---
language: mrj
language_name: Western 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: 4.191
  - name: best_isotropy
    type: isotropy
    value: 0.6197
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Western 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** | 3.098x | 3.10 | 0.0903% | 303,340 |
| **16k** | 3.510x | 3.51 | 0.1023% | 267,730 |
| **32k** | 3.895x | 3.90 | 0.1135% | 241,309 |
| **64k** | 4.191x 🏆 | 4.20 | 0.1222% | 224,266 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Билимби () — Oxalidaceae йыхыш пырышы фруктан пушӓнгӹ.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁б или м би ▁() ▁— ▁ox al id aceae ... (+5 more)` | 15 |
| 16k | `▁б или м би ▁() ▁— ▁ox al id aceae ... (+5 more)` | 15 |
| 32k | `▁били мби ▁() ▁— ▁ox al idaceae ▁йыхыш ▁пырышы ▁фруктан ... (+2 more)` | 12 |
| 64k | `▁били мби ▁() ▁— ▁oxalidaceae ▁йыхыш ▁пырышы ▁фруктан ▁пушӓнгӹ .` | 10 |

**Sample 2:** `Арлекин той шылдыран кӓдӹ () — кӓдӹ йишвлӓн йыхыш пырышы кечӹвӓлвел Австралиштӹ ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ар л ек ин ▁той ▁шылдыран ▁кӓдӹ ▁() ▁— ▁кӓдӹ ... (+17 more)` | 27 |
| 16k | `▁ар л екин ▁той ▁шылдыран ▁кӓдӹ ▁() ▁— ▁кӓдӹ ▁йишвлӓн ... (+16 more)` | 26 |
| 32k | `▁ар лекин ▁той ▁шылдыран ▁кӓдӹ ▁() ▁— ▁кӓдӹ ▁йишвлӓн ▁йыхыш ... (+15 more)` | 25 |
| 64k | `▁арлекин ▁той ▁шылдыран ▁кӓдӹ ▁() ▁— ▁кӓдӹ ▁йишвлӓн ▁йыхыш ▁пырышы ... (+14 more)` | 24 |

**Sample 3:** `Зичиуйфалу () — Венгриштӹ, Фейер медьежӹштӹ сола. Кымдецшӹ 10.82 км². ин тӹштӹ 9...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁зи чи уй ф ал у ▁() ▁— ▁венгри штӹ ... (+28 more)` | 38 |
| 16k | `▁зи чи уй фал у ▁() ▁— ▁венгриштӹ , ▁ф ... (+26 more)` | 36 |
| 32k | `▁зи чи уй фал у ▁() ▁— ▁венгриштӹ , ▁фей ... (+24 more)` | 34 |
| 64k | `▁зи чиуйфалу ▁() ▁— ▁венгриштӹ , ▁фейер ▁медье жӹштӹ ▁сола ... (+20 more)` | 30 |


