---
language: ba
language_name: Bashkir
language_family: turkic_kipchak
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-turkic_kipchak
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: 4.674
  - name: best_isotropy
    type: isotropy
    value: 0.7711
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Bashkir** 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** | 3.561x | 3.56 | 0.3982% | 1,530,967 |
| **16k** | 3.999x | 4.00 | 0.4471% | