---
language: hr
language_name: Croatian
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: 4.592
  - name: best_isotropy
    type: isotropy
    value: 0.7990
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Croatian** 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** | 3.541x | 3.54 | 0.0441% | 1,061,585 |
| **16k** | 3.929x | 3.93 | 0.0489% | 956,840 |
| **32k** | 4.292x | 4.29 | 0.0534% | 875,971 |
| **64k** | 4.592x 🏆 | 4.59 | 0.0572% | 818,812 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `NGC je galaksija u zviježđu Vodenoj zmiji. Izvori Vanjske poveznice NGC`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ngc ▁je ▁galaksija ▁u ▁zviježđu ▁vode noj ▁z mi ji ... (+5 more)` | 15 |
| 16k | `▁ngc ▁je ▁galaksija ▁u ▁zviježđu ▁vode noj ▁z miji . ... (+4 more)` | 14 |
| 32k | `▁ngc ▁je ▁galaksija ▁u ▁zviježđu ▁vodenoj ▁zmiji . ▁izvori ▁vanjske ... (+2 more)` | 12 |
| 64k | `▁ngc ▁je ▁galaksija ▁u ▁zviježđu ▁vodenoj ▁zmiji . ▁izvori ▁vanjske ... (+2 more)` | 12 |

**Sample 2:** `Hrvatska: Kostadinovac (Križevci), gradsko naselje Križevaca Srbija: Kostadinova...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁hrvatska : ▁kosta di novac ▁( križe vci ), ▁grad ... (+24 more)` | 34 |
| 16k | `▁hrvatska : ▁kosta di novac ▁( križe vci ), ▁gradsko ... (+20 more)` | 30 |
| 32k | `▁hrvatska : ▁kosta di novac ▁( križe vci ), ▁gradsko ... (+19 more)` | 29 |
| 64k | `▁hrvatska : ▁kosta di novac ▁( križevci ), ▁gradsko ▁naselje ... (+17 more)` | 27 |

**Sample 3:** `NGC 587 je galaksija u zviježđu Trokut. Izvori Vanjske poveznice NGC`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ngc ▁ 5 8 7 ▁je ▁galaksija ▁u ▁zviježđu ▁troku ... (+6 more)` | 16 |
| 16k | `▁ngc ▁ 5 8 7 ▁je ▁galaksija ▁u ▁zviježđu ▁troku ... (+6 more)` | 16 |
| 32k | `▁ngc ▁ 5 8 7 ▁je ▁galaksija ▁u ▁zviježđu ▁trokut ... (+5 more)` | 15 |
| 64k | `▁ngc ▁ 5 8 7 ▁je ▁galaksija ▁u ▁zviježđu ▁trokut ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.592x compression
- **Lowest UNK Rate:** 8k with 0.0441% 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 | 267,023 | 18.03 | 1,536,962 | 6.2% | 15.5% |
| **2-gram** | Subword | 314 🏆 | 8.29 | 17,412 | 63.2% | 99.0% |
| **3-gram** | Word | 860,543 | 19.71 | 2,568,958 | 2.9% | 8.5% |
| **3-gram** | Subword | 3,101 | 11.60 | 146,611 | 21.1% | 65.0% |
| **4-gram** | Word | 2,007,494 | 20.94 | 4,346,865 | 2.5% | 6.6% |
| **4-gram** | Subword | 21,614 | 14.40 | 870,800 | 8.5% | 30.3% |
| **5-gram** | Word | 1,554,489 | 20.57 | 3,187,745 | 3.2% | 7.7% |
| **5-gram** | Subword | 106,845 | 16.71 | 3,145,742 | 3.9% | 15.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `je u` | 105,341 |
| 2 | `vanjske poveznice` | 93,834 |
| 3 | `koji je` | 79,115 |
| 4 | `da je` | 76,085 |
| 5 | `bio je` | 64,808 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `izvori vanjske poveznice` | 48,503 |
| 2 | `bosne i hercegovine` | 15,350 |
| 3 | `0 0 0` | 15,157 |
| 4 | `prema popisu stanovništva` | 14,804 |
| 5 | `popisu stanovništva iz` | 14,603 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `prema popisu stanovništva iz` | 13,965 |
| 2 | `popisu stanovništva iz godine` | 9,055 |
| 3 | `0 0 0 0` | 7,718 |
| 4 | `stanovništvo prema popisu stanovništva` | 7,610 |
| 5 | `u bosni i hercegovini` | 7,346 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `prema popisu stanovništva iz godine` | 8,505 |
| 2 | `stanovništvo prema popisu stanovništva iz` | 7,504 |
| 3 | `iz godine naselje je imalo` | 6,432 |
| 4 | `popisu stanovništva iz godine naselje` | 6,074 |
| 5 | `klub ut pob ner por` | 6,053 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 11,772,034 |
| 2 | `e _` | 10,057,232 |
| 3 | `j e` | 9,032,733 |
| 4 | `i _` | 7,983,271 |
| 5 | `_ s` | 7,190,572 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j e _` | 3,895,077 |
| 2 | `_ j e` | 2,710,825 |
| 3 | `_ p o` | 2,506,868 |
| 4 | `_ p r` | 2,383,257 |
| 5 | `_ n a` | 2,336,425 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ j e _` | 2,225,392 |
| 2 | `_ n a _` | 884,954 |
| 3 | `_ s e _` | 864,331 |
| 4 | `_ p r o` | 684,557 |
| 5 | `_ k o j` | 681,175 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ j e _` | 584,793 |
| 2 | `o _ j e _` | 536,381 |
| 3 | `_ g o d i` | 464,832 |
| 4 | `g o d i n` | 453,046 |
| 5 | `o d i n e` | 358,859 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 314
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~16% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Contexts](visualizations/markov_contexts.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Variant | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | Word | 1.0357 | 2.050 | 12.27 | 1,815,273 | 0.0% |
| **1** | Subword | 1.2283 | 2.343 | 8.11 | 7,670 | 0.0% |
| **2** | Word | 0.3287 | 1.256 | 2.06 | 22,242,688 | 67.1% |
| **2** | Subword | 0.7670 | 1.702 | 5.14 | 62,088 | 23.3% |
| **3** | Word | 0.1208 | 1.087 | 1.25 | 45,802,650 | 87.9% |
| **3** | Subword | 0.8038 | 1.746 | 4.62 | 318,839 | 19.6% |
| **4** | Word | 0.0449 🏆 | 1.032 | 1.07 | 57,168,259 | 95.5% |
| **4** | Subword | 0.7427 | 1.673 | 3.77 | 1,471,918 | 25.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `je jedini gol bod1 orijent expressu od do polufinala nastupila je manji zbog toga dragocjena u`
2. `u 56 km kvadratnih kilometara je postao vodeći u dundu maroju armandu kemičara i bečki i`
3. `i izraz malo energije na njihovo je također povezivanje svakoga naroda onaj za istraživanje je minog...`

