---
language: udm
language_name: Udmurt
language_family: uralic_permian
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-uralic_permian
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: 4.565
  - name: best_isotropy
    type: isotropy
    value: 0.6980
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Udmurt** 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** | 3.543x | 3.55 | 0.1375% | 258,898 |
| **16k** | 3.952x | 3.96 | 0.1534% | 232,054 |
| **32k** | 4.311x | 4.32 | 0.1673% | 212,774 |
| **64k** | 4.565x 🏆 | 4.57 | 0.1772% | 200,933 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Байраншур () — Удмуртиысь пичи шур. Бызе Яр ёрослэн музъеметӥз но усе Тум шуре. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁бай ран шур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ... (+23 more)` | 33 |
| 16k | `▁бай ран шур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ... (+22 more)` | 32 |
| 32k | `▁байран шур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ▁яр ... (+20 more)` | 30 |
| 64k | `▁байраншур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ▁яр ▁ёрослэн ... (+19 more)` | 29 |

**Sample 2:** `Олеся Журакивська (; Киев, СССР, — Украин актриса. Фильмъёс Остров Донбас алфави...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ол ес я ▁ж ур ак ив ська ▁(; ▁киев ... (+13 more)` | 23 |
| 16k | `▁ол ес я ▁ж ур ак ив ська ▁(; ▁киев ... (+12 more)` | 22 |
| 32k | `▁ол еся ▁жур акив ська ▁(; ▁киев , ▁ссср , ... (+9 more)` | 19 |
| 64k | `▁ол еся ▁журакив ська ▁(; ▁киев , ▁ссср , ▁— ... (+8 more)` | 18 |

**Sample 3:** `Кривой Рог метротрам ( укр. Криворізький швидкісний трамвай )`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁кр ив ой ▁ро г ▁метро т рам ▁( ▁ук ... (+17 more)` | 27 |
| 16k | `▁крив ой ▁рог ▁метро т рам ▁( ▁ук р . ... (+12 more)` | 22 |
| 32k | `▁крив ой ▁рог ▁метро трам ▁( ▁укр . ▁крив ор ... (+10 more)` | 20 |
| 64k | `▁кривой ▁рог ▁метротрам ▁( ▁укр . ▁крив ор і зь ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.565x compression
- **Lowest UNK Rate:** 8k with 0.1375% 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 | 4,224 | 12.04 | 9,045 | 20.2% | 51.2% |
| **2-gram** | Subword | 646 🏆 | 9.34 | 3,769 | 43.9% | 95.6% |
| **3-gram** | Word | 4,567 | 12.16 | 10,317 | 20.4% | 49.5% |
| **3-gram** | Subword | 5,398 | 12.40 | 30,259 | 15.9% | 50.6% |
| **4-gram** | Word | 9,357 | 13.19 | 19,488 | 14.9% | 37.3% |
| **4-gram** | Subword | 23,964 | 14.55 | 134,461 | 8.6% | 28.8% |
| **5-gram** | Word | 7,868 | 12.94 | 14,631 | 14.0% | 37.7% |
| **5-gram** | Subword | 56,525 | 15.79 | 261,817 | 5.4% | 21.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j j` | 743 |
| 2 | `1 тӥ` | 662 |
| 3 | `synonym of` | 638 |
| 4 | `now synonym` | 606 |
| 5 | `rchb f` | 601 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `now synonym of` | 604 |
| 2 | `j j sm` | 569 |
| 3 | `ёросысь улон интыос` | 559 |
| 4 | `арын 1 тӥ` | 533 |
| 5 | `1 тӥ толшоре` | 490 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `арын 1 тӥ толшоре` | 484 |
| 2 | `улӥсьёс арын 1 тӥ` | 482 |
| 3 | `1 тӥ толшоре гуртын` | 478 |
| 4 | `ёросысь улон интыос ёросысь` | 414 |
| 5 | `улон интыос ёросысь гуртъёс` | 414 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `улӥсьёс арын 1 тӥ толшоре` | 482 |
| 2 | `арын 1 тӥ толшоре гуртын` | 478 |
| 3 | `ёросысь улон интыос ёросысь гуртъёс` | 414 |
| 4 | `адями лыдъяськиз ёросысь улон интыос` | 404 |
| 5 | `лыдъяськиз ёросысь улон интыос ёросысь` | 396 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _` | 53,739 |
| 2 | `. _` | 52,122 |
| 3 | `с ь` | 44,748 |
| 4 | `_ к` | 43,958 |
| 5 | `, _` | 37,972 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `с ь _` | 23,826 |
| 2 | `_ — _` | 21,444 |
| 3 | `ы с ь` | 19,313 |
| 4 | `ъ ё с` | 19,179 |
| 5 | `ы н _` | 19,081 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы с ь _` | 17,835 |
| 2 | `л э н _` | 16,383 |
| 3 | `_ н о _` | 10,521 |
| 4 | `. _ — _` | 9,347 |
| 5 | `ъ ё с _` | 7,031 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `у д м у р` | 5,330 |
| 2 | `д м у р т` | 5,329 |
| 3 | `_ у д м у` | 4,783 |
| 4 | `_ ё р о с` | 4,592 |
| 5 | `и ы с ь _` | 4,529 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 646
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~21% 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 | 0.6992 | 1.624 | 3.81 | 87,992 | 30.1% |
| **1** | Subword | 0.9862 | 1.981 | 7.60 | 1,200 | 1.4% |
| **2** | Word | 0.1500 | 1.110 | 1.29 | 333,544 | 85.0% |
| **2** | Subword | 0.9701 | 1.959 | 6.05 | 9,108 | 3.0% |
| **3** | Word | 0.0464 | 1.033 | 1.08 | 427,340 | 95.4% |
| **3** | Subword | 0.8614 | 1.817 | 4.08 | 55,078 | 13.9% |
| **4** | Word | 0.0213 🏆 | 1.015 | 1.04 | 457,825 | 97.9% |
| **4** | Subword | 0.5986 | 1.514 | 2.45 | 224,742 | 40.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `но юскаре атаез агнешка но дунай мм пала адями лыдъяськиз пурга ёрослэн музъеметӥз шунды пуксён палл...`
2. `арын 1 58 арын распределение бере кузон нефтеразведка участокъёс сад ёросын камбарка карын казахстан...`
3. `тӥ мае пичи пургаысь сельлесхоз озьы ик сезьы кӧжы ӝук пӧзьто вӧсьсы бере баушев софин ӟуч`

