---
language: rsk
language_name: Unknown language [rsk]
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: 4.008
  - name: best_isotropy
    type: isotropy
    value: 0.8518
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Unknown language [rsk] - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Unknown language [rsk]** 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** | 3.410x | 3.41 | 0.1603% | 1,061,780 |
| **16k** | 3.743x | 3.74 | 0.1760% | 967,123 |
| **32k** | 4.008x 🏆 | 4.01 | 0.1884% | 903,354 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Митра (вецейзначна одреднїца) Митра (церковне швето) Митра (владикова коруна)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁митра ▁( вецейзначна ▁одреднїца ) ▁митра ▁( цер ков не ... (+9 more)` | 19 |
| 16k | `▁митра ▁( вецейзначна ▁одреднїца ) ▁митра ▁( цер ков не ... (+8 more)` | 18 |
| 32k | `▁митра ▁( вецейзначна ▁одреднїца ) ▁митра ▁( церковне ▁швето ) ... (+5 more)` | 15 |

**Sample 2:** `<div solid background: overflow:hidden; Витайце на Википедиї, шлєбодней енциклоп...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ < div ▁sol id ▁b ack g ro und ... (+27 more)` | 37 |
| 16k | `▁ < div ▁sol id ▁b ack g ro und ... (+21 more)` | 31 |
| 32k | `▁ < div ▁solid ▁background : ▁overflow : hidden ; ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 32k achieves 4.008x compression
- **Lowest UNK Rate:** 8k with 0.1603% 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 | 5,656 | 12.47 | 10,854 | 16.5% | 43.9% |
| **2-gram** | Subword | 418 🏆 | 8.71 | 3,221 | 57.2% | 97.6% |
| **3-gram** | Word | 5,139 | 12.33 | 9,203 | 16.8% | 43.6% |
| **3-gram** | Subword | 3,606 | 11.82 | 24,224 | 19.5% | 60.9% |
| **4-gram** | Word | 10,090 | 13.30 | 15,965 | 12.8% | 31.2% |
| **4-gram** | Subword | 18,492 | 14.17 | 103,003 | 8.7% | 30.6% |
| **5-gram** | Word | 6,783 | 12.73 | 10,762 | 16.1% | 35.7% |
| **5-gram** | Subword | 55,733 | 15.77 | 218,834 | 4.8% | 18.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `же би` | 1,021 |
| 2 | `нови сад` | 886 |
| 3 | `у руским` | 884 |
| 4 | `руским керестуре` | 755 |
| 5 | `и у` | 655 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `у руским керестуре` | 720 |
| 2 | `у новим садзе` | 430 |
| 3 | `нови сад б` | 373 |
| 4 | `style text align` | 373 |
| 5 | `же би ше` | 338 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `руски язик литературу и` | 234 |
| 2 | `за руски язик литературу` | 234 |
| 3 | `язик литературу и културу` | 233 |
| 4 | `дружтво за руски язик` | 177 |
| 5 | `style text align center` | 171 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `за руски язик литературу и` | 234 |
| 2 | `руски язик литературу и културу` | 233 |
| 3 | `дружтво за руски язик литературу` | 158 |
| 4 | `div style text align center` | 122 |
| 5 | `литература словнїк руского народного язика` | 115 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `и _` | 87,099 |
| 2 | `а _` | 60,960 |
| 3 | `_ п` | 47,637 |
| 4 | `, _` | 44,841 |
| 5 | `у _` | 39,787 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ и _` | 21,998 |
| 2 | `_ н а` | 19,764 |
| 3 | `_ п о` | 18,942 |
| 4 | `_ у _` | 17,122 |
| 5 | `_ п р` | 16,568 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ш е _` | 8,610 |
| 2 | `о г о _` | 8,549 |
| 3 | `_ н а _` | 8,281 |
| 4 | `_ п р е` | 6,885 |
| 5 | `_ р у с` | 6,730 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ з о з _` | 5,978 |
| 2 | `_ х т о р` | 4,704 |
| 3 | `_ р у с к` | 4,379 |
| 4 | `_ р о к у` | 3,977 |
| 5 | `х т о р и` | 3,051 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 418
- **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 | 0.8135 | 1.757 | 4.52 | 76,178 | 18.7% |
| **1** | Subword | 1.8736 | 3.664 | 18.30 | 336 | 0.0% |
| **2** | Word | 0.1957 | 1.145 | 1.39 | 343,743 | 80.4% |
| **2** | Subword | 1.2490 | 2.377 | 7.30 | 6,150 | 0.0% |
| **3** | Word | 0.0496 | 1.035 | 1.08 | 475,706 | 95.0% |
| **3** | Subword | 0.8955 | 1.860 | 4.03 | 44,870 | 10.5% |
| **4** | Word | 0.0165 🏆 | 1.011 | 1.02 | 511,199 | 98.4% |
| **4** | Subword | 0.6155 | 1.532 | 2.54 | 180,969 | 38.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `и редактор и створел виведол формулу у другей шветовей войни експериментованє у комисиї у рускей мат...`
2. `у жеми биоґрафия исидор баїч миниятура за шицких виводзачох уметнїкох хтори у нїх предлужовал до шей...`
3. `ше риши найдзена квадратна єдначина достанє ше року дзецкового живота руснацох у руским керестуре у ...`