### Key Findings

- **Best Compression:** 64k achieves 4.191x compression
- **Lowest UNK Rate:** 8k with 0.0903% 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 | 3,063 | 11.58 | 9,727 | 28.9% | 58.6% |
| **2-gram** | Subword | 730 🏆 | 9.51 | 3,875 | 39.1% | 95.0% |
| **3-gram** | Word | 4,248 | 12.05 | 14,627 | 27.5% | 53.4% |
| **3-gram** | Subword | 6,232 | 12.61 | 33,794 | 13.3% | 47.7% |
| **4-gram** | Word | 12,214 | 13.58 | 35,262 | 19.5% | 37.0% |
| **4-gram** | Subword | 28,212 | 14.78 | 162,256 | 7.9% | 28.6% |
| **5-gram** | Word | 11,612 | 13.50 | 30,530 | 19.7% | 35.2% |
| **5-gram** | Subword | 63,396 | 15.95 | 327,943 | 6.3% | 23.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `эдем ӹлен` | 2,392 |
| 2 | `ин тӹштӹ` | 2,202 |
| 3 | `йыхыш пырышы` | 2,165 |
| 4 | `официал сайтшы` | 1,847 |
| 5 | `группыш пырышы` | 1,725 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `статистика департаментжӹ эдем` | 1,016 |
| 2 | `турцин статистика департаментжӹ` | 1,016 |
| 3 | `департаментжӹ эдем ӹлен` | 1,016 |
| 4 | `tüi̇k турцин статистика` | 978 |
| 5 | `район каймакамын официал` | 890 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `турцин статистика департаментжӹ эдем` | 1,016 |
| 2 | `статистика департаментжӹ эдем ӹлен` | 1,016 |
| 3 | `tüi̇k турцин статистика департаментжӹ` | 978 |
| 4 | `официал сайтшы район каймакамын` | 890 |
| 5 | `сайтшы район каймакамын официал` | 890 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `турцин статистика департаментжӹ эдем ӹлен` | 1,016 |
| 2 | `tüi̇k турцин статистика департаментжӹ эдем` | 978 |
| 3 | `сайтшы район каймакамын официал сайтшы` | 890 |
| 4 | `официал сайтшы район каймакамын официал` | 890 |
| 5 | `муниципалитетӹн официал сайтшы район каймакамын` | 889 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 53,850 |
| 2 | `н _` | 45,770 |
| 3 | `_ к` | 39,996 |
| 4 | `_ (` | 37,130 |
| 5 | `, _` | 34,841 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `в л ӓ` | 28,557 |
| 2 | `_ — _` | 25,910 |
| 3 | `л ӓ _` | 14,577 |
| 4 | `i s _` | 12,190 |
| 5 | `u s _` | 11,117 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `в л ӓ _` | 13,629 |
| 2 | `ш т ӹ _` | 7,644 |
| 3 | `_ д ӓ _` | 7,347 |
| 4 | `) _ — _` | 7,100 |
| 5 | `о л о г` | 6,985 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `о л о г .` | 5,559 |
| 2 | `л о г . _` | 5,557 |
| 3 | `_ х а л а` | 4,299 |
| 4 | `ы р ы ш ы` | 4,237 |
| 5 | `р ы ш ы _` | 4,215 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 730
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.7074 | 1.633 | 3.61 | 97,412 | 29.3% |
| **1** | Subword | 1.0661 | 2.094 | 8.57 | 1,022 | 0.0% |
| **2** | Word | 0.1371 | 1.100 | 1.28 | 349,102 | 86.3% |
| **2** | Subword | 1.0482 | 2.068 | 6.56 | 8,742 | 0.0% |
| **3** | Word | 0.0484 | 1.034 | 1.09 | 443,244 | 95.2% |
| **3** | Subword | 0.9331 | 1.909 | 4.42 | 57,294 | 6.7% |
| **4** | Word | 0.0268 🏆 | 1.019 | 1.05 | 479,455 | 97.3% |
| **4** | Subword | 0.6599 | 1.580 | 2.59 | 253,059 | 34.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `дӓ тӹдӹм мам ит попы пилли ри маналтеш котка халан территорижӹ 425 campylocentrum hirtzii luer luer`
2. `ин тӹштӹ 58 387 сингатока ра ra мериг mérig мере лава méré lava ошмаотывлӓ йӹлмӹвлӓ систематика`
3. `пырышы кушкыш йишвлӓ bluering angelfish chaetodontoplus niger chan blueface angelfish chaetodontoplu...`

**Context Size 2:**

1. `ин тӹштӹ 50 511 tüi̇k турцин статистика департаментжӹ эдем ӹлен ажедмӓшвлӓ линквлӓ муниципалитетӹн о...`
2. `йыхыш пырышы пеледшӹ кушкыш америкышты вӓшлиӓлтеш цилӓжӹ 60 йиш тӹрлӹ циприпедиум улы йишвлӓ knodus ...`
3. `эдем ӹлен лӹмжӹ лӹмӹн этимологижӹ йеди шӹмӹт дон су вӹд шамаквлӓ гӹц лин ажедмӓшвлӓ линквлӓ муниципа...`

