---
language: bs
language_name: Bosnian
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: 4.709
  - name: best_isotropy
    type: isotropy
    value: 0.6791
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Bosnian** 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** | 3.626x | 3.63 | 0.1221% | 1,306,515 |
| **16k** | 4.032x | 4.03 | 0.1358% | 1,174,869 |
| **32k** | 4.404x | 4.40 | 0.1483% | 1,075,596 |
| **64k** | 4.709x 🏆 | 4.71 | 0.1586% | 1,005,898 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Vrpolje Ljubomir je naseljeno mjesto u gradu Trebinju, Bosna i Hercegovina. Stan...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁vr polje ▁lju bo mir ▁je ▁naseljeno ▁mjesto ▁u ▁gradu ... (+16 more)` | 26 |
| 16k | `▁vr polje ▁ljubo mir ▁je ▁naseljeno ▁mjesto ▁u ▁gradu ▁trebinju ... (+13 more)` | 23 |
| 32k | `▁vr polje ▁ljubomir ▁je ▁naseljeno ▁mjesto ▁u ▁gradu ▁trebinju , ... (+12 more)` | 22 |
| 64k | `▁vrpolje ▁ljubomir ▁je ▁naseljeno ▁mjesto ▁u ▁gradu ▁trebinju , ▁bosna ... (+11 more)` | 21 |

**Sample 2:** `Kobatovci su naseljeno mjesto u gradu Laktaši, Bosna i Hercegovina. Stanovništvo...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ko ba to vci ▁su ▁naseljeno ▁mjesto ▁u ▁gradu ▁la ... (+17 more)` | 27 |
| 16k | `▁koba to vci ▁su ▁naseljeno ▁mjesto ▁u ▁gradu ▁lakta ši ... (+14 more)` | 24 |
| 32k | `▁koba tovci ▁su ▁naseljeno ▁mjesto ▁u ▁gradu ▁laktaši , ▁bosna ... (+11 more)` | 21 |
| 64k | `▁koba tovci ▁su ▁naseljeno ▁mjesto ▁u ▁gradu ▁laktaši , ▁bosna ... (+11 more)` | 21 |

**Sample 3:** `Decenija 780-ih trajala je od 1. januara 780. do 31. decembra 789. godine. Događ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁dece nija ▁ 7 8 0 - ih ▁traja la ... (+31 more)` | 41 |
| 16k | `▁decenija ▁ 7 8 0 - ih ▁trajala ▁je ▁od ... (+29 more)` | 39 |
| 32k | `▁decenija ▁ 7 8 0 - ih ▁trajala ▁je ▁od ... (+29 more)` | 39 |
| 64k | `▁decenija ▁ 7 8 0 - ih ▁trajala ▁je ▁od ... (+29 more)` | 39 |