**Context Size 2:**

1. `же би ше огранїчел лєм на атлетских и маратонских обеговачох алє нє и на менши оправяня ремеселнїцтв...`
2. `нови сад б 7 26 микола м русинська веб книга сайт о литературѣ и языку webnode моя`
3. `у руским керестуре од та по 30 авґуст одроснул у шидзе студирал на универзитетох у бувшей югославиї`

**Context Size 3:**

1. `у руским керестуре 22 децембра року оцец владо и мац серафина родз раґаї силвестер мал младшу шестру...`
2. `у новим садзе закончела економску штредню школу попри роботи вона ше уписала на висшу педаґоґийну шк...`
3. `нови сад б 688 оксана тимко дїтко назви рошлїнох и животиньох у руским язику вуковар б 57 59`

**Context Size 4:**

1. `руски язик литературу и културу ч 11 б 185 184 владимир сабо дайко рецензия на хромишов квиток младо...`
2. `за руски язик литературу и културу нови сад бок 57 тамаш др юлиян дом културиˮ руски керестур лїтопи...`
3. `язик литературу и културу ч 29 б 29 мр гелена медєши два ювилеї нашей науки о писаню 100 роки`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_хтитеру_бловянґ`
2. `овета_воса_то_oz`
3. `и_linsičktv_ити_`

**Context Size 2:**

1. `и_проперестивою_у`
2. `а_понутонски_зоз_`
3. `_пре,_и_миї_молоґ`

**Context Size 3:**

1. `_и_до_кед_шеступка`
2. `_на_по_рого_робел_`
3. `_под_свою_як_членд`

**Context Size 4:**

1. `_ше_друкавого_пах,_`
2. `ого_владимир_соло_и`
3. `_на_придаваюци_3,2_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (180,969 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 | 33,434 |
| Total Tokens | 506,343 |
| Mean Frequency | 15.14 |
| Median Frequency | 3 |
| Frequency Std Dev | 188.98 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | и | 22,158 |
| 2 | у | 17,326 |
| 3 | ше | 8,771 |
| 4 | на | 8,454 |
| 5 | зоз | 6,045 |
| 6 | за | 5,768 |
| 7 | а | 4,186 |
| 8 | року | 3,943 |
| 9 | як | 3,813 |
| 10 | з | 3,723 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | кабла | 2 |
| 2 | чурчку | 2 |
| 3 | мутлянку | 2 |
| 4 | bunar | 2 |
| 5 | дробизґ | 2 |
| 6 | шопи | 2 |
| 7 | пойдзик | 2 |
| 8 | шедали | 2 |
| 9 | банти | 2 |
| 10 | фармох | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9446 |
| R² (Goodness of Fit) | 0.995835 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.4% |
| Top 1,000 | 56.7% |
| Top 5,000 | 77.3% |
| Top 10,000 | 86.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9958 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.4% of corpus
- **Long Tail:** 23,434 words needed for remaining 13.9% 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 | 0.8518 | 0.3416 | N/A | N/A |
| **mono_64d** | 64 | 0.5299 | 0.2930 | N/A | N/A |
| **mono_128d** | 128 | 0.1154 | 0.2705 | N/A | N/A |
| **aligned_32d** | 32 | 0.8518 🏆 | 0.3287 | 0.0060 | 0.0540 |
| **aligned_64d** | 64 | 0.5299 | 0.2873 | 0.0160 | 0.1020 |
| **aligned_128d** | 128 | 0.1154 | 0.2730 | 0.0300 | 0.1520 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8518 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2990. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.0% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.959** | 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 |
|--------|----------|
| `-п` | просвитни, прохоров, прескакованє |
| `-по` | посцигнуцох, полних, почитованє |
| `-с` | строгосц, сцихшованє, сербскому |
| `-к` | карате, комуналней, крайняк |
| `-пр` | просвитни, прохоров, прескакованє |
| `-д` | драги, директним, доставанє |
| `-в` | влапели, вей, виплокованє |
| `-на` | напущованє, нацийох, националносцох |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-и` | влапели, просвитни, явносци |
| `-а` | лиґа, бела, универзитета |
| `-х` | нотних, тамбурашох, посцигнуцох |
| `-о` | микийово, канио, цепко |
| `-ох` | тамбурашох, посцигнуцох, рядох |
| `-ни` | просвитни, елементарни, зєдинєни |
| `-у` | широку, инсбруку, сербскому |
| `-м` | директним, ширеньом, филиґраном |

