---
language: rmy
language_name: Vlax Romani
language_family: indoaryan_romani
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-indoaryan_romani
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: 3.596
  - name: best_isotropy
    type: isotropy
    value: 0.1310
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Vlax Romani - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Vlax Romani** 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** | 3.064x | 3.07 | 0.1507% | 195,120 |
| **16k** | 3.303x | 3.31 | 0.1625% | 180,964 |
| **32k** | 3.596x 🏆 | 3.60 | 0.1768% | 166,245 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `E Portugaliya (portekezikanes: Portugal) si yek them andi Sudutni Evropa. Common...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁e ▁portugaliya ▁( port ek ez ikanes : ▁portugal ) ... (+8 more)` | 18 |
| 16k | `▁e ▁portugaliya ▁( port ek ez ikanes : ▁portugal ) ... (+8 more)` | 18 |
| 32k | `▁e ▁portugaliya ▁( portekezikanes : ▁portugal ) ▁si ▁yek ▁them ... (+5 more)` | 15 |

**Sample 2:** `Renieblas si ekh gav kay Provinciya Soriya, ande Komunitatya Kastiliya thay Leon...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ren ie blas ▁si ▁ekh ▁gav ▁kay ▁provinciya ▁soriya , ... (+11 more)` | 21 |
| 16k | `▁ren ie blas ▁si ▁ekh ▁gav ▁kay ▁provinciya ▁soriya , ... (+11 more)` | 21 |
| 32k | `▁renieblas ▁si ▁ekh ▁gav ▁kay ▁provinciya ▁soriya , ▁ande ▁komunitatya ... (+9 more)` | 19 |

**Sample 3:** `I paradàjka si jekh loli lugùma, barăli and-i manuśeski bar.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁i ▁parad àj ka ▁si ▁jekh ▁loli ▁l ug ùma ... (+11 more)` | 21 |
| 16k | `▁i ▁parad àj ka ▁si ▁jekh ▁loli ▁lugùma , ▁bar ... (+9 more)` | 19 |
| 32k | `▁i ▁paradàjka ▁si ▁jekh ▁loli ▁lugùma , ▁barăli ▁and - ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 32k achieves 3.596x compression
- **Lowest UNK Rate:** 8k with 0.1507% 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 | 750 | 9.55 | 1,357 | 40.4% | 90.1% |
| **2-gram** | Subword | 338 🏆 | 8.40 | 1,845 | 63.1% | 98.6% |
| **3-gram** | Word | 593 | 9.21 | 1,259 | 43.3% | 90.3% |
| **3-gram** | Subword | 2,745 | 11.42 | 11,649 | 22.8% | 67.2% |
| **4-gram** | Word | 898 | 9.81 | 2,105 | 37.8% | 70.1% |
| **4-gram** | Subword | 12,493 | 13.61 | 42,942 | 10.9% | 37.5% |
| **5-gram** | Word | 455 | 8.83 | 1,299 | 48.0% | 88.0% |
| **5-gram** | Subword | 25,019 | 14.61 | 65,011 | 7.9% | 27.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `anθ o` | 268 |
| 2 | `si yek` | 258 |
| 3 | `si o` | 212 |
| 4 | `si ekh` | 211 |
| 5 | `gav kay` | 190 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ande komunitatya kastiliya` | 180 |
| 2 | `soriya ande komunitatya` | 178 |
| 3 | `leon spaniya provinciya` | 176 |
| 4 | `si ekh gav` | 174 |
| 5 | `ekh gav kay` | 173 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `soriya ande komunitatya kastiliya` | 178 |
| 2 | `si ekh gav kay` | 173 |
| 3 | `ekh gav kay provinciya` | 168 |
| 4 | `komunitatya kastiliya thay leon` | 167 |
| 5 | `ande komunitatya kastiliya thay` | 167 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `si ekh gav kay provinciya` | 168 |
| 2 | `ande komunitatya kastiliya thay leon` | 167 |
| 3 | `ekh gav kay provinciya soriya` | 166 |
| 4 | `gav kay provinciya soriya ande` | 166 |
| 5 | `kay provinciya soriya ande komunitatya` | 166 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n` | 12,580 |
| 2 | `o _` | 11,862 |
| 3 | `e _` | 11,640 |
| 4 | `a _` | 10,755 |
| 5 | `i _` | 9,139 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a n` | 3,349 |
| 2 | `a n d` | 2,854 |
| 3 | `_ k a` | 2,732 |
| 4 | `_ o _` | 2,720 |
| 5 | `_ s i` | 2,633 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s i _` | 1,959 |
| 2 | `_ a n d` | 1,835 |
| 3 | `_ t h a` | 1,643 |
| 4 | `i k a n` | 1,579 |
| 5 | `r o m a` | 1,107 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i p e n _` | 840 |
| 2 | `i k a n e` | 803 |
| 3 | `r o m a n` | 767 |
| 4 | `t h a j _` | 717 |
| 5 | `_ r o m a` | 717 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 338
- **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 | 0.6472 | 1.566 | 3.15 | 22,311 | 35.3% |
| **1** | Subword | 0.8874 | 1.850 | 5.98 | 867 | 11.3% |
| **2** | Word | 0.1372 | 1.100 | 1.24 | 69,729 | 86.3% |
| **2** | Subword | 0.8895 | 1.852 | 4.76 | 5,185 | 11.1% |
| **3** | Word | 0.0377 | 1.026 | 1.05 | 85,861 | 96.2% |
| **3** | Subword | 0.7852 | 1.723 | 3.33 | 24,644 | 21.5% |
| **4** | Word | 0.0126 🏆 | 1.009 | 1.02 | 89,426 | 98.7% |
| **4** | Subword | 0.5431 | 1.457 | 2.11 | 81,993 | 45.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `o personalune pronomengo parudipe personalune pronomya si cultura rromilor curs audio de boliviabosn...`
2. `si i chexaya tay e rromane ʒene sas anθ o manushengro vi patrinipen le balkanosko kai`
3. `e rroma te avel o bućh kerdăs butĭ te del nina e romengi chib sudutne brazilyako`

