---
language: mhr
language_name: Eastern Mari
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: 4.335
  - name: best_isotropy
    type: isotropy
    value: 0.8198
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Eastern Mari - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Eastern Mari** 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** | 3.658x | 3.66 | 0.0886% | 476,276 |
| **16k** | 3.968x | 3.97 | 0.0961% | 439,027 |
| **32k** | 4.189x | 4.19 | 0.1015% | 415,901 |
| **64k** | 4.335x 🏆 | 4.34 | 0.1050% | 401,897 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ворзель () — Украиныште Киев велыште Буча кундемыштыже верланыше посёлко. Калыкч...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more)` | 26 |
| 16k | `▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more)` | 26 |
| 32k | `▁вор з ель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ... (+16 more)` | 26 |
| 64k | `▁ворзель ▁() ▁— ▁украиныште ▁киев ▁велыште ▁буча ▁кундемыштыже ▁верланыше ▁посёлко ... (+14 more)` | 24 |

**Sample 2:** `Пункт () — дюймын 1/72 наре ужашыже лийше кӱшычын ӱлык шрифтын висымкугытшо.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁пункт ▁() ▁— ▁д юй мын ▁ 1 / 7 ... (+17 more)` | 27 |
| 16k | `▁пункт ▁() ▁— ▁дюй мын ▁ 1 / 7 2 ... (+15 more)` | 25 |
| 32k | `▁пункт ▁() ▁— ▁дюй мын ▁ 1 / 7 2 ... (+10 more)` | 20 |
| 64k | `▁пункт ▁() ▁— ▁дюймын ▁ 1 / 7 2 ▁наре ... (+8 more)` | 18 |

**Sample 3:** `238 ий — III курымын ийже. Мо лийын Кӧ шочын Кӧ колен курым`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more)` | 17 |
| 16k | `▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more)` | 17 |
| 32k | `▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more)` | 17 |
| 64k | `▁ 2 3 8 ▁ий ▁— ▁iii ▁курымын ▁ийже . ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.335x compression
- **Lowest UNK Rate:** 8k with 0.0886% 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 | 3,582 | 11.81 | 26,265 | 34.2% | 60.8% |
| **2-gram** | Subword | 439 🏆 | 8.78 | 3,878 | 54.6% | 97.4% |
| **3-gram** | Word | 4,130 | 12.01 | 36,566 | 34.5% | 60.2% |
| **3-gram** | Subword | 3,337 | 11.70 | 33,949 | 19.6% | 64.9% |
| **4-gram** | Word | 7,186 | 12.81 | 70,518 | 30.8% | 54.1% |
| **4-gram** | Subword | 13,025 | 13.67 | 159,935 | 11.7% | 42.2% |
| **5-gram** | Word | 6,518 | 12.67 | 62,229 | 31.1% | 55.2% |
| **5-gram** | Subword | 29,667 | 14.86 | 355,981 | 9.8% | 34.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `марий эл` | 13,258 |
| 2 | `йошкар ола` | 10,954 |
| 3 | `республики марий` | 9,354 |
| 4 | `великой отечественной` | 6,261 |
| 5 | `отечественной войне` | 6,227 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `республики марий эл` | 9,353 |
| 2 | `великой отечественной войне` | 6,227 |
| 3 | `в великой отечественной` | 6,214 |
| 4 | `народа в великой` | 6,200 |
| 5 | `подвиг народа в` | 6,199 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `в великой отечественной войне` | 6,214 |
| 2 | `народа в великой отечественной` | 6,200 |
| 3 | `документов подвиг народа в` | 6,199 |
| 4 | `подвиг народа в великой` | 6,199 |
| 5 | `банк документов подвиг народа` | 6,196 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `народа в великой отечественной войне` | 6,200 |
| 2 | `документов подвиг народа в великой` | 6,199 |
| 3 | `подвиг народа в великой отечественной` | 6,199 |
| 4 | `банк документов подвиг народа в` | 6,196 |
| 5 | `в великой отечественной войне гг` | 6,196 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 184,996 |
| 2 | `е _` | 147,576 |
| 3 | `л а` | 134,439 |
| 4 | `_ к` | 133,534 |
| 5 | `а р` | 121,950 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `и й _` | 64,060 |
| 2 | `ы н _` | 57,801 |
| 3 | `_ м а` | 49,403 |
| 4 | `м а р` | 48,489 |
| 5 | `р и й` | 42,988 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `м а р и` | 41,511 |
| 2 | `_ м а р` | 41,069 |
| 3 | `а р и й` | 40,250 |
| 4 | `в л а к` | 32,702 |
| 5 | `р и й _` | 32,360 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `м а р и й` | 39,931 |
| 2 | `_ м а р и` | 36,163 |
| 3 | `- в л а к` | 32,274 |
| 4 | `а р и й _` | 30,689 |
| 5 | `в л а к _` | 23,835 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 439
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.8000 | 1.741 | 5.03 | 109,319 | 20.0% |
| **1** | Subword | 1.2025 | 2.301 | 10.94 | 715 | 0.0% |
| **2** | Word | 0.2053 | 1.153 | 1.44 | 547,819 | 79.5% |
| **2** | Subword | 1.1275 | 2.185 | 7.46 | 7,818 | 0.0% |
| **3** | Word | 0.0723 | 1.051 | 1.14 | 786,559 | 92.8% |
| **3** | Subword | 0.9049 | 1.872 | 4.46 | 58,298 | 9.5% |
| **4** | Word | 0.0392 🏆 | 1.028 | 1.08 | 893,046 | 96.1% |
| **4** | Subword | 0.6302 | 1.548 | 2.69 | 260,070 | 37.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `марий эл юринский район 304 с 123 лашт тыгак ончо тылзын коло ияш туныктен тӱвырам кучылтмаш`
2. `влак историк влак посёлок боровской российыште вологда вел виче да калабрий регионын рӱдолаже сарман...`
3. `с 35 ч 1 еҥ ий численность населения городских населенных пунктов звениговский муниципальный район с...`

