---
language: sh
language_name: Serbian (Latin)
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: 4.489
  - name: best_isotropy
    type: isotropy
    value: 0.6562
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-17
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Serbian (Latin)** 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** | 3.351x | 3.35 | 0.1426% | 3,710,049 |
| **16k** | 3.751x | 3.75 | 0.1597% | 3,313,984 |
| **32k** | 4.136x | 4.14 | 0.1761% | 3,005,948 |
| **64k** | 4.489x 🏆 | 4.49 | 0.1911% | 2,769,508 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Galbenu ima više značenja: Galbenu, Galbenu Opština Galbenu, Brăila`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gal ben u ▁ima ▁više ▁značenja : ▁gal ben u ... (+12 more)` | 22 |
| 16k | `▁gal benu ▁ima ▁više ▁značenja : ▁gal benu , ▁gal ... (+8 more)` | 18 |
| 32k | `▁gal benu ▁ima ▁više ▁značenja : ▁gal benu , ▁gal ... (+7 more)` | 17 |
| 64k | `▁gal benu ▁ima ▁više ▁značenja : ▁gal benu , ▁gal ... (+6 more)` | 16 |

**Sample 2:** `Molekulska formula se može odnositi na: Deksrazoksan Pentostatin Acetilkarnozin`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁molekulska ▁formula ▁se ▁može ▁odnositi ▁na : ▁de ks ra ... (+12 more)` | 22 |
| 16k | `▁molekulska ▁formula ▁se ▁može ▁odnositi ▁na : ▁de ks ra ... (+10 more)` | 20 |
| 32k | `▁molekulska ▁formula ▁se ▁može ▁odnositi ▁na : ▁de ks ra ... (+10 more)` | 20 |
| 64k | `▁molekulska ▁formula ▁se ▁može ▁odnositi ▁na : ▁de ks ra ... (+8 more)` | 18 |

**Sample 3:** `Marcucci ima više značenja: Marcucci, Lucca Marcucci, Macerata`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mar cu c ci ▁ima ▁više ▁značenja : ▁mar cu ... (+10 more)` | 20 |
| 16k | `▁mar cu cci ▁ima ▁više ▁značenja : ▁mar cu cci ... (+7 more)` | 17 |
| 32k | `▁mar cu cci ▁ima ▁više ▁značenja : ▁mar cu cci ... (+7 more)` | 17 |
| 64k | `▁mar cu cci ▁ima ▁više ▁značenja : ▁mar cu cci ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.489x compression
- **Lowest UNK Rate:** 8k with 0.1426% 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 | 70,231 | 16.10 | 1,297,205 | 17.5% | 34.2% |
| **2-gram** | Subword | 308 🏆 | 8.26 | 17,425 | 63.9% | 99.1% |
| **3-gram** | Word | 71,253 | 16.12 | 1,947,671 | 20.3% | 38.7% |
| **3-gram** | Subword | 2,856 | 11.48 | 140,131 | 21.8% | 67.0% |
| **4-gram** | Word | 77,932 | 16.25 | 3,159,151 | 21.1% | 41.0% |
| **4-gram** | Subword | 17,451 | 14.09 | 805,205 | 10.3% | 34.9% |
| **5-gram** | Word | 47,310 | 15.53 | 2,271,520 | 22.4% | 44.2% |
| **5-gram** | Subword | 72,387 | 16.14 | 2,854,449 | 6.9% | 22.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `vanjske veze` | 365,724 |
| 2 | `reference literatura` | 253,293 |
| 3 | `u opštini` | 249,864 |
| 4 | `literatura vanjske` | 239,013 |
| 5 | `se nalazi` | 230,020 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `literatura vanjske veze` | 239,012 |
| 2 | `reference literatura vanjske` | 231,740 |
| 3 | `nadmorskoj visini od` | 206,227 |
| 4 | `se nalazi na` | 199,011 |
| 5 | `na nadmorskoj visini` | 195,919 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `reference literatura vanjske veze` | 231,739 |
| 2 | `na nadmorskoj visini od` | 195,753 |
| 3 | `nalazi na nadmorskoj visini` | 194,264 |
| 4 | `se nalazi na nadmorskoj` | 194,263 |
| 5 | `naselje se nalazi na` | 176,984 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `se nalazi na nadmorskoj visini` | 194,261 |
| 2 | `nalazi na nadmorskoj visini od` | 194,261 |
| 3 | `stanovnika naselje se nalazi na` | 176,911 |
| 4 | `naselje se nalazi na nadmorskoj` | 176,909 |
| 5 | `m reference literatura vanjske veze` | 158,235 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 11,868,424 |
| 2 | `e _` | 11,387,649 |
| 3 | `i _` | 8,439,887 |
| 4 | `j e` | 7,898,306 |
| 5 | `_ s` | 7,108,466 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j e _` | 4,332,062 |
| 2 | `_ n a` | 3,400,063 |
| 3 | `_ j e` | 2,962,324 |
| 4 | `_ u _` | 2,805,413 |
| 5 | `_ p r` | 2,640,480 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ j e _` | 2,500,801 |
| 2 | `_ n a _` | 1,012,547 |
| 3 | `_ s e _` | 987,234 |
| 4 | `_ p r o` | 943,243 |
| 5 | `e _ n a` | 846,873 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n a s e l` | 702,873 |
| 2 | `_ n a s e` | 702,329 |
| 3 | `a s e l j` | 701,918 |
| 4 | `a _ j e _` | 594,535 |
| 5 | `_ g o d i` | 573,498 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 308
- **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 | 1.0184 | 2.026 | 11.40 | 1,765,275 | 0.0% |
| **1** | Subword | 1.2791 | 2.427 | 8.32 | 8,241 | 0.0% |
| **2** | Word | 0.3197 | 1.248 | 2.00 | 20,074,468 | 68.0% |
| **2** | Subword | 0.7024 | 1.627 | 4.69 | 68,441 | 29.8% |
| **3** | Word | 0.1128 | 1.081 | 1.23 | 40,113,108 | 88.7% |
| **3** | Subword | 0.7622 | 1.696 | 4.36 | 320,739 | 23.8% |
| **4** | Word | 0.0405 🏆 | 1.028 | 1.07 | 49,336,446 | 96.0% |
| **4** | Subword | 0.7216 | 1.649 | 3.66 | 1,398,820 | 27.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `u opštini querétaro u rumunskom okrugu cvikau nojkirhen vorm springs je bilo je ukinuta četiri temen...`
2. `je zaštićena kraška vrela na početku svoje karijere ona postala glavnom gradu radom unhcr provodi i`
3. `i teritorijalnim gubicima mp3 on buddhist art of mathematics logic of roman history italy primary do...`

