---
language: csb
language_name: Kashubian
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: 4.520
  - name: best_isotropy
    type: isotropy
    value: 0.7585
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kashubian** 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** | 3.576x | 3.58 | 0.1685% | 179,827 |
| **16k** | 3.912x | 3.92 | 0.1843% | 164,376 |
| **32k** | 4.229x | 4.24 | 0.1993% | 152,042 |
| **64k** | 4.520x 🏆 | 4.53 | 0.2130% | 142,258 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Mòrzebób abò lësy ògón (Lycopodium clavatum L.) - to je wielelatnô roscëna z rod...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mòrze b ób ▁abò ▁lë sy ▁ògón ▁( ly co ... (+29 more)` | 39 |
| 16k | `▁mòrze b ób ▁abò ▁lë sy ▁ògón ▁( ly copo ... (+26 more)` | 36 |
| 32k | `▁mòrze b ób ▁abò ▁lë sy ▁ògón ▁( lycopo dium ... (+22 more)` | 32 |
| 64k | `▁mòrze b ób ▁abò ▁lë sy ▁ògón ▁( lycopodium ▁cla ... (+21 more)` | 31 |

**Sample 2:** `Niemieckô Karznica (pòl. Karzniczka) - to je wies w pòmòrsczim wòjewództwie, w s...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁niemie ckô ▁ka rz nica ▁( pòl . ▁ka rz ... (+19 more)` | 29 |
| 16k | `▁niemieckô ▁karz nica ▁( pòl . ▁karz niczka ) ▁- ... (+16 more)` | 26 |
| 32k | `▁niemieckô ▁karznica ▁( pòl . ▁karz niczka ) ▁- ▁to ... (+15 more)` | 25 |
| 64k | `▁niemieckô ▁karznica ▁( pòl . ▁karzniczka ) ▁- ▁to ▁je ... (+14 more)` | 24 |

**Sample 3:** `Wëdarzenia Pòlsczi król Władisłôw I Herman wëdôł rozkôz spôleniô gardów w Gduńsc...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wëdarzenia ▁pòlsczi ▁król ▁władisłôw ▁i ▁her man ▁wëdôł ▁roz kôz ... (+6 more)` | 16 |
| 16k | `▁wëdarzenia ▁pòlsczi ▁król ▁władisłôw ▁i ▁her man ▁wëdôł ▁roz kôz ... (+6 more)` | 16 |
| 32k | `▁wëdarzenia ▁pòlsczi ▁król ▁władisłôw ▁i ▁herman ▁wëdôł ▁roz kôz ▁spô ... (+5 more)` | 15 |
| 64k | `▁wëdarzenia ▁pòlsczi ▁król ▁władisłôw ▁i ▁herman ▁wëdôł ▁rozkôz ▁spôleniô ▁gardów ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 4.520x compression
- **Lowest UNK Rate:** 8k with 0.1685% 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 | 1,947 | 10.93 | 6,180 | 31.4% | 68.7% |
| **2-gram** | Subword | 457 🏆 | 8.84 | 2,749 | 53.5% | 98.1% |
| **3-gram** | Word | 2,094 | 11.03 | 7,716 | 31.5% | 69.0% |
| **3-gram** | Subword | 3,953 | 11.95 | 22,499 | 18.9% | 58.2% |
| **4-gram** | Word | 3,732 | 11.87 | 15,312 | 28.0% | 59.5% |
| **4-gram** | Subword | 18,873 | 14.20 | 102,765 | 10.0% | 33.1% |
| **5-gram** | Word | 3,059 | 11.58 | 12,171 | 29.4% | 62.6% |
| **5-gram** | Subword | 46,114 | 15.49 | 210,801 | 7.4% | 25.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `to je` | 2,500 |
| 2 | `bùtnowé lënczi` | 1,440 |
| 3 | `ùrodzëlë sã` | 991 |
| 4 | `w gminie` | 982 |
| 5 | `m jin` | 870 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wëdarzenia ùrodzëlë sã` | 849 |
| 2 | `ùrodzëlë sã ùmarlë` | 814 |
| 3 | `w pòmòrsczim wòjewództwie` | 642 |
| 4 | `p p p` | 601 |
| 5 | `pòmòrsczim wòjewództwie w` | 543 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wëdarzenia ùrodzëlë sã ùmarlë` | 753 |
| 2 | `p p p p` | 566 |
| 3 | `w pòmòrsczim wòjewództwie w` | 537 |
| 4 | `i jinëch słowiańsczich krajów` | 489 |
| 5 | `królestwa i jinëch słowiańsczich` | 489 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `p p p p p` | 532 |
| 2 | `pòlsczégò królestwa i jinëch słowiańsczich` | 489 |
| 3 | `królestwa i jinëch słowiańsczich krajów` | 489 |
| 4 | `słowôrzu pòlsczégò królestwa i jinëch` | 488 |
| 5 | `geògraficznym słowôrzu pòlsczégò królestwa i` | 487 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c z` | 39,727 |
| 2 | `a _` | 38,964 |
| 3 | `_ w` | 38,073 |
| 4 | `. _` | 33,276 |
| 5 | `_ p` | 32,909 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c z i` | 17,503 |
| 2 | `_ w _` | 16,830 |
| 3 | `s c z` | 14,512 |
| 4 | `_ p ò` | 12,375 |
| 5 | `n a _` | 10,995 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s c z i` | 9,919 |
| 2 | `c z i _` | 8,412 |
| 3 | `_ j e _` | 7,786 |
| 4 | `é g ò _` | 7,710 |
| 5 | `_ n a _` | 6,352 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a s z` | 5,271 |
| 2 | `k a s z ë` | 4,572 |
| 3 | `a s z ë b` | 4,569 |
| 4 | `s c z i _` | 4,317 |
| 5 | `z é g ò _` | 4,004 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 457
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.5411 | 1.455 | 2.97 | 80,925 | 45.9% |
| **1** | Subword | 1.0139 | 2.019 | 7.32 | 979 | 0.0% |
| **2** | Word | 0.1312 | 1.095 | 1.25 | 237,972 | 86.9% |
| **2** | Subword | 0.9776 | 1.969 | 6.00 | 7,156 | 2.2% |
| **3** | Word | 0.0409 | 1.029 | 1.07 | 295,594 | 95.9% |
| **3** | Subword | 0.8837 | 1.845 | 4.13 | 42,873 | 11.6% |
| **4** | Word | 0.0202 🏆 | 1.014 | 1.03 | 312,105 | 98.0% |
| **4** | Subword | 0.6519 | 1.571 | 2.59 | 176,892 | 34.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `w drëdżich wëstąpiwo nacygnienié i bùtnową z eùropejsczégò partnerstwa pòrtë to ekònomicznô rzôdzëzn...`
2. `je w geògraficznym słowôrzu pòlsczégò królestwa i pierre bourdieu francësczi jãzëk to bëło jich rozm...`
3. `i jedzenié wedle wielënë lëdztwa z kaszëbsczégò krôjòbraznégò parkù òn béł wërëti òn pisôł m jin`

