---
language: scn
language_name: Sicilian
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: 4.491
  - name: best_isotropy
    type: isotropy
    value: 0.8559
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sicilian** 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** | 3.628x | 3.63 | 0.0737% | 333,830 |
| **16k** | 3.960x | 3.96 | 0.0804% | 305,808 |
| **32k** | 4.255x | 4.26 | 0.0864% | 284,572 |
| **64k** | 4.491x 🏆 | 4.49 | 0.0912% | 269,653 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Samo è nu cumuni di 1.005 abbitanti dâ pruvincia di Riggiu Calabbria. dâ pruvinc...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sa mo ▁è ▁nu ▁cumuni ▁di ▁ 1 . 0 ... (+15 more)` | 25 |
| 16k | `▁samo ▁è ▁nu ▁cumuni ▁di ▁ 1 . 0 0 ... (+14 more)` | 24 |
| 32k | `▁samo ▁è ▁nu ▁cumuni ▁di ▁ 1 . 0 0 ... (+14 more)` | 24 |
| 64k | `▁samo ▁è ▁nu ▁cumuni ▁di ▁ 1 . 0 0 ... (+14 more)` | 24 |

**Sample 2:** `è un cumuni talianu dâ pruvincia di Sondriu ntâ Lummardìa. dâ pruvincia di Sondr...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁sondriu ▁ntâ ▁lummardìa ... (+5 more)` | 15 |
| 16k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁sondriu ▁ntâ ▁lummardìa ... (+5 more)` | 15 |
| 32k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁sondriu ▁ntâ ▁lummardìa ... (+5 more)` | 15 |
| 64k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁sondriu ▁ntâ ▁lummardìa ... (+5 more)` | 15 |

**Sample 3:** `è un cumuni talianu dâ pruvincia di Cremona ntâ Lummardìa. dâ pruvincia di Cremo...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁cremona ▁ntâ ▁lummardìa ... (+5 more)` | 15 |
| 16k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁cremona ▁ntâ ▁lummardìa ... (+5 more)` | 15 |
| 32k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁cremona ▁ntâ ▁lummardìa ... (+5 more)` | 15 |
| 64k | `▁è ▁un ▁cumuni ▁talianu ▁dâ ▁pruvincia ▁di ▁cremona ▁ntâ ▁lummardìa ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.491x compression
- **Lowest UNK Rate:** 8k with 0.0737% 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 | 16,384 | 14.00 | 58,233 | 15.6% | 34.5% |
| **2-gram** | Subword | 244 🏆 | 7.93 | 4,404 | 70.4% | 99.0% |
| **3-gram** | Word | 24,141 | 14.56 | 72,090 | 12.9% | 28.3% |
| **3-gram** | Subword | 2,050 | 11.00 | 34,045 | 29.2% | 74.5% |
| **4-gram** | Word | 36,264 | 15.15 | 109,633 | 12.4% | 28.1% |
| **4-gram** | Subword | 12,335 | 13.59 | 174,994 | 13.1% | 41.0% |
| **5-gram** | Word | 23,643 | 14.53 | 73,924 | 12.6% | 32.9% |
| **5-gram** | Subword | 48,581 | 15.57 | 458,275 | 7.8% | 23.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pruvincia di` | 15,198 |
| 2 | `dâ pruvincia` | 14,084 |
| 3 | `di l` | 11,236 |
| 4 | `è un` | 5,502 |
| 5 | `è nu` | 5,227 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dâ pruvincia di` | 13,755 |
| 2 | `è un cumuni` | 4,935 |
| 3 | `talianu dâ pruvincia` | 4,537 |
| 4 | `cumuni talianu dâ` | 4,533 |
| 5 | `un cumuni talianu` | 4,497 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `cumuni talianu dâ pruvincia` | 4,533 |
| 2 | `è un cumuni talianu` | 4,497 |
| 3 | `un cumuni talianu dâ` | 4,420 |
| 4 | `talianu dâ pruvincia di` | 4,404 |
| 5 | `abbitanti dâ pruvincia di` | 1,920 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `è un cumuni talianu dâ` | 4,420 |
| 2 | `un cumuni talianu dâ pruvincia` | 4,420 |
| 3 | `cumuni talianu dâ pruvincia di` | 4,400 |
| 4 | `ntâ lummardìa dâ pruvincia di` | 1,512 |
| 5 | `nu cumuni dâ pruvincia di` | 1,411 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _` | 648,749 |
| 2 | `a _` | 449,210 |
| 3 | `u _` | 428,360 |
| 4 | `_ d` | 299,061 |
| 5 | `_ c` | 245,777 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i` | 173,046 |
| 2 | `d i _` | 150,142 |
| 3 | `n i _` | 97,798 |
| 4 | `t i _` | 93,979 |
| 5 | `i _ d` | 89,842 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i _` | 140,256 |
| 2 | `i _ d i` | 52,971 |
| 3 | `_ l u _` | 51,883 |
| 4 | `a _ d i` | 47,082 |
| 5 | `_ l a _` | 44,178 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _ d i _` | 43,124 |
| 2 | `a _ d i _` | 41,391 |
| 3 | `u _ d i _` | 29,866 |
| 4 | `_ d i _ l` | 28,707 |
| 5 | `i o n i _` | 27,862 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 244
- **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 | 0.8233 | 1.769 | 5.57 | 202,619 | 17.7% |
| **1** | Subword | 1.0275 | 2.038 | 8.59 | 1,252 | 0.0% |
| **2** | Word | 0.2739 | 1.209 | 1.68 | 1,121,596 | 72.6% |
| **2** | Subword | 1.0284 | 2.040 | 6.37 | 10,748 | 0.0% |
| **3** | Word | 0.0907 | 1.065 | 1.15 | 1,872,306 | 90.9% |
| **3** | Subword | 0.8687 | 1.826 | 4.42 | 68,346 | 13.1% |
| **4** | Word | 0.0294 🏆 | 1.021 | 1.04 | 2,146,546 | 97.1% |
| **4** | Subword | 0.6923 | 1.616 | 3.02 | 301,807 | 30.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `di l utilizzu eni uguali n maduna surmuntatu spissu china occupies a spidercam telecamera e di`
2. `e in ebbica abbastanza nichi e riazzioni tinta tinta ntô 480 a parallassi dâ prima ranni`
3. `lu divintaru famusi macari li pupulazzioni di fora dû branu cu la situazzioni 1 cor damaya`

