---
language: fur
language_name: Friulian
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: 4.179
  - name: best_isotropy
    type: isotropy
    value: 0.8456
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Friulian** 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** | 3.499x | 3.50 | 0.0442% | 298,836 |
| **16k** | 3.763x | 3.77 | 0.0475% | 277,903 |
| **32k** | 4.005x | 4.01 | 0.0506% | 261,078 |
| **64k** | 4.179x 🏆 | 4.18 | 0.0528% | 250,188 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Angelo Angeli (Tarcint al è stât un chimic furlan. Angeli, Angelo`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁angelo ▁ang eli ▁( tar cint ▁al ▁è ▁stât ▁un ... (+7 more)` | 17 |
| 16k | `▁angelo ▁ang eli ▁( tar cint ▁al ▁è ▁stât ▁un ... (+7 more)` | 17 |
| 32k | `▁angelo ▁angeli ▁( tarcint ▁al ▁è ▁stât ▁un ▁chimic ▁furlan ... (+4 more)` | 14 |
| 64k | `▁angelo ▁angeli ▁( tarcint ▁al ▁è ▁stât ▁un ▁chimic ▁furlan ... (+4 more)` | 14 |

**Sample 2:** `Futurama e jè une serie televisive merecane fate di Matt Groening, creadôr dai S...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁fut ura ma ▁e ▁jè ▁une ▁serie ▁televis ive ▁merecane ... (+20 more)` | 30 |
| 16k | `▁fut ura ma ▁e ▁jè ▁une ▁serie ▁televisive ▁merecane ▁fate ... (+16 more)` | 26 |
| 32k | `▁fut ura ma ▁e ▁jè ▁une ▁serie ▁televisive ▁merecane ▁fate ... (+15 more)` | 25 |
| 64k | `▁futurama ▁e ▁jè ▁une ▁serie ▁televisive ▁merecane ▁fate ▁di ▁matt ... (+10 more)` | 20 |

**Sample 3:** `La gjenerazion cidine (Silent Generation par inglês) e je la coort demografiche ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁la ▁gjenerazion ▁cid ine ▁( s il ent ▁gener ation ... (+16 more)` | 26 |
| 16k | `▁la ▁gjenerazion ▁cid ine ▁( s il ent ▁gener ation ... (+15 more)` | 25 |
| 32k | `▁la ▁gjenerazion ▁cidine ▁( sil ent ▁generation ▁par ▁inglês ) ... (+12 more)` | 22 |
| 64k | `▁la ▁gjenerazion ▁cidine ▁( silent ▁generation ▁par ▁inglês ) ▁e ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.179x compression
- **Lowest UNK Rate:** 8k with 0.0442% 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 | 6,387 | 12.64 | 19,666 | 20.3% | 46.3% |
| **2-gram** | Subword | 248 🏆 | 7.96 | 2,671 | 70.2% | 99.2% |
| **3-gram** | Word | 8,833 | 13.11 | 24,038 | 19.0% | 41.2% |
| **3-gram** | Subword | 1,960 | 10.94 | 19,755 | 29.1% | 74.5% |
| **4-gram** | Word | 13,956 | 13.77 | 38,236 | 17.7% | 36.5% |
| **4-gram** | Subword | 10,511 | 13.36 | 89,752 | 14.0% | 41.5% |
| **5-gram** | Word | 8,136 | 12.99 | 25,386 | 22.1% | 44.1% |
| **5-gram** | Subword | 34,761 | 15.09 | 204,100 | 7.7% | 25.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `al è` | 7,101 |
| 2 | `e je` | 3,936 |
| 3 | `che al` | 2,795 |
| 4 | `d c` | 2,492 |
| 5 | `a son` | 2,477 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `p d c` | 2,382 |
| 2 | `al è un` | 2,096 |
| 3 | `c p d` | 1,011 |
| 4 | `d c p` | 1,011 |
| 5 | `e je la` | 898 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c p d c` | 1,011 |
| 2 | `d c p d` | 1,011 |
| 3 | `p d c p` | 1,011 |
| 4 | `al è un comun` | 793 |
| 5 | `friûl vie pal mont` | 658 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `p d c p d` | 1,011 |
| 2 | `d c p d c` | 1,011 |
| 3 | `c p d c p` | 1,002 |
| 4 | `in friûl vie pal mont` | 653 |
| 5 | `cjale ancje storie an par` | 623 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 162,437 |
| 2 | `_ d` | 109,050 |
| 3 | `i _` | 91,782 |
| 4 | `l _` | 85,238 |
| 5 | `_ c` | 77,432 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l _` | 50,711 |
| 2 | `_ d i` | 47,425 |
| 3 | `d i _` | 41,307 |
| 4 | `_ e _` | 27,541 |
| 5 | `_ d a` | 27,491 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i _` | 38,921 |
| 2 | `_ a l _` | 22,205 |
| 3 | `_ d a l` | 18,305 |
| 4 | `d a l _` | 18,054 |
| 5 | `c h e _` | 17,262 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a l _` | 17,925 |
| 2 | `_ c h e _` | 11,800 |
| 3 | `e _ d i _` | 9,488 |
| 4 | `_ p a r _` | 7,670 |
| 5 | `a z i o n` | 7,163 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 248
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.8172 | 1.762 | 4.95 | 72,772 | 18.3% |
| **1** | Subword | 1.1868 | 2.277 | 8.98 | 739 | 0.0% |
| **2** | Word | 0.2892 | 1.222 | 1.68 | 358,823 | 71.1% |
| **2** | Subword | 0.9716 | 1.961 | 5.88 | 6,634 | 2.8% |
| **3** | Word | 0.0992 | 1.071 | 1.17 | 599,633 | 90.1% |
| **3** | Subword | 0.8300 | 1.778 | 3.99 | 38,974 | 17.0% |
| **4** | Word | 0.0329 🏆 | 1.023 | 1.05 | 698,598 | 96.7% |
| **4** | Subword | 0.6457 | 1.564 | 2.69 | 155,477 | 35.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `di març nassût intal vivaldi al continuà il plui famôs il cjampanîl di ferruccio valcareggi dilunc`
2. `e al è un an par descrivi in lui intal bahrain a cjaval di lôr al`
3. `al deficit dal stelon l an par latin si c p d c 502 p d`

