---
language: cv
language_name: Chuvash
language_family: turkic_other
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-turkic_other
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: 3.778
  - name: best_isotropy
    type: isotropy
    value: 0.8326
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Chuvash** 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** | 3.075x | 3.08 | 0.2413% | 246,622 |
| **16k** | 3.345x | 3.35 | 0.2625% | 226,699 |
| **32k** | 3.576x | 3.58 | 0.2806% | 212,069 |
| **64k** | 3.778x 🏆 | 3.78 | 0.2964% | 200,734 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Вики: Вики Wiki Wiki WIKI (FM) Wiki wiki dollar Wiki Wiki Shuttle WikiWikiWeb Ви...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁вики : ▁вики ▁wik i ▁wik i ▁wik i ▁( ... (+41 more)` | 51 |
| 16k | `▁вики : ▁вики ▁wiki ▁wiki ▁wiki ▁( f m ) ... (+28 more)` | 38 |
| 32k | `▁вики : ▁вики ▁wiki ▁wiki ▁wiki ▁( fm ) ▁wiki ... (+25 more)` | 35 |
| 64k | `▁вики : ▁вики ▁wiki ▁wiki ▁wiki ▁( fm ) ▁wiki ... (+23 more)` | 33 |

**Sample 2:** `Хро́мпик — ят е мар ят. Хромпик — калий Топоним Хромпик — çул Первоуральск (стан...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁х ро ́м п ик ▁— ▁ят ▁е ▁мар ▁ят ... (+51 more)` | 61 |
| 16k | `▁х ро ́м п ик ▁— ▁ят ▁е ▁мар ▁ят ... (+43 more)` | 53 |
| 32k | `▁х ро ́м пик ▁— ▁ят ▁е ▁мар ▁ят . ... (+36 more)` | 46 |
| 64k | `▁х ро ́м пик ▁— ▁ят ▁е ▁мар ▁ят . ... (+32 more)` | 42 |

**Sample 3:** `Мушар — Республикин Куславкка ял. ял Коричев АССР Халах Вуламалли алфавитпа`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁му шар ▁— ▁республикин ▁куславкка ▁ял . ▁ял ▁кори чев ... (+4 more)` | 14 |
| 16k | `▁му шар ▁— ▁республикин ▁куславкка ▁ял . ▁ял ▁кори чев ... (+4 more)` | 14 |
| 32k | `▁му шар ▁— ▁республикин ▁куславкка ▁ял . ▁ял ▁коричев ▁асср ... (+3 more)` | 13 |
| 64k | `▁му шар ▁— ▁республикин ▁куславкка ▁ял . ▁ял ▁коричев ▁асср ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 3.778x compression
- **Lowest UNK Rate:** 8k with 0.2413% 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 | 9,473 | 13.21 | 71,211 | 26.6% | 47.9% |
| **2-gram** | Subword | 532 🏆 | 9.06 | 7,908 | 52.7% | 95.2% |
| **3-gram** | Word | 8,325 | 13.02 | 89,585 | 30.3% | 52.2% |
| **3-gram** | Subword | 4,929 | 12.27 | 69,351 | 17.2% | 56.3% |
| **4-gram** | Word | 14,593 | 13.83 | 169,630 | 26.4% | 47.5% |
| **4-gram** | Subword | 26,364 | 14.69 | 378,926 | 10.1% | 32.1% |
| **5-gram** | Word | 12,306 | 13.59 | 144,170 | 27.1% | 49.1% |
| **5-gram** | Subword | 81,182 | 16.31 | 1,007,721 | 7.9% | 24.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `шыв шыв` | 22,911 |
| 2 | `территоринчи юханшыв` | 14,353 |
| 3 | `территорипе юхать` | 13,579 |
| 4 | `юхса юханшыв` | 13,517 |
| 5 | `экологи министерстви` | 11,703 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `рф экологи министерстви` | 11,700 |
| 2 | `территорин шыв геоинформаци` | 11,389 |
| 3 | `геоинформаци системин шыв` | 11,389 |
| 4 | `федераци агентстви рф` | 11,389 |
| 5 | `шыв федераци агентстви` | 11,389 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `геоинформаци системин шыв шыв` | 11,389 |
| 2 | `рф территорин шыв геоинформаци` | 11,389 |
| 3 | `агентстви рф территорин шыв` | 11,389 |
| 4 | `федераци агентстви рф территорин` | 11,389 |
| 5 | `территорин шыв геоинформаци системин` | 11,389 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `агентстви рф территорин шыв геоинформаци` | 11,389 |
| 2 | `федераци агентстви рф территорин шыв` | 11,389 |
| 3 | `шыв геоинформаци системин шыв шыв` | 11,389 |
| 4 | `территорин шыв геоинформаци системин шыв` | 11,389 |
| 5 | `шыв федераци агентстви рф территорин` | 11,389 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 465,426 |
| 2 | `а _` | 402,164 |
| 3 | `и _` | 363,006 |
| 4 | `— _` | 346,175 |
| 5 | `_ —` | 343,660 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ — _` | 342,728 |
| 2 | `ш ы в` | 149,577 |
| 3 | `ы в _` | 121,922 |
| 4 | `_ ю х` | 94,718 |
| 5 | `т е р` | 86,508 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ш ы в _` | 121,828 |
| 2 | `_ ш ы в` | 85,484 |
| 3 | `_ ю х а` | 76,914 |
| 4 | `ю х а н` | 63,379 |
| 5 | `х а н ш` | 63,281 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ш ы в _` | 83,923 |
| 2 | `ю х а н ш` | 63,268 |
| 3 | `х а н ш ы` | 63,265 |
| 4 | `а н ш ы в` | 63,263 |
| 5 | `_ ю х а н` | 62,475 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 532
- **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 | 0.7800 | 1.717 | 5.34 | 352,836 | 22.0% |
| **1** | Subword | 0.6157 | 1.532 | 6.03 | 3,635 | 38.4% |
| **2** | Word | 0.1829 | 1.135 | 1.40 | 1,869,675 | 81.7% |
| **2** | Subword | 0.9040 | 1.871 | 6.19 | 21,903 | 9.6% |
| **3** | Word | 0.0525 | 1.037 | 1.09 | 2,591,084 | 94.7% |
| **3** | Subword | 0.8721 | 1.830 | 4.70 | 135,543 | 12.8% |
| **4** | Word | 0.0223 🏆 | 1.016 | 1.04 | 2,792,400 | 97.8% |
| **4** | Subword | 0.7095 | 1.635 | 3.14 | 636,890 | 29.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `шыв гидрологи бассейн шыв шыв геоинформаци системин шыв федераци агентстви рф территорин шыв геоинфо...`
2. `юханшыв двина печора шыв федераци агентстви рф экологи министерстви республикин ао коми республики т...`
3. `в цене чем предпочитают вспоминать и дефекты зрения м советская энциклопедия в унисон с любашей леро...`