**Context Size 2:**

1. `vanjske veze boeing com mcdonnell douglas md 80 md 90 s druge strane antiohovi maloazijski posedi po...`
2. `reference literatura vanjske veze serije star trek deep space nine izvori vanjske veze by the cia fa...`
3. `u opštini tezontepec de aldama prema proceni iz godine u naselju je živelo 15 stanovnika naselje se`

**Context Size 3:**

1. `literatura vanjske veze by the cia factbook italian railways italian national and regional parks his...`
2. `reference literatura vanjske veze zvanični sajt opštine nem savezni zavod za statistiku stalna konfe...`
3. `nadmorskoj visini od m reference literatura vanjske veze u opštini tapalpa halisko`

**Context Size 4:**

1. `reference literatura vanjske veze u opštini tlachichilco verakruz`
2. `na nadmorskoj visini od m reference literatura vanjske veze by the cia factbook italian railways ita...`
3. `nalazi na nadmorskoj visini od 753 m reference literatura vanjske veze baza podataka insee cornas na...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_-znove_očkmnaca`
2. `a_stastorari,_kr`
3. `i_cizno._ičeći_u`

**Context Size 2:**

1. `a_lianje_bel_poša`
2. `e_oarem_pro_pozič`
3. `i_3_(pri_na_jevno`

**Context Size 3:**

1. `je_od_96._-_zapano`
2. `_nastime_bilantoma`
3. `_je_odnormaturesut`

**Context Size 4:**

1. `_je_bio_je_nalazima`
2. `_na_wolfgang_su_dje`
3. `_se_iznosi_0,36_m._`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,398,820 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 | 831,692 |
| Total Tokens | 73,187,626 |
| Mean Frequency | 88.00 |
| Median Frequency | 4 |
| Frequency Std Dev | 5458.78 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | u | 2,835,134 |
| 2 | je | 2,539,203 |
| 3 | i | 1,828,128 |
| 4 | na | 1,024,921 |
| 5 | se | 996,788 |
| 6 | od | 740,498 |
| 7 | su | 563,164 |
| 8 | iz | 480,024 |
| 9 | godine | 465,533 |
| 10 | za | 457,009 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | fretzera | 2 |
| 2 | kartif | 2 |
| 3 | karnion | 2 |
| 4 | kartifove | 2 |
| 5 | trifulgasov | 2 |
| 6 | rouxa | 2 |
| 7 | pikrata | 2 |
| 8 | chancelloru | 2 |
| 9 | jynxstrop | 2 |
| 10 | shahristoni | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9867 |
| R² (Goodness of Fit) | 0.999465 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 35.4% |
| Top 1,000 | 55.2% |
| Top 5,000 | 69.8% |
| Top 10,000 | 76.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9995 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 35.4% of corpus
- **Long Tail:** 821,692 words needed for remaining 23.8% 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 | 0.6562 🏆 | 0.3601 | N/A | N/A |
| **mono_64d** | 64 | 0.6544 | 0.2950 | N/A | N/A |
| **mono_128d** | 128 | 0.6020 | 0.2379 | N/A | N/A |
| **aligned_32d** | 32 | 0.6562 | 0.3559 | 0.2600 | 0.6660 |
| **aligned_64d** | 64 | 0.6544 | 0.2879 | 0.4620 | 0.8340 |
| **aligned_128d** | 128 | 0.6020 | 0.2418 | 0.5900 | 0.8740 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6562 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2964. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 59.0% 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 | **0.982** | 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` | smatram, sekeré, szucsáva |
