README.md

---
language: myv
language_name: Erzya
language_family: uralic_volgaic
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_volgaic
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: 4.104
  - name: best_isotropy
    type: isotropy
    value: 0.8628
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Erzya** 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** | 3.359x | 3.36 | 0.1174% | 282,726 |
| **16k** | 3.657x | 3.66 | 0.1279% | 259,662 |
| **32k** | 3.923x | 3.93 | 0.1371% | 242,074 |
| **64k** | 4.104x 🏆 | 4.11 | 0.1435% | 231,386 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Киислова () — те велесь Эстэнь Масторсо Вырумаа ёнкссо. Сёрм. Мастор Масторонть ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |
| 16k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |
| 32k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |
| 64k | `▁киислова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ▁ёнкссо . ... (+5 more)` | 15 |

**Sample 2:** `Лепамиця лымбамот — лымбиця лыкамось, кона альмезэ аламолгады шканьберть.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ле па м иця ▁лы мба мот ▁— ▁лы мб ... (+16 more)` | 26 |
| 16k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+15 more)` | 25 |
| 32k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+12 more)` | 22 |
| 64k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+9 more)` | 19 |

**Sample 3:** `Мария Гулегина (); чач. Умарьковонь 9 чистэ, Одесса ош, СССР) — морыця (сопрано)...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁мария ▁гу ле г ина ▁(); ▁чач . ▁умарьковонь ▁ ... (+14 more)` | 24 |
| 16k | `▁мария ▁гу ле гина ▁(); ▁чач . ▁умарьковонь ▁ 9 ... (+12 more)` | 22 |
| 32k | `▁мария ▁гу ле гина ▁(); ▁чач . ▁умарьковонь ▁ 9 ... (+12 more)` | 22 |
| 64k | `▁мария ▁гулегина ▁(); ▁чач . ▁умарьковонь ▁ 9 ▁чистэ , ... (+10 more)` | 20 |


### Key Findings

- **Best Compression:** 64k achieves 4.104x compression
- **Lowest UNK Rate:** 8k with 0.1174% 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 | 5,234 | 12.35 | 13,565 | 19.1% | 50.0% |
| **2-gram** | Subword | 451 🏆 | 8.82 | 4,411 | 55.9% | 96.7% |
| **3-gram** | Word | 5,809 | 12.50 | 17,643 | 20.4% | 49.4% |
| **3-gram** | Subword | 3,849 | 11.91 | 34,647 | 20.1% | 61.1% |
| **4-gram** | Word | 9,800 | 13.26 | 32,090 | 18.1% | 43.0% |
| **4-gram** | Subword | 19,085 | 14.22 | 156,710 | 10.3% | 34.9% |
| **5-gram** | Word | 7,606 | 12.89 | 25,413 | 19.9% | 46.5% |
| **5-gram** | Subword | 51,060 | 15.64 | 321,204 | 6.8% | 24.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `вн истяжо` | 1,572 |
| 2 | `содавикс ломанть` | 1,490 |
| 3 | `ломанть те` | 1,467 |
| 4 | `те велестэнть` | 1,405 |
| 5 | `веленть лемденть` | 1,393 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `содавикс ломанть те` | 1,461 |
| 2 | `ломанть те велестэнть` | 1,405 |
| 3 | `эрицятне раськень состав` | 1,059 |
| 4 | `раськень состав весероссиянь` | 1,054 |
| 5 | `состав весероссиянь перепись` | 1,039 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `содавикс ломанть те велестэнть` | 1,405 |
| 2 | `эрицятне раськень состав весероссиянь` | 1,044 |
| 3 | `раськень состав весероссиянь перепись` | 1,039 |
| 4 | `весероссиянь перепись населения ие` | 1,039 |
| 5 | `состав весероссиянь перепись населения` | 1,039 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `состав весероссиянь перепись населения ие` | 1,039 |
| 2 | `раськень состав весероссиянь перепись населения` | 1,039 |
| 3 | `эрицятне раськень состав весероссиянь перепись` | 1,032 |
| 4 | `содавикс ломанть те велестэнть эрицятне` | 946 |
| 5 | `эрямозо содавикс ломанть те велестэнть` | 917 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ь _` | 153,248 |
| 2 | `. _` | 92,452 |
| 3 | `н ь` | 90,818 |
| 4 | `с т` | 68,788 |
| 5 | `, _` | 66,880 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н ь _` | 80,150 |
| 2 | `т ь _` | 36,047 |
| 3 | `_ — _` | 29,408 |
| 4 | `о н ь` | 26,266 |
| 5 | `е н ь` | 26,109 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `о н ь _` | 24,242 |
| 2 | `е н ь _` | 22,554 |
| 3 | `н т ь _` | 20,388 |
| 4 | `_ в е л` | 13,694 |
| 5 | `в е л е` | 12,902 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ в е л е` | 12,574 |
| 2 | `е н т ь _` | 8,208 |
| 3 | `в о н ь _` | 7,157 |
| 4 | `о в о н ь` | 6,844 |
| 5 | `и я н ь _` | 6,197 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 451
- **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 | 0.6530 | 1.572 | 3.67 | 122,977 | 34.7% |
| **1** | Subword | 1.2973 | 2.458 | 11.50 | 833 | 0.0% |
| **2** | Word | 0.1469 | 1.107 | 1.28 | 449,631 | 85.3% |
| **2** | Subword | 1.1429 | 2.208 | 6.92 | 9,577 | 0.0% |
| **3** | Word | 0.0456 | 1.032 | 1.08 | 573,707 | 95.4% |
| **3** | Subword | 0.8768 | 1.836 | 4.15 | 66,234 | 12.3% |
| **4** | Word | 0.0224 🏆 | 1.016 | 1.04 | 613,293 | 97.8% |
| **4** | Subword | 0.6169 | 1.534 | 2.56 | 274,547 | 38.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ды касы седе ламо м и б в финно угорский прорыв текст биографический фильм без источников`
2. `в суздаль на южния полюс с рус эрзян isbn url consultato il 21 8 чистэ калиновка`
3. `и д в рузанкин н новгород англо хинди русский словарь ок назв а кенерезь лёмзёркссо почодозь`