**Context Size 2:**

1. `je u sabirni logor za zarobljene španjolske muškarce i žene koji su bez uspjeha robert lowie je`
2. `vanjske poveznice hrvatske kazališne manifestacije u hrvatskoj reformsko krilo koje se smatra normal...`
3. `koji je osvojio pojedinačnu medalju na austrian openu u osmini završnice osam i protjerivan sedam pu...`

**Context Size 3:**

1. `izvori vanjske poveznice hartmut frommert revidirani novi opći katalog eng izvangalaktička baza poda...`
2. `0 0 0 0 0 4 1 kvalifikacije za afrički kup nacija 08 17 21 lipnja abuja national`
3. `bosne i hercegovine postao je slobodno područje izabran je za izvanrednog profesora na harvardu te v...`

**Context Size 4:**

1. `prema popisu stanovništva iz godine rajčići su imali 4 stanovnika vanjske poveznice o blažević dolu ...`
2. `popisu stanovništva iz godine naselje je imalo 0 stanovnikapopis stanovništva www dzs hr te 25 obite...`
3. `0 0 0 0 0 hispanoamerikanci 4 0 9 12 1 4 ukupno 844 861 vrela vanjske poveznice u`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_poskovopr._vi_d`
2. `av_jeni_staog_1.`
3. `ire_zbe._n_pledo`