**Context Size 2:**

1. `al è iessut il 28 chês di chei timps a vevin sielzût in riferiment ae lenghe te`
2. `e je la ilustrazion de vedue che e je l uniche eruzion tal cjamp des circoscrizions che`
3. `che al conte 40 670 puescj 31 533 omologâts dal la glesie parochiâl di foresto sparso dedicade`

**Context Size 3:**

1. `p d c 459 p d c 983 p d c 818 p d c al vûl dî`
2. `al è un an dal secul xvii acjadiments nassûts muarts cjale ancje storie an par an dal friûl`
3. `c p d c 680 p d c 327 p d c fint al p d c 73`

**Context Size 4:**

1. `p d c p d c p d c p d c p d c p d c p`
2. `d c p d c p d c p d c p d c p d c p d`
3. `c p d c p d c p d c p d c p d c p d c`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_rda_3871570prtâ`
2. `icjoba_ili_a_pal`
3. `entisal_asi_ant_`

**Context Size 2:**

1. `e_e_abitadôr_a_em`
2. `_diulnunellonobum`
3. `i_riodellan_de_mi`

**Context Size 3:**

1. `al_riveligjôs_pera`
2. `_di_un_si_day_28_d`
3. `di_la_maxister_(†_`

**Context Size 4:**

1. `_di_2-3_fin_a_un_fu`
2. `_al_à_1.353)_tris_c`
3. `_dal_mâr_dai_piçule`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (155,477 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 | 32,145 |
| Total Tokens | 790,046 |
| Mean Frequency | 24.58 |
| Median Frequency | 4 |
| Frequency Std Dev | 397.72 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | di | 39,085 |
| 2 | e | 28,112 |
| 3 | al | 22,659 |
| 4 | a | 19,048 |
| 5 | dal | 18,049 |
| 6 | la | 17,389 |
| 7 | il | 14,910 |
| 8 | de | 12,230 |
| 9 | che | 12,124 |
| 10 | in | 9,877 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | sorunsuz | 2 |
| 2 | honorem | 2 |
| 3 | mariie | 2 |
| 4 | zeni | 2 |
| 5 | prestato | 2 |
| 6 | colomps | 2 |
| 7 | mariotti | 2 |
| 8 | acoustic | 2 |
| 9 | hayreddin | 2 |
| 10 | mitilen | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0527 |
| R² (Goodness of Fit) | 0.998570 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 47.2% |
| Top 1,000 | 70.1% |
| Top 5,000 | 85.4% |
| Top 10,000 | 91.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9986 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 47.2% of corpus
- **Long Tail:** 22,145 words needed for remaining 8.7% 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 | 0.8456 🏆 | 0.3453 | N/A | N/A |
| **mono_64d** | 64 | 0.7362 | 0.2912 | N/A | N/A |
| **mono_128d** | 128 | 0.3656 | 0.2659 | N/A | N/A |
| **aligned_32d** | 32 | 0.8456 | 0.3331 | 0.0580 | 0.2960 |
| **aligned_64d** | 64 | 0.7362 | 0.2849 | 0.1000 | 0.3420 |
| **aligned_128d** | 128 | 0.3656 | 0.2575 | 0.1500 | 0.4140 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8456 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2963. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 15.0% 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 | **0.707** | 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` | comme, concentrâts, conventu |
| `-pr` | programadis, protagoniscj, prestazions |