| `-a` | arsenija, amsterdamove, aharski |
| `-ma` | marshom, malvinu, mashrou |
| `-m` | marshom, malvinu, mashrou |
| `-p` | puruborá, prenatalni, prejak |
| `-k` | kopitarovo, kačketi, kaftarinska |
| `-b` | bettis, bobovište, belavića |
| `-d` | drăgești, dekorisani, dobel |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | arsenija, kaftarinska, szucsáva |
| `-e` | amsterdamove, natpolovične, bobovište |
| `-i` | prenatalni, zatrudniti, kačketi |
| `-m` | smatram, marshom, copernicanism |
| `-u` | malvinu, mashrou, severinsku |
| `-om` | marshom, migratornom, probuđenom |
| `-n` | warleggan, wallisian, voisin |
| `-o` | kopitarovo, eskimsko, afipo |

### 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 |
|------|----------|------------------|----------|
| `efer` | 2.11x | 96 contexts | nefer, lefer, hefer |
| `dmor` | 2.17x | 60 contexts | odmor, edmor, odmoru |
| `admo` | 2.57x | 31 contexts | kadmo, nadmoć, tadmor |
| `anjs` | 1.63x | 226 contexts | vanjse, vanjsk, banjsku |
| `elje` | 1.48x | 378 contexts | relje, celje, kelje |
| `acij` | 1.51x | 295 contexts | lacij, acija, aciju |
| `njsk` | 1.56x | 183 contexts | vnjske, vanjsk, banjsku |
| `alaz` | 1.77x | 92 contexts | zalaz, nalaz, kalaz |
| `rsko` | 1.36x | 261 contexts | mrsko, drsko, irsko |
| `ržav` | 1.54x | 130 contexts | držav, kržava, državu |
| `ocen` | 1.46x | 126 contexts | kocen, ocenu, bocen |
| `pšti` | 1.82x | 39 contexts | opšti, uopšti, opštim |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-a` | 182 words | prigorja, palmata |
| `-p` | `-e` | 132 words | poljepšavanje, planiranje |
| `-s` | `-a` | 126 words | stoogesa, strtenica |
| `-k` | `-a` | 124 words | korijenja, klericima |
| `-p` | `-i` | 118 words | puhati, prokoagulansi |
| `-b` | `-a` | 101 words | bajkerska, brgata |
| `-d` | `-a` | 89 words | diližansama, došašća |
| `-s` | `-e` | 87 words | saksofoniste, srednjoafričke |
| `-a` | `-a` | 82 words | ariola, agatoerga |
| `-p` | `-m` | 79 words | plimskim, pečuškim |

### 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 |
|------|-----------------|------------|------|
| talasemiju | **`talasem-i-ju`** | 7.5 | `i` |
| šestokraku | **`šestok-ra-ku`** | 7.5 | `ra` |
| divanhane | **`divanh-a-ne`** | 7.5 | `a` |
| sadržavat | **`sadržav-a-t`** | 7.5 | `a` |
| zaštitilo | **`zaštiti-l-o`** | 7.5 | `l` |
| jednadžbama | **`jednadžb-a-ma`** | 7.5 | `a` |
| eliminisane | **`eliminis-a-ne`** | 7.5 | `a` |
| kanalizirane | **`kanalizir-a-ne`** | 7.5 | `a` |
| kiiyaahaan | **`kiiyaah-a-an`** | 7.5 | `a` |
| prostirati | **`prostir-a-ti`** | 7.5 | `a` |
| uranographia | **`uranograph-i-a`** | 7.5 | `i` |
| nesputane | **`nespu-ta-ne`** | 7.5 | `ta` |
| asfaltirane | **`asfaltir-a-ne`** | 7.5 | `a` |
| transalpina | **`transalp-i-na`** | 7.5 | `i` |
| parametrizovano | **`parametrizov-a-no`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Serbian (Latin) 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 (4.49x) |
| N-gram | **2-gram** | Lowest perplexity (308) |
| Markov | **Context-4** | Highest predictability (96.0%) |
| 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: 2026-01-17 05:35:37*