---
language: mdf
language_name: Moksha
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: 4.225
  - name: best_isotropy
    type: isotropy
    value: 0.7339
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Moksha** 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** | 3.231x | 3.23 | 0.1355% | 438,468 |
| **16k** | 3.531x | 3.53 | 0.1481% | 401,156 |
| **32k** | 3.913x | 3.92 | 0.1641% | 362,030 |
| **64k** | 4.225x 🏆 | 4.23 | 0.1772% | 335,301 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `433 киза. Тядде мезе ульсь Тядде шачсть Тядде кулость`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 4 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 16k | `▁ 4 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 32k | `▁ 4 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 64k | `▁ 4 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |

**Sample 2:** `465 киза. Тядде мезе ульсь Тядде шачсть Тядде кулость`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 4 6 5 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 16k | `▁ 4 6 5 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 32k | `▁ 4 6 5 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 64k | `▁ 4 6 5 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |

**Sample 3:** `233 киза. Тядде мезе ульсь Тядде шачсть Тядде кулость`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 2 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 16k | `▁ 2 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 32k | `▁ 2 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |
| 64k | `▁ 2 3 3 ▁киза . ▁тядде ▁мезе ▁ульсь ▁тядде ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 4.225x compression
- **Lowest UNK Rate:** 8k with 0.1355% 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 | 2,477 | 11.27 | 10,854 | 30.8% | 65.4% |
| **2-gram** | Subword | 691 🏆 | 9.43 | 4,360 | 41.1% | 94.9% |
| **3-gram** | Word | 2,969 | 11.54 | 15,781 | 29.1% | 63.0% |
| **3-gram** | Subword | 5,307 | 12.37 | 34,065 | 14.5% | 52.9% |
| **4-gram** | Word | 4,572 | 12.16 | 28,280 | 24.9% | 57.4% |
| **4-gram** | Subword | 19,794 | 14.27 | 143,320 | 9.8% | 35.0% |
| **5-gram** | Word | 4,394 | 12.10 | 24,669 | 24.1% | 57.6% |
| **5-gram** | Subword | 37,913 | 15.21 | 276,991 | 8.2% | 30.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ушеширень кучфтемат` | 3,889 |
| 2 | `лятфтамат ушеширень` | 3,799 |
| 3 | `культурась тонадомась` | 3,172 |
| 4 | `тонадомась спортсь` | 3,096 |
| 5 | `экономикась культурась` | 3,087 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `лятфтамат ушеширень кучфтемат` | 3,749 |
| 2 | `культурась тонадомась спортсь` | 3,086 |
| 3 | `экономикась культурась тонадомась` | 3,079 |
| 4 | `географиясь климатсь историясь` | 2,705 |
| 5 | `эряйхне экономикась культурась` | 2,570 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `экономикась культурась тонадомась спортсь` | 3,071 |
| 2 | `эряйхне экономикась культурась тонадомась` | 2,565 |
| 3 | `лятфтамат ушеширень кучфтемат официалонь` | 2,370 |
| 4 | `ушеширень кучфтемат официалонь лопа` | 2,344 |
| 5 | `тонадомась спортсь ошт ялгат` | 2,095 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `эряйхне экономикась культурась тонадомась спортсь` | 2,559 |
| 2 | `лятфтамат ушеширень кучфтемат официалонь лопа` | 2,313 |
| 3 | `культурась тонадомась спортсь ошт ялгат` | 2,093 |
| 4 | `экономикась культурась тонадомась спортсь ошт` | 2,090 |
| 5 | `кизоня эряйхне экономикась культурась тонадомась` | 1,823 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 103,097 |
| 2 | `ь _` | 96,627 |
| 3 | `, _` | 55,915 |
| 4 | `с ь` | 53,283 |
| 5 | `_ к` | 50,925 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `с ь _` | 45,627 |
| 2 | `н ь _` | 32,529 |
| 3 | `ь _ к` | 21,160 |
| 4 | `_ — _` | 18,491 |
| 5 | `м а т` | 16,761 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а с ь _` | 13,278 |
| 2 | `е н ь _` | 13,229 |
| 3 | `о н ь _` | 11,418 |
| 4 | `м а т _` | 8,971 |
| 5 | `с ь _ к` | 8,248 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `и я с ь _` | 7,473 |
| 2 | `_ i s b n` | 7,317 |
| 3 | `i s b n _` | 7,306 |
| 4 | `ф т а м а` | 6,520 |
| 5 | `_ л я т ф` | 6,479 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 691
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.6555 | 1.575 | 3.59 | 82,101 | 34.5% |
| **1** | Subword | 1.0880 | 2.126 | 9.78 | 877 | 0.0% |
| **2** | Word | 0.1207 | 1.087 | 1.29 | 292,280 | 87.9% |
| **2** | Subword | 1.0621 | 2.088 | 6.70 | 8,573 | 0.0% |
| **3** | Word | 0.0435 | 1.031 | 1.11 | 374,255 | 95.6% |
| **3** | Subword | 0.8308 | 1.779 | 4.03 | 57,391 | 16.9% |
| **4** | Word | 0.0248 🏆 | 1.017 | 1.06 | 411,850 | 97.5% |
| **4** | Subword | 0.5684 | 1.483 | 2.42 | 231,406 | 43.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `isbn le figaro одри дана british north state corporate university of saxe gotha and the royal`
2. `с isbn robert l lamb in gilbert bouriquet hrsg encyclopédie biologique band xlvi paul lechevalier pa...`
3. `тядде мезе ульсь тядде мезе ульсь апатиты кнц ран с с энциклопедия городов и мордовская инструментал...`

