---
language: sk
language_name: Slovak
language_family: slavic_west
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_west
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: 4.618
  - name: best_isotropy
    type: isotropy
    value: 0.7762
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Slovak** 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** | 3.384x | 3.39 | 0.1078% | 1,294,485 |
| **16k** | 3.810x | 3.81 | 0.1214% | 1,149,866 |
| **32k** | 4.234x | 4.24 | 0.1349% | 1,034,640 |
| **64k** | 4.618x 🏆 | 4.62 | 0.1472% | 948,528 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Teatrálnosť je strojené správanie, vystupovanie; strojenosť; okázalosť. Externé ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁te at rál nosť ▁je ▁stroj ené ▁sprá vanie , ... (+14 more)` | 24 |
| 16k | `▁te at rál nosť ▁je ▁stroj ené ▁správanie , ▁vystup ... (+12 more)` | 22 |
| 32k | `▁te at rál nosť ▁je ▁stroj ené ▁správanie , ▁vystup ... (+11 more)` | 21 |
| 64k | `▁te at rál nosť ▁je ▁stroj ené ▁správanie , ▁vystupovanie ... (+10 more)` | 20 |

**Sample 2:** `205 Martha je planétka v hlavnom páse planétok. Iné projekty Externé odkazy 1 – ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 2 0 5 ▁mar tha ▁je ▁planétka ▁v ▁hlavnom ... (+20 more)` | 30 |
| 16k | `▁ 2 0 5 ▁mar tha ▁je ▁planétka ▁v ▁hlavnom ... (+19 more)` | 29 |
| 32k | `▁ 2 0 5 ▁mar tha ▁je ▁planétka ▁v ▁hlavnom ... (+18 more)` | 28 |
| 64k | `▁ 2 0 5 ▁martha ▁je ▁planétka ▁v ▁hlavnom ▁páse ... (+17 more)` | 27 |

**Sample 3:** `Mopsus môže byť: latinský názov gréckej mytologickej postavy, pozri Mopsos rod p...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mo ps us ▁môže ▁byť : ▁latin ský ▁názov ▁gréckej ... (+22 more)` | 32 |
| 16k | `▁mo ps us ▁môže ▁byť : ▁latin ský ▁názov ▁gréckej ... (+19 more)` | 29 |
| 32k | `▁mo ps us ▁môže ▁byť : ▁latinský ▁názov ▁gréckej ▁myto ... (+18 more)` | 28 |
| 64k | `▁mo ps us ▁môže ▁byť : ▁latinský ▁názov ▁gréckej ▁myto ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 64k achieves 4.618x compression
- **Lowest UNK Rate:** 8k with 0.1078% 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 | 194,679 | 17.57 | 1,294,124 | 9.6% | 19.4% |
| **2-gram** | Subword | 436 🏆 | 8.77 | 14,570 | 55.9% | 97.9% |
| **3-gram** | Word | 313,082 | 18.26 | 1,894,773 | 11.8% | 18.9% |
| **3-gram** | Subword | 4,546 | 12.15 | 139,891 | 17.1% | 55.9% |
| **4-gram** | Word | 450,373 | 18.78 | 2,990,666 | 13.9% | 19.7% |
| **4-gram** | Subword | 29,988 | 14.87 | 892,283 | 7.0% | 26.0% |
| **5-gram** | Word | 245,160 | 17.90 | 2,133,494 | 17.8% | 24.5% |
| **5-gram** | Subword | 135,044 | 17.04 | 3,317,079 | 3.9% | 15.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `v roku` | 239,095 |
| 2 | `externé odkazy` | 86,205 |
| 3 | `v departemente` | 81,770 |
| 4 | `pozri aj` | 80,426 |
| 5 | `iné projekty` | 61,467 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `pozri aj zoznam` | 55,568 |
| 2 | `referencie pozri aj` | 53,094 |
| 3 | `aj zoznam obcí` | 41,598 |
| 4 | `sa nachádza v` | 41,376 |
| 5 | `ktorá sa nachádza` | 37,349 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referencie pozri aj zoznam` | 44,925 |
| 2 | `pozri aj zoznam obcí` | 41,597 |
| 3 | `ktorá sa nachádza v` | 36,794 |
| 4 | `dostupné online po francúzsky` | 36,767 |
| 5 | `insee dostupné online po` | 36,760 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referencie pozri aj zoznam obcí` | 41,480 |
| 2 | `insee dostupné online po francúzsky` | 36,760 |
| 3 | `má rozlohu najvyšší bod je` | 36,532 |
| 4 | `institut national de la statistique` | 36,530 |
| 5 | `national de la statistique et` | 36,529 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 8,087,656 |
| 2 | `_ p` | 5,509,644 |
| 3 | `_ s` | 5,383,985 |
| 4 | `e _` | 5,252,691 |
| 5 | `_ v` | 4,866,750 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ p r` | 2,185,530 |
| 2 | `_ p o` | 2,090,423 |
| 3 | `_ v _` | 1,919,460 |
| 4 | `_ n a` | 1,809,529 |
| 5 | `_ a _` | 1,552,905 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a _` | 904,134 |
| 2 | `_ s a _` | 814,412 |
| 3 | `_ p r e` | 785,964 |
| 4 | `_ j e _` | 682,133 |
| 5 | `ý c h _` | 668,796 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k t o r` | 496,744 |
| 2 | `, _ k t o` | 404,467 |
| 3 | `_ r o k u` | 369,877 |
| 4 | `r o k u _` | 354,960 |
| 5 | `_ v _ r o` | 291,692 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 436
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~15% 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 | 1.0430 | 2.060 | 11.55 | 1,699,952 | 0.0% |
| **1** | Subword | 1.0314 | 2.044 | 7.25 | 6,754 | 0.0% |
| **2** | Word | 0.3261 | 1.254 | 1.98 | 19,608,492 | 67.4% |
| **2** | Subword | 0.7796 | 1.717 | 5.79 | 48,928 | 22.0% |
| **3** | Word | 0.1115 | 1.080 | 1.22 | 38,651,293 | 88.9% |
| **3** | Subword | 0.8417 | 1.792 | 5.12 | 283,324 | 15.8% |
| **4** | Word | 0.0420 🏆 | 1.030 | 1.07 | 46,960,073 | 95.8% |
| **4** | Subword | 0.7681 | 1.703 | 3.95 | 1,449,998 | 23.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `v lese i video z medzinárodnej únie členovia pátracích technikách v rámci ukrajinskej po jej kritiko...`
2. `a jej hmoty ktorá pôsobila ako spotrebiteľ spoliehal na predaj viac skomplikovala proti aerodactylov...`
3. `na rozjazd prostredníctvom svojich smarfónov túto procedúru nízkoúrovňového formátovania príspevkov ...`

