---
language: got
language_name: Gothic
language_family: germanic_historical
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-germanic_historical
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: 2.884
  - name: best_isotropy
    type: isotropy
    value: 0.1831
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Gothic** 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** | 2.525x | 2.53 | 0.0669% | 260,190 |
| **16k** | 2.674x | 2.68 | 0.0708% | 245,725 |
| **32k** | 2.884x 🏆 | 2.89 | 0.0764% | 227,819 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `𐌺𐌰𐌽𐌰𐌳𐌰 𐌹𐍃𐍄 𐌻𐌰𐌽𐌳 𐌰𐌽𐌰 𐌰𐌹𐍂𐌸𐌰𐌳𐌰𐌹𐌻𐌰𐌹 𐌽𐌰𐌿𐍂𐌸𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰 𐌾𐌰𐌷 𐌲𐌰𐌼𐌰𐍂𐌺𐍉𐌸 𐌲𐌰𐌲𐌰𐌷𐌰𐍆𐍄𐌹𐌳𐌰 𐍂𐌴𐌹𐌺𐌾𐌰𐌹. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁𐌺𐌰𐌽𐌰𐌳𐌰 ▁𐌹𐍃𐍄 ▁𐌻𐌰𐌽𐌳 ▁𐌰𐌽𐌰 ▁𐌰𐌹𐍂𐌸𐌰𐌳𐌰𐌹𐌻 𐌰𐌹 ▁𐌽𐌰𐌿𐍂𐌸 𐌰𐌼𐌰𐌹𐍂𐌹𐌺 𐌰 ▁𐌾𐌰𐌷 ... (+20 more)` | 30 |
| 16k | `▁𐌺𐌰𐌽𐌰𐌳𐌰 ▁𐌹𐍃𐍄 ▁𐌻𐌰𐌽𐌳 ▁𐌰𐌽𐌰 ▁𐌰𐌹𐍂𐌸𐌰𐌳𐌰𐌹𐌻𐌰𐌹 ▁𐌽𐌰𐌿𐍂𐌸 𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰 ▁𐌾𐌰𐌷 ▁𐌲𐌰𐌼𐌰𐍂𐌺𐍉𐌸 ▁𐌲𐌰𐌲𐌰𐌷𐌰𐍆𐍄𐌹𐌳𐌰 ... (+16 more)` | 26 |
| 32k | `▁𐌺𐌰𐌽𐌰𐌳𐌰 ▁𐌹𐍃𐍄 ▁𐌻𐌰𐌽𐌳 ▁𐌰𐌽𐌰 ▁𐌰𐌹𐍂𐌸𐌰𐌳𐌰𐌹𐌻𐌰𐌹 ▁𐌽𐌰𐌿𐍂𐌸𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰 ▁𐌾𐌰𐌷 ▁𐌲𐌰𐌼𐌰𐍂𐌺𐍉𐌸 ▁𐌲𐌰𐌲𐌰𐌷𐌰𐍆𐍄𐌹𐌳𐌰 ▁𐍂𐌴𐌹𐌺𐌾𐌰𐌹 ... (+12 more)` | 22 |

**Sample 2:** `𐌰𐍀𐌻𐍃 — 𐌰𐌺𐍂𐌰𐌽 𐌰𐍀𐌻𐌰𐌱𐌰𐌲𐌼𐌴 𐌾𐌰𐌷 𐍅𐌰𐌹𐌻𐌰𐌺𐌿𐌽𐌸𐌰 𐍆𐍉𐌳𐌴𐌹𐌽𐍃 𐌹𐍃𐍄·`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁𐌰𐍀𐌻𐍃 ▁— ▁𐌰𐌺𐍂𐌰𐌽 ▁𐌰𐍀 𐌻 𐌰𐌱𐌰𐌲𐌼𐌴 ▁𐌾𐌰𐌷 ▁𐍅𐌰𐌹𐌻 𐌰𐌺𐌿𐌽𐌸𐌰 ▁𐍆𐍉𐌳𐌴𐌹𐌽𐍃 ... (+2 more)` | 12 |
| 16k | `▁𐌰𐍀𐌻𐍃 ▁— ▁𐌰𐌺𐍂𐌰𐌽 ▁𐌰𐍀 𐌻 𐌰𐌱𐌰𐌲𐌼𐌴 ▁𐌾𐌰𐌷 ▁𐍅𐌰𐌹𐌻 𐌰𐌺𐌿𐌽𐌸𐌰 ▁𐍆𐍉𐌳𐌴𐌹𐌽𐍃 ... (+2 more)` | 12 |
| 32k | `▁𐌰𐍀𐌻𐍃 ▁— ▁𐌰𐌺𐍂𐌰𐌽 ▁𐌰𐍀𐌻𐌰𐌱𐌰𐌲𐌼𐌴 ▁𐌾𐌰𐌷 ▁𐍅𐌰𐌹𐌻𐌰𐌺𐌿𐌽𐌸𐌰 ▁𐍆𐍉𐌳𐌴𐌹𐌽𐍃 ▁𐌹𐍃𐍄 ·` | 9 |