**Context Size 2:**

1. `вн истяжо таштамковонь 12 чистэ саран ошсо калмазо апак ёвта секскак велень продештяст истямо сынст ...`
2. `содавикс ломанть те велестэнть веленть эрямозо содавикс ломанть те велестэнть веленть эрямозо содави...`
3. `ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 56 велеть ошо...`

**Context Size 3:**

1. `содавикс ломанть те велестэнть веленть эрямозо эрицятне раськень состав весероссиянь перепись населе...`
2. `ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 93 велеть вел...`
3. `эрицятне раськень состав весероссиянь эрицятнень сёрмадстоманть ие коряс рузт 100 содавикс ломанть т...`

**Context Size 4:**

1. `содавикс ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 95 с...`
2. `эрицятне раськень состав весероссиянь перепись населения ие рузт 100 велеть буень велеть`
3. `весероссиянь перепись населения ие печкаст 100 велеть велеть`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_вень_кулмиистес`
2. `олияморх_с_мениз`
3. `ав_покрявась_а_к`

**Context Size 2:**

1. `ь_ких_новияс_эле_`
2. `._валриц_мень_(юу`
3. `нь_эритортаранили`

**Context Size 3:**

1. `нь_аштемантоликани`
2. `ть_экось_оплангсо_`
3. `_—_ведческие_с_евр`

**Context Size 4:**

1. `онь_сал,_запись_нас`
2. `ень_ды_уманический_`
3. `нть_эрямонзо_токаль`


### 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 (274,547 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 | 47,484 |
| Total Tokens | 705,946 |
| Mean Frequency | 14.87 |
| Median Frequency | 3 |
| Frequency Std Dev | 119.73 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ды | 10,760 |
| 2 | в | 8,187 |
| 3 | и | 6,467 |
| 4 | с | 6,350 |
| 5 | а | 5,547 |
| 6 | те | 5,228 |
| 7 | м | 4,398 |
| 8 | иестэ | 3,988 |
| 9 | ульнесь | 3,596 |
| 10 | ие | 3,563 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | якшаматянть | 2 |
| 2 | аналогозо | 2 |
| 3 | доминияк | 2 |
| 4 | indeks | 2 |
| 5 | grup | 2 |
| 6 | zawodowych | 2 |
| 7 | muzea | 2 |
| 8 | britishpedia | 2 |
| 9 | osobistości | 2 |
| 10 | bph | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0126 |
| R² (Goodness of Fit) | 0.996053 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 27.1% |
| Top 1,000 | 55.8% |
| Top 5,000 | 75.1% |
| Top 10,000 | 83.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9961 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 27.1% of corpus
- **Long Tail:** 37,484 words needed for remaining 17.0% 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 | 0.8628 🏆 | 0.3405 | N/A | N/A |
| **mono_64d** | 64 | 0.7101 | 0.2786 | N/A | N/A |
| **mono_128d** | 128 | 0.2558 | 0.2702 | N/A | N/A |
| **aligned_32d** | 32 | 0.8628 | 0.3424 | 0.0280 | 0.1300 |
| **aligned_64d** | 64 | 0.7101 | 0.2772 | 0.0360 | 0.1540 |
| **aligned_128d** | 128 | 0.2558 | 0.2675 | 0.0700 | 0.2380 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8628 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2961. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 7.0% 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 | **0.892** | 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` | кемкавтово, кантнить, клавдий |