**Context Size 2:**

1. `шыв шыв тури обь иртыш шыв федераци агентстви рф территорин шыв геоинформаци системин шыв шыв тури о...`
2. `территоринчи юханшыв рейн вестфали территорипе юхать юханшыв негус ях сулахай 13 км шыв шыв тури бас...`
3. `территорипе юхать юханшыв мăн салым сулахай 220 км юхса юханшыв 12 км шыв шыв гидрологи бассейн том`

**Context Size 3:**

1. `федераци агентстви рф территорин шыв геоинформаци системин шыв шыв гидрологи гт бассейн том гт 15 гт...`
2. `шыв федераци агентстви рф территорин шыв геоинформаци системин шыв шыв гидрологи бассейн том 15 3 рф...`
3. `шыв геоинформаци системин шыв шыв гидрологи гт бассейн том гт 11 гт 1 рф экологи министерстви респуб...`

**Context Size 4:**

1. `шыв геоинформаци системин шыв шыв гидрологи гт бассейн том гт 03 гт 0 рф экологи министерстви ао рес...`
2. `территорин шыв геоинформаци системин шыв шыв гидрологи бассейн том 15 3 рф экологи министерстви авто...`
3. `геоинформаци системин шыв шыв гидрологи гт бассейн том гт 03 гт 0 рф экологи министерстви ао республ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_—_фикулигинци_в`
2. `а,_;_улслаки_пид`
3. `и_каспалименияни`