| `-in` | insets, inventôrs, interpretazions |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | murçalis, programadis, carateristichis |
| `-e` | que, croniche, vicenze |
| `-is` | murçalis, programadis, carateristichis |
| `-ts` | insets, falâts, possidents |
| `-on` | perfezion, chiampon, ambientazion |
| `-ât` | bonât, popolaritât, staticitât |
| `-de` | alimentade, liende, einöde |
| `-in` | rabin, montafin, bandonin |

### 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 |
|------|----------|------------------|----------|
| `azio` | 2.07x | 55 contexts | lazio, azion, spazio |
| `uart` | 1.84x | 71 contexts | fuart, puart, muart |
| `razi` | 2.17x | 30 contexts | razis, orazi, grazie |
| `iche` | 1.93x | 44 contexts | piche, laiche, criche |
| `entr` | 1.81x | 43 contexts | centr, entre, entri |
| `lian` | 1.92x | 34 contexts | zelian, zulian, talian |
| `itât` | 1.95x | 30 contexts | citât, mitât, zitât |
| `imen` | 1.95x | 27 contexts | imens, timent, ciment |
| `ions` | 2.24x | 16 contexts | lions, zions, grions |
| `omun` | 2.07x | 18 contexts | comun, comune, comuni |
| `isti` | 1.48x | 52 contexts | esisti, listis, istint |
| `ntri` | 1.85x | 20 contexts | entri, cintri, contri |

### 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` | 88 words | comunâls, comics |
| `-co` | `-e` | 64 words | couture, completade |
| `-pr` | `-e` | 50 words | predicjave, protagoniste |
| `-pr` | `-s` | 48 words | principinonpais, provocatoris |
| `-in` | `-s` | 46 words | invetivis, industriis |
| `-in` | `-e` | 38 words | invistidure, incirche |
| `-co` | `-is` | 34 words | contraris, convicinis |
| `-co` | `-on` | 31 words | concession, cosson |
| `-co` | `-in` | 24 words | costin, condividevin |
| `-co` | `-nt` | 21 words | costituint, corispondent |

### 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 |
|------|-----------------|------------|------|
| studentis | **`stude-nt-is`** | 6.0 | `stude` |
| costantin | **`co-stant-in`** | 6.0 | `stant` |
| incontaminât | **`in-co-ntam-in-ât`** | 6.0 | `ntam` |
| friulinis | **`friul-in-is`** | 6.0 | `friul` |
| indreçâts | **`in-dreçâ-ts`** | 6.0 | `dreçâ` |
| filipinis | **`filip-in-is`** | 6.0 | `filip` |
| grandonis | **`grand-on-is`** | 6.0 | `grand` |
| venetopontinis | **`venetopo-nt-in-is`** | 4.5 | `venetopo` |
| bandonâts | **`bandonâ-ts`** | 4.5 | `bandonâ` |
| favorevulis | **`favorevul-is`** | 4.5 | `favorevul` |
| indagjinis | **`in-dagj-in-is`** | 4.5 | `dagj` |
| segretariât | **`segretari-ât`** | 4.5 | `segretari` |
| designâts | **`designâ-ts`** | 4.5 | `designâ` |
| associâts | **`associâ-ts`** | 4.5 | `associâ` |
| cuviertis | **`cuviert-is`** | 4.5 | `cuviert` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Friulian 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 (4.18x) |
| N-gram | **2-gram** | Lowest perplexity (248) |
| Markov | **Context-4** | Highest predictability (96.7%) |
| 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: 2026-01-04 14:49:50*