| `-с` | сайнелень, сабан, скульптуры |
| `-п` | пильгеоскань, политиканьветий, паросто |
| `-ка` | кантнить, казаньсэ, кайсеви |
| `-а` | абус, андонь, англиясо |
| `-т` | тамары, таштоюрьево, туинек |
| `-в` | венстизе, вагриус, венок |
| `-м` | матвеево, монастырень, массрэнь |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ь` | пильгеоскань, сайнелень, кантнить |
| `-нь` | пильгеоскань, сайнелень, раввинэнь |
| `-о` | кемкавтово, матвеево, ярмаконзо |
| `-ть` | кантнить, художникенть, эрсить |
| `-а` | задонска, божена, улянка |
| `-е` | венстизе, характеристикатне, европе |
| `-й` | клавдий, политиканьветий, учебной |
| `-сь` | ловомась, куломачись, кельесь |

### 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 |
|------|----------|------------------|----------|
| `ково` | 2.01x | 50 contexts | ковол, беково, ковозо |
| `енть` | 1.92x | 55 contexts | генть, денть, менть |
| `овон` | 2.23x | 30 contexts | човонь, ловонь, ковонь |
| `арка` | 2.00x | 42 contexts | парка, тарка, аркат |
| `риця` | 2.25x | 20 contexts | эриця, триця, мариця |
| `ской` | 1.90x | 34 contexts | арской, южской, ямской |
| `анть` | 1.83x | 38 contexts | канть, панть, манть |
| `вонь` | 2.26x | 18 contexts | орвонь, сёвонь, лувонь |
| `асто` | 1.74x | 44 contexts | тасто, састо, часто |
| `стор` | 1.63x | 48 contexts | сторож, мастор, стороны |
| `ятне` | 1.76x | 33 contexts | цятне, ятнень, атятне |
| `тарк` | 2.14x | 16 contexts | тарка, таркат, тарксо |

### 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` | `-ь` | 242 words | компаниянть, кшить |
| `-п` | `-ь` | 182 words | палсь, политикень |
| `-с` | `-ь` | 168 words | семиянь, сельмтнень |
| `-в` | `-ь` | 134 words | вирьавань, вейсветямонь |
| `-т` | `-ь` | 123 words | токалить, термодинамикань |
| `-м` | `-ь` | 118 words | марясть, максоманть |
| `-к` | `-нь` | 117 words | каминь, клеткантень |
| `-а` | `-ь` | 103 words | ашомештень, азребайджанонь |
| `-л` | `-ь` | 94 words | лемдезь, людикинь |
| `-п` | `-нь` | 85 words | политикень, псакань |

### 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 |
|------|-----------------|------------|------|
| инязорава | **`инязор-а-ва`** | 7.5 | `а` |
| материалам | **`материал-а-м`** | 7.5 | `а` |
| пандомась | **`пандо-ма-сь`** | 7.5 | `ма` |
| группанень | **`группа-не-нь`** | 7.5 | `не` |
| экономистов | **`экономи-ст-ов`** | 7.5 | `ст` |
| васеньценть | **`васеньце-н-ть`** | 7.5 | `н` |
| маритьнень | **`марить-не-нь`** | 7.5 | `не` |
| участкась | **`участ-ка-сь`** | 7.5 | `ка` |
| ломаньстэ | **`ломань-ст-э`** | 7.5 | `ст` |
| кемекстись | **`кемекст-и-сь`** | 7.5 | `и` |
| невтемакс | **`невте-ма-кс`** | 7.5 | `ма` |
| чугункасто | **`чугунка-ст-о`** | 7.5 | `ст` |
| велетнесэ | **`велет-не-сэ`** | 7.5 | `не` |
| премиятне | **`премия-т-не`** | 7.5 | `т` |
| медицинань | **`медици-на-нь`** | 7.5 | `на` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Erzya 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 (4.10x) |
| N-gram | **2-gram** | Lowest perplexity (451) |
| 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: 2026-01-10 14:15:51*