**Context Size 2:**

1. `pruvincia di salernu havi na pupulazzioni di 1 chistu pirmetti ô browser di mozilla firefox sunnu sc...`
2. `dâ pruvincia di frusinuni havi na vota ntô 147º e na storia assai àutru centru di lu`
3. `di l aquila havi na pupulazzioni di 1 a 29 annu e ô dramma sacru di la`

**Context Size 3:**

1. `dâ pruvincia di asti ntô piemunti dâ pruvincia di palermu la notti dû 22 di dicèmmiru fu nu`
2. `è un cumuni talianu dâ pruvincia di cremona ntâ lummardìa havi na pupulazzioni di 2 807 abbitanti dâ`
3. `talianu dâ pruvincia di sarausa puru si la vilucitati dâ luci sia isutropica ossia ca avi u stissu`

**Context Size 4:**

1. `cumuni talianu dâ pruvincia di carbonia iglesias ntâ sardigna dâ pruvincia di oristanu ntâ sardigna ...`
2. `è un cumuni talianu dâ pruvincia di nuvara ntô piemunti dâ pruvincia di cuneu ntô piemunti dâ pruvin...`
3. `un cumuni talianu dâ pruvincia di pavìa ntâ lummardìa dâ pruvincia di bèrgamu ntâ lummardìa dâ pruvi...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pìu_duvi_nta_dî`
2. `imprersio_ncidi_`
3. `a_di_le_antô_–_s`

