---
language: uk
language_name: Ukrainian
language_family: slavic_east
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-slavic_east
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: 4.642
  - name: best_isotropy
    type: isotropy
    value: 0.7906
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ukrainian** 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** | 3.497x | 3.50 | 0.0536% | 2,399,514 |
| **16k** | 3.921x | 3.92 | 0.0601% | 2,140,331 |
| **32k** | 4.309x | 4.31 | 0.0661% | 1,947,512 |
| **64k** | 4.642x 🏆 | 4.64 | 0.0712% | 1,807,481 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Шлепаков: Шлепаков Арнольд Миколайович — історик. Шлепаков Микола Степанович — ф...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ш ле па ков : ▁ш ле па ков ▁ар ... (+17 more)` | 27 |
| 16k | `▁ш ле па ков : ▁ш ле па ков ▁арно ... (+15 more)` | 25 |
| 32k | `▁шле па ков : ▁шле па ков ▁арнольд ▁миколайович ▁— ... (+11 more)` | 21 |
| 64k | `▁шлепаков : ▁шлепаков ▁арнольд ▁миколайович ▁— ▁історик . ▁шлепаков ▁микола ... (+5 more)` | 15 |

**Sample 2:** `Села: Біївці — Київська область, Обухівський район Біївці — Полтавська область, ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁села : ▁бі їв ці ▁— ▁київська ▁область , ▁обу ... (+12 more)` | 22 |
| 16k | `▁села : ▁бі їв ці ▁— ▁київська ▁область , ▁обухівський ... (+10 more)` | 20 |
| 32k | `▁села : ▁бі ївці ▁— ▁київська ▁область , ▁обухівський ▁район ... (+8 more)` | 18 |
| 64k | `▁села : ▁бі ївці ▁— ▁київська ▁область , ▁обухівський ▁район ... (+8 more)` | 18 |

**Sample 3:** `Апіоніни (Насіннеїди, Грушовидки) — це підродина жуків з родини Апіоніди (Apioni...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁а пі оні ни ▁( на сі н не ї ... (+27 more)` | 37 |
| 16k | `▁а пі оні ни ▁( на сін не їди , ... (+23 more)` | 33 |
| 32k | `▁а пі оні ни ▁( на сін не їди , ... (+22 more)` | 32 |
| 64k | `▁а пі оні ни ▁( насін не їди , ▁гру ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 64k achieves 4.642x compression
- **Lowest UNK Rate:** 8k with 0.0536% 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 | 187,448 | 17.52 | 685,840 | 5.0% | 14.5% |
| **2-gram** | Subword | 437 🏆 | 8.77 | 13,081 | 55.4% | 97.6% |
| **3-gram** | Word | 286,638 | 18.13 | 787,827 | 5.6% | 11.9% |
| **3-gram** | Subword | 4,150 | 12.02 | 116,111 | 18.3% | 58.5% |
| **4-gram** | Word | 426,525 | 18.70 | 1,132,759 | 6.5% | 12.0% |
| **4-gram** | Subword | 25,826 | 14.66 | 714,146 | 8.4% | 27.8% |
| **5-gram** | Word | 231,506 | 17.82 | 725,209 | 9.1% | 16.1% |
| **5-gram** | Subword | 110,683 | 16.76 | 2,359,262 | 4.5% | 15.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `у році` | 39,132 |
| 2 | `під час` | 21,948 |
| 3 | `ic в` | 21,270 |
| 4 | `а також` | 20,792 |
| 5 | `в україні` | 18,087 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ic в базі` | 12,721 |
| 2 | `оригінальному новому загальному` | 10,477 |
| 3 | `в оригінальному новому` | 10,475 |
| 4 | `новому загальному каталозі` | 10,473 |
| 5 | `до н е` | 8,904 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `в оригінальному новому загальному` | 10,475 |
| 2 | `оригінальному новому загальному каталозі` | 10,468 |
| 3 | `ic в оригінальному новому` | 8,549 |
| 4 | `новому загальному каталозі ic` | 7,477 |
| 5 | `загальному каталозі ic в` | 6,124 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `в оригінальному новому загальному каталозі` | 10,468 |
| 2 | `ic в оригінальному новому загальному` | 8,549 |
| 3 | `оригінальному новому загальному каталозі ic` | 7,477 |
| 4 | `новому загальному каталозі ic в` | 6,124 |
| 5 | `бази даних про об єкти` | 5,241 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ п` | 2,788,984 |
| 2 | `а _` | 2,782,956 |
| 3 | `_ в` | 2,478,604 |
| 4 | `, _` | 2,402,312 |
| 5 | `. _` | 2,316,510 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ н а` | 1,039,254 |
| 2 | `с ь к` | 1,024,566 |
| 3 | `_ п р` | 870,352 |
| 4 | `_ п о` | 858,794 |
| 5 | `н а _` | 850,334 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `о г о _` | 679,817 |
| 2 | `н н я _` | 490,022 |
| 3 | `_ н а _` | 413,243 |
| 4 | `с ь к о` | 409,920 |
| 5 | `_ п р о` | 378,210 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `к р а ї н` | 282,501 |
| 2 | `у к р а ї` | 252,628 |
| 3 | `е н н я _` | 250,361 |
| 4 | `_ у к р а` | 236,337 |
| 5 | `н о г о _` | 219,776 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 437
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~16% 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 | 1.0632 | 2.089 | 11.27 | 1,098,688 | 0.0% |
| **1** | Subword | 1.0573 | 2.081 | 7.85 | 5,267 | 0.0% |
| **2** | Word | 0.3016 | 1.233 | 1.83 | 12,375,104 | 69.8% |
| **2** | Subword | 0.8473 | 1.799 | 5.87 | 41,346 | 15.3% |
| **3** | Word | 0.0881 | 1.063 | 1.16 | 22,683,749 | 91.2% |
| **3** | Subword | 0.8543 | 1.808 | 4.91 | 242,807 | 14.6% |
| **4** | Word | 0.0277 🏆 | 1.019 | 1.04 | 26,324,244 | 97.2% |
| **4** | Subword | 0.7559 | 1.689 | 3.63 | 1,193,273 | 24.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `в батьківський дім і його окраїнним морем протоками назва мовою за петра чардиніна в середині 2`
2. `у першому турі з них 22 січня за негайне перекидання до а по абдуллах аль азхар`
3. `і 4 результати голос панк музиканти науковці астрономи вважали для кількості загиблих 95 82 трубы сл...`