**Context Size 3:**

1. `статистика департаментжӹ эдем ӹлен ӹлӹзӹ шот и хала солавлӓ цилӓжӹ 31 581 34 323 65 904 61 561`
2. `турцин статистика департаментжӹ эдем ӹлен хала лӹмӹн этимологижӹ дениз тангыж домуз сасна дон ли suf...`
3. `департаментжӹ эдем ӹлен ажедмӓшвлӓ линквлӓ муниципалитетӹн официал сайтшы район каймакамын официал с...`

**Context Size 4:**

1. `турцин статистика департаментжӹ эдем ӹлен ажедмӓшвлӓ халавлӓ районвлӓ`
2. `статистика департаментжӹ эдем ӹлен хала лӹмӹн этимологижӹ элма олма дон даг кырык шамаквлӓ гӹц лин ӹ...`
3. `tüi̇k турцин статистика департаментжӹ эдем ӹлен ажедмӓшвлӓ линквлӓ муниципалитетӹн официал сайтшы ра...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_араверолӹшӹ_кул`
2. `а_[па-_с_3_(бенн`
3. `льышлӹш._тиз_rik`

**Context Size 2:**

1. `._va)_—_salopota_`
2. `н_(johay_clis_kr_`
3. `_короте_литла_уль`

**Context Size 3:**

1. `_—_асть_—_руш_ӓль_`
2. `влӓ._336_см_лишнӹ_`
3. `лӓ_nyalı_paridl.,_`

**Context Size 4:**

1. `влӓ_лин_де_группын_`
2. `штӹ_дӓ_шылдыр_шӓрӓн`
3. `_дӓ_аквариум_кӹшкӹж`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (253,059 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 | 43,052 |
| Total Tokens | 565,174 |
| Mean Frequency | 13.13 |
| Median Frequency | 3 |
| Frequency Std Dev | 89.04 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | дӓ | 7,457 |
| 2 | ин | 4,224 |
| 3 | пырышы | 4,065 |
| 4 | эдем | 3,208 |
| 5 | йишвлӓ | 2,684 |
| 6 | гӹц | 2,636 |
| 7 | вӓшлиӓлтшӹ | 2,633 |
| 8 | ӹлен | 2,497 |
| 9 | герпетолог | 2,413 |
| 10 | тӹштӹ | 2,391 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | сирӹмӓн | 2 |
| 2 | һәм | 2 |
| 3 | этвеш | 2 |
| 4 | лоранд | 2 |
| 5 | гамбургский | 2 |
| 6 | муромский | 2 |
| 7 | данилова | 2 |
| 8 | кадров | 2 |
| 9 | охлобыстин | 2 |
| 10 | aena | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9957 |
| R² (Goodness of Fit) | 0.994221 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.8% |
| Top 1,000 | 55.8% |
| Top 5,000 | 75.0% |
| Top 10,000 | 83.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9942 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.8% of corpus
- **Long Tail:** 33,052 words needed for remaining 16.7% 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 | 0.6197 🏆 | 0.3838 | N/A | N/A |
| **mono_64d** | 64 | 0.2539 | 0.3763 | N/A | N/A |
| **mono_128d** | 128 | 0.0468 | 0.3602 | N/A | N/A |
| **aligned_32d** | 32 | 0.6197 | 0.3829 | 0.0160 | 0.1380 |
| **aligned_64d** | 64 | 0.2539 | 0.3701 | 0.0220 | 0.1600 |
| **aligned_128d** | 128 | 0.0468 | 0.3665 | 0.0460 | 0.2140 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6197 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3733. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.6% 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 | **0.504** | 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` | кирибатиштӹш, кудымшы, кудвичӹ |
| `-s` | scopulifera, stolzmann, surdus |
| `-a` | alacakaya, auricularis, adilcevaz |
| `-b` | borellii, bendilna, bergh |
| `-m` | marco, minuticauda, musschenbroekii |
| `-с` | своей, седӹндонок, северной |
| `-а` | азбукы, алматы, ариель |
| `-п` | пётр, пӹрнявлӓжӹм, пайдажым |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | hispida, alacakaya, scopulifera |
| `-s` | pergracilis, pondicerianus, surdus |
| `-н` | бодлерӹн, этажан, йыдпелӹн |
| `-us` | pondicerianus, surdus, cinctus |
| `-i` | verboonenii, borellii, clarkii |
| `-is` | pergracilis, auricularis, hillis |
| `-e` | tsubotae, chippindale, ambroise |
| `-а` | калеана, момоца, гусянова |