**Context Size 2:**

1. `i_rinciriglia,_«c`
2. `a_a_acquersanuota`
3. `u_acquagnu_do'_va`

**Context Size 3:**

1. `_di_l'asempion:_th`
2. `di_mai_di_gueva_nz`
3. `ni_tantironali_a_j`

**Context Size 4:**

1. `_di_giugnu_'n_arban`
2. `i_di_cuntra_venneme`
3. `_lu_nùmmuru_nizo_ne`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (301,807 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 | 86,322 |
| Total Tokens | 2,462,744 |
| Mean Frequency | 28.53 |
| Median Frequency | 4 |
| Frequency Std Dev | 696.15 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | di | 140,762 |
| 2 | e | 60,379 |
| 3 | lu | 55,075 |
| 4 | a | 51,553 |
| 5 | la | 47,116 |
| 6 | l | 39,892 |
| 7 | dâ | 32,478 |
| 8 | è | 31,791 |
| 9 | li | 30,388 |
| 10 | n | 24,459 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | artificaili | 2 |
| 2 | degeneratu | 2 |
| 3 | impress | 2 |
| 4 | escaldes | 2 |
| 5 | engordany | 2 |
| 6 | sabigotho | 2 |
| 7 | reiter | 2 |
| 8 | homestuck | 2 |
| 9 | manganelli | 2 |
| 10 | emiciclu | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0191 |
| R² (Goodness of Fit) | 0.998927 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.6% |
| Top 1,000 | 63.1% |
| Top 5,000 | 78.3% |
| Top 10,000 | 84.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9989 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.6% of corpus
- **Long Tail:** 76,322 words needed for remaining 15.5% 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 | 0.8559 🏆 | 0.3184 | N/A | N/A |
| **mono_64d** | 64 | 0.8517 | 0.2317 | N/A | N/A |
| **mono_128d** | 128 | 0.7450 | 0.1848 | N/A | N/A |
| **aligned_32d** | 32 | 0.8559 | 0.3200 | 0.0900 | 0.3440 |
| **aligned_64d** | 64 | 0.8517 | 0.2295 | 0.1380 | 0.4440 |
| **aligned_128d** | 128 | 0.7450 | 0.1777 | 0.2000 | 0.5420 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8559 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2437. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 20.0% 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 |
|--------|----------|
| `-s` | schianari, straputiri, spirimintàvanu |
| `-a` | aglabita, abbunata, azzurri |
| `-c` | chidja, calculatu, catenanuova |
| `-m` | mladic, medioevo, mintennu |
| `-p` | presu, puvuredda, puacu |
| `-ca` | calculatu, catenanuova, calabbra |
| `-n` | negroponte, nnustri, ntitulata |
| `-ma` | magistri, majistrìa, maladzečna |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-i` | schianari, liberi, itali |
| `-u` | calculatu, mintennu, presu |
| `-a` | chidja, aglabita, catenanuova |
| `-ti` | acuti, disignati, fimmati |
| `-ni` | moroni, littoni, valanzuni |
| `-ri` | schianari, liberi, azzurri |
| `-tu` | calculatu, scuraggiatu, nzignatu |
| `-nu` | mintennu, infantinu, spirimintàvanu |

### 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 |
|------|----------|------------------|----------|
| `azzi` | 2.30x | 147 contexts | tazzi, yazzi, mazzi |
| `izzi` | 2.03x | 166 contexts | pizzi, rizzi, nizzi |
| `itat` | 2.12x | 103 contexts | citat, itati, vitatu |
| `zion` | 2.21x | 73 contexts | zione, zioni, azione |
| `zzio` | 2.32x | 44 contexts | zzioni, azziona, azzioni |
| `vinc` | 2.14x | 39 contexts | vinci, vincì, vince |
| `iggi` | 1.65x | 109 contexts | siggi, liggi, figgi |
| `nali` | 1.91x | 43 contexts | anali, linali, fanali |
| `ncia` | 1.61x | 80 contexts | uncia, ancia, lancia |
| `lian` | 1.58x | 70 contexts | julian, alianu, eliana |
| `inci` | 1.46x | 96 contexts | jinci, vinci, linci |
| `ilia` | 1.52x | 77 contexts | dilia, filia, iliadi |

### 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` | `-i` | 299 words | crudili, ciampi |
| `-a` | `-i` | 257 words | arrisbigghiari, avvrazzari |
| `-a` | `-u` | 247 words | albergu, arrinneru |
| `-c` | `-u` | 225 words | colledimenzu, chiu |
| `-c` | `-a` | 203 words | catilina, caldea |
| `-s` | `-u` | 201 words | sassòfunu, suffru |
| `-p` | `-i` | 200 words | pinitrari, picciriddi |
| `-s` | `-i` | 200 words | sumenzi, sanguinari |
| `-a` | `-a` | 157 words | adriatica, amatura |
| `-m` | `-i` | 153 words | mustri, matrici |

### 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 |
|------|-----------------|------------|------|
| eremitaggiu | **`eremitagg-i-u`** | 7.5 | `i` |
| intellighentsia | **`intellighents-i-a`** | 7.5 | `i` |
| impiegati | **`impieg-a-ti`** | 7.5 | `a` |
| gghiùnciri | **`gghiùnc-i-ri`** | 7.5 | `i` |
| cunsidiratu | **`cunsidir-a-tu`** | 7.5 | `a` |
| melitensis | **`melitens-i-s`** | 7.5 | `i` |
| nfruinzatu | **`nfruinz-a-tu`** | 7.5 | `a` |
| fortificata | **`fortific-a-ta`** | 7.5 | `a` |
| agghìunciri | **`agghìunc-i-ri`** | 7.5 | `i` |
| madeleine | **`madele-i-ne`** | 7.5 | `i` |
| munarchii | **`munarch-i-i`** | 7.5 | `i` |
| baudelaire | **`baudela-i-re`** | 7.5 | `i` |
| ndividuari | **`ndividu-a-ri`** | 7.5 | `a` |
| ncintivati | **`ncintiv-a-ti`** | 7.5 | `a` |
| vintagghiu | **`vintaggh-i-u`** | 7.5 | `i` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Sicilian 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 (4.49x) |
| N-gram | **2-gram** | Lowest perplexity (244) |
| Markov | **Context-4** | Highest predictability (97.1%) |
| 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: 2026-01-10 19:53:23*