**Sample 3:** `𐌺𐌰𐌿𐌻𐌿𐌼𐌱𐌾𐌰 (Colombia) 𐌹𐍃𐍄 𐌻𐌰𐌽𐌳 𐌹𐌽 𐍃𐌿𐌽𐌸𐍂𐌰𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹. 𐌰𐌼𐌴𐍂𐌹𐌺𐌰 This page is brought t...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁𐌺𐌰𐌿𐌻𐌿𐌼𐌱 𐌾𐌰 ▁( col om b ia ) ▁𐌹𐍃𐍄 ▁𐌻𐌰𐌽𐌳 ... (+19 more)` | 29 |
| 16k | `▁𐌺𐌰𐌿𐌻𐌿𐌼𐌱𐌾𐌰 ▁( colombia ) ▁𐌹𐍃𐍄 ▁𐌻𐌰𐌽𐌳 ▁𐌹𐌽 ▁𐍃𐌿𐌽𐌸𐍂𐌰𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹 . ▁𐌰𐌼𐌴𐍂𐌹𐌺𐌰 ... (+12 more)` | 22 |
| 32k | `▁𐌺𐌰𐌿𐌻𐌿𐌼𐌱𐌾𐌰 ▁( colombia ) ▁𐌹𐍃𐍄 ▁𐌻𐌰𐌽𐌳 ▁𐌹𐌽 ▁𐍃𐌿𐌽𐌸𐍂𐌰𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹 . ▁𐌰𐌼𐌴𐍂𐌹𐌺𐌰 ... (+10 more)` | 20 |