**Context Size 2:**

1. `j j wood in j j sm ex koord schum galeola kuhlii rchb f hook f summerh`
2. `1 тӥ толшоре гуртын 77 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыоссы ёросысь ул...`
3. `synonym of didactylus paradoxa luer dalström эквадор stelis nana lindl эквадор stelis pudens luer эк...`

**Context Size 3:**

1. `now synonym of crocodeilanthe cauliflora lindl luer pleurothallis pilostoma коста рика now synonym o...`
2. `j j sm liparis cyperifolia ridl liparis dalessandroi dodson liparis dalzellii hook f liparis xanthin...`
3. `арын 1 тӥ толшоре гуртын 378 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыоссы`

**Context Size 4:**

1. `арын 1 тӥ толшоре гуртын 1 адями лыдъяськиз пурга ёросысь улон интыос пурга ёросысь гуртъёс улон инт...`
2. `улӥсьёс арын 1 тӥ толшоре гуртын 82 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыос...`
3. `1 тӥ толшоре гуртын 43 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыоссы`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_кеныст_чыни_._д`
2. `ай,_ктерспёсканы`
3. `сь._taccyncrs_ва`

**Context Size 2:**

1. `н_1-тӥсь_болос._e`
2. `._—_вылэсовитич_(`
3. `сь._—_aglowiedipt`

**Context Size 3:**

1. `сь_выль_венграв_мо`
2. `_—_кость_садово_пр`
3. `ысь_еврок_(hoehne_`

**Context Size 4:**

1. `ысь_улос,_кубикет_с`
2. `лэн_быдӟалаз_дӥсько`
3. `_но_пичи_луыса._а._`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (224,742 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 | 35,258 |
| Total Tokens | 485,306 |
| Mean Frequency | 13.76 |
| Median Frequency | 3 |
| Frequency Std Dev | 88.68 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | но | 10,962 |
| 2 | арын | 3,468 |
| 3 | тӥ | 2,839 |
| 4 | удмурт | 2,798 |
| 5 | luer | 2,289 |
| 6 | гурт | 2,284 |
| 7 | ёросысь | 2,189 |
| 8 | 1 | 2,085 |
| 9 | со | 1,987 |
| 10 | j | 1,734 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | телеграм | 2 |
| 2 | феминизмлы | 2 |
| 3 | вотчина | 2 |
| 4 | феминизм | 2 |
| 5 | глобалистъёслэн | 2 |
| 6 | пельмень | 2 |
| 7 | секта | 2 |
| 8 | версиозы | 2 |
| 9 | вераськет | 2 |
| 10 | эрис | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0076 |
| R² (Goodness of Fit) | 0.990825 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.1% |
| Top 1,000 | 54.2% |
| Top 5,000 | 76.3% |
| Top 10,000 | 85.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9908 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.1% of corpus
- **Long Tail:** 25,258 words needed for remaining 14.9% 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 | 0.6980 | 0.3482 | N/A | N/A |
| **mono_64d** | 64 | 0.4125 | 0.3188 | N/A | N/A |
| **mono_128d** | 128 | 0.0749 | 0.3189 | N/A | N/A |
| **aligned_32d** | 32 | 0.6980 🏆 | 0.3505 | 0.0080 | 0.1280 |
| **aligned_64d** | 64 | 0.4125 | 0.3252 | 0.0260 | 0.1660 |
| **aligned_128d** | 128 | 0.0749 | 0.3271 | 0.0420 | 0.1880 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6980 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3314. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.2% 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 | **0.793** | 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 |
|--------|----------|
| `-к` | кит, кубоказ, косметической |
| `-с` | списокезлэн, серем, сюрреализм |
| `-п` | петра, прокурорез, пӧйшурало |
| `-в` | выжонни, выжыысьтызы, валаз |
| `-б` | берлинэ, бавариысь, борок |
| `-а` | алжирлэн, австрия, александрович |
| `-м` | мазунинской, механик, мозмытӥсь |
| `-т` | театральная, теориен, талибъёслы |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | алжирлэн, гвинеяын, набережнойын |
| `-эн` | алжирлэн, цехезлэн, ельцинлэн |
| `-a` | parvula, michelia, glaucophylla |
| `-з` | валаз, кубоказ, прокурорез |
| `-сь` | бавариысь, мозмытӥсь, дэремлэсь |
| `-ь` | бавариысь, мозмытӥсь, дэремлэсь |
| `-ын` | гвинеяын, набережнойын, европаын |
| `-ы` | выжыысьтызы, ӝутӥськизы, шудӥсьлы |