**Context Size 2:**

1. `марий эл по делам архивов государственный архив республики марий эл республикын йӱдвел кипр турций р...`
2. `йошкар ола с 125 158 15 ключева м а чап тамга орденын кавалерж кылвер влак хутор балезина`
3. `республики марий эл по делам архивов государственный архив республики марий эл администрация муницип...`

**Context Size 3:**

1. `республики марий эл оршанский район сборник документальных очерков йошкар ола комитет республики мар...`
2. `великой отечественной войне гг кузнецов михаил сарманаевич i степенян ачамланде сар орден да йошкар ...`
3. `в великой отечественной войне гг аралымылан степенян чап орден влакын кавалерже ийласе кугу ачамланд...`

**Context Size 4:**

1. `в великой отечественной войне гг заровняев василий фёдорович ийласе кугу ачамланде сарын участникше ...`
2. `народа в великой отечественной войне гг 11px i степенян ачамланде сар орденын кавалерже ийласе кугу ...`
3. `документов подвиг народа в великой отечественной войне гг суаплан медальэлектронный банк документов ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_165_ушктренынап`
2. `аск_-штлик_je_йс`
3. `еше_«стэл:_ичий)`

**Context Size 2:**

1. `._*_matheleptedia`
2. `е_ке,_эҥеш_марсти`
3. `_кӧ_кумарий)_jah_`

**Context Size 3:**

1. `ий_элын,_марий_йӱл`
2. `ын_моча_куснен_кун`
3. `_мари-кушто_дене_в`

**Context Size 4:**

1. `марий-влак_кундемыш`
2. `_марий_эл,_админист`
3. `арий_эл_по_делам_ар`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (260,070 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 | 48,490 |
| Total Tokens | 1,425,889 |
| Mean Frequency | 29.41 |
| Median Frequency | 4 |
| Frequency Std Dev | 331.81 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | марий | 30,639 |
| 2 | влак | 26,643 |
| 3 | с | 22,173 |
| 4 | в | 15,995 |
| 5 | эл | 13,818 |
| 6 | йошкар | 13,689 |
| 7 | ола | 13,467 |
| 8 | ий | 11,834 |
| 9 | ял | 11,645 |
| 10 | и | 11,569 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | слегка | 2 |
| 2 | расстроены | 2 |
| 3 | покачав | 2 |
| 4 | брать | 2 |
| 5 | поглаживая | 2 |
| 6 | настраивать | 2 |
| 7 | взял | 2 |
| 8 | взмахнул | 2 |
| 9 | поплыла | 2 |
| 10 | комнате | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1394 |
| R² (Goodness of Fit) | 0.995171 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.4% |
| Top 1,000 | 67.2% |
| Top 5,000 | 84.2% |
| Top 10,000 | 90.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9952 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.4% of corpus
- **Long Tail:** 38,490 words needed for remaining 10.0% 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 | 0.8198 🏆 | 0.3483 | N/A | N/A |
| **mono_64d** | 64 | 0.7400 | 0.2927 | N/A | N/A |
| **mono_128d** | 128 | 0.3509 | 0.2627 | N/A | N/A |
| **aligned_32d** | 32 | 0.8198 | 0.3439 | 0.0120 | 0.1120 |
| **aligned_64d** | 64 | 0.7400 | 0.2932 | 0.0280 | 0.1860 |
| **aligned_128d** | 128 | 0.3509 | 0.2652 | 0.0520 | 0.2340 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8198 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3010. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.2% 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 | **0.590** | 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` | кертшылан, кравцов, капитон |
| `-п` | пургыж, пайгусово, пырысым |
| `-с` | саксофон, составитель, садретдинов |
| `-т` | такая, таҥаса, тимофеевский |
| `-ко` | командирын, кокыте, колмо |
| `-м` | мурымыж, марийкалыкым, модшын |
| `-а` | автора, аквалангым, акр |
| `-в` | вашталтыш, ведра, веткино |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-е` | культовые, литературйылме, руэмское |
| `-н` | кертшылан, капитон, чурийвылышан |
| `-а` | хайруллина, дата, таҥаса |
| `-й` | флоренций, тимофеевский, заведующий |
| `-м` | яким, редакцийжым, марийкалыкым |
| `-о` | пайгусово, общественно, качейкино |
| `-ым` | редакцийжым, марийкалыкым, иктешлымашым |
| `-ий` | флоренций, тимофеевский, заведующий |

