---
language: sr
language_name: Serbian
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: 4.463
  - name: best_isotropy
    type: isotropy
    value: 0.7304
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Serbian** 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** | 3.437x | 3.44 | 0.0903% | 3,193,783 |
| **16k** | 3.819x | 3.82 | 0.1004% | 2,874,429 |
| **32k** | 4.168x | 4.17 | 0.1095% | 2,633,814 |
| **64k** | 4.463x 🏆 | 4.46 | 0.1173% | 2,459,404 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Сабо () је веома често мађарско презиме као на пример код Срба Јовановић, Николи...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁сабо ▁() ▁је ▁веома ▁често ▁мађар ско ▁презиме ▁као ▁на ... (+22 more)` | 32 |
| 16k | `▁сабо ▁() ▁је ▁веома ▁често ▁мађарско ▁презиме ▁као ▁на ▁пример ... (+17 more)` | 27 |
| 32k | `▁сабо ▁() ▁је ▁веома ▁често ▁мађарско ▁презиме ▁као ▁на ▁пример ... (+17 more)` | 27 |
| 64k | `▁сабо ▁() ▁је ▁веома ▁често ▁мађарско ▁презиме ▁као ▁на ▁пример ... (+17 more)` | 27 |

**Sample 2:** `Еребус се може односити на: Еребус, божанство из грчке митологије планину на Ант...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ере бу с ▁се ▁може ▁односити ▁на : ▁ере бу ... (+29 more)` | 39 |
| 16k | `▁ере бус ▁се ▁може ▁односити ▁на : ▁ере бус , ... (+22 more)` | 32 |
| 32k | `▁ере бус ▁се ▁може ▁односити ▁на : ▁ере бус , ... (+17 more)` | 27 |
| 64k | `▁ере бус ▁се ▁може ▁односити ▁на : ▁ере бус , ... (+17 more)` | 27 |

**Sample 3:** `Ово је страница за вишезначну одредницу појма Лимбо. Лимбо (програмски језик) Ли...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ово ▁је ▁страница ▁за ▁више зна чну ▁одре дни цу ... (+27 more)` | 37 |
| 16k | `▁ово ▁је ▁страница ▁за ▁више зна чну ▁одре дни цу ... (+26 more)` | 36 |
| 32k | `▁ово ▁је ▁страница ▁за ▁више зна чну ▁одре дницу ▁појма ... (+22 more)` | 32 |
| 64k | `▁ово ▁је ▁страница ▁за ▁вишезна чну ▁одре дницу ▁појма ▁лимбо ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.463x compression
- **Lowest UNK Rate:** 8k with 0.0903% 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 | 101,010 | 16.62 | 541,740 | 10.5% | 23.1% |
| **2-gram** | Subword | 417 🏆 | 8.70 | 10,655 | 57.4% | 97.8% |
| **3-gram** | Word | 173,243 | 17.40 | 753,336 | 12.1% | 19.9% |
| **3-gram** | Subword | 3,794 | 11.89 | 91,805 | 20.7% | 60.8% |
| **4-gram** | Word | 303,317 | 18.21 | 1,236,985 | 12.9% | 18.9% |
| **4-gram** | Subword | 23,753 | 14.54 | 568,494 | 8.7% | 30.0% |
| **5-gram** | Word | 175,057 | 17.42 | 859,857 | 15.7% | 23.0% |
| **5-gram** | Subword | 103,293 | 16.66 | 1,934,363 | 4.2% | 16.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `да се` | 37,569 |
| 2 | `да је` | 37,093 |
| 3 | `који је` | 32,864 |
| 4 | `је у` | 32,694 |
| 5 | `у француској` | 28,666 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `референце спољашње везе` | 17,332 |
| 2 | `географија насеља у` | 14,556 |
| 3 | `из године у` | 12,667 |
| 4 | `подацима из године` | 12,386 |
| 5 | `по подацима из` | 12,385 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `географија насеља у француској` | 12,290 |
| 2 | `у француској географија насеља` | 12,231 |
| 3 | `француској географија насеља у` | 12,231 |
| 4 | `по подацима из године` | 12,218 |
| 5 | `у општини је живело` | 12,073 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `француској географија насеља у француској` | 12,231 |
| 2 | `у француској географија насеља у` | 12,231 |
| 3 | `а густина насељености је износила` | 12,019 |
| 4 | `године у општини је живело` | 12,013 |
| 5 | `по подацима из године у` | 12,009 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 4,254,775 |
| 2 | `е _` | 3,484,880 |
| 3 | `и _` | 2,798,461 |
| 4 | `_ с` | 2,402,734 |
| 5 | `_ п` | 2,167,464 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ј е _` | 1,227,613 |
| 2 | `_ ј е` | 1,007,997 |
| 3 | `_ н а` | 904,776 |
| 4 | `_ п о` | 898,886 |
| 5 | `н а _` | 849,756 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ј е _` | 832,365 |
| 2 | `_ н а _` | 351,709 |
| 3 | `_ с е _` | 341,716 |
| 4 | `, _ - {` | 333,041 |
| 5 | `_ с у _` | 265,965 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _ ј е _` | 233,666 |
| 2 | `_ г о д и` | 196,626 |
| 3 | `г о д и н` | 193,637 |
| 4 | `о _ ј е _` | 179,487 |
| 5 | `о д и н е` | 149,943 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 417
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~17% 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 | 1.0281 | 2.039 | 9.57 | 1,005,421 | 0.0% |
| **1** | Subword | 0.9082 | 1.877 | 7.42 | 4,016 | 9.2% |
| **2** | Word | 0.2993 | 1.231 | 1.87 | 9,615,248 | 70.1% |
| **2** | Subword | 0.9001 | 1.866 | 6.18 | 29,746 | 10.0% |
| **3** | Word | 0.1002 | 1.072 | 1.20 | 17,985,483 | 90.0% |
| **3** | Subword | 0.8701 | 1.828 | 4.99 | 183,681 | 13.0% |
| **4** | Word | 0.0325 🏆 | 1.023 | 1.05 | 21,482,040 | 96.7% |
| **4** | Subword | 0.7815 | 1.719 | 3.70 | 916,341 | 21.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `је само састављали збирке одељења за члана председништва цк кпј у уметничко друштво је русија је`
2. `у овом делу sidereus nuncius године националност срби плаћали променила велики рептили који вређа кр...`
3. `и најавни део провансе и након што су поставили војску је 404 метара максималној 634 године`

**Context Size 2:**

1. `да се никада не напушта ни наду децу треба научити до 6 маја по црквеном а 6`
2. `да је основна обрада добро изведена и претежно сува са највећим избором литературе са исказима свјед...`
3. `који је стекао и велики број лоше васпитане деце из брака са марином севером и игра финале`

**Context Size 3:**

1. `референце спољашње везе база података insee арбукав на страници националног географског института фр...`
2. `географија насеља у француској север у француској географија насеља у француској мозел у француској ...`
3. `из године у општини је живело 41 становника а густина насељености је износила 37 47 општина се прост...`

**Context Size 4:**

1. `француској географија насеља у француској аверон у француској географија насеља у француској север у...`
2. `у француској географија насеља у француској алије у француској географија насеља у француској арјеж ...`
3. `по подацима из године у општини је живело становника а густина насељености је износила 148 84 општин...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_хе_фенсјутрават`
2. `а_рин-{cetote,_с`
3. `и,_ка_овезе_е_".`

**Context Size 2:**

1. `а_18._евојмаљивин`
2. `е_се_дембрановод_`
3. `и_мрепрата_и_ствр`

**Context Size 3:**

1. `је_у_бела_милазе_м`
2. `_је_(трна_тесаветс`
3. `_на_са_редињени_од`

**Context Size 4:**

1. `_је_насељености_чиј`
2. `_на_светом,_и_мишље`
3. `_се_раку.потребљено`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (916,341 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 | 517,888 |
| Total Tokens | 24,596,294 |
| Mean Frequency | 47.49 |
| Median Frequency | 4 |
| Frequency Std Dev | 2239.63 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | је | 841,603 |
| 2 | у | 779,149 |
| 3 | и | 778,274 |
| 4 | на | 355,146 |
| 5 | се | 345,085 |
| 6 | су | 272,433 |
| 7 | да | 243,646 |
| 8 | од | 217,292 |
| 9 | за | 179,897 |
| 10 | са | 153,021 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | astropixels | 2 |
| 2 | astron | 2 |
| 3 | periodicities | 2 |
| 4 | tjeenk | 2 |
| 5 | morsels | 2 |
| 6 | heatseekers | 2 |
| 7 | млађака | 2 |
| 8 | espenak | 2 |
| 9 | пба | 2 |
| 10 | пбка | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9204 |
| R² (Goodness of Fit) | 0.998749 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 29.3% |
| Top 1,000 | 48.4% |
| Top 5,000 | 64.3% |
| Top 10,000 | 71.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9987 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 29.3% of corpus
- **Long Tail:** 507,888 words needed for remaining 28.4% 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 | 0.7304 | 0.4041 | N/A | N/A |
| **mono_64d** | 64 | 0.6931 | 0.3311 | N/A | N/A |
| **mono_128d** | 128 | 0.6524 | 0.2382 | N/A | N/A |
| **aligned_32d** | 32 | 0.7304 🏆 | 0.4084 | 0.0400 | 0.2700 |
| **aligned_64d** | 64 | 0.6931 | 0.3210 | 0.1200 | 0.4240 |
| **aligned_128d** | 128 | 0.6524 | 0.2421 | 0.1280 | 0.4500 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7304 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3242. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 12.8% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.390** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