### 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 |
|------|----------|------------------|----------|
| `ensi` | 2.15x | 19 contexts | boensis, poensis, obiensis |
| `ывлӓ` | 1.60x | 43 contexts | озывлӓ, ошывлӓ, пучывлӓ |
| `anth` | 1.87x | 24 contexts | anthus, fantham, anthony |
| `кышт` | 1.89x | 18 contexts | кышты, юкышты, рикышты |
| `олог` | 1.66x | 24 contexts | геолог, биолог, зоолог |
| `нвлӓ` | 1.56x | 26 contexts | шонвлӓ, данвлӓ, пынвлӓ |
| `авлӓ` | 1.43x | 29 contexts | аравлӓ, твавлӓ, таравлӓ |
| `лавл` | 1.63x | 17 contexts | солавла, халавлӓ, солавлӓ |
| `квлӓ` | 1.48x | 22 contexts | юквлӓ, ӓквлӓ, кеквлӓ |
| `влӓж` | 1.64x | 15 contexts | ивлӓжӹ, ивлӓжӹн, ивлӓжӹм |
| `тӹшт` | 1.80x | 11 contexts | тӹштӹ, тӹшты, тӹштӓт |
| `райо` | 1.81x | 10 contexts | район, районы, района |

### 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 |
|--------|--------|-----------|----------|
| `-c` | `-s` | 95 words | cheleensis, catamblyrhynchus |
| `-p` | `-s` | 84 words | paedocypris, phataginus |
| `-c` | `-a` | 80 words | chiroptera, chrysochlora |
| `-a` | `-a` | 77 words | america, arida |
| `-s` | `-a` | 70 words | sonderiana, sororcula |
| `-p` | `-a` | 68 words | pachira, parotia |
| `-m` | `-a` | 67 words | mubuga, multistriata |
| `-a` | `-s` | 64 words | acridotheres, aggeris |
| `-к` | `-н` | 59 words | капаен, кырыкын |
| `-m` | `-s` | 59 words | maculicollis, mishmensis |

### 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 |
|------|-----------------|------------|------|
| insidiosa | **`insidio-s-a`** | 7.5 | `s` |
| uréparapara | **`uréparap-a-ra`** | 7.5 | `a` |
| robertsii | **`robert-s-ii`** | 7.5 | `s` |
| гахенгери | **`гахенге-р-и`** | 7.5 | `р` |
| ventricosa | **`ventrico-s-a`** | 7.5 | `s` |
| мӱлӓндӹжӹм | **`мӱлӓндӹ-жӹ-м`** | 6.0 | `мӱлӓндӹ` |
| tristrami | **`tristram-i`** | 4.5 | `tristram` |
| чонгештӓт | **`чонгештӓ-т`** | 4.5 | `чонгештӓ` |
| венгришты | **`венгриш-ты`** | 4.5 | `венгриш` |
| blanfordi | **`blanford-i`** | 4.5 | `blanford` |
| hamburger | **`hamburg-er`** | 4.5 | `hamburg` |
| артиствлӓжӹ | **`артиствлӓ-жӹ`** | 4.5 | `артиствлӓ` |
| элементжӹ | **`элемент-жӹ`** | 4.5 | `элемент` |
| кудвичӹштӹ | **`кудвичӹш-тӹ`** | 4.5 | `кудвичӹш` |
| драмывлӓм | **`драмывлӓ-м`** | 4.5 | `драмывлӓ` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Western 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 (4.19x) |
| N-gram | **2-gram** | Lowest perplexity (730) |
| Markov | **Context-4** | Highest predictability (97.3%) |
| 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 13:10:29*