---
language: mn
language_name: Mongolian
language_family: mongolic
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-mongolic
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: 4.859
  - name: best_isotropy
    type: isotropy
    value: 0.8474
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Mongolian** 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** | 3.843x | 3.84 | 0.0664% | 1,203,793 |
| **16k** | 4.276x | 4.28 | 0.0738% | 1,082,049 |
| **32k** | 4.612x | 4.61 | 0.0797% | 1,003,132 |
| **64k** | 4.859x 🏆 | 4.86 | 0.0839% | 952,134 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Акстафа (Ağstafa rayonu) — Азербайжан улсын 8 түмэн хүнтэй район. Засаг захиргаа...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ак ст аф а ▁( a ğ st af a ... (+33 more)` | 43 |
| 16k | `▁ак ст афа ▁( a ğ st af a ▁r ... (+31 more)` | 41 |
| 32k | `▁ак ст афа ▁( a ğ st af a ▁ray ... (+29 more)` | 39 |
| 64k | `▁ак стафа ▁( ağ st af a ▁rayonu ) ▁— ... (+25 more)` | 35 |

**Sample 2:** `«Янаг дурлалын дууль» — онд Монгол улсад монгол хэлээр бүтсэн уран сайхны кино. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁« ян аг ▁дур лалын ▁дуул ь » ▁— ▁онд ... (+15 more)` | 25 |
| 16k | `▁« ян аг ▁дурлалын ▁дуул ь » ▁— ▁онд ▁монгол ... (+14 more)` | 24 |
| 32k | `▁« ян аг ▁дурлалын ▁дууль » ▁— ▁онд ▁монгол ▁улсад ... (+13 more)` | 23 |
| 64k | `▁« ян аг ▁дурлалын ▁дууль » ▁— ▁онд ▁монгол ▁улсад ... (+13 more)` | 23 |

**Sample 3:** `Олимпын VIII наадам буюу оны Парисын олимп () нь оны 5 сарын 4-нөөс 7 сарын 27-н...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁олимпын ▁v iii ▁наадам ▁буюу ▁оны ▁парисын ▁олимп ▁() ▁нь ... (+27 more)` | 37 |
| 16k | `▁олимпын ▁viii ▁наадам ▁буюу ▁оны ▁парисын ▁олимп ▁() ▁нь ▁оны ... (+26 more)` | 36 |
| 32k | `▁олимпын ▁viii ▁наадам ▁буюу ▁оны ▁парисын ▁олимп ▁() ▁нь ▁оны ... (+26 more)` | 36 |
| 64k | `▁олимпын ▁viii ▁наадам ▁буюу ▁оны ▁парисын ▁олимп ▁() ▁нь ▁оны ... (+26 more)` | 36 |


### Key Findings

- **Best Compression:** 64k achieves 4.859x compression
- **Lowest UNK Rate:** 8k with 0.0664% 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 | 68,727 | 16.07 | 220,179 | 6.8% | 20.8% |
| **2-gram** | Subword | 413 🏆 | 8.69 | 10,809 | 57.9% | 97.3% |
| **3-gram** | Word | 111,379 | 16.77 | 257,301 | 5.1% | 15.7% |
| **3-gram** | Subword | 3,439 | 11.75 | 80,850 | 22.4% | 63.9% |
| **4-gram** | Word | 225,307 | 17.78 | 414,540 | 3.9% | 10.7% |
| **4-gram** | Subword | 18,056 | 14.14 | 452,951 | 10.9% | 35.4% |
| **5-gram** | Word | 178,177 | 17.44 | 286,398 | 3.6% | 10.0% |
| **5-gram** | Subword | 63,519 | 15.95 | 1,205,940 | 6.3% | 22.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `р сарын` | 13,394 |
| 2 | `онд төрсөн` | 10,821 |
| 3 | `монгол улсын` | 9,521 |
| 4 | `энэ нь` | 7,945 |
| 5 | `олон улсын` | 6,568 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `онд нас барсан` | 3,190 |
| 2 | `төрсөн онд өнгөрсөн` | 2,725 |
| 3 | `онд төрсөн онд` | 2,565 |
| 4 | `тоглогч багийн тоглогч` | 2,249 |
| 5 | `багийн тоглогч багийн` | 2,217 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `онд төрсөн онд өнгөрсөн` | 2,503 |
| 2 | `багийн тоглогч багийн тоглогч` | 2,210 |
| 3 | `оны зуны олимпод оролцогч` | 1,481 |
| 4 | `оролцогч оны зуны олимпод` | 1,046 |
| 5 | `оны 3 р сарын` | 1,027 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `оролцогч оны зуны олимпод оролцогч` | 1,046 |
| 2 | `тоглогч багийн тоглогч багийн тоглогч` | 979 |
| 3 | `багийн тоглогч багийн тоглогч багийн` | 975 |
| 4 | `оны зуны олимпод оролцогч оны` | 727 |
| 5 | `хүн онд төрсөн онд өнгөрсөн` | 679 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _` | 2,065,189 |
| 2 | `_ б` | 982,662 |
| 3 | `и й` | 971,304 |
| 4 | `_ х` | 933,182 |
| 5 | `а н` | 813,213 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `й н _` | 630,284 |
| 2 | `и й н` | 596,746 |
| 3 | `ы н _` | 466,998 |
| 4 | `_ б а` | 433,581 |
| 5 | `а н _` | 329,680 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `и й н _` | 582,887 |
| 2 | `_ б а й` | 257,407 |
| 3 | `г и й н` | 207,050 |
| 4 | `_ н ь _` | 172,147 |
| 5 | `_ б о л` | 171,235 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `г и й н _` | 202,980 |
| 2 | `л и й н _` | 88,000 |
| 3 | `_ б о л о` | 85,950 |
| 4 | `_ о н д _` | 83,407 |
| 5 | `и й н _ х` | 73,490 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 413
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.9549 | 1.938 | 9.40 | 425,053 | 4.5% |
| **1** | Subword | 1.2682 | 2.409 | 7.77 | 6,078 | 0.0% |
| **2** | Word | 0.3001 | 1.231 | 1.76 | 3,989,426 | 70.0% |
| **2** | Subword | 0.6382 | 1.556 | 4.13 | 47,189 | 36.2% |
| **3** | Word | 0.0919 | 1.066 | 1.16 | 7,019,958 | 90.8% |
| **3** | Subword | 0.7262 | 1.654 | 4.12 | 194,932 | 27.4% |
| **4** | Word | 0.0319 🏆 | 1.022 | 1.05 | 8,133,129 | 96.8% |
| **4** | Subword | 0.6730 | 1.594 | 3.05 | 802,473 | 32.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `нь нийгмийн болон анадолугийн их хурлын тогтоолоор албан ёсны цахим холбоос article from the coup d`
2. `онд нас бие монгол нь ангилж нэрлэж болно оху ын төлөөлөгч эсэргүүцлийн хандлага нь нарийвчлал бага`
3. `оны 5 танхим нба гийн аваргаар онд бнмау ын холбооны нэгдсэн хөдөлгөөн багатай боловч жон лиллигийн`

**Context Size 2:**

1. `р сарын 1 нд компьень хотод төрсөн америкийн мэргэжлийн хөлбөмбөгийн карьераа онд серие виченца бага...`
2. `монгол улсын засгийн газар сонгуульд ялснаар важпи энэтхэг улсын карнатака мужийн үндэс нь морзе код...`
3. `энэ нь ажиллуулах боломжтой болгосон ромын эзэн хаан вильхельмийн нийгэмлэг гэдэг нэртэй болжээ хоёу...`

**Context Size 3:**

1. `онд нас барсан америкийн геологич хүний үүслийн судлаач бөгөөд палеонтолог олон жил нью йорк дахь нү...`
2. `онд төрсөн онд өнгөрсөн хаан хүн монголын түүх үндэстэн зуунд төрсөн онд өнгөрсөн түрэгийн хаад зуун...`
3. `тоглогч багийн тоглогч 05 багийн тоглогч багийн тоглогч багийн тоглогч багийн тоглогч марсель багийн...`

**Context Size 4:**

1. `багийн тоглогч багийн тоглогч багийн тоглогч онд төрсөн онд өнгөрсөн хүн улс төрч байгаль орчны сайд`
2. `оны зуны олимпод оролцогч оны зуны олимпод оролцогч онд төрсөн онд өнгөрсөн улсын жанжин улсын улс т...`
3. `оролцогч оны зуны олимпод оролцогч хамгаалагч хотспур багийн тоглогч лигийн тоглогч ирландчууд`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_нги_тэ_ты_хүдай`
2. `аагэмьтой_штөлго`
3. `ндөөлар_дгөөван_`

**Context Size 2:**

1. `н_ол_бай_бөмжилца`
2. `_бөглог_он_өөрсөн`
3. `ий_сургийн_цай._ч`

**Context Size 3:**

1. `йн_түүхээс_их_бөги`
2. `ийн_фран_гарахарим`
3. `ын_холбоотой_бөмбө`

**Context Size 4:**

1. `ийн_улсын_отограмма`
2. `_байршилын_үед_холб`
3. `гийн_босгодог._эдий`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (802,473 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 | 188,243 |
| Total Tokens | 9,012,621 |
| Mean Frequency | 47.88 |
| Median Frequency | 4 |
| Frequency Std Dev | 695.98 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | нь | 175,668 |
| 2 | онд | 84,299 |
| 3 | оны | 67,254 |
| 4 | юм | 49,881 |
| 5 | улсын | 48,832 |
| 6 | байна | 43,613 |
| 7 | сарын | 43,501 |
| 8 | болон | 40,408 |
| 9 | байсан | 38,901 |
| 10 | их | 36,525 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | аюудайн | 2 |
| 2 | хэргииг | 2 |
| 3 | сайханчдыг | 2 |
| 4 | нимсан | 2 |
| 5 | агваандоной | 2 |
| 6 | гольдоны | 2 |
| 7 | тожин | 2 |
| 8 | хэшидэй | 2 |
| 9 | иезуитүүдийн | 2 |
| 10 | хванчкара | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0408 |
| R² (Goodness of Fit) | 0.986627 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.0% |
| Top 1,000 | 51.5% |
| Top 5,000 | 73.5% |
| Top 10,000 | 81.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9866 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.0% of corpus
- **Long Tail:** 178,243 words needed for remaining 18.7% 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 | 0.8474 🏆 | 0.3711 | N/A | N/A |
| **mono_64d** | 64 | 0.8353 | 0.2813 | N/A | N/A |
| **mono_128d** | 128 | 0.8031 | 0.2224 | N/A | N/A |
| **aligned_32d** | 32 | 0.8474 | 0.3608 | 0.0800 | 0.3720 |
| **aligned_64d** | 64 | 0.8353 | 0.2867 | 0.0800 | 0.4280 |
| **aligned_128d** | 128 | 0.8031 | 0.2290 | 0.1740 | 0.5200 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8474 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2919. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 17.4% 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 | **-0.547** | Low formulaic 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 |
|--------|----------|
| `-а` | аарцаг, аргад, апулиа |
| `-х` | хүрэлцэхүйц, хё, ханцуйны |
| `-б` | бнрау, багаад, баянзүрхулсын |
| `-с` | сурагчидтай, сэтэлж, субстраттай |
| `-ха` | ханцуйны, ханноверийн, хасан |
| `-т` | туулах, телескопыг, тансаглал |
| `-к` | кэмби, кронбергийн, кмтаван |
| `-ба` | багаад, баянзүрхулсын, баттулгахөвсгөл |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | мөнхтөрзавхан, латеран, гуалин |
| `-йн` | яшкулийн, кронбергийн, ерөөлтийн |
| `-г` | аарцаг, мессежийг, телескопыг |
| `-ын` | баянзүрхулсын, дизайнерын, харрисын |
| `-д` | давшаад, багаад, аргад |
| `-й` | всемирный, сурагчидтай, зориулалтай |
| `-р` | мейнор, нууцлалаар, конр |
| `-с` | гулагаас, шанс, хараалаас |