**Context Size 2:**

1. `._—_торф_тыслана_`
2. `а_медилостви_тута`
3. `и_йышши_баллина_з`

**Context Size 3:**

1. `_—_теминисем_астар`
2. `шыв_—_мар_монтовол`
3. `ыв_шыв._команицы:_`

**Context Size 4:**

1. `шыв_шыв_—_венгрла._`
2. `_шыв_федераци_агент`
3. `_юханшыв_шыв_геоинф`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (636,890 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 | 149,054 |
| Total Tokens | 3,895,916 |
| Mean Frequency | 26.14 |
| Median Frequency | 4 |
| Frequency Std Dev | 439.39 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | шыв | 84,160 |
| 2 | юханшыв | 53,731 |
| 3 | в | 45,242 |
| 4 | и | 41,204 |
| 5 | с | 37,543 |
| 6 | тата | 34,625 |
| 7 | бассейн | 28,455 |
| 8 | км | 25,026 |
| 9 | м | 24,932 |
| 10 | рф | 24,450 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | дустлик | 2 |
| 2 | галляарал | 2 |
| 3 | зарбдар | 2 |
| 4 | джизакской | 2 |
| 5 | сардоба | 2 |
| 6 | баяут | 2 |
| 7 | хаваст | 2 |
| 8 | сырдарьинской | 2 |
| 9 | пайт | 2 |
| 10 | клинов | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0393 |
| R² (Goodness of Fit) | 0.997747 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 30.0% |
| Top 1,000 | 56.1% |
| Top 5,000 | 72.5% |
| Top 10,000 | 79.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9977 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 30.0% of corpus
- **Long Tail:** 139,054 words needed for remaining 21.0% 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 | 0.8326 🏆 | 0.3463 | N/A | N/A |
| **mono_64d** | 64 | 0.8301 | 0.2835 | N/A | N/A |
| **mono_128d** | 128 | 0.7992 | 0.2278 | N/A | N/A |
| **aligned_32d** | 32 | 0.8326 | 0.3575 | 0.0120 | 0.1340 |
| **aligned_64d** | 64 | 0.8301 | 0.2722 | 0.0400 | 0.2360 |
| **aligned_128d** | 128 | 0.7992 | 0.2219 | 0.0680 | 0.3000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8326 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2849. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 6.8% 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 | **1.001** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | курска, никсона, подвига |
| `-ен` | америкасен, слышен, судьясен |
| `-не` | взводне, очерксене, болгарине |
| `-ов` | резюков, коршунов, щенков |
| `-ем` | сикекенсем, символсем, перуанецсем |
| `-ий` | выступлений, парфентий, праславянский |

### 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 |
|------|----------|------------------|----------|
| `олог` | 2.08x | 173 contexts | геолог, пологи, эколог |
| `сейн` | 2.92x | 24 contexts | сейнер, хусейн, хасейн |
| `ссей` | 2.92x | 17 contexts | ессей, эссей, рассей |
| `огра` | 1.78x | 95 contexts | богра, ограды, ограда |
| `рито` | 2.46x | 26 contexts | ритон, крито, приток |
| `ншыв` | 2.79x | 17 contexts | юшаншыв, юханшыв, юханшыве |
| `ерри` | 2.45x | 22 contexts | черри, ферри, дерри |
| `орин` | 1.72x | 74 contexts | дорин, шорин, борин |
| `аншы` | 2.79x | 13 contexts | юшаншыв, юханшыв, юханшыве |
| `исте` | 1.81x | 57 contexts | листе, хистет, истерн |
| `блик` | 2.25x | 17 contexts | облик, облика, коблик |
| `нист` | 1.86x | 30 contexts | финист, пианист, капнист |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| айсбергов | **`айсберг-ов`** | 4.5 | `айсберг` |
| фахрутдинов | **`фахрутдин-ов`** | 4.5 | `фахрутдин` |
| экономикине | **`экономики-не`** | 4.5 | `экономики` |
| пурнӑҫланине | **`пурнӑҫлани-не`** | 4.5 | `пурнӑҫлани` |
| ансамбльне | **`ансамбль-не`** | 4.5 | `ансамбль` |
| хрустальне | **`хрусталь-не`** | 4.5 | `хрусталь` |
| анатомине | **`анатоми-не`** | 4.5 | `анатоми` |
| инженеров | **`инженер-ов`** | 4.5 | `инженер` |
| багдасаров | **`багдасар-ов`** | 4.5 | `багдасар` |
| фотографий | **`фотограф-ий`** | 4.5 | `фотограф` |
| ассамблейине | **`ассамблейи-не`** | 4.5 | `ассамблейи` |
| символикине | **`символики-не`** | 4.5 | `символики` |
| бриллиантов | **`бриллиант-ов`** | 4.5 | `бриллиант` |
| кинокритиков | **`кинокритик-ов`** | 4.5 | `кинокритик` |
| наводнений | **`наводн-ен-ий`** | 3.0 | `наводн` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Chuvash 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 (3.78x) |
| N-gram | **2-gram** | Lowest perplexity (532) |
| Markov | **Context-4** | Highest predictability (97.8%) |
| 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: 2026-01-03 23:50:11*