**Context Size 2:**

1. `v roku štatistický úrad slovenskej republiky bratislava úrad geodézie a kartografie č z z baláž 3 00`
2. `externé odkazy fridrich viliam bol vnukom kréthea zakladateľa iólku v tesálii boli bojovníkmi v tora...`
3. `v departemente vienne v departemente seine maritime mestom preteká rieka ploučnice ktorá sa nachádza...`

**Context Size 3:**

1. `pozri aj zoznam obcí departementu eure et loir v departemente eure v regióne horná normandia poloha ...`
2. `referencie pozri aj zoznam obcí v česku iné projekty externé odkazy arthur penn na fdb cz fedor bart...`
3. `aj zoznam obcí departementu haute marne v regióne champagne ardenne poloha obec má rozlohu najvyšší ...`

**Context Size 4:**

1. `referencie pozri aj zoznam obcí departementu manche v departemente manche svetového dedičstva vo fra...`
2. `pozri aj zoznam obcí departementu corse du sud v regióne korzika poloha obec má rozlohu najvyšší bod...`
3. `ktorá sa nachádza v departemente landes v regióne akvitánsko poloha obec má rozlohu najvyšší bod je ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pu_ora_pova_ov-`
2. `ou_famuhl_vy_svn`
3. `a_prekupokoduln_`