### 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 |
|------|----------|------------------|----------|
| `иськ` | 1.61x | 95 contexts | иськем, миськон, иськеме |
| `anth` | 2.47x | 18 contexts | euanthe, panther, anthrax |
| `тъёс` | 1.67x | 59 contexts | юртъёс, кутъёс, катъёс |
| `тэмы` | 2.15x | 22 contexts | итэмын, актэмыр, ватэмын |
| `ръёс` | 1.52x | 81 contexts | ӧръёс, аръёс, шуръёс |
| `тӥсь` | 1.61x | 61 contexts | кутӥсь, чутӥсь, потӥсь |
| `эмын` | 2.07x | 23 contexts | улэмын, алэмын, луэмын |
| `ъёсы` | 1.46x | 83 contexts | ожъёсы, аръёсы, ужъёсыз |
| `ской` | 2.07x | 20 contexts | чудской, рижской, вотской |
| `нъёс` | 1.70x | 39 contexts | дунъёс, вынъёс, синъёс |
| `яськ` | 1.57x | 28 contexts | сяська, сяськае, сяськая |
| `емын` | 1.71x | 18 contexts | ваемын, ошемын, утемын |

### 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 |
|--------|--------|-----------|----------|
| `-к` | `-н` | 157 words | кубертен, кудымкарын |
| `-т` | `-н` | 71 words | тропинин, трактэн |
| `-п` | `-н` | 70 words | петровичлэн, план |
| `-к` | `-з` | 70 words | катэныз, коллегиез |
| `-к` | `-ы` | 64 words | кивалтӥсезлы, кузьымлы |
| `-п` | `-з` | 64 words | пыронэз, палозяз |
| `-к` | `-эн` | 64 words | кивалтэтэзлэн, калыкъёслэн |
| `-с` | `-н` | 63 words | суданлэн, спринтын |
| `-в` | `-н` | 61 words | валамон, валтӥсьёсызлэн |
| `-г` | `-н` | 53 words | героезлэн, гербезлэн |

### 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 |
|------|-----------------|------------|------|
| комитетсы | **`комитет-с-ы`** | 7.5 | `с` |
| факультетсэ | **`факультет-с-э`** | 7.5 | `с` |
| процентысь | **`процент-ы-сь`** | 6.0 | `процент` |
| ссылкаысь | **`ссылка-ы-сь`** | 6.0 | `ссылка` |
| шормуӵысь | **`шормуӵ-ы-сь`** | 6.0 | `шормуӵ` |
| школаослы | **`школа-ос-лы`** | 6.0 | `школа` |
| группаослы | **`группа-ос-лы`** | 6.0 | `группа` |
| историысь | **`истори-ы-сь`** | 6.0 | `истори` |
| округъёсы | **`округъёс-ы`** | 4.5 | `округъёс` |
| планетаос | **`планета-ос`** | 4.5 | `планета` |
| журналистикая | **`журналистика-я`** | 4.5 | `журналистика` |
| системаын | **`система-ын`** | 4.5 | `система` |
| куартолэзен | **`куартолэзе-н`** | 4.5 | `куартолэзе` |
| возьматон | **`возьмато-н`** | 4.5 | `возьмато` |
| разделъёсыз | **`разделъёс-ыз`** | 4.5 | `разделъёс` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Udmurt 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 (4.56x) |
| N-gram | **2-gram** | Lowest perplexity (646) |
| Markov | **Context-4** | Highest predictability (97.9%) |
| 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 02:18:53*