### 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 |
|------|----------|------------------|----------|
| `одзе` | 1.55x | 89 contexts | водзел, годзен, сходзе |
| `ован` | 1.57x | 78 contexts | йован, јован, ковани |
| `оста` | 1.56x | 78 contexts | коста, поста, моста |
| `ного` | 2.00x | 23 contexts | ногох, усного, южного |
| `овал` | 1.65x | 46 contexts | ковал, овални, коваля |
| `тори` | 1.73x | 31 contexts | хтори, хторим, хторих |
| `снов` | 1.47x | 57 contexts | основе, основы, основу |
| `ског` | 1.93x | 21 contexts | ческого, српског, ирского |
| `скей` | 1.80x | 26 contexts | ирскей, рускей, епскей |
| `наро` | 1.87x | 22 contexts | народ, народи, народа |
| `дзен` | 1.51x | 47 contexts | дзень, єдзенє, годзен |
| `школ` | 2.07x | 15 contexts | школе, школу, школи |

### 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 |
|--------|--------|-----------|----------|
| `-п` | `-и` | 198 words | подзековносци, предшедуюци |
| `-п` | `-а` | 132 words | пса, положа |
| `-п` | `-х` | 94 words | принципох, паноцох |
| `-с` | `-и` | 85 words | суши, стандардни |
| `-с` | `-а` | 81 words | самца, спектакла |
| `-п` | `-о` | 78 words | полно, повойново |
| `-к` | `-и` | 75 words | композиторови, косци |
| `-в` | `-и` | 68 words | вирабяли, влапели |
| `-о` | `-и` | 66 words | опарти, оспособени |
| `-п` | `-ни` | 63 words | присутни, посадзени |

### 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 |
|------|-----------------|------------|------|
| приповеданя | **`приповед-а-ня`** | 7.5 | `а` |
| сербского | **`сербск-о-го`** | 7.5 | `о` |
| дошлєбодзує | **`дошлєбодз-у-є`** | 7.5 | `у` |
| мандарини | **`мандар-и-ни`** | 7.5 | `и` |
| рошлїнами | **`рошлї-на-ми`** | 7.5 | `на` |
| транспортних | **`транспорт-ни-х`** | 6.0 | `транспорт` |
| животного | **`живот-но-го`** | 6.0 | `живот` |
| текстуални | **`тексту-ал-ни`** | 6.0 | `тексту` |
| преостава | **`п-ре-остава`** | 6.0 | `остава` |
| нєзвичайни | **`нє-звичай-ни`** | 6.0 | `звичай` |
| животинями | **`животи-ня-ми`** | 6.0 | `животи` |
| правилами | **`прави-ла-ми`** | 6.0 | `прави` |
| вишпивани | **`ви-шпива-ни`** | 6.0 | `шпива` |
| согласносци | **`согласносц-и`** | 4.5 | `согласносц` |
| инспировало | **`инспировал-о`** | 4.5 | `инспировал` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Unknown language [rsk] 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 | **32k BPE** | Best compression (4.01x) |
| N-gram | **2-gram** | Lowest perplexity (418) |
| Markov | **Context-4** | Highest predictability (98.4%) |
| 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 18:54:11*