**Context Size 2:**

1. `ушеширень кучфтемат ямусукра encyclopædia universalis брайтон internetowa encyklopedia pwn тромбоцит...`
2. `лятфтамат ушеширень кучфтемат офицалонь лопа мартвили georgian travel guide мумбва zambia info org г...`
3. `культурась тонадомась спортсь ошт ялгат лятфтамат ушеширень кучфтемат кранцмастор encyclopædia brita...`

**Context Size 3:**

1. `лятфтамат ушеширень кучфтемат кола снегирёв мордовиянь литературонь библиотек живайкина`
2. `культурась тонадомась спортсь ошт ялгат фотоархтофкс кяльвалсь hannu tarmio pentti papunen kalevi ko...`
3. `экономикась культурась тонадомась спортсь кяльвалсь в д алемайкина материалы по языку и фольклору се...`

**Context Size 4:**

1. `экономикась культурась тонадомась спортсь содаф ломатть виктор гудожников мокшень театрань налхкись ...`
2. `эряйхне экономикась культурась тонадомась спортсь содаф ломатть ошт ялгат кяльвалсь hans h hansen ís...`
3. `лятфтамат ушеширень кучфтемат официалонь лопа копэр geonames копэр encyclopædia britannica копэр sto...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_саранес,_ддаялэ`
2. `а_(amise._4_кобу`
3. `опутайн_stogeadi`

**Context Size 2:**

1. `._epin_вих_ная_с.`
2. `ь_пинно-морта_пре`
3. `,_ine_deekonlä,_д`

**Context Size 3:**

1. `сь_шачсть_матсь_ис`
2. `нь_ошть_сёрмат_офи`
3. `ь_климат_фотоархто`

**Context Size 4:**

1. `ась_тядде_мезе_ульс`
2. `ень_кяль_ди_семитиз`
3. `онь_лопа_ниленди_бо`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (231,406 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 | 34,162 |
| Total Tokens | 679,791 |
| Mean Frequency | 19.90 |
| Median Frequency | 4 |
| Frequency Std Dev | 148.72 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | isbn | 7,327 |
| 2 | с | 6,258 |
| 3 | тядде | 5,664 |
| 4 | кизоня | 5,463 |
| 5 | of | 5,325 |
| 6 | лятфтамат | 5,117 |
| 7 | ошсь | 5,082 |
| 8 | j | 4,358 |
| 9 | m | 4,287 |
| 10 | a | 4,231 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kissinger | 2 |
| 2 | franziskanerkloster | 2 |
| 3 | eisenstadt | 2 |
| 4 | südburgenlandes | 2 |
| 5 | forschungsgesellschaft | 2 |
| 6 | содафтомс | 2 |
| 7 | фирма | 2 |
| 8 | музейнь | 2 |
| 9 | sõlmed | 2 |
| 10 | püsinäitus | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0114 |
| R² (Goodness of Fit) | 0.995653 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 33.2% |
| Top 1,000 | 63.0% |
| Top 5,000 | 80.7% |
| Top 10,000 | 88.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9957 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 33.2% of corpus
- **Long Tail:** 24,162 words needed for remaining 11.4% 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 | 0.7339 | 0.3952 | N/A | N/A |
| **mono_64d** | 64 | 0.4331 | 0.3884 | N/A | N/A |
| **mono_128d** | 128 | 0.0795 | 0.3673 | N/A | N/A |
| **aligned_32d** | 32 | 0.7339 🏆 | 0.3886 | 0.0260 | 0.2120 |
| **aligned_64d** | 64 | 0.4331 | 0.3862 | 0.0400 | 0.2520 |
| **aligned_128d** | 128 | 0.0795 | 0.3771 | 0.0480 | 0.3180 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7339 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3838. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.8% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.907** | 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` | косач, кабомпа, кемерова |
| `-s` | streda, suur, springfield |
| `-с` | своеобразие, свэдру, сёксенда |
| `-п` | пянакуд, программа, палуоя |
| `-a` | alainii, arietinum, auxopus |
| `-а` | асмара, аля, антропоморфизмась |
| `-p` | pallas, pelican, primulinum |
| `-m` | museer, montigena, modestissima |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ь` | мысль, тарнамась, максфоль |
| `-а` | валста, асмара, кабомпа |
| `-a` | montigena, streda, modestissima |
| `-нь` | модатнень, венгеронь, мордвань |
| `-s` | pallas, inputs, dupuis |
| `-сь` | тарнамась, перьфпяльсь, антропоморфизмась |
| `-e` | balansae, rice, livermore |
| `-n` | volkstrachten, wan, erzählungen |