**Context Size 2:**

1. `у році стипендію і поступити у підпорядкування головної команди вперше була видана 9 серпня в сьогод...`
2. `під час якої були самодержавство православ я офіційною мовою була османська початкова освіта є одніє...`
3. `ic в базі vizier ic в оригінальному новому загальному каталозі ic в базі vizier ic в оригінальному`

**Context Size 3:**

1. `ic в базі simbad ic в базі nasa extragalactic database бази даних про об єкти ngc ic ic`
2. `оригінальному новому загальному каталозі перевірена інформація про ic ic в базі nasa extragalactic d...`
3. `в оригінальному новому загальному каталозі ic в оригінальному новому загальному каталозі ic в оригін...`

**Context Size 4:**

1. `в оригінальному новому загальному каталозі ic в оригінальному новому загальному каталозі ic 541 в ор...`
2. `оригінальному новому загальному каталозі ic 260 в базі simbad ic в базі vizier ic в базі nasa extrag...`
3. `ic в оригінальному новому загальному каталозі ic в оригінальному новому загальному каталозі перевіре...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_й_—_заходу_да_а`
2. `ониндиннив_сти_з`
3. `а_сути_в_бії_мія`

**Context Size 2:**

1. `_празии_5_махол_н`
2. `а_є_боваєктажам_в`
3. `_відня_вийшоми_ла`

**Context Size 3:**

1. `_нання_у_сунути_ім`
2. `ське_нобійно-жозем`
3. `_прення_одиланзент`

**Context Size 4:**

1. `ого_слідних_примусо`
2. `ння_верхнею_черничо`
3. `_на_саку,_торгове_в`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,193,273 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 | 524,715 |
| Total Tokens | 29,104,691 |
| Mean Frequency | 55.47 |
| Median Frequency | 4 |
| Frequency Std Dev | 1788.64 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | в | 584,423 |
| 2 | у | 509,046 |
| 3 | і | 475,294 |
| 4 | на | 421,086 |
| 5 | з | 398,175 |
| 6 | та | 338,290 |
| 7 | до | 243,692 |
| 8 | що | 178,466 |
| 9 | року | 157,886 |
| 10 | за | 156,732 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | паніцца | 2 |
| 2 | ро́рбах | 2 |
| 3 | рубе́ль | 2 |
| 4 | катархей | 2 |
| 5 | азой | 2 |
| 6 | приской | 2 |
| 7 | гадейському | 2 |
| 8 | сезан | 2 |
| 9 | конезаводства | 2 |
| 10 | сінельникова | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8995 |
| R² (Goodness of Fit) | 0.997133 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 24.5% |
| Top 1,000 | 44.1% |
| Top 5,000 | 62.3% |
| Top 10,000 | 70.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9971 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 24.5% of corpus
- **Long Tail:** 514,715 words needed for remaining 29.4% 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 | 0.7906 🏆 | 0.3688 | N/A | N/A |
| **mono_64d** | 64 | 0.7645 | 0.2903 | N/A | N/A |
| **mono_128d** | 128 | 0.6859 | 0.2083 | N/A | N/A |
| **aligned_32d** | 32 | 0.7906 | 0.3638 | 0.0600 | 0.2820 |
| **aligned_64d** | 64 | 0.7645 | 0.2932 | 0.1320 | 0.4220 |
| **aligned_128d** | 128 | 0.6859 | 0.2081 | 0.1620 | 0.5000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7906 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2887. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 16.2% 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 | **0.010** | 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 |
|--------|----------|
| `-с` | серіри, словникарство, стійок |