**Context Size 2:**

1. `anθ o atlantikano baro pani pala i phakh kaj dǎs tele o diktatòro o jon antonesko thai`
2. `si yek mesto teritoriyo kay si rugisarime thay luvudime but manushendar ande avere thema kadea but p...`
3. `si o foro thaj o maj baro genetikano diverzitèto sar rezultato so si kay bukereshto tay may`

**Context Size 3:**

1. `ande komunitatya kastiliya thay leon spaniya provinciya`
2. `soriya ande komunitatya kastiliya tay leon spaniya provinciya`
3. `si ekh gav kay provinciya soriya ande komunitatya kastiliya thay leon spaniya provinciya`

**Context Size 4:**

1. `soriya ande komunitatya kastiliya thay leon spaniya provinciya`
2. `si ekh gav kay provinciya soriya ande komunitatya kastiliya thay leon spaniya provinciya`
3. `ekh gav kay provinciya soriya ande komunitatya kastiliya tay leon spaniya provinciya`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ni_b_răl_sisuči`
2. `an_s_serorrio,2_`
3. `e_je:_esizo_rage`

**Context Size 2:**

1. `anai_si_tu_o_mosf`
2. `o_palno;_ro_dukka`
3. `e_pola_ladaushama`

**Context Size 3:**

1. `_and-i_janglunetwo`
2. `ando-aripuritustro`
3. `_katar)_biphuro-ps`

**Context Size 4:**

1. `_si_andar_i_hiśtòri`
2. `_ande_island_is_is_`
3. `_thay_diskutire_(xu`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (81,993 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 | 8,383 |
| Total Tokens | 83,700 |
| Mean Frequency | 9.98 |
| Median Frequency | 3 |
| Frequency Std Dev | 60.21 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | o | 3,442 |
| 2 | si | 2,006 |
| 3 | e | 1,630 |
| 4 | i | 1,274 |
| 5 | le | 1,057 |
| 6 | te | 972 |
| 7 | thaj | 721 |
| 8 | 1 | 708 |
| 9 | sas | 698 |
| 10 | sar | 686 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | balkano | 2 |
| 2 | praktično | 2 |
| 3 | misticizmo | 2 |
| 4 | tehnikani | 2 |
| 5 | patjavipa | 2 |
| 6 | eksperiencije | 2 |
| 7 | mistikane | 2 |
| 8 | muslimanura | 2 |
| 9 | statuso | 2 |
| 10 | źanglimata | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8979 |
| R² (Goodness of Fit) | 0.986680 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 40.7% |
| Top 1,000 | 67.3% |
| Top 5,000 | 91.8% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9867 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 40.7% of corpus
- **Long Tail:** -1,617 words needed for remaining 100.0% 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 | 0.1310 🏆 | 0.5085 | N/A | N/A |
| **mono_64d** | 64 | 0.0226 | 0.4891 | N/A | N/A |
| **mono_128d** | 128 | 0.0034 | 0.4954 | N/A | N/A |
| **aligned_32d** | 32 | 0.1310 | 0.5051 | 0.0080 | 0.0920 |
| **aligned_64d** | 64 | 0.0226 | 0.4861 | 0.0280 | 0.1140 |
| **aligned_128d** | 128 | 0.0034 | 0.4910 | 0.0280 | 0.1100 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.1310 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4959. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 2.8% 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 | **2.264** | 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` | sindh, septèmbro, sherutni |
| `-a` | auraiya, acest, arakh |
| `-p` | polynesia, paulo, prima |
| `-b` | been, barabanki, barǎrel |
| `-m` | marley, manush, madagaskar |
| `-k` | kuzko, kongeriget, kontrakto |
| `-d` | dǎs, dikhel, diskografiya |
| `-l` | lovo, lekhipnaske, literature |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | fatima, hagiwara, auraiya |
| `-o` | śingalo, septèmbro, kuzko |
| `-e` | themutne, lekhipnaske, irane |
| `-i` | anderyarindoi, sherutni, religǎqi |
| `-n` | ćoren, jordan, meren |
| `-ya` | auraiya, diskografiya, edeya |
| `-s` | dǎs, signalées, fragments |
| `-en` | ćoren, meren, kideren |