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

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-s` | schiffer, slotove, saposchnikowii |
| `-с` | сеља, сажела, социјалиста |
| `-a` | amonijak, abnormal, amundsen |
| `-к` | корисника, квасци, конвективну |
| `-а` | анализатори, алентаун, атеници |
| `-ма` | марашли, мауретаније, маленченко |
| `-по` | поморишки, подстрекивани, покајањем |
| `-b` | base, berlencourt, bessins |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | екосистемска, дикава, пауза |
| `-s` | entomopisthius, walkers, knottnerus |
| `-a` | taeniifera, jouvea, pillaia |
| `-и` | марашли, темперовани, анализатори |
| `-е` | пасуљанске, ларе, мауретаније |
| `-us` | entomopisthius, knottnerus, ovigerus |
| `-м` | деутеријумом, фруктозом, истакнутим |
| `-у` | упу, досежу, бубну |

### 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 |
|------|----------|------------------|----------|
| `ости` | 1.98x | 208 contexts | рости, аости, остин |
| `ском` | 2.03x | 155 contexts | уском, еском, воском |
| `ност` | 2.07x | 99 contexts | ностра, ностер, иностр |
| `анск` | 1.44x | 640 contexts | данск, канск, јански |
| `нски` | 1.73x | 187 contexts | јански, шонски, сенски |
| `асељ` | 2.49x | 36 contexts | насељу, насеље, засеље |
| `општ` | 1.98x | 83 contexts | опште, општу, општи |
| `држа` | 1.66x | 187 contexts | држао, држач, одржа |
| `егов` | 1.78x | 120 contexts | његов, негов, бегов |
| `ациј` | 1.66x | 153 contexts | лациј, ација, нације |
| `пшти` | 2.16x | 38 contexts | општи, уопшти, општио |
| `ориј` | 1.50x | 191 contexts | орија, морији, морије |

### 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 |
|--------|--------|-----------|----------|
| `-с` | `-а` | 93 words | светила, сенахирима |
| `-a` | `-s` | 89 words | avidus, abiskoensis |
| `-к` | `-а` | 84 words | капитализација, краварица |
| `-s` | `-s` | 79 words | spretus, synechogobius |
| `-a` | `-a` | 61 words | albopicta, anamaera |
| `-с` | `-и` | 56 words | сокобањи, сасечени |
| `-с` | `-е` | 54 words | стручне, смртнице |
| `-а` | `-а` | 52 words | ангажманима, астрофизичка |
| `-с` | `-м` | 51 words | сопством, севиљском |
| `-к` | `-и` | 49 words | касноантички, карантанији |

### 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 |
|------|-----------------|------------|------|
| електрана | **`електр-а-на`** | 7.5 | `а` |
| одгурнути | **`одгурн-у-ти`** | 7.5 | `у` |
| областимаи | **`области-ма-и`** | 7.5 | `ма` |
| оправдани | **`оправд-а-ни`** | 7.5 | `а` |
| меканском | **`ме-канск-ом`** | 6.0 | `канск` |
| поштовану | **`пошто-ва-ну`** | 6.0 | `пошто` |
| јованкину | **`јован-ки-ну`** | 6.0 | `јован` |
| коминикеи | **`комини-ке-и`** | 6.0 | `комини` |
| проживети | **`пр-оживе-ти`** | 6.0 | `оживе` |
| катаринин | **`катари-ни-н`** | 6.0 | `катари` |
| примењену | **`приме-ње-ну`** | 6.0 | `приме` |
| фосфолипида | **`фосфолипид-а`** | 4.5 | `фосфолипид` |
| зеведејева | **`зеведејев-а`** | 4.5 | `зеведејев` |
| радиоактивности | **`радиоактивност-и`** | 4.5 | `радиоактивност` |
| скорпиона | **`скорпион-а`** | 4.5 | `скорпион` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Serbian 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 | **64k BPE** | Best compression (4.46x) |
| N-gram | **2-gram** | Lowest perplexity (417) |
| Markov | **Context-4** | Highest predictability (96.7%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-11 00:46:21*