---
language: mwl
language_name: Mirandese
language_family: romance_iberian
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_iberian
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: 4.578
  - name: best_isotropy
    type: isotropy
    value: 0.8323
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Mirandese** 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** | 3.793x | 3.79 | 0.0216% | 2,683,483 |
| **16k** | 4.139x | 4.14 | 0.0236% | 2,459,597 |
| **32k** | 4.421x | 4.42 | 0.0252% | 2,302,588 |
| **64k** | 4.578x 🏆 | 4.58 | 0.0261% | 2,223,729 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Propebela miona ye ua spece de gastrópode de l género Propebela, pertencente la ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pro pe bela ▁mi ona ▁ye ▁ua ▁spece ▁de ▁gas ... (+16 more)` | 26 |
| 16k | `▁pro pe bela ▁mi ona ▁ye ▁ua ▁spece ▁de ▁gastrópode ... (+13 more)` | 23 |
| 32k | `▁pro pe bela ▁mi ona ▁ye ▁ua ▁spece ▁de ▁gastrópode ... (+12 more)` | 22 |
| 64k | `▁propebela ▁mi ona ▁ye ▁ua ▁spece ▁de ▁gastrópode ▁de ▁l ... (+8 more)` | 18 |

**Sample 2:** `Pingnan ye un cundado de la porbinça Fujian ne la China. Ten ua sobrefiç de km² ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ping nan ▁ye ▁un ▁cundado ▁de ▁la ▁porbinça ▁fujian ▁ne ... (+21 more)` | 31 |
| 16k | `▁ping nan ▁ye ▁un ▁cundado ▁de ▁la ▁porbinça ▁fujian ▁ne ... (+21 more)` | 31 |
| 32k | `▁ping nan ▁ye ▁un ▁cundado ▁de ▁la ▁porbinça ▁fujian ▁ne ... (+21 more)` | 31 |
| 64k | `▁ping nan ▁ye ▁un ▁cundado ▁de ▁la ▁porbinça ▁fujian ▁ne ... (+21 more)` | 31 |

**Sample 3:** `Paízes Baixos ye un paíç localizado na Ouropa. A sua capital ye Amsterdam de la ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁paízes ▁baixos ▁ye ▁un ▁paíç ▁localizado ▁na ▁ouropa . ▁a ... (+10 more)` | 20 |
| 16k | `▁paízes ▁baixos ▁ye ▁un ▁paíç ▁localizado ▁na ▁ouropa . ▁a ... (+10 more)` | 20 |
| 32k | `▁paízes ▁baixos ▁ye ▁un ▁paíç ▁localizado ▁na ▁ouropa . ▁a ... (+10 more)` | 20 |
| 64k | `▁paízes ▁baixos ▁ye ▁un ▁paíç ▁localizado ▁na ▁ouropa . ▁a ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.578x compression
- **Lowest UNK Rate:** 8k with 0.0216% 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 | 15,343 | 13.91 | 73,697 | 17.8% | 35.6% |
| **2-gram** | Subword | 225 🏆 | 7.81 | 4,011 | 72.6% | 99.4% |
| **3-gram** | Word | 43,244 | 15.40 | 99,993 | 7.1% | 21.5% |
| **3-gram** | Subword | 1,730 | 10.76 | 30,226 | 30.5% | 76.9% |
| **4-gram** | Word | 83,756 | 16.35 | 139,745 | 4.6% | 13.5% |
| **4-gram** | Subword | 9,145 | 13.16 | 149,701 | 15.4% | 43.2% |
| **5-gram** | Word | 53,205 | 15.70 | 77,395 | 5.4% | 14.4% |
| **5-gram** | Subword | 33,248 | 15.02 | 377,533 | 9.3% | 26.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de l` | 58,173 |
| 2 | `de la` | 48,036 |
| 3 | `ne l` | 20,582 |
| 4 | `de ls` | 12,372 |
| 5 | `de las` | 10,382 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de l seclo` | 1,892 |
| 2 | `ls stados ounidos` | 1,436 |
| 3 | `a partir de` | 1,328 |
| 4 | `i de l` | 1,327 |
| 5 | `i de la` | 1,270 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de ls stados ounidos` | 710 |
| 2 | `i ua poblaçon de` | 453 |
| 3 | `km i ua poblaçon` | 453 |
| 4 | `la china ten ua` | 447 |
| 5 | `china ten ua sobrefiç` | 445 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `km i ua poblaçon de` | 453 |
| 2 | `china ten ua sobrefiç de` | 445 |
| 3 | `la china ten ua sobrefiç` | 445 |
| 4 | `ne la china ten ua` | 342 |
| 5 | `stados ounidos de la américa` | 309 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 591,904 |
| 2 | `a _` | 499,400 |
| 3 | `s _` | 411,342 |
| 4 | `_ l` | 403,980 |
| 5 | `d e` | 400,252 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 310,441 |
| 2 | `d e _` | 308,352 |
| 3 | `e _ l` | 194,993 |
| 4 | `_ l a` | 160,851 |
| 5 | `l a _` | 145,857 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 270,574 |
| 2 | `d e _ l` | 136,607 |
| 3 | `_ l a _` | 127,081 |
| 4 | `e _ l _` | 83,501 |
| 5 | `e _ l a` | 74,074 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _ l` | 133,195 |
| 2 | `e _ l a _` | 60,089 |
| 3 | `d e _ l a` | 59,980 |
| 4 | `o _ d e _` | 56,259 |
| 5 | `d e _ l _` | 54,129 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 225
- **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 | 1.0545 | 2.077 | 7.75 | 149,145 | 0.0% |
| **1** | Subword | 0.8887 | 1.852 | 6.01 | 2,125 | 11.1% |
| **2** | Word | 0.3376 | 1.264 | 1.92 | 1,155,292 | 66.2% |
| **2** | Subword | 0.8016 | 1.743 | 4.96 | 12,756 | 19.8% |
| **3** | Word | 0.1237 | 1.090 | 1.24 | 2,212,454 | 87.6% |
| **3** | Subword | 0.7949 | 1.735 | 4.10 | 63,188 | 20.5% |
| **4** | Word | 0.0452 🏆 | 1.032 | 1.07 | 2,748,862 | 95.5% |
| **4** | Subword | 0.6515 | 1.571 | 2.89 | 258,945 | 34.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de participaçon de l príncepe tutmés morriu na mesma família turbenidae apersentan porte las cuostas...`
2. `l liezi recebírun mais de la stória bai siempre porjetan este al gerar todas las ciéncias`
3. `la proposiçon cumpuosta por misson apollo fazírun ancursones de la region de trabalhadores renobában...`