**Context Size 2:**

1. `a_prednog_reba_me`
2. `e_urisamom_kakvu.`
3. `jedina_jensih_fij`

**Context Size 3:**

1. `je_udružen_uglavno`
2. `_je_je_meki_držana`
3. `_postavu_i_murski_`

**Context Size 4:**

1. `_je_i_„bijedložili_`
2. `_na_bio_je_breedler`
3. `_se_tada_satenu_dat`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,471,918 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 | 865,837 |
| Total Tokens | 68,760,487 |
| Mean Frequency | 79.42 |
| Median Frequency | 4 |
| Frequency Std Dev | 4611.66 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | je | 2,245,537 |
| 2 | u | 2,108,487 |
| 3 | i | 2,058,490 |
| 4 | na | 897,376 |
| 5 | se | 873,737 |
| 6 | su | 661,725 |
| 7 | za | 564,276 |
| 8 | od | 535,634 |
| 9 | s | 445,590 |
| 10 | a | 436,542 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | uerpmann | 2 |
| 2 | cociancicha | 2 |
| 3 | fornasari | 2 |
| 4 | federighi | 2 |
| 5 | ulanoff | 2 |
| 6 | svelteov | 2 |
| 7 | ractive | 2 |
| 8 | jsdoc | 2 |
| 9 | vercel | 2 |
| 10 | onsubmit | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9105 |
| R² (Goodness of Fit) | 0.998328 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 29.2% |
| Top 1,000 | 47.5% |
| Top 5,000 | 64.0% |
| Top 10,000 | 71.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9983 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 29.2% of corpus
- **Long Tail:** 855,837 words needed for remaining 28.5% 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 | 0.7990 | 0.3752 | N/A | N/A |
| **mono_64d** | 64 | 0.7419 | 0.2943 | N/A | N/A |
| **mono_128d** | 128 | 0.6113 | 0.2735 | N/A | N/A |
| **aligned_32d** | 32 | 0.7990 🏆 | 0.3713 | 0.2440 | 0.6400 |
| **aligned_64d** | 64 | 0.7419 | 0.2911 | 0.4700 | 0.8320 |
| **aligned_128d** | 128 | 0.6113 | 0.2771 | 0.6240 | 0.8980 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7990 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3137. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 62.4% 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 | **-0.514** | 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 |
|--------|----------|
| `-s` | saccharina, stažem, sieversia |
| `-a` | appleton, aromatika, antipatros |
| `-ma` | macv, mahajangu, manfredonija |
| `-m` | mešetari, midp, megasten |
| `-k` | konfederacije, kumarom, karlovačku |
| `-p` | prostalih, portulani, panopticum |
| `-b` | breviarium, bandašica, botticellija |
| `-t` | terpenoide, tamnocrvenkast, teregova |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | saccharina, sieversia, premašenima |
| `-e` | konfederacije, terpenoide, elaboracije |
| `-i` | portulani, vori, mešetari |
| `-m` | stažem, panopticum, breviarium |
| `-u` | nahalu, ikonostasu, karlovačku |
| `-om` | kumarom, samarom, kokom |
| `-s` | servas, winos, clupeoides |
| `-o` | dezorijentirano, dsno, papio |

### 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` | 1.67x | 1068 contexts | anove, hanov, banov |
| `cije` | 2.00x | 238 contexts | cijel, cijev, cijem |
| `acij` | 1.85x | 273 contexts | lacij, acije, racij |
| `ijel` | 1.69x | 293 contexts | cijel, ijele, dijel |
| `ansk` | 1.35x | 1078 contexts | ansko, anski, dansk |
| `ljen` | 1.42x | 618 contexts | kljen, pljen, ljeni |
| `avlj` | 1.51x | 394 contexts | javlja, vavlje, lavlji |
| `elik` | 1.71x | 176 contexts | melik, jelik, çelik |
| `ijsk` | 1.36x | 538 contexts | hijska, bijsku, kijski |
| `egov` | 1.60x | 208 contexts | negov, begov, egove |
| `novn` | 1.84x | 95 contexts | onovno, pnovno, ponovno |
| `telj` | 1.66x | 146 contexts | atelj, artelj, stelje |

### 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` | 202 words | prekorava, petruša |
| `-s` | `-a` | 178 words | suverenizma, sritna |
| `-p` | `-e` | 114 words | produbljavanje, perenense |
| `-k` | `-a` | 106 words | kanatima, koruška |
| `-p` | `-i` | 97 words | protoni, poigravati |
| `-a` | `-a` | 93 words | almanusa, alžirka |
| `-s` | `-i` | 88 words | svesokolski, saeculi |
| `-d` | `-a` | 88 words | disonancija, denzimetrija |
| `-b` | `-a` | 85 words | barista, bhattija |
| `-p` | `-m` | 85 words | perfectum, punicum |

### 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 |
|------|-----------------|------------|------|
| auchenipteridae | **`auchenipterid-a-e`** | 7.5 | `a` |
| neprikazane | **`neprikaz-a-ne`** | 7.5 | `a` |
| arunkumar | **`arunkum-a-r`** | 7.5 | `a` |
| intervjuua | **`intervju-u-a`** | 7.5 | `u` |
| domeciidae | **`domeciid-a-e`** | 7.5 | `a` |
| ventricosus | **`ventrico-s-us`** | 7.5 | `s` |
| codiaceae | **`codiace-a-e`** | 7.5 | `a` |
| anastasiju | **`anastas-i-ju`** | 7.5 | `i` |
| sistemsko | **`sistem-s-ko`** | 7.5 | `s` |
| pattalophyllia | **`pattalophyll-i-a`** | 7.5 | `i` |
| studenske | **`studen-s-ke`** | 7.5 | `s` |
| modernizirani | **`modernizir-a-ni`** | 7.5 | `a` |
| filtrirani | **`filtrir-a-ni`** | 7.5 | `a` |
| postavljane | **`postavlj-a-ne`** | 7.5 | `a` |
| coriariaceae | **`coriariace-a-e`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Croatian 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 (4.59x) |
| N-gram | **2-gram** | Lowest perplexity (314) |
| Markov | **Context-4** | Highest predictability (95.5%) |
| 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: 2026-01-10 10:10:35*