### Key Findings

- **Best Compression:** 32k achieves 2.884x compression
- **Lowest UNK Rate:** 8k with 0.0669% 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 | 773 | 9.60 | 1,213 | 36.4% | 92.9% |
| **2-gram** | Subword | 546 🏆 | 9.09 | 2,316 | 47.1% | 96.7% |
| **3-gram** | Word | 630 | 9.30 | 1,041 | 40.1% | 98.0% |
| **3-gram** | Subword | 4,140 | 12.02 | 14,315 | 17.0% | 56.1% |
| **4-gram** | Word | 3,152 | 11.62 | 3,669 | 12.9% | 38.4% |
| **4-gram** | Subword | 17,609 | 14.10 | 51,785 | 8.9% | 30.1% |
| **5-gram** | Word | 2,230 | 11.12 | 2,508 | 13.1% | 46.3% |
| **5-gram** | Subword | 36,495 | 15.16 | 84,401 | 6.7% | 21.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i to` | 325 |
| 2 | `wv i` | 315 |
| 3 | `akin to` | 129 |
| 4 | `iii to` | 106 |
| 5 | `𐌹𐌽 𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹` | 102 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wv i to` | 276 |
| 2 | `akin to eng` | 78 |
| 3 | `sv vii to` | 64 |
| 4 | `sv iii to` | 61 |
| 5 | `𐌹𐍃𐍄 𐌻𐌰𐌽𐌳 𐌹𐌽` | 54 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽` | 48 |
| 2 | `𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽 𐌷𐌰𐌱𐌰𐌽` | 48 |
| 3 | `𐍃𐌴𐌹𐌳𐍉 𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃` | 48 |
| 4 | `𐌹𐌽 𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹 𐌲𐌰𐍅𐌹𐍃𐍃𐌴𐌹𐍃 www` | 48 |
| 5 | `𐌹𐌽 𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹 𐌷𐌰𐌿𐌱𐌹𐌳𐌰𐌱𐌰𐌿𐍂𐌲𐍃 𐌹𐍃𐍄` | 40 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `𐍃𐌴𐌹𐌳𐍉 𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽` | 48 |
| 2 | `𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽 𐌷𐌰𐌱𐌰𐌽` | 48 |
| 3 | `𐌹𐍃𐍄 𐌲𐌰𐍅𐌹 𐌹𐌽 𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹 𐌷𐌰𐌿𐌱𐌹𐌳𐌰𐌱𐌰𐌿𐍂𐌲𐍃` | 36 |
| 4 | `𐌲𐌰𐍅𐌹 𐌹𐌽 𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹 𐌷𐌰𐌿𐌱𐌹𐌳𐌰𐌱𐌰𐌿𐍂𐌲𐍃 𐌹𐍃𐍄` | 36 |
| 5 | `𐌷𐌰𐌿𐌱𐌹𐌳𐌰𐌱𐌰𐌿𐍂𐌲𐍃 𐌾𐌰𐌷 𐍃𐍉 𐌼𐌰𐌹𐍃𐍄𐍉 𐌱𐌰𐌿𐍂𐌲𐍃` | 21 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `, _` | 17,634 |
| 2 | `. _` | 14,540 |
| 3 | `𐌰 𐌹` | 7,870 |
| 4 | `𐍃 _` | 7,637 |
| 5 | `𐌹 𐍃` | 6,470 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ - _` | 2,452 |
| 2 | `n , _` | 2,251 |
| 3 | `s , _` | 2,187 |
| 4 | `𐌹 𐌽 _` | 2,125 |
| 5 | `, _ s` | 2,064 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ 𐌹 𐌽 _` | 1,670 |
| 2 | `_ t o _` | 1,483 |
| 3 | `_ 𐌾 𐌰 𐌷` | 1,475 |
| 4 | `𐌾 𐌰 𐌷 _` | 1,472 |
| 5 | `a n , _` | 1,390 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ 𐌾 𐌰 𐌷 _` | 1,469 |
| 2 | `_ 𐌹 𐍃 𐍄 _` | 1,060 |
| 3 | `_ t h e _` | 885 |
| 4 | `, _ t o _` | 881 |
| 5 | `_ o e . _` | 839 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 546
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.5463 | 1.460 | 2.78 | 26,779 | 45.4% |
| **1** | Subword | 1.3185 | 2.494 | 9.24 | 600 | 0.0% |
| **2** | Word | 0.1349 | 1.098 | 1.22 | 73,655 | 86.5% |
| **2** | Subword | 0.9989 | 1.999 | 5.20 | 5,543 | 0.1% |
| **3** | Word | 0.0401 | 1.028 | 1.06 | 89,056 | 96.0% |
| **3** | Subword | 0.7885 | 1.727 | 3.23 | 28,771 | 21.2% |
| **4** | Word | 0.0157 🏆 | 1.011 | 1.02 | 93,235 | 98.4% |
| **4** | Subword | 0.5184 | 1.432 | 2.05 | 92,872 | 48.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `𐌹𐌽 𐍅𐌹𐍃𐍄𐍂𐌰𐌹 𐌰𐍃𐌹𐌰𐌹 𐌽𐌴𐌷𐍅𐌿𐌽𐌳𐍉𐍃 𐌿𐍆𐌰𐍂 500 𐍆𐌰𐌿𐍂𐌰 𐍇𐍂𐌹𐍃𐍄𐌰𐌿 𐍃𐌰 𐌼𐌰𐌹𐍃𐍄𐌰 𐌰𐌻𐌻𐌰𐌹𐌶𐌴 𐌰𐌹𐍅𐌴 𐍃𐌴𐌹𐌳𐍉 𐌸𐍉𐌶𐌴𐌹 𐌵𐌹𐌼𐌰𐌽𐌳 𐍆𐍂𐌰𐌼`
2. `to tame 170 182 354 fulla ga náitjan wv i am trying to call cry aloud`
3. `𐌾𐌰𐌷 𐌰𐌽𐌸𐌰𐍂𐌰𐌹𐌼 𐌱𐌰𐍂𐌱𐌰𐍂𐌹𐍅𐌴 𐌸𐌰𐌹𐌴𐌹 𐌺𐌿𐌽𐌽𐌰𐌽 𐍈𐌰 𐌹𐌽 𐌾𐌴𐍂𐌰 𐌿𐍃𐍅𐌰𐌹𐍂𐍀𐌰𐌽 𐌼𐌰𐌷𐍄𐌴𐌹𐌲 𐍅𐌰𐍃 𐌸𐌰𐍄𐌴𐌹 𐌰𐍂𐌰𐌱𐌹𐍃𐌺𐌰 𐍂𐌰𐌶𐌳𐌰 𐍂𐌰𐌶𐌳𐌰 𐌿𐌺𐍂𐌰...`