**Context Size 2:**

1. `de l testo de l japon residentes strangeiros eilegales besitado an 28 de dezembre de l católicos`
2. `de la tierra ye to berde cun un sistema político i houmanitário dreitos de ls nomes de`
3. `ne l sou purmeiro trabalho na astronomie geofísica angenharie eiquenomie etc einicialmente la rebolu...`

**Context Size 3:**

1. `de l seclo xiv i xv antre las percipales obras de la eigreija i sin antermediários repersentantes ó`
2. `ls stados ounidos an stephen r cobey outor de l yoga eilhes son ls mais amportantes silicatos custit...`
3. `a partir de anton la reboluçon stendiu se al campo adonde çparou un tiro de canhon i l`

**Context Size 4:**

1. `de ls stados ounidos ne l bietname promobida por lyndon johnson debediu ls amaricanos an campos oupo...`
2. `km i ua poblaçon de 116 mil ingros an`
3. `i ua poblaçon de 431 mil ingros an`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_xor_gri_bes,_ca`
2. `a_",_ye_"birrter`
3. `ebefrmel_las_gog`

**Context Size 2:**

1. `e_lha_pe,_bólicar`
2. `a_ambregeiriencia`
3. `s_oute_l_ra_eisei`

**Context Size 3:**

1. `_de_subre_formas._`
2. `de_31_de_mera_qu'e`
3. `e_l_ciclónia_de_l_`

**Context Size 4:**

1. `_de_l_de_an_cente_s`
2. `de_l_telscópio_lhio`
3. `_la_sue_tenente,_d.`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (258,945 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 | 74,297 |
| Total Tokens | 3,042,544 |
| Mean Frequency | 40.95 |
| Median Frequency | 4 |
| Frequency Std Dev | 1358.50 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 272,017 |
| 2 | l | 154,267 |
| 3 | la | 129,771 |
| 4 | i | 87,959 |
| 5 | an | 48,574 |
| 6 | que | 42,608 |
| 7 | ls | 41,935 |
| 8 | a | 31,842 |
| 9 | las | 29,271 |
| 10 | se | 25,391 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | quedó | 2 |
| 2 | debut | 2 |
| 3 | haldane | 2 |
| 4 | xenopus | 2 |
| 5 | werskey | 2 |
| 6 | loom | 2 |
| 7 | bodmer | 2 |
| 8 | birminghan | 2 |
| 9 | maureen | 2 |
| 10 | correspondência | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0129 |
| R² (Goodness of Fit) | 0.994529 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 45.6% |
| Top 1,000 | 65.5% |
| Top 5,000 | 81.7% |
| Top 10,000 | 87.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9945 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 45.6% of corpus
- **Long Tail:** 64,297 words needed for remaining 12.1% 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 | 0.8157 | 0.3421 | N/A | N/A |
| **mono_64d** | 64 | 0.8323 🏆 | 0.2544 | N/A | N/A |
| **mono_128d** | 128 | 0.8007 | 0.1810 | N/A | N/A |
| **aligned_32d** | 32 | 0.8157 | 0.3370 | 0.0960 | 0.3740 |
| **aligned_64d** | 64 | 0.8323 | 0.2524 | 0.1680 | 0.5300 |
| **aligned_128d** | 128 | 0.8007 | 0.1744 | 0.2420 | 0.5960 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.8323 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2569. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 24.2% 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 | **-0.446** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-a` | ambencíbel, altas, atacante |
| `-s` | surprende, spaçonabes, seguiren |
