---
language: bg
language_name: Bulgarian
language_family: slavic_south
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_south
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: 4.373
  - name: best_isotropy
    type: isotropy
    value: 0.7975
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-07
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Bulgarian** 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** | 3.452x | 3.45 | 0.0493% | 2,552,470 |
| **16k** | 3.809x | 3.81 | 0.0544% | 2,313,214 |
| **32k** | 4.120x | 4.12 | 0.0589% | 2,138,945 |
| **64k** | 4.373x 🏆 | 4.37 | 0.0625% | 2,015,292 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Часово отместване UTC-11 се използва в: : Американска Самоа, Атол Мидуей : Ниуе ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ча сово ▁от мест ване ▁utc - 1 1 ▁се ... (+17 more)` | 27 |
| 16k | `▁ча сово ▁от мест ване ▁utc - 1 1 ▁се ... (+15 more)` | 25 |
| 32k | `▁ча сово ▁от местване ▁utc - 1 1 ▁се ▁използва ... (+13 more)` | 23 |
| 64k | `▁часово ▁отместване ▁utc - 1 1 ▁се ▁използва ▁в : ... (+9 more)` | 19 |

**Sample 2:** `Synodontis ouemeensis е вид лъчеперка от семейство Mochokidae. Разпространение В...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁s yn od ont is ▁o u em e ensis ... (+22 more)` | 32 |
| 16k | `▁syn odont is ▁o u em e ensis ▁е ▁вид ... (+20 more)` | 30 |
| 32k | `▁syn odont is ▁ou em e ensis ▁е ▁вид ▁лъчеперка ... (+19 more)` | 29 |
| 64k | `▁synodontis ▁ou eme ensis ▁е ▁вид ▁лъчеперка ▁от ▁семейство ▁mochokidae ... (+13 more)` | 23 |

**Sample 3:** `Orthotomus derbianus е вид птица от семейство Cisticolidae. Разпространение Видъ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁or th ot om us ▁der b ian us ▁е ... (+22 more)` | 32 |
| 16k | `▁or th ot omus ▁der b ianus ▁е ▁вид ▁птица ... (+17 more)` | 27 |
| 32k | `▁orth ot omus ▁der b ianus ▁е ▁вид ▁птица ▁от ... (+14 more)` | 24 |
| 64k | `▁orth ot omus ▁der b ianus ▁е ▁вид ▁птица ▁от ... (+13 more)` | 23 |


### Key Findings

- **Best Compression:** 64k achieves 4.373x compression
- **Lowest UNK Rate:** 8k with 0.0493% 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 | 246,747 | 17.91 | 2,004,902 | 5.8% | 16.2% |
| **2-gram** | Subword | 385 🏆 | 8.59 | 20,810 | 61.1% | 97.4% |
| **3-gram** | Word | 1,033,483 | 19.98 | 4,251,847 | 2.5% | 8.2% |
| **3-gram** | Subword | 3,528 | 11.78 | 189,319 | 23.2% | 62.6% |
| **4-gram** | Word | 2,692,464 | 21.36 | 7,308,829 | 1.5% | 5.1% |
| **4-gram** | Subword | 21,676 | 14.40 | 1,191,303 | 10.4% | 32.6% |
| **5-gram** | Word | 2,278,792 | 21.12 | 5,264,454 | 1.8% | 5.4% |
| **5-gram** | Subword | 93,842 | 16.52 | 4,256,227 | 5.4% | 19.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `през г` | 371,674 |
| 2 | `да се` | 178,835 |
| 3 | `през година` | 109,499 |
| 4 | `външни препратки` | 108,119 |
| 5 | `е на` | 90,144 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `по време на` | 72,585 |
| 2 | `източници външни препратки` | 52,888 |
| 3 | `пр н е` | 38,682 |
| 4 | `може да се` | 32,598 |
| 5 | `през г е` | 28,945 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `разпространение видът е разпространен` | 11,928 |
| 2 | `видът е разпространен в` | 11,811 |
| 3 | `може да се отнася` | 9,394 |
| 4 | `външни препратки официален сайт` | 9,248 |
| 5 | `застрашен от изчезване разпространение` | 9,061 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `разпространение видът е разпространен в` | 11,030 |
| 2 | `може да се отнася за` | 8,323 |
| 3 | `е вид птица от семейство` | 8,165 |
| 4 | `източници външни препратки уебсайт на` | 7,757 |
| 5 | `външни препратки уебсайт на общината` | 7,230 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 22,221,689 |
| 2 | `н а` | 13,044,169 |
| 3 | `и _` | 12,174,707 |
| 4 | `_ с` | 10,248,868 |
| 5 | `_ н` | 9,602,446 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н а _` | 8,421,175 |
| 2 | `_ н а` | 7,714,836 |
| 3 | `_ п р` | 3,824,613 |
| 4 | `т а _` | 3,691,871 |
| 5 | `т о _` | 3,556,816 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ н а _` | 5,969,377 |
| 2 | `а т а _` | 2,454,178 |
| 3 | `_ о т _` | 2,129,103 |
| 4 | `а _ н а` | 1,914,071 |
| 5 | `_ п р е` | 1,889,917 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _ н а _` | 1,515,525 |
| 2 | `е _ н а _` | 949,109 |
| 3 | `_ п р е з` | 882,206 |
| 4 | `п р е з _` | 849,611 |
| 5 | `о _ н а _` | 755,344 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 385
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~19% 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 | 0.9743 | 1.965 | 12.25 | 1,896,771 | 2.6% |
| **1** | Subword | 1.0920 | 2.132 | 7.98 | 9,126 | 0.0% |
| **2** | Word | 0.3814 | 1.303 | 2.47 | 23,216,480 | 61.9% |
| **2** | Subword | 0.7778 | 1.714 | 5.53 | 72,830 | 22.2% |
| **3** | Word | 0.1657 | 1.122 | 1.39 | 57,272,367 | 83.4% |
| **3** | Subword | 0.8207 | 1.766 | 4.91 | 403,072 | 17.9% |
| **4** | Word | 0.0723 🏆 | 1.051 | 1.13 | 79,394,777 | 92.8% |
| **4** | Subword | 0.7498 | 1.682 | 3.81 | 1,979,446 | 25.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `на излезли преди тази система от общинския център е най доброто от контекстовото запитване за написв...`
2. `в миналото корабите от своето поведение и актриси актьори рок група в колекциониране на военноморска...`
3. `и денчевци и е посрещала годеницата на черноморец бургас община палеор φούφας антиполохагос атина за...`