**Context Size 2:**

1. `i to lighten 424 ohg lohazzen láun sn pay reward 22 141 175 211 oe ht a`
2. `wv i see ga eitjan eits aj white 140 165 oe hwt ohg hw 329a an av`
3. `akin to eng ask treat shamefully oe ntan ohg neien ga nasjan wv i to permit allow`

**Context Size 3:**

1. `wv i to give light 63 85 105 320 oe lehtan liuhten liusan sv ii see af skiuban`
2. `akin to eng arrow arrow arjan distantly akin to lat anima spirit pant comp uzanan exhale and anda`
3. `sv vii to call to one profess confess acknowledge give thanks to and háusjan wv i to sin`

**Context Size 4:**

1. `𐍃𐌴𐌹𐌳𐍉 𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽 𐌷𐌰𐌱𐌰𐌽 𐍃𐌴𐌹𐌳𐍉 𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽 𐌷𐌰𐌱𐌰𐌽 𐌱𐌰𐌽𐌳𐌰𐍂𐌴𐌹𐌺𐌾𐌹𐍃`
2. `𐌹𐌽 𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌰𐌹 𐌲𐌰𐍅𐌹𐍃𐍃𐌴𐌹𐍃 www stpaul gov`
3. `𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽 𐌷𐌰𐌱𐌰𐌽 𐍃𐌴𐌹𐌳𐍉 𐌸𐍉𐌶𐌴𐌹 𐌰𐌻𐌻𐍉𐍃 𐍅𐌹𐌺𐌹𐍀𐌰𐌹𐌳𐌾𐍉𐍃 𐍃𐌺𐌿𐌻𐌿𐌽 𐌷𐌰𐌱𐌰𐌽 𐌱𐌰𐌽𐌳𐌰𐍂𐌴𐌹𐌺𐌾𐌹𐍃`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_sl_1_scoperutce`
2. `𐌰𐌹𐌺𐌿𐌸_mago_𐌸𐌰_k,`
3. `𐌹𐍈𐌰𐌷𐌹_(*wve._bal`

**Context Size 2:**

1. `,_𐍃𐌴𐌹𐌽𐍃_𐌾𐌰𐌳𐌰,_ble`
2. `._oe._arkjan_ram,`
3. `𐌰𐌹._infornarusess`

**Context Size 3:**

1. `_-_chimess,_munia)`
2. `n,_with_kaúlustriv`
3. `s,_mallmers_but_at`

**Context Size 4:**

1. `_𐌹𐌽_𐌰𐌼𐌰𐌹𐍂𐌹𐌺𐌹𐍃_𐌿𐌽𐌳_𐌳`
2. `_to_restone_...hadu`
3. `_𐌾𐌰𐌷_𐌻𐌹𐌿𐌲𐍉𐍃𐌻𐌰𐌱𐌹𐍃𐌺𐌹𐍃`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (92,872 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 | 10,445 |
| Total Tokens | 85,682 |
| Mean Frequency | 8.20 |
| Median Frequency | 3 |
| Frequency Std Dev | 41.75 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 𐌹𐌽 | 1,691 |
| 2 | to | 1,570 |
| 3 | 𐌾𐌰𐌷 | 1,478 |
| 4 | 𐌹𐍃𐍄 | 1,269 |
| 5 | the | 906 |
| 6 | i | 903 |
| 7 | oe | 851 |
| 8 | ohg | 841 |
| 9 | a | 719 |
| 10 | 𐍅𐌰𐍃 | 616 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 𐌳𐌿𐍄𐍄𐌴 | 2 |
| 2 | 𐍆𐌹𐌲𐌲𐍂𐌰𐌽𐍃 | 2 |
| 3 | 𐍃𐌹𐌿𐌺𐌰𐌹𐌶𐌴 | 2 |
| 4 | 𐌺𐌿𐌺𐌾𐌰𐌽𐌳 | 2 |
| 5 | 𐌷𐌰𐌹𐍄𐌹𐍃 | 2 |
| 6 | 𐍃𐌿𐌽𐌸𐍂𐌹𐍃 | 2 |
| 7 | 𐌷𐌹𐌱𐌰𐌹𐍂𐌾𐍉𐍃 | 2 |
| 8 | citerior | 2 |
| 9 | ulterior | 2 |
| 10 | 𐌸𐌿𐍂𐌺𐌴𐌹𐍃 | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8663 |
| R² (Goodness of Fit) | 0.982156 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 33.8% |
| Top 1,000 | 63.2% |
| Top 5,000 | 86.7% |
| Top 10,000 | 99.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9822 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 33.8% of corpus
- **Long Tail:** 445 words needed for remaining 1.0% 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 | 0.1831 🏆 | 0.4505 | N/A | N/A |
| **mono_64d** | 64 | 0.0766 | 0.4301 | N/A | N/A |
| **mono_128d** | 128 | 0.0136 | 0.4355 | N/A | N/A |
| **aligned_32d** | 32 | 0.1831 | 0.4429 | 0.0080 | 0.0680 |
| **aligned_64d** | 64 | 0.0766 | 0.4301 | 0.0080 | 0.0740 |
| **aligned_128d** | 128 | 0.0136 | 0.4348 | 0.0160 | 0.0900 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.1831 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4373. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.6% 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 | **1.146** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-an` | ocean, wan, hauhjan |
| `-𐌽𐍃` | 𐌵𐌴𐌽𐍃, 𐌺𐌰𐌷𐍅𐌴𐌹𐌽𐍃, 𐌱𐍂𐌿𐌺𐌴𐌹𐌽𐍃 |