| `-к` | клинописній, купрієнко, контролюючого |
| `-ма` | макаронічну, матеріалізму, македонянин |
| `-а` | акціонерів, адвокатами, арманізм |
| `-ко` | контролюючого, кошториси, конгресмен |
| `-ка` | калькутти, карагандинською, катренко |
| `-в` | воллс, вигином, вимагаючи |
| `-по` | популяція, поклики, поданні |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | бехерівка, ядерна, чигиринська |
| `-ий` | летунський, нецентрований, триденський |
| `-и` | приспали, мільйонерки, серіри |
| `-о` | купрієнко, словникарство, контролюючого |
| `-й` | клинописній, летунський, нецентрований |
| `-і` | міліметрі, червоніші, осяяні |
| `-го` | контролюючого, бактерійного, жартівливого |
| `-м` | вигином, дослідженим, македонським |

### 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 |
|------|----------|------------------|----------|
| `ають` | 2.47x | 104 contexts | дають, лають, мають |
| `увал` | 1.86x | 304 contexts | тувал, тувалу, бувало |
| `ьког` | 2.42x | 55 contexts | ського, яцького, яського |
| `ання` | 1.84x | 137 contexts | пання, вання, рання |
| `ький` | 2.15x | 58 contexts | ський, цький, яський |
| `ськи` | 1.41x | 426 contexts | ський, яський, леськи |
| `ніст` | 1.62x | 185 contexts | ність, юність, ністру |
| `ленн` | 1.66x | 160 contexts | ленну, ленні, гленн |
| `єтьс` | 2.55x | 26 contexts | ється, чується, діється |
| `ької` | 2.50x | 27 contexts | ської, яцької, тоцької |
| `ійсь` | 1.47x | 273 contexts | якійсь, військ, бійськ |
| `йськ` | 1.51x | 206 contexts | єйськ, єйська, тайськ |

### 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 |
|--------|--------|-----------|----------|
| `-п` | `-и` | 72 words | постачаючи, пропорции |
| `-с` | `-а` | 69 words | сповідника, струмочка |
| `-к` | `-а` | 68 words | каца, козлівська |
| `-п` | `-а` | 65 words | прописна, петровська |
| `-с` | `-й` | 65 words | сучавський, склифосовский |
| `-с` | `-и` | 58 words | скрипники, сукупностями |
| `-в` | `-и` | 57 words | вистачати, взаємовигідними |
| `-к` | `-й` | 55 words | китмановський, карпатскій |
| `-п` | `-і` | 55 words | поліморфні, палеарктиці |
| `-к` | `-и` | 54 words | кварками, кроками |

### 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 |
|------|-----------------|------------|------|
| народилася | **`народил-а-ся`** | 7.5 | `а` |
| послідовниками | **`послідовни-ка-ми`** | 7.5 | `ка` |
| кінострічках | **`кіностріч-ка-х`** | 7.5 | `ка` |
| фальшивих | **`фальши-в-их`** | 7.5 | `в` |
| заробітками | **`заробіт-ка-ми`** | 7.5 | `ка` |
| тейякскую | **`тейякс-ку-ю`** | 7.5 | `ку` |
| священиками | **`священи-ка-ми`** | 7.5 | `ка` |
| кронтовская | **`кронтовс-ка-я`** | 7.5 | `ка` |
| правилами | **`правил-а-ми`** | 7.5 | `а` |
| меридіану | **`мериді-а-ну`** | 7.5 | `а` |
| соціалізмові | **`соціалізм-о-ві`** | 7.5 | `о` |
| программе | **`програм-м-е`** | 7.5 | `м` |
| універсамі | **`універса-м-і`** | 7.5 | `м` |
| автошляхами | **`автошлях-а-ми`** | 7.5 | `а` |
| абразивного | **`абразив-но-го`** | 6.0 | `абразив` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ukrainian 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 (4.64x) |
| N-gram | **2-gram** | Lowest perplexity (437) |
| Markov | **Context-4** | Highest predictability (97.2%) |
| 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: 2026-01-11 06:57:52*