**Context Size 2:**

1. `през г тъй като години българия медал за на барила през г в битката е част от`
2. `да се шуми около връзката ѝ с република българия собствеността на международна научна конференция га...`
3. `външни препратки официален сайт схема на телескопа е било напълно елиминирано съмнението на ръководс...`

**Context Size 3:**

1. `по време на празничния сезон и стачката в метрото в токио vx не се използва от национално музикално`
2. `източници външни препратки официален сайт на метеор първите ѝ постановки са дипломният ѝ спектакъл с...`
3. `пр н е и са изключително популярни на балканите и втората най обща сред мъжете по онова време`

**Context Size 4:**

1. `разпространение видът е разпространен в малави мозамбик и j placidochromis johnstoni in iucn iucn re...`
2. `видът е разпространен в демократична република t lamprologus lethops in iucn iucn red list of threat...`
3. `може да се отнася до фердинандо i де медичи за да приюти извънбрачните дъщери на алесандро за разлик...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_трхтвътва_бъно_`
2. `а_ma_верг._п_ц_м`
3. `ита_менизандиясн`

**Context Size 2:**

1. `а_преват_и_с_ко_к`
2. `на_сед_хеърши_ак:`
3. `и_от_стори_те_съе`

**Context Size 3:**

1. `на_кампийский_став`
2. `_на_от_вите_ръчепе`
3. `_прически_баваща_с`

**Context Size 4:**

1. `_на_шаламброзиеолог`
2. `ата_е_важна_космиче`
3. `_от_попов_конвойна_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,979,446 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 | 888,624 |
| Total Tokens | 105,654,230 |
| Mean Frequency | 118.90 |
| Median Frequency | 4 |
| Frequency Std Dev | 9303.24 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | на | 5,995,585 |
| 2 | в | 3,186,690 |
| 3 | и | 3,167,004 |
| 4 | е | 2,175,525 |
| 5 | от | 2,154,986 |
| 6 | за | 1,348,073 |
| 7 | се | 1,261,391 |
| 8 | г | 1,205,312 |
| 9 | с | 1,088,412 |
| 10 | през | 849,597 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | кепевци | 2 |
| 2 | сарджовци | 2 |
| 3 | мъндън | 2 |
| 4 | талиевия | 2 |
| 5 | carbonato | 2 |
| 6 | tallio | 2 |
| 7 | разр | 2 |
| 8 | барутхана | 2 |
| 9 | азадлу | 2 |
| 10 | шталаг | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9425 |
| R² (Goodness of Fit) | 0.997405 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 35.2% |
| Top 1,000 | 53.9% |
| Top 5,000 | 70.2% |
| Top 10,000 | 77.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9974 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 35.2% of corpus
- **Long Tail:** 878,624 words needed for remaining 22.8% 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 | 0.7975 🏆 | 0.3595 | N/A | N/A |
| **mono_64d** | 64 | 0.7851 | 0.2896 | N/A | N/A |
| **mono_128d** | 128 | 0.7344 | 0.2334 | N/A | N/A |
| **aligned_32d** | 32 | 0.7975 | 0.3609 | 0.1560 | 0.5140 |
| **aligned_64d** | 64 | 0.7851 | 0.2794 | 0.3420 | 0.7340 |
| **aligned_128d** | 128 | 0.7344 | 0.2326 | 0.4740 | 0.8180 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7975 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2926. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 47.4% 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 | **-0.715** | 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 |