**Context Size 2:**

1. `to je susk z rodzëznë swiniowatëch suidae na kaszëbach ten łëzgôcz żëwi sã roscënama`
2. `bùtnowé lënczi picus viridis to je roscëna z rodzëznë cyperaceae òn rosce m jin w gardze dérowałë`
3. `ùrodzëlë sã ùmarlë gregòriańsczi kalãdôrz zaczął bëc ùżiwóny dopiérze w na zôczątkù leno w niechtërn...`

**Context Size 3:**

1. `wëdarzenia ùrodzëlë sã ùmarlë przësłowia barbara swiãtô ò rëbôkach pamiãtô jak na barbarã mróz schòw...`
2. `ùrodzëlë sã ùmarlë augùstin dominik chtëren napisôł m jin że kaszëbi cassubiorum gôdają pò wandalskù...`
3. `w pòmòrsczim wòjewództwie w bëtowsczim krézu w pòmòrsczim wòjewództwie tu je pałac a w nim klôsztór ...`

**Context Size 4:**

1. `wëdarzenia ùrodzëlë sã ùmarlë przësłowié w stôrim piéckù diabeł pôli`
2. `p p p p p p p p p p p p p p p swiãta ë ùroczëznë midzënôrodné`
3. `w pòmòrsczim wòjewództwie w kartësczim krézu w gminie kartuzë tu ùrodzył sã gerard labùda niedalek ò...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_jeczącz_wierëne`
2. `a_xycok_w_słowin`
3. `i_pò_aromstë_adz`