### 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 |
|------|----------|------------------|----------|
| `ther` | 2.06x | 24 contexts | there, other, others |
| `𐌰𐌿𐍂𐌳` | 1.98x | 18 contexts | 𐍅𐌰𐌿𐍂𐌳, 𐍅𐌰𐌿𐍂𐌳𐌴, 𐍅𐌰𐌿𐍂𐌳𐌰 |
| `tion` | 2.11x | 14 contexts | option, motion, nation |
| `𐌴𐌹𐌽𐌰` | 1.83x | 16 contexts | 𐌺𐌴𐌹𐌽𐌰, 𐌼𐌴𐌹𐌽𐌰, 𐍅𐌴𐌹𐌽𐌰 |
| `𐍅𐌰𐌿𐍂` | 1.80x | 14 contexts | 𐍅𐌰𐌿𐍂𐌳, 𐍅𐌰𐌿𐍂𐌳𐌴, 𐍅𐌰𐌿𐍂𐌳𐌰 |
| `𐌿𐌳𐌰𐌽` | 2.08x | 9 contexts | 𐌲𐌿𐌳𐌰𐌽𐍃, 𐌸𐌹𐌿𐌳𐌰𐌽, 𐌸𐌹𐌿𐌳𐌰𐌽𐍃 |
| `𐌹𐌿𐌳𐌰` | 1.71x | 14 contexts | 𐌻𐌹𐌿𐌳𐌰, 𐌸𐌹𐌿𐌳𐌰, 𐌸𐌹𐌿𐌳𐌰𐌹 |
| `𐌾𐌰𐌽𐌳` | 1.62x | 16 contexts | 𐍃𐍉𐌺𐌾𐌰𐌽𐌳, 𐍅𐌰𐌲𐌾𐌰𐌽𐌳, 𐌼𐌰𐍄𐌾𐌰𐌽𐌳 |
| `𐍂𐌰𐌶𐌳` | 1.98x | 9 contexts | 𐍂𐌰𐌶𐌳𐍉, 𐍂𐌰𐌶𐌳𐌰, 𐍂𐌰𐌶𐌳𐍉𐌼 |
| `𐌹𐌽𐌰𐌹` | 1.88x | 10 contexts | 𐌰𐌹𐌽𐌰𐌹, 𐍃𐌹𐌽𐌰𐌹, 𐍃𐌴𐌹𐌽𐌰𐌹 |
| `𐌷𐌰𐌱𐌰` | 1.91x | 9 contexts | 𐌷𐌰𐌱𐌰𐌽, 𐌷𐌰𐌱𐌰𐌼, 𐌷𐌰𐌱𐌰𐌹𐌸 |
| `𐍂𐌴𐌹𐌺` | 1.82x | 10 contexts | 𐍂𐌴𐌹𐌺𐍃, 𐍂𐌴𐌹𐌺𐌹, 𐍂𐌴𐌹𐌺𐌹𐍃 |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| 𐍃𐌺𐌰𐌿𐌽𐌴𐌹𐌽𐍃 | **`𐍃𐌺𐌰𐌿𐌽𐌴𐌹-𐌽𐍃`** | 4.5 | `𐍃𐌺𐌰𐌿𐌽𐌴𐌹` |
| 𐍆𐍂𐌿𐌼𐌹𐍃𐍄𐍉𐌽𐍃 | **`𐍆𐍂𐌿𐌼𐌹𐍃𐍄𐍉-𐌽𐍃`** | 4.5 | `𐍆𐍂𐌿𐌼𐌹𐍃𐍄𐍉` |
| 𐌼𐌿𐌽𐌳𐍂𐌴𐌹𐌽𐍃 | **`𐌼𐌿𐌽𐌳𐍂𐌴𐌹-𐌽𐍃`** | 4.5 | `𐌼𐌿𐌽𐌳𐍂𐌴𐌹` |
