---
language: bxr
language_name: Russia Buriat
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: 4.402
  - name: best_isotropy
    type: isotropy
    value: 0.9019
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

# Russia Buriat - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Russia Buriat** 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** | 3.459x | 3.46 | 0.1450% | 616,507 |
| **16k** | 3.854x | 3.86 | 0.1615% | 553,408 |
| **32k** | 4.159x | 4.16 | 0.1743% | 512,788 |
| **64k** | 4.402x 🏆 | 4.40 | 0.1845% | 484,538 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Мэйси - Ород Википеэдийн Үбэр Монголой долоо хоногой үгүүлэл. Мүн үзэхэ Үбэр Мон...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁мэй си ▁- ▁ород ▁википеэдийн ▁үбэр ▁монголой ▁долоо ▁хоногой ▁үгүүлэл ... (+7 more)` | 17 |
| 16k | `▁мэй си ▁- ▁ород ▁википеэдийн ▁үбэр ▁монголой ▁долоо ▁хоногой ▁үгүүлэл ... (+7 more)` | 17 |
| 32k | `▁мэй си ▁- ▁ород ▁википеэдийн ▁үбэр ▁монголой ▁долоо ▁хоногой ▁үгүүлэл ... (+7 more)` | 17 |
| 64k | `▁мэйси ▁- ▁ород ▁википеэдийн ▁үбэр ▁монголой ▁долоо ▁хоногой ▁үгүүлэл . ... (+6 more)` | 16 |

**Sample 2:** `Уһан далайн сэрэгэй авиаци — уһан соо бууха ба уһан дээрэһээ ниидэжэ гараха онго...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁уһан ▁далайн ▁сэрэгэй ▁ав иа ци ▁— ▁уһан ▁соо ▁буу ... (+16 more)` | 26 |
| 16k | `▁уһан ▁далайн ▁сэрэгэй ▁авиа ци ▁— ▁уһан ▁соо ▁бууха ▁ба ... (+13 more)` | 23 |
| 32k | `▁уһан ▁далайн ▁сэрэгэй ▁авиаци ▁— ▁уһан ▁соо ▁бууха ▁ба ▁уһан ... (+12 more)` | 22 |
| 64k | `▁уһан ▁далайн ▁сэрэгэй ▁авиаци ▁— ▁уһан ▁соо ▁бууха ▁ба ▁уһан ... (+12 more)` | 22 |