|--------|----------|
| `-пр` | предхождащ, прихлупена, правнообвързващи |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | исаака, жижавица, гамета |
| `-та` | гамета, лопатовидната, малинката |
| `-те` | врапчиште, древноиндийските, регресионните |
| `-ите` | древноиндийските, регресионните, циментовите |
| `-ата` | лопатовидната, малинката, покойницата |
| `-ни` | пълнозначни, шекони, капсулни |
| `-ки` | весегонски, гаговски, бачовски |
| `-ия` | шумния, напрежения, валутния |

### 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 |
|------|----------|------------------|----------|
| `лгар` | 2.07x | 163 contexts | елгар, илгар, юлгар |
| `нска` | 1.82x | 254 contexts | анска, энска, юнска |
| `анск` | 1.39x | 921 contexts | данск, анска, банск |
| `ийск` | 1.57x | 389 contexts | бийск, ийски, лийски |
| `нски` | 1.49x | 508 contexts | янски, ански, онски |
| `ълга` | 2.34x | 39 contexts | дълга, бълга, ългаз |
| `емвр` | 2.64x | 21 contexts | ноемвр, декемвр, нпември |
| `рски` | 1.42x | 269 contexts | юрски, врски, ерски |
| `точн` | 1.58x | 134 contexts | точни, точно, точна |
| `ичес` | 1.43x | 204 contexts | бичес, уичес, ическ |
| `остр` | 1.37x | 215 contexts | остри, остро, остра |
| `ение` | 1.49x | 123 contexts | пение, шение, мение |

### 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 |
|--------|--------|-----------|----------|
| `-пр` | `-а` | 59 words | пріложіха, приложната |
| `-пр` | `-те` | 21 words | притеснявайте, профилиращите |
| `-пр` | `-та` | 20 words | приложната, притежаващата |
| `-пр` | `-ите` | 18 words | профилиращите, пребогатите |
| `-пр` | `-ата` | 16 words | приложната, притежаващата |
| `-пр` | `-ия` | 15 words | противоракетния, притежания |
| `-пр` | `-то` | 13 words | прозводството, препострояването |
| `-пр` | `-ни` | 9 words | производни, предхождани |
| `-пр` | `-ки` | 7 words | прокарвайки, правейки |
| `-пр` | `-на` | 6 words | приблизителна, престъпна |

### 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 |
|------|-----------------|------------|------|
| пробитите | **`пр-обит-ите`** | 6.0 | `обит` |
| натрупванията | **`натрупван-ия-та`** | 6.0 | `натрупван` |
| смразяващата | **`смразяващ-ата`** | 4.5 | `смразяващ` |
| лишаването | **`лишаване-то`** | 4.5 | `лишаване` |
| телепатия | **`телепат-ия`** | 4.5 | `телепат` |
| плодородното | **`плодородно-то`** | 4.5 | `плодородно` |
| маловажното | **`маловажно-то`** | 4.5 | `маловажно` |
| стигналите | **`стигнал-ите`** | 4.5 | `стигнал` |
| латинизирани | **`латинизира-ни`** | 4.5 | `латинизира` |
| уругвайското | **`уругвайско-то`** | 4.5 | `уругвайско` |
| паразитология | **`паразитолог-ия`** | 4.5 | `паразитолог` |
| реализираната | **`реализиран-ата`** | 4.5 | `реализиран` |
| изчислимостта | **`изчислимост-та`** | 4.5 | `изчислимост` |
| истинностни | **`истинност-ни`** | 4.5 | `истинност` |
| паратаксалното | **`паратаксално-то`** | 4.5 | `паратаксално` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Bulgarian 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 (4.37x) |
| N-gram | **2-gram** | Lowest perplexity (385) |
| Markov | **Context-4** | Highest predictability (92.8%) |
| 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: 2026-01-07 00:49:27*