### Key Findings

- **Best Compression:** 64k achieves 4.709x compression
- **Lowest UNK Rate:** 8k with 0.1221% 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 | 80,810 | 16.30 | 664,455 | 9.9% | 28.7% |
| **2-gram** | Subword | 328 🏆 | 8.36 | 10,943 | 62.1% | 98.9% |
| **3-gram** | Word | 100,258 | 16.61 | 924,847 | 11.7% | 30.0% |
| **3-gram** | Subword | 3,216 | 11.65 | 100,916 | 20.8% | 64.5% |
| **4-gram** | Word | 134,611 | 17.04 | 1,482,132 | 12.9% | 30.8% |
| **4-gram** | Subword | 20,996 | 14.36 | 689,460 | 8.6% | 31.6% |
| **5-gram** | Word | 88,861 | 16.44 | 1,107,611 | 15.0% | 34.2% |
| **5-gram** | Subword | 89,572 | 16.45 | 2,357,541 | 4.7% | 18.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `spiralna galaksija` | 91,078 |
| 2 | `vanjski linkovi` | 68,061 |
| 3 | `se u` | 45,470 |
| 4 | `reference vanjski` | 44,256 |
| 5 | `ngc ic` | 40,015 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `reference vanjski linkovi` | 44,193 |
| 2 | `prečkasta spiralna galaksija` | 32,671 |
| 3 | `zavod za statistiku` | 22,679 |
| 4 | `popisu stanovništva godine` | 20,723 |
| 5 | `na popisu stanovništva` | 20,184 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `na popisu stanovništva godine` | 20,088 |
| 2 | `državni zavod za statistiku` | 14,619 |
| 3 | `broj stanovnika po popisima` | 13,853 |
| 4 | `reference vanjski linkovi u` | 13,677 |
| 5 | `novi opći katalog spisak` | 13,518 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `također pogledajte novi opći katalog` | 13,518 |
| 2 | `pogledajte novi opći katalog spisak` | 13,517 |
| 3 | `historija do teritorijalne reorganizacije u` | 13,436 |
| 4 | `interaktivni ngc online katalog astronomska` | 13,248 |
| 5 | `ngc online katalog astronomska baza` | 13,248 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 5,724,674 |
| 2 | `e _` | 4,473,918 |
| 3 | `j e` | 3,904,782 |
| 4 | `i _` | 3,802,145 |
| 5 | `_ s` | 3,388,803 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j e _` | 1,738,823 |
| 2 | `n a _` | 1,237,973 |
| 3 | `_ n a` | 1,177,081 |
| 4 | `_ j e` | 1,128,189 |
| 5 | `_ p o` | 1,086,240 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ j e _` | 924,709 |
| 2 | `i j a _` | 457,403 |
| 3 | `_ n a _` | 454,266 |
| 4 | `_ s e _` | 399,769 |
| 5 | `i j e _` | 316,944 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ j e _` | 263,188 |
| 2 | `_ g o d i` | 195,374 |
| 3 | `g o d i n` | 192,967 |
| 4 | `o _ j e _` | 190,942 |
| 5 | `_ n g c _` | 158,105 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 328
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~18% 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 | 0.9835 | 1.977 | 9.99 | 1,096,434 | 1.7% |
| **1** | Subword | 1.0155 | 2.022 | 7.71 | 3,863 | 0.0% |
| **2** | Word | 0.3071 | 1.237 | 1.90 | 10,934,441 | 69.3% |
| **2** | Subword | 0.9460 | 1.927 | 6.59 | 29,789 | 5.4% |
| **3** | Word | 0.1029 | 1.074 | 1.20 | 20,758,711 | 89.7% |
| **3** | Subword | 0.9514 | 1.934 | 5.47 | 196,125 | 4.9% |
| **4** | Word | 0.0378 🏆 | 1.027 | 1.06 | 24,939,260 | 96.2% |
| **4** | Subword | 0.9416 | 1.921 | 4.19 | 1,073,504 | 5.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i sfrj popis ostali su nove ere ce espanyol olímpic lluís d očigledno drevni grad u`
2. `je počeo zanimati za testiranje je holoenzim počinje u genima patofiziološki mehanizam samouništenja...`
3. `u zemaljskom muzeju i rukama do teritorijalne reorganizacije u 13 33 923 0 plesni parovi još`

**Context Size 2:**

1. `spiralna galaksija s ic 0 51 nepoznato 3 0 3 uglovnih minuta s a d p gdje`
2. `vanjski linkovi ic ic na aladin pregledaču ic katalog na ngc ic objekti sljedeći spisak sadrži deset`
3. `se u četvrtfinale potom je bila poljska glumica koja iza sebe thomasa morgensterna koch vor morgenst...`

**Context Size 3:**

1. `reference vanjski linkovi zvanični sajt općine teslić`
2. `prečkasta spiralna galaksija sbab p ngc 5 41 emisijska maglina en također pogledajte novi opći katal...`
3. `zavod za statistiku i evidenciju fnrj i sfrj popis stanovništva i godine knjiga narodnosni i vjerski...`

**Context Size 4:**

1. `na popisu stanovništva godine naseljeno mjesto majkovi je imalo 273 stanovnika broj stanovnika po po...`
2. `državni zavod za statistiku naselja i stanovništvo republike hrvatske 23 0 84 85 129 118 110 149 130...`
3. `broj stanovnika po popisima 31 38 napomena u nastalo izdvajanjem dijela iz naselja buk vlaka i opuze...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_diintk,_d,_pri_`
2. `arafužde_0452)_b`
3. `inavjuc_stodite_`