**Sample 3:** `Денонсаци — нэгэ гүрэнэй нүгөө гүрэндэ өөр—хоорондохи ябажа байгаа хэрээ, хэлсээ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁д ен он са ци ▁— ▁нэгэ ▁гүрэнэй ▁нүгөө ▁гүрэндэ ... (+16 more)` | 26 |
| 16k | `▁ден он са ци ▁— ▁нэгэ ▁гүрэнэй ▁нүгөө ▁гүрэндэ ▁өөр ... (+14 more)` | 24 |
| 32k | `▁ден он са ци ▁— ▁нэгэ ▁гүрэнэй ▁нүгөө ▁гүрэндэ ▁өөр ... (+14 more)` | 24 |
| 64k | `▁денонсаци ▁— ▁нэгэ ▁гүрэнэй ▁нүгөө ▁гүрэндэ ▁өөр — хоорондохи ▁ябажа ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 64k achieves 4.402x compression
- **Lowest UNK Rate:** 8k with 0.1450% 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 | 4,087 | 12.00 | 8,036 | 19.8% | 49.7% |
| **2-gram** | Subword | 452 🏆 | 8.82 | 3,815 | 56.9% | 96.7% |
| **3-gram** | Word | 3,571 | 11.80 | 7,655 | 25.2% | 48.6% |
| **3-gram** | Subword | 3,726 | 11.86 | 29,176 | 20.6% | 62.2% |
| **4-gram** | Word | 7,283 | 12.83 | 14,462 | 19.6% | 35.4% |
| **4-gram** | Subword | 17,919 | 14.13 | 123,764 | 9.4% | 34.6% |
| **5-gram** | Word | 5,323 | 12.38 | 10,833 | 22.1% | 38.6% |
| **5-gram** | Subword | 48,261 | 15.56 | 234,708 | 6.1% | 22.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `энэ үдэр` | 1,109 |
| 2 | `гү али` | 1,021 |
| 3 | `of the` | 462 |
| 4 | `байна энэ` | 425 |
| 5 | `бүгэдэ найрамдаха` | 396 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `үйлэ ябадалай жагсаалта` | 366 |
| 2 | `энэ үдэр тохёоһон` | 366 |
| 3 | `тохёоһон үйлэ ябадалай` | 366 |
| 4 | `үдэр наһа бараһаниинь` | 366 |
| 5 | `энэ үдэр наһа` | 366 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `үдэр тохёоһон үйлэ ябадалай` | 366 |
| 2 | `энэ үдэр наһа бараһаниинь` | 366 |
| 3 | `энэ үдэр тохёоһон үйлэ` | 366 |
| 4 | `тохёоһон үйлэ ябадалай жагсаалта` | 366 |
| 5 | `энэ үдэрэй тэмдэглэлтэ баяр` | 358 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `энэ үдэр тохёоһон үйлэ ябадалай` | 366 |
| 2 | `үдэр тохёоһон үйлэ ябадалай жагсаалта` | 366 |
| 3 | `тохёоһон үйлэ ябадалай жагсаалта энэ` | 340 |
| 4 | `ябадалай жагсаалта энэ үдэр түрэһэниинь` | 340 |
| 5 | `үйлэ ябадалай жагсаалта энэ үдэр` | 340 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _` | 81,065 |
| 2 | `й _` | 55,911 |
| 3 | `_ б` | 53,676 |
| 4 | `_ х` | 49,355 |
| 5 | `а й` | 47,888 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а й _` | 24,178 |
| 2 | `_ б а` | 23,944 |
| 3 | `ы н _` | 18,168 |
| 4 | `э й _` | 17,283 |
| 5 | `а н _` | 16,564 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ б а й` | 12,726 |
| 2 | `_ б о л` | 11,040 |
| 3 | `б о л о` | 8,901 |
| 4 | `и и н _` | 6,846 |
| 5 | `_ у л а` | 6,751 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ б о л о` | 8,849 |
| 2 | `_ у л а с` | 5,743 |
| 3 | `о н о й _` | 4,950 |
| 4 | `а н а й _` | 4,619 |
| 5 | `э һ э н _` | 4,162 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 452
- **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 | 0.7365 | 1.666 | 4.12 | 92,015 | 26.3% |
| **1** | Subword | 0.8645 | 1.821 | 5.69 | 2,131 | 13.5% |
| **2** | Word | 0.1428 | 1.104 | 1.26 | 378,037 | 85.7% |
| **2** | Subword | 0.8166 | 1.761 | 5.04 | 12,123 | 18.3% |
| **3** | Word | 0.0341 | 1.024 | 1.05 | 476,205 | 96.6% |
| **3** | Subword | 0.7973 | 1.738 | 3.76 | 61,012 | 20.3% |
| **4** | Word | 0.0112 🏆 | 1.008 | 1.02 | 497,992 | 98.9% |
| **4** | Subword | 0.5747 | 1.489 | 2.39 | 229,261 | 42.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ба дайшадай толгойнууд олдоо һэн мүн магрибай араб уласай 5 сая ажаһуугшад боложо үгэһэн бэлэй ниисл...`
2. `юм исаак ньютон джон нэрэтэй байгаад наһа бараа үйлэшэлгын хэлтэстэ хубаагдана эдэ олон жэлэй 189 дэ...`
3. `энэ үдэр түрэһэниинь парацельс алхимик эмшэ эсперантогой байгуулагша гээд хэдэн нөлөө дэндүү их гүрн...`

**Context Size 2:**

1. `энэ үдэр тохёоһон үйлэ ябадалай жагсаалта 324 римэй эзэнтэ гүрэнэй үндэһэлэгшэд отто фон бисмарк фри...`
2. `гү али зүрхэнэй өөрынхинь мэдэрэлэй тогтолсоогоор ябагдана агшалтын үеэр шуһанай һудаһуудта шуһан ша...`
3. `of the iaea itu upu and wipo and a permanently functioning legislative administrative and supervisor...`