### 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 |
|------|----------|------------------|----------|
| `kerd` | 1.74x | 25 contexts | kerdi, kerda, kerde |
| `ikan` | 1.55x | 26 contexts | nikana, vatikan, bikaner |
| `ipen` | 1.73x | 17 contexts | jipen, ekipen, butipen |
| `akar` | 1.95x | 10 contexts | makar, vakar, vakara |
| `angl` | 1.43x | 24 contexts | angle, anglo, angla |
| `imat` | 1.75x | 11 contexts | pimata, marimata, cacimata |
| `rutn` | 1.45x | 19 contexts | avrutno, forutne, forutno |
| `utno` | 1.69x | 12 contexts | avutno, paśutno, telutno |
| `utne` | 1.64x | 12 contexts | beśutne, forutne, marutne |
| `sard` | 1.90x | 8 contexts | alsardo, xasardi, alosardo |
| `hiba` | 1.67x | 10 contexts | čhiba, shiba, ćhiba |
| `manu` | 1.44x | 12 contexts | manuś, manuš, manus |

### 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 |
|--------|--------|-----------|----------|
| `-m` | `-a` | 71 words | manușha, mothavela |
| `-a` | `-a` | 69 words | auraiya, algèbra |
| `-k` | `-a` | 63 words | kolaja, karnataka |
| `-p` | `-o` | 62 words | paulo, parlimento |
| `-p` | `-a` | 59 words | polynesia, prima |
| `-s` | `-a` | 56 words | shtatura, shunyola |
| `-s` | `-o` | 54 words | septèmbro, somdasno |
| `-p` | `-e` | 54 words | pachanpe, phandipe |
| `-k` | `-e` | 53 words | kourthiade, kote |
| `-b` | `-a` | 47 words | barca, baramula |

### 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 |
|------|-----------------|------------|------|
| makyarekani | **`makyarek-a-ni`** | 7.5 | `a` |
| deshtonai | **`deshto-na-i`** | 7.5 | `na` |
| barodvipkane | **`barodvip-ka-ne`** | 7.5 | `ka` |
| australian | **`australi-a-n`** | 7.5 | `a` |
| xitajkane | **`xitaj-ka-ne`** | 7.5 | `ka` |
| kalifornaki | **`kaliforn-a-ki`** | 7.5 | `a` |
| religikane | **`religi-ka-ne`** | 7.5 | `ka` |
| tehsilurya | **`tehsil-ur-ya`** | 6.0 | `tehsil` |
| dharmesko | **`dharm-es-ko`** | 6.0 | `dharm` |
| arakhenpe | **`arakh-en-pe`** | 6.0 | `arakh` |
| manuśenqe | **`manuś-en-qe`** | 6.0 | `manuś` |
| chhibyako | **`chhib-ya-ko`** | 6.0 | `chhib` |
| brazilyako | **`brazil-ya-ko`** | 6.0 | `brazil` |
| bersheski | **`bersh-es-ki`** | 6.0 | `bersh` |
| bershende | **`bersh-en-de`** | 6.0 | `bersh` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Vlax Romani 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 | **32k BPE** | Best compression (3.60x) |
| N-gram | **2-gram** | Lowest perplexity (338) |
| Markov | **Context-4** | Highest predictability (98.7%) |
| 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 18:41:21*