### 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 |
|------|----------|------------------|----------|
| `тори` | 1.92x | 23 contexts | история, истории, арторима |
| `мась` | 1.98x | 19 contexts | юмась, тумась, амасья |
| `кизо` | 1.97x | 16 contexts | кизот, кизоц, кизос |
| `асто` | 1.74x | 23 contexts | астон, мастор, вастоц |
| `ьтур` | 1.95x | 16 contexts | культур, культуры, культуре |
| `огра` | 1.62x | 27 contexts | биоград, бэоград, географа |
| `мокш` | 1.86x | 17 contexts | мокши, мокша, мокшет |
| `tion` | 1.88x | 16 contexts | tiona, nation, motion |
| `омас` | 1.74x | 15 contexts | томас, азомась, явомась |
| `ульт` | 1.94x | 11 contexts | культ, культсь, культур |
| `фоль` | 1.92x | 11 contexts | афоль, явфоль, тифоль |
| `исто` | 1.83x | 11 contexts | истоки, кристоз, история |

### 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` | 132 words | корольсь, качамсь |
| `-п` | `-ь` | 97 words | пичень, позань |
| `-к` | `-а` | 88 words | койса, кстова |
| `-с` | `-ь` | 80 words | стрелецнень, соборсь |
| `-а` | `-ь` | 74 words | аннополь, алсь |
| `-s` | `-a` | 65 words | susanna, secunda |
| `-a` | `-a` | 62 words | asta, acuminata |
| `-м` | `-ь` | 60 words | макссесь, марсэль |
| `-p` | `-a` | 58 words | paradoxa, pandurifera |
| `-к` | `-нь` | 54 words | книгань, кельмеширень |

### 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 |
|------|-----------------|------------|------|
| kotschyana | **`kotschy-a-na`** | 7.5 | `a` |
| регионтне | **`регион-т-не`** | 7.5 | `т` |
| stanislovas | **`stanislov-a-s`** | 7.5 | `a` |
| retrieved | **`retriev-e-d`** | 7.5 | `e` |
| bafoussam | **`bafouss-a-m`** | 7.5 | `a` |
| экономиконь | **`экономик-о-нь`** | 7.5 | `о` |
| orchidaceous | **`orchidace-o-us`** | 7.5 | `o` |
| nationalism | **`national-is-m`** | 6.0 | `national` |
| сёрмадыень | **`сёрмады-е-нь`** | 6.0 | `сёрмады` |
| веленятне | **`веленят-не`** | 4.5 | `веленят` |
| вологдань | **`вологда-нь`** | 4.5 | `вологда` |
| монголиянь | **`монголия-нь`** | 4.5 | `монголия` |
| сёрмадыть | **`сёрмады-ть`** | 4.5 | `сёрмады` |
| transformations | **`transformation-s`** | 4.5 | `transformation` |
| alphabets | **`alphabet-s`** | 4.5 | `alphabet` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Moksha 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 (4.23x) |
| N-gram | **2-gram** | Lowest perplexity (691) |
| Markov | **Context-4** | Highest predictability (97.5%) |
| 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 11:39:40*