**Context Size 2:**

1. `cz_gmik_47_iniewò`
2. `a_z_pòzwëbski)_na`
3. `_w_rok_drólotam_p`

**Context Size 3:**

1. `czim_jãzëkã._strzé`
2. `_w_pòzwa_«lucjonal`
3. `sczi_kaszëbsczégò_`

**Context Size 4:**

1. `sczi)._wiesłowie_ho`
2. `czi_lëdztwa_kaszëbs`
3. `_je_w_tim_célu_gduń`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (176,892 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 | 28,419 |
| Total Tokens | 363,789 |
| Mean Frequency | 12.80 |
| Median Frequency | 3 |
| Frequency Std Dev | 147.85 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | w | 17,269 |
| 2 | je | 7,835 |
| 3 | i | 6,858 |
| 4 | na | 6,665 |
| 5 | z | 4,968 |
| 6 | to | 4,725 |
| 7 | sã | 3,705 |
| 8 | do | 3,388 |
| 9 | rok | 3,182 |
| 10 | a | 2,483 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | krakowska | 2 |
| 2 | włãczëne | 2 |
| 3 | союз | 2 |
| 4 | eliminowanié | 2 |
| 5 | pòliticznich | 2 |
| 6 | pôłna | 2 |
| 7 | kòntrola | 2 |
| 8 | ùmòwã | 2 |
| 9 | stalinizm | 2 |
| 10 | fssr | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9915 |
| R² (Goodness of Fit) | 0.995964 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.1% |
| Top 1,000 | 63.4% |
| Top 5,000 | 80.0% |
| Top 10,000 | 87.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9960 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.1% of corpus
- **Long Tail:** 18,419 words needed for remaining 12.4% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.7585 | 0.3620 | N/A | N/A |
| **mono_64d** | 64 | 0.5824 | 0.3234 | N/A | N/A |
| **mono_128d** | 128 | 0.1382 | 0.3213 | N/A | N/A |
| **aligned_32d** | 32 | 0.7585 🏆 | 0.3595 | 0.0200 | 0.1880 |
| **aligned_64d** | 64 | 0.5824 | 0.3217 | 0.0600 | 0.2480 |
| **aligned_128d** | 128 | 0.1382 | 0.3200 | 0.1040 | 0.3580 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7585 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3347. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.4% 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 | **1.504** | 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` | przednik, przistãpną, prowincëjã |
| `-pò` | pòzycji, pòkòrë, pòdôwô |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | gdùńska, chòrobama, tradycja |
| `-ch` | griphenberch, błãdnëch, pòdwòrzach |
| `-zi` | czedrowsczi, krëszczi, amerikansczi |
| `-czi` | czedrowsczi, krëszczi, amerikansczi |
| `-ów` | ùrządzeniów, wëdôwków, dzélëków |

### 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 |
|------|----------|------------------|----------|
| `tërn` | 1.98x | 29 contexts | chtërny, chtërno, chtërnë |
| `chtë` | 2.02x | 27 contexts | chtërë, sëchtë, zëchtë |
| `htër` | 2.06x | 23 contexts | chtërë, chtëre, chtërô |
| `szëb` | 2.02x | 22 contexts | kaszëb, kaszëbą, kaszëbã |
| `sczi` | 1.43x | 67 contexts | bùsczi, łasczi, bòsczi |
| `zeni` | 1.61x | 32 contexts | zenice, grzenia, ùczeniô |
| `odzë` | 1.76x | 23 contexts | rodzëc, rodzënë, rodzëcë |
| `stol` | 1.81x | 20 contexts | stolp, stole, stolpe |
| `rodz` | 1.40x | 45 contexts | rodzą, rodzy, rodze |
| `aszë` | 1.93x | 14 contexts | kaszëb, kaszëbą, kaszëbã |
| `sczé` | 1.44x | 30 contexts | rusczé, nisczé, wąsczé |
| `zëbs` | 2.09x | 9 contexts | kaszëbsko, kaszëbsce, kaszëbskù |

### 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` | `-ów` | 23 words | prawów, przezeblôkańców |
| `-pr` | `-a` | 20 words | procesama, praha |
| `-pò` | `-a` | 14 words | pòsłëga, pòlsczima |
| `-pò` | `-ch` | 13 words | pòłączeniach, pòdwòdnëch |
| `-pò` | `-ów` | 9 words | pòzwów, pòspólnotów |
| `-pr` | `-ch` | 7 words | prawach, prezidencczich |
| `-pò` | `-zi` | 6 words | pòlszczi, pòmerénczi |
| `-pò` | `-czi` | 6 words | pòlszczi, pòmerénczi |
| `-pr` | `-zi` | 6 words | prëczkòwsczi, prasczi |
| `-pr` | `-czi` | 4 words | prëczkòwsczi, prasczi |

### 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 |
|------|-----------------|------------|------|
| państwòwich | **`państwòwi-ch`** | 4.5 | `państwòwi` |
| mòdlëtwów | **`mòdlëtw-ów`** | 4.5 | `mòdlëtw` |
| przebendowsczich | **`pr-zebendows-czi-ch`** | 4.5 | `zebendows` |
| czerënków | **`czerënk-ów`** | 4.5 | `czerënk` |
| gòspòdarztwach | **`gòspòdarztwa-ch`** | 4.5 | `gòspòdarztwa` |
| kòmpùtrach | **`kòmpùtra-ch`** | 4.5 | `kòmpùtra` |
| chternych | **`chterny-ch`** | 4.5 | `chterny` |
| instrumentów | **`instrument-ów`** | 4.5 | `instrument` |
| wiérztczi | **`wiérzt-czi`** | 4.5 | `wiérzt` |
| etnicznych | **`etniczny-ch`** | 4.5 | `etniczny` |
| kònkùrsów | **`kònkùrs-ów`** | 4.5 | `kònkùrs` |
| wòjskòwich | **`wòjskòwi-ch`** | 4.5 | `wòjskòwi` |
| miemiecczich | **`miemiec-czi-ch`** | 3.0 | `miemiec` |
| pòległëch | **`pò-ległë-ch`** | 3.0 | `ległë` |
| programach | **`pr-ograma-ch`** | 3.0 | `ograma` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kashubian 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 (4.52x) |
| N-gram | **2-gram** | Lowest perplexity (457) |
| Markov | **Context-4** | Highest predictability (98.0%) |
| 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: 2026-01-03 20:55:59*