**Context Size 2:**

1. `a_stal)_teiftupng`
2. `e_podilnetskimost`
3. `jedin_štvoji_izvi`

**Context Size 3:**

1. `je_nazi_se_daklene`
2. `na_predočan_heime_`
3. `_nama_prija,_datim`

**Context Size 4:**

1. `_je_od_na_15_462_sb`
2. `ija_deset_na_od_tri`
3. `_na_prema_oltara_ko`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,073,504 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 | 504,813 |
| Total Tokens | 32,497,466 |
| Mean Frequency | 64.38 |
| Median Frequency | 4 |
| Frequency Std Dev | 2777.29 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 945,166 |
| 2 | je | 931,753 |
| 3 | u | 924,423 |
| 4 | na | 457,967 |
| 5 | se | 403,233 |
| 6 | su | 292,637 |
| 7 | od | 271,227 |
| 8 | za | 266,768 |
| 9 | 1 | 253,853 |
| 10 | ngc | 206,389 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | antiinfektivne | 2 |
| 2 | veditors | 2 |
| 3 | esac | 2 |
| 4 | martirosyan | 2 |
| 5 | neuzimanje | 2 |
| 6 | spekarski | 2 |
| 7 | probabilizamski | 2 |
| 8 | dtl | 2 |
| 9 | setap | 2 |
| 10 | visoravani | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9660 |
| R² (Goodness of Fit) | 0.999467 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.1% |
| Top 1,000 | 53.1% |
| Top 5,000 | 68.7% |
| Top 10,000 | 75.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9995 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.1% of corpus
- **Long Tail:** 494,813 words needed for remaining 24.3% 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 | 0.6791 🏆 | 0.3557 | N/A | N/A |
| **mono_64d** | 64 | 0.6789 | 0.2931 | N/A | N/A |
| **mono_128d** | 128 | 0.6505 | 0.2294 | N/A | N/A |
| **aligned_32d** | 32 | 0.6791 | 0.3517 | 0.1940 | 0.5160 |
| **aligned_64d** | 64 | 0.6789 | 0.2923 | 0.3680 | 0.7380 |
| **aligned_128d** | 128 | 0.6505 | 0.2262 | 0.4520 | 0.7800 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6791 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2914. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 45.2% 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 | **0.860** | 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 |
|--------|----------|
| `-pr` | promotriti, pristrasno, priznavajući |
| `-po` | podstilova, postporođajno, položene |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | ćamila, afrića, canaima |
| `-e` | candace, emilie, feničane |
| `-i` | izrađujući, promotriti, opstruktivni |
| `-om` | holivudskom, ekvatorom, mckaganom |
| `-na` | odoljena, zloćudna, interamericana |
| `-ni` | opstruktivni, bogobojazni, normani |
| `-og` | vazdušnog, nanizanog, modularnog |
| `-ja` | inkrustacija, gaskonja, bradikardija |

### 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 |
|------|----------|------------------|----------|
| `anov` | 1.53x | 627 contexts | panov, šanov, anova |
| `ijsk` | 1.54x | 411 contexts | ijski, šijska, azijske |
| `renc` | 2.13x | 74 contexts | renca, renci, renco |
| `kovi` | 1.39x | 620 contexts | okovi, ković, kovič |
| `alak` | 2.51x | 33 contexts | malak, talak, malaku |
| `selj` | 1.97x | 81 contexts | selja, seljo, crselj |
| `jekt` | 1.94x | 77 contexts | objekt, subjekt, objektu |
| `iral` | 1.65x | 165 contexts | viral, ziral, miral |
| `ksij` | 2.04x | 55 contexts | iksija, oleksij, taksiju |
| `vanj` | 1.56x | 169 contexts | vanju, vanji, kvanj |
| `acij` | 1.45x | 219 contexts | acije, acija, lacij |
| `bjek` | 2.29x | 27 contexts | ribjek, žabjek, objeki |

### 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 |
|--------|--------|-----------|----------|
| `-pr` | `-a` | 64 words | pripaja, prezentska |
| `-po` | `-a` | 56 words | posttestikulska, pokroviteljima |
| `-pr` | `-e` | 50 words | prijestupne, pregljeve |
| `-pr` | `-i` | 45 words | prevareni, prebacivani |
| `-po` | `-e` | 39 words | potterove, polusušne |
| `-po` | `-i` | 36 words | populaciji, potterovi |
| `-pr` | `-om` | 14 words | pramajkom, prustom |
| `-pr` | `-na` | 14 words | pravougaona, pretražena |
| `-pr` | `-ni` | 12 words | prevareni, prebacivani |
| `-po` | `-na` | 11 words | ponosna, polipropilena |

### 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 |
|------|-----------------|------------|------|
| nerazvijenog | **`nerazvijen-og`** | 4.5 | `nerazvijen` |
| langleyja | **`langley-ja`** | 4.5 | `langley` |
| nadvratnikom | **`nadvratnik-om`** | 4.5 | `nadvratnik` |
| zahvaćenog | **`zahvaćen-og`** | 4.5 | `zahvaćen` |
| posigurno | **`po-sigurno`** | 4.5 | `sigurno` |
| nepostojanja | **`nepostojan-ja`** | 4.5 | `nepostojan` |
| dramatizirana | **`dramatizira-na`** | 4.5 | `dramatizira` |
| newtonovom | **`newtonov-om`** | 4.5 | `newtonov` |
| bertoluccija | **`bertolucci-ja`** | 4.5 | `bertolucci` |
| uravnoteženog | **`uravnotežen-og`** | 4.5 | `uravnotežen` |
| ilustriranom | **`ilustriran-om`** | 4.5 | `ilustriran` |
| saobraćajne | **`saobraćaj-ne`** | 4.5 | `saobraćaj` |
| herlihyja | **`herlihy-ja`** | 4.5 | `herlihy` |
| čehovljevog | **`čehovljev-og`** | 4.5 | `čehovljev` |
| rječnikom | **`rječnik-om`** | 4.5 | `rječnik` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Bosnian 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 (4.71x) |
| N-gram | **2-gram** | Lowest perplexity (328) |
| Markov | **Context-4** | Highest predictability (96.2%) |
| 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: 2026-01-04 01:24:53*