------------|----------|
| `çion` | 1.98x | 61 contexts | açion, leçion, seçion |
| `ment` | 1.67x | 123 contexts | mente, menti, mentæ |
| `açió` | 2.28x | 26 contexts | açión, façión, naçión |
| `açio` | 1.61x | 71 contexts | façio, açion, laçio |
| `çión` | 2.18x | 22 contexts | açión, seçión, leçión |
| `nter` | 1.72x | 51 contexts | nterò, inter, interä |
| `rovi` | 1.74x | 45 contexts | rovie, rovinn, rovine |
| `stru` | 1.52x | 75 contexts | austru, mestru, castru |
| `rchi` | 1.48x | 65 contexts | archi, ærchi, erchi |
| `raçi` | 1.52x | 48 contexts | graçia, oraçio, graçie |
| `taçi` | 1.53x | 40 contexts | staçión, staçion, staçiun |
| `hite` | 2.05x | 13 contexts | white, architetu, architetü |

### 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` | `-a` | 168 words | carbònica, chionea |
| `-c` | `-o` | 136 words | càspio, caldaréllo |
| `-c` | `-e` | 128 words | circe, crìste |
| `-s` | `-a` | 121 words | servia, svevia |
| `-s` | `-e` | 117 words | scenette, særavàlle |
| `-p` | `-e` | 112 words | prutešte, provvidde |
| `-p` | `-o` | 111 words | petto, prononçiao |
| `-p` | `-a` | 109 words | puiia, preminença |
| `-s` | `-o` | 103 words | spartio, satûrno |
| `-a` | `-a` | 103 words | achela, atella |

### 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 |
|------|-----------------|------------|------|
| prescidiâ | **`prescid-i-â`** | 7.5 | `i` |
| continoava | **`contino-a-va`** | 7.5 | `a` |
| economìsta | **`economì-s-ta`** | 7.5 | `s` |
| imprezaio | **`imprez-a-io`** | 7.5 | `a` |
| attribuii | **`attribu-i-i`** | 7.5 | `i` |
| gianfranco | **`gi-an-franco`** | 7.5 | `franco` |
| consonanti | **`consona-n-ti`** | 7.5 | `n` |
| élémentaire | **`élémenta-i-re`** | 7.5 | `i` |
| manifèsti | **`manifè-s-ti`** | 7.5 | `s` |
| travagiòu | **`travag-i-òu`** | 7.5 | `i` |
| mangiâvan | **`mangiâ-va-n`** | 6.0 | `mangiâ` |
| parallela | **`par-alle-la`** | 6.0 | `alle` |
| borgorato | **`borgo-ra-to`** | 6.0 | `borgo` |
| incontrao | **`in-contra-o`** | 6.0 | `contra` |
| codevilla | **`co-de-villa`** | 6.0 | `villa` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ligurian 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 (3.66x) |
| N-gram | **2-gram** | Lowest perplexity (320) |
| Markov | **Context-4** | Highest predictability (95.7%) |
| 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 10:57:38*