| 𐌰𐌿𐍃𐍄𐍂𐌰𐌲𐌿𐍄𐌰𐌽𐍃 | **`𐌰𐌿𐍃𐍄𐍂𐌰𐌲𐌿𐍄𐌰-𐌽𐍃`** | 4.5 | `𐌰𐌿𐍃𐍄𐍂𐌰𐌲𐌿𐍄𐌰` |
| 𐌰𐌽𐌳𐌽𐌿𐌼𐌰𐌽𐍃 | **`𐌰𐌽𐌳𐌽𐌿𐌼𐌰-𐌽𐍃`** | 1.5 | `𐌰𐌽𐌳𐌽𐌿𐌼𐌰` |
| 𐌲𐌰𐌲𐌰𐌷𐌰𐍆𐍄𐌾𐌰𐌽𐌳𐌰𐌽𐍃 | **`𐌲𐌰𐌲𐌰𐌷𐌰𐍆𐍄𐌾𐌰𐌽𐌳𐌰-𐌽𐍃`** | 1.5 | `𐌲𐌰𐌲𐌰𐌷𐌰𐍆𐍄𐌾𐌰𐌽𐌳𐌰` |
| porthpean | **`porthpe-an`** | 1.5 | `porthpe` |
| barbarian | **`barbari-an`** | 1.5 | `barbari` |
| scandinavian | **`scandinavi-an`** | 1.5 | `scandinavi` |
| 𐍆𐍂𐌹𐌾𐌰𐍄𐌹𐌼𐍂𐌴𐌹𐌽𐍃 | **`𐍆𐍂𐌹𐌾𐌰𐍄𐌹𐌼𐍂𐌴𐌹-𐌽𐍃`** | 1.5 | `𐍆𐍂𐌹𐌾𐌰𐍄𐌹𐌼𐍂𐌴𐌹` |
| 𐌷𐍂𐌿𐌲𐌾𐌰𐌱𐌰𐌹𐌽𐌰𐌽𐍃 | **`𐌷𐍂𐌿𐌲𐌾𐌰𐌱𐌰𐌹𐌽𐌰-𐌽𐍃`** | 1.5 | `𐌷𐍂𐌿𐌲𐌾𐌰𐌱𐌰𐌹𐌽𐌰` |
| 𐌼𐌰𐌾𐌰𐌹𐌽𐌾𐍉𐌽𐍃 | **`𐌼𐌰𐌾𐌰𐌹𐌽𐌾𐍉-𐌽𐍃`** | 1.5 | `𐌼𐌰𐌾𐌰𐌹𐌽𐌾𐍉` |
| macmillan | **`macmill-an`** | 1.5 | `macmill` |
| 𐌼𐌹𐌻𐌿𐌺𐍃𐍆𐍉𐌳𐌾𐌰𐌽𐍃 | **`𐌼𐌹𐌻𐌿𐌺𐍃𐍆𐍉𐌳𐌾𐌰-𐌽𐍃`** | 1.5 | `𐌼𐌹𐌻𐌿𐌺𐍃𐍆𐍉𐌳𐌾𐌰` |
| 𐌽𐌹𐍂𐌱𐌰𐌽𐌹𐌽𐍃 | **`𐌽𐌹𐍂𐌱𐌰𐌽𐌹-𐌽𐍃`** | 1.5 | `𐌽𐌹𐍂𐌱𐌰𐌽𐌹` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Gothic 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 (2.88x) |
| N-gram | **2-gram** | Lowest perplexity (546) |
| Markov | **Context-4** | Highest predictability (98.4%) |
| 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 15:24:37*