### 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 |
|------|----------|------------------|----------|
| `ндем` | 2.44x | 22 contexts | киндем, шындем, тандем |
| `ланд` | 2.03x | 35 contexts | ландау, юланда, мланде |
| `рлан` | 1.84x | 37 contexts | арлан, ерлан, хорлан |
| `айон` | 2.14x | 19 contexts | район, района, районе |
| `демы` | 2.09x | 20 contexts | айдемын, айдемыш, айдемым |
| `райо` | 2.14x | 16 contexts | район, района, районе |
| `унде` | 2.45x | 10 contexts | кундем, кундемна, кундемже |
| `альн` | 1.70x | 25 contexts | дальний, дальние, вокально |
| `енно` | 1.95x | 16 contexts | фенно, именно, военно |
| `кунд` | 2.26x | 9 contexts | кунда, кундем, секунд |
| `лект` | 1.38x | 36 contexts | лекте, лектыш, лектыт |
| `верл` | 2.01x | 8 contexts | верла, верлам, уверла |

### 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` | `-е` | 122 words | комнате, каҥашыме |
| `-п` | `-е` | 121 words | правление, периодике |
| `-к` | `-н` | 109 words | клапан, катян |
| `-с` | `-е` | 90 words | савырнымыже, следовательже |
| `-п` | `-н` | 71 words | пӧлкажын, пуртыман |
| `-с` | `-н` | 69 words | скревын, савырашлан |
| `-к` | `-о` | 69 words | колжо, кузьменко |
| `-т` | `-е` | 65 words | тиде, тюркское |
| `-к` | `-а` | 63 words | куклина, коведяева |
| `-м` | `-н` | 60 words | мардежан, музыкан |

### 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 |
|------|-----------------|------------|------|
| автономный | **`автоном-н-ый`** | 7.5 | `н` |
| диалектный | **`диалект-н-ый`** | 7.5 | `н` |
| отвлеченный | **`отвлечен-н-ый`** | 7.5 | `н` |
| министертвын | **`министерт-в-ын`** | 7.5 | `в` |
| всемарийском | **`в-се-марийском`** | 7.5 | `марийском` |
| материалах | **`материал-а-х`** | 7.5 | `а` |
| фильмыште | **`фильм-ыш-те`** | 6.0 | `фильм` |
| биологийын | **`биолог-ий-ын`** | 6.0 | `биолог` |
| тунемыныт | **`тунем-ын-ыт`** | 6.0 | `тунем` |
| комплексыште | **`комплекс-ыш-те`** | 6.0 | `комплекс` |
| абхазийын | **`абхаз-ий-ын`** | 6.0 | `абхаз` |
| каҥашымаш | **`каҥаш-ым-аш`** | 6.0 | `каҥаш` |
| шотландийын | **`шотланд-ий-ын`** | 6.0 | `шотланд` |
| философийже | **`философ-ий-же`** | 6.0 | `философ` |
| вашталтымаш | **`вашталт-ым-аш`** | 6.0 | `вашталт` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Eastern Mari 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 (4.34x) |
| N-gram | **2-gram** | Lowest perplexity (439) |
| Markov | **Context-4** | Highest predictability (96.1%) |
| 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 11:49:08*