**Context Size 2:**

1. `a_prvé_do_isymba_`
2. `_prí_otnú,_ktoréc`
3. `_sanský_v_proje,_`

**Context Size 3:**

1. `_predoventaina..._`
2. `_po_udržby_kom_pod`
3. `_v_za_na_na_sa_vym`

**Context Size 4:**

1. `_na_tzv._etapokojný`
2. `_sa_celkovej_afroam`
3. `_pre_rôzneho_hudby_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,449,998 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 | 820,443 |
| Total Tokens | 58,682,268 |
| Mean Frequency | 71.53 |
| Median Frequency | 4 |
| Frequency Std Dev | 3539.87 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | v | 1,958,659 |
| 2 | a | 1,592,669 |
| 3 | na | 911,291 |
| 4 | sa | 823,676 |
| 5 | je | 689,206 |
| 6 | z | 435,689 |
| 7 | s | 419,380 |
| 8 | roku | 369,840 |
| 9 | do | 304,080 |
| 10 | aj | 295,406 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | reorganizačnú | 2 |
| 2 | kamb | 2 |
| 3 | patenting | 2 |
| 4 | časobitie | 2 |
| 5 | cápizu | 2 |
| 6 | capizu | 2 |
| 7 | bookstagramovej | 2 |
| 8 | bookstagrame | 2 |
| 9 | nevzlietne | 2 |
| 10 | marusov | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9228 |
| R² (Goodness of Fit) | 0.998599 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 27.5% |
| Top 1,000 | 47.2% |
| Top 5,000 | 63.8% |
| Top 10,000 | 71.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9986 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 27.5% of corpus
- **Long Tail:** 810,443 words needed for remaining 28.6% 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 | 0.7762 🏆 | 0.3424 | N/A | N/A |
| **mono_64d** | 64 | 0.7460 | 0.2848 | N/A | N/A |
| **mono_128d** | 128 | 0.6617 | 0.2475 | N/A | N/A |
| **aligned_32d** | 32 | 0.7762 | 0.3486 | 0.2660 | 0.6020 |
| **aligned_64d** | 64 | 0.7460 | 0.2779 | 0.4740 | 0.8420 |
| **aligned_128d** | 128 | 0.6617 | 0.2466 | 0.5920 | 0.8620 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7762 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2913. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 59.2% 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 | **0.588** | 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` | skákať, skeptika, spišká |
| `-a` | aiolského, augie, avermaet |
| `-p` | pygmejských, pozlovice, plouich |
| `-m` | malárovej, medvědskej, maltskému |
| `-k` | konkubínou, kolomajstrovstvá, krampová |
| `-ma` | malárovej, maltskému, marjinke |
| `-b` | bacteroidetes, belanského, bonsanto |
| `-d` | dagestanského, devolučnú, dorsey |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | translokácia, skeptika, holocephalimorpha |
| `-e` | wace, augie, pozlovice |
| `-i` | zapnutými, accorsi, temetői |
| `-u` | konkubínou, tereziánsku, aẗu |
| `-m` | ťažením, ábdálím, diolom |
| `-ch` | pygmejských, plouich, sturmbusch |
| `-o` | štvorvrstvového, dagestanského, aiolského |
| `-ho` | štvorvrstvového, dagestanského, aiolského |

### 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 |
|------|----------|------------------|----------|
| `ovan` | 1.47x | 866 contexts | bovan, jovan, hovan |
| `ensk` | 1.54x | 455 contexts | ženská, jenská, svensk |
| `vens` | 1.99x | 101 contexts | ivens, svensk, civens |
| `iest` | 1.70x | 184 contexts | piest, diest, siest |
| `stre` | 1.40x | 457 contexts | astre, stret, stres |
| `hádz` | 1.69x | 150 contexts | hádzal, hádzať, hádzaný |
| `ranc` | 1.56x | 223 contexts | ranco, rancy, rance |
| `emen` | 1.43x | 352 contexts | zemen, hemen, femen |
| `nost` | 1.57x | 197 contexts | anost, noste, cnosti |
| `enci` | 1.54x | 179 contexts | nenci, ženci, benci |
| `ádza` | 1.41x | 257 contexts | hrádza, sádzať, zvádza |
| `chád` | 1.50x | 85 contexts | chádža, chádim, nacháda |

### 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` | 106 words | poczesna, pesera |
| `-p` | `-e` | 78 words | paleozoologie, pernidae |
| `-s` | `-e` | 77 words | slintačke, strategiaage |
| `-p` | `-m` | 76 words | plénom, perlmutterom |
| `-p` | `-u` | 71 words | poškrabaniu, poisťovňou |
| `-s` | `-a` | 63 words | skia, spela |
| `-p` | `-i` | 61 words | parlamentami, páni |
| `-k` | `-a` | 61 words | krajčovičkatarína, kodaka |
| `-m` | `-a` | 57 words | mulatta, matola |
| `-b` | `-a` | 51 words | biljana, burna |

### 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 |
|------|-----------------|------------|------|
| željezničar | **`željeznič-a-r`** | 7.5 | `a` |
| zawistowski | **`zawistows-k-i`** | 7.5 | `k` |
| fralignes | **`fralig-ne-s`** | 7.5 | `ne` |
| stromčekom | **`stromče-k-om`** | 7.5 | `k` |
| dvojzáprah | **`dvojzápr-a-h`** | 7.5 | `a` |
| textúrové | **`textúr-ov-é`** | 6.0 | `textúr` |
| turgenevovej | **`turgenev-ov-ej`** | 6.0 | `turgenev` |
| fulbrightova | **`fulbright-ov-a`** | 6.0 | `fulbright` |
| neohraničeného | **`ne-ohraničené-ho`** | 6.0 | `ohraničené` |
| finálovou | **`finál-ov-ou`** | 6.0 | `finál` |
| miroslavov | **`miroslav-ov`** | 4.5 | `miroslav` |
| josephina | **`josephi-na`** | 4.5 | `josephi` |
| englewoode | **`englewood-e`** | 4.5 | `englewood` |
| flindersa | **`flinders-a`** | 4.5 | `flinders` |
| wheatleya | **`wheatley-a`** | 4.5 | `wheatley` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Slovak 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 (4.62x) |
| N-gram | **2-gram** | Lowest perplexity (436) |
| Markov | **Context-4** | Highest predictability (95.8%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-11 02:39:37*