| `-c` | certificación, cruzou, cungestionamientos |
| `-b` | balioso, bissau, birginia |
| `-p` | pioneiros, paredones, prague |
| `-m` | márteres, menimamente, munshiganj |
| `-ma` | malaquias, matricula, mayas |
| `-t` | telégrafo, tóxicas, templo |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | pioneiros, márteres, flabonóides |
| `-o` | etiológico, telégrafo, eisilado |
| `-a` | gmina, júnia, ria |
| `-os` | pioneiros, cungestionamientos, canídeos |
| `-e` | menimamente, çcubre, surprende |
| `-as` | tóxicas, altas, águas |
| `-es` | márteres, flabonóides, paredones |
| `-n` | çporen, certificación, seguiren |

### 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 |
|------|----------|------------------|----------|
| `ones` | 2.27x | 105 contexts | mones, cones, pones |
| `ados` | 2.37x | 66 contexts | lados, fados, dados |
| `idad` | 2.30x | 59 contexts | idade, lidado, unidad |
| `ento` | 2.05x | 80 contexts | cento, mento, lento |
| `çone` | 2.62x | 29 contexts | açones, maçones, raçones |
| `ista` | 1.91x | 102 contexts | pista, bista, mista |
| `ient` | 1.97x | 77 contexts | niente, ciento, biento |
| `tado` | 1.80x | 102 contexts | atado, stado, betado |
| `amie` | 2.49x | 26 contexts | jamie, tamien, amiens |
| `dade` | 2.18x | 42 contexts | idade, edades, cidade |
| `mien` | 2.27x | 35 contexts | miente, tamien, amiens |
| `ment` | 1.82x | 84 contexts | mento, mente, menta |

### 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 |
|--------|--------|-----------|----------|
| `-a` | `-s` | 247 words | ancenadas, anterspecíficas |
| `-c` | `-s` | 203 words | cunsequentes, caseiras |
| `-a` | `-a` | 194 words | angloba, alicia |
| `-a` | `-o` | 182 words | atípico, assimilado |
| `-p` | `-s` | 177 words | porgramados, perjuízos |
| `-s` | `-s` | 167 words | saturadas, surinamés |
| `-c` | `-o` | 140 words | cometimiento, caindo |
| `-c` | `-a` | 139 words | cántabra, cunceituada |
| `-p` | `-a` | 126 words | plaka, pesquisa |
| `-m` | `-s` | 124 words | mostradas, mosteiros |

### 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 |
|------|-----------------|------------|------|
| campanapse | **`campanap-s-e`** | 7.5 | `s` |
| corumbaenses | **`corumbaen-s-es`** | 7.5 | `s` |
| machucado | **`machu-ca-do`** | 7.5 | `ca` |
| cuncluísse | **`cuncluís-s-e`** | 7.5 | `s` |
| antressando | **`antress-an-do`** | 7.5 | `an` |
| eilegíaco | **`eilegí-a-co`** | 7.5 | `a` |
| albergaba | **`alberg-a-ba`** | 7.5 | `a` |
| alcançasse | **`alcanças-s-e`** | 7.5 | `s` |
| portucalenses | **`portucalen-s-es`** | 7.5 | `s` |
| ancluírun | **`ancluí-r-un`** | 7.5 | `r` |
| ampatando | **`ampat-an-do`** | 7.5 | `an` |
| neubauten | **`neubau-te-n`** | 7.5 | `te` |
| asturiense | **`asturien-s-e`** | 7.5 | `s` |
| banguardista | **`banguardi-s-ta`** | 7.5 | `s` |
| cumpostelana | **`cumpostel-an-a`** | 7.5 | `an` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Mirandese shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.58x) |
| N-gram | **2-gram** | Lowest perplexity (225) |
| Markov | **Context-4** | Highest predictability (95.5%) |
| 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 13:50:43*