### 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 |
|------|----------|------------------|----------|
| `гуул` | 1.71x | 228 contexts | угуул, гууль, гуульд |
| `байс` | 2.78x | 18 contexts | байса, байсн, байсаг |
| `айса` | 2.10x | 44 contexts | байса, хайса, кайса |
| `йсан` | 2.07x | 40 contexts | айсан, хийсан, зайсан |
| `йгуу` | 2.43x | 22 contexts | уйгуур, байгуу, байгуул |
| `нгол` | 1.78x | 68 contexts | ангол, нгола, онгол |
| `олбо` | 1.91x | 49 contexts | олбол, толбо, колбо |
| `лсан` | 1.74x | 63 contexts | улсан, үлсан, алсан |
| `үүлэ` | 1.38x | 187 contexts | үүлэн, үүлээ, шүүлэг |
| `агаа` | 1.40x | 140 contexts | агаан, цагаа, жагаа |
| `ргуу` | 1.56x | 79 contexts | шаргуу, аргууд, шургуу |
| `сург` | 2.31x | 18 contexts | сурга, сурган, сургах |

### 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 |
|--------|--------|-----------|----------|
| `-б` | `-н` | 133 words | бичсэнчлэн, баясахын |
| `-х` | `-н` | 122 words | хүлэгүгийн, хашлагдсан |
| `-с` | `-н` | 118 words | сүсэглэн, станцийн |
| `-а` | `-н` | 106 words | адамирангийн, абатсүхийн |
| `-т` | `-н` | 103 words | тонуулын, талстжисан |
| `-м` | `-н` | 75 words | металлын, миникомпьютерын |
| `-х` | `-г` | 66 words | хуйраг, хүрснийг |
| `-д` | `-н` | 65 words | дармаагийн, дамдингийн |
| `-х` | `-й` | 64 words | хугархай, хаштай |
| `-к` | `-н` | 64 words | кондратьевын, кантабрийн |

### 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 |
|------|-----------------|------------|------|
| борлуулагчдаараа | **`борлуулагчда-ар-аа`** | 7.5 | `ар` |
| нийлэгжүүлнэ | **`нийлэгжүүл-н-э`** | 7.5 | `н` |
| өргөжүүлнэ | **`өргөжүүл-н-э`** | 7.5 | `н` |
| сургуулилт | **`сургуули-л-т`** | 7.5 | `л` |
| тэмүжиний | **`тэмүжи-н-ий`** | 7.5 | `н` |
| халдлаганд | **`халдлага-н-д`** | 7.5 | `н` |
| ойлгоцгоож | **`ойлгоцго-о-ж`** | 7.5 | `о` |
| бэрнаскони | **`бэрнаско-н-и`** | 7.5 | `н` |
| бүжигчний | **`бүжигч-н-ий`** | 7.5 | `н` |
| өрнөдийнхний | **`өрнөдийнх-н-ий`** | 7.5 | `н` |
| наносекунд | **`наносеку-н-д`** | 7.5 | `н` |
| биндусара | **`биндус-ар-а`** | 7.5 | `ар` |
| диоксидыг | **`диокси-д-ыг`** | 7.5 | `д` |
| товчоодыг | **`товчоо-д-ыг`** | 7.5 | `д` |
| хадгалалтанд | **`хадгалалта-н-д`** | 7.5 | `н` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Mongolian shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.86x) |
| N-gram | **2-gram** | Lowest perplexity (413) |
| Markov | **Context-4** | Highest predictability (96.8%) |
| 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 13:03:40*