**Context Size 3:**

1. `тохёоһон үйлэ ябадалай жагсаалта энэ үдэр түрэһэниинь энэ үдэр наһа бараһаниинь энэ үдэрэй тэмдэглэл...`
2. `үйлэ ябадалай жагсаалта энэ үдэр түрэһэниинь энэ үдэр наһа бараһаниинь энэ үдэрэй тэмдэглэлтэ баяр э...`
3. `энэ үдэр түрэһэниинь энэ үдэр наһа бараһаниинь энэ үдэрэй тэмдэглэлтэ баяр энэ үдэр тохёоһон үйлэ яб...`

**Context Size 4:**

1. `үдэр тохёоһон үйлэ ябадалай жагсаалта энэ үдэр түрэһэниинь оной урда үе энэ үдэр наһа бараһаниинь эн...`
2. `тохёоһон үйлэ ябадалай жагсаалта энэ үдэр түрэһэниинь энэ үдэр наһа бараһаниинь энэ үдэрэй тэмдэглэл...`
3. `энэ үдэр тохёоһон үйлэ ябадалай жагсаалта энэ үдэр түрэһэниинь оной урда үе энэ үдэр наһа бараһаниин...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_6,_сэн»_г,_үүга`
2. `а_тэршэгай_гаһэд`
3. `эраре_бан_каасэй`

**Context Size 2:**

1. `н_зари,_хажа._бан`
2. `й_лэгэ,_plearunt_`
3. `_баран._захмерита`

**Context Size 3:**

1. `ай_гэшүүн_хубиин_1`
2. `_бан_холбоон_ба_ту`
3. `ын_аралай_марилсуу`

**Context Size 4:**

1. `_байна._антика._мож`
2. `_болоһоншье_үлүү_эр`
3. `болобошье,_каирай_н`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (229,261 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 | 35,751 |
| Total Tokens | 485,385 |
| Mean Frequency | 13.58 |
| Median Frequency | 3 |
| Frequency Std Dev | 73.26 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ба | 3,777 |
| 2 | юм | 3,165 |
| 3 | энэ | 3,056 |
| 4 | ондо | 2,831 |
| 5 | болон | 2,629 |
| 6 | байна | 2,533 |
| 7 | оной | 2,521 |
| 8 | улас | 2,428 |
| 9 | the | 2,147 |
| 10 | үдэр | 2,079 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ᠮᠠᠨᠠᠶ | 2 |
| 2 | ᠲᠠᠢ | 2 |
| 3 | ᠮᠣᠩᠭᠤᠯ | 2 |
| 4 | ᠤᠷᠤᠨ | 2 |
| 5 | ᠮᠢᠨᠢ | 2 |
| 6 | ᠦᠷ | 2 |
| 7 | ᠵᠢᠷᠭᠠᠯ | 2 |
| 8 | дүхэригтэй | 2 |
| 9 | исибагай | 2 |
| 10 | ылын | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9688 |
| R² (Goodness of Fit) | 0.993514 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.2% |
| Top 1,000 | 52.4% |
| Top 5,000 | 74.8% |
| Top 10,000 | 84.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9935 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.2% of corpus
- **Long Tail:** 25,751 words needed for remaining 15.7% 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 | 0.9019 🏆 | 0.3176 | N/A | N/A |
| **mono_64d** | 64 | 0.7924 | 0.2625 | N/A | N/A |
| **mono_128d** | 128 | 0.3620 | 0.2359 | N/A | N/A |
| **aligned_32d** | 32 | 0.9019 | 0.3203 | 0.0100 | 0.1160 |
| **aligned_64d** | 64 | 0.7924 | 0.2588 | 0.0220 | 0.1580 |
| **aligned_128d** | 128 | 0.3620 | 0.2402 | 0.0480 | 0.2140 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.9019 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2725. 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 | **0.728** | 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 |
|--------|----------|
| `-ба` | байгаар, байр, баряуд |
| `-ха` | харагдана, халимагууд, хангахын |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | шатааһан, португалиин, догшин |
| `-й` | монголой, шэрхэгтэй, санхүүгай |
| `-ай` | санхүүгай, билзуухай, байгуулгануудтай |
| `-ан` | шатааһан, урлаһан, абатан |
| `-эй` | шэрхэгтэй, ерэнхэй, нүхэтэй |
| `-ые` | диграфые, конгрессые, логикые |
| `-ын` | хилын, нэмэгдэхын, хангахын |
| `-нь` | уклонь, утаашань, вангиинь |

### 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` | 1.87x | 66 contexts | уугуул, хайгуул, агуулжа |
| `энэй` | 1.92x | 53 contexts | сэнэй, эзэнэй, энэнэй |
| `анай` | 1.74x | 74 contexts | манай, танай, ванай |
| `ниин` | 1.99x | 40 contexts | ниинь, даниин, кениин |
| `азар` | 2.36x | 21 contexts | газар, базар, лазарь |
| `нүүд` | 1.92x | 41 contexts | үенүүд, гүнүүд, эснүүд |
| `алай` | 1.85x | 47 contexts | һалай, малай, алайр |
| `дэһэ` | 1.87x | 44 contexts | гэдэһэ, үндэһэ, үдэһэн |
| `эдэг` | 1.76x | 56 contexts | хэдэг, гэдэг, үзэдэг |
| `эгдэ` | 1.57x | 91 contexts | жэгдэ, дэгдэн, нэгдэн |
| `оһон` | 1.91x | 40 contexts | тоһон, хооһон, ороһон |
| `ууда` | 1.72x | 57 contexts | уудам, уудаг, буудал |

### 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 |
|--------|--------|-----------|----------|
| `-ба` | `-н` | 36 words | багамын, байгуулсан |
| `-ха` | `-н` | 29 words | хамаарһан, харбаан |
| `-ба` | `-й` | 28 words | байгууламжануудай, баттерфляй |
| `-ха` | `-й` | 26 words | харбинай, хатарай |
| `-ха` | `-ай` | 23 words | харбинай, хатарай |
| `-ха` | `-ан` | 21 words | хамаарһан, харбаан |
| `-ба` | `-ан` | 21 words | байгуулсан, барилдаан |
| `-ба` | `-ай` | 18 words | байгууламжануудай, баатарай |
| `-ха` | `-аа` | 13 words | хаанһаа, харууллаа |
| `-ба` | `-аа` | 11 words | байдалаараа, бараа |

### 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 |
|------|-----------------|------------|------|
| басаганай | **`ба-саган-ай`** | 6.0 | `саган` |
| онсолигые | **`онсолиг-ые`** | 4.5 | `онсолиг` |
| гибралтарай | **`гибралтар-ай`** | 4.5 | `гибралтар` |
| оронуудаа | **`оронууд-аа`** | 4.5 | `оронууд` |
| туристуудай | **`туристууд-ай`** | 4.5 | `туристууд` |
| эблэрэлэй | **`эблэрэл-эй`** | 4.5 | `эблэрэл` |
| шалгалтые | **`шалгалт-ые`** | 4.5 | `шалгалт` |
| шулуунуудые | **`шулуунууд-ые`** | 4.5 | `шулуунууд` |
| хүсэнүүдые | **`хүсэнүүд-ые`** | 4.5 | `хүсэнүүд` |
| бэшэхэдэнь | **`бэшэхэдэ-нь`** | 4.5 | `бэшэхэдэ` |
| хубилбаринь | **`хубилбари-нь`** | 4.5 | `хубилбари` |
| үзүүрнүүдые | **`үзүүрнүүд-ые`** | 4.5 | `үзүүрнүүд` |
| моринойнь | **`мориной-нь`** | 4.5 | `мориной` |
| реализмын | **`реализм-ын`** | 4.5 | `реализм` |
| сэрэгүүдые | **`сэрэгүүд-ые`** | 4.5 | `сэрэгүүд` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Russia Buriat 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 (4.40x) |
| N-gram | **2-gram** | Lowest perplexity (452) |
| Markov | **Context-4** | Highest predictability (98.9%) |
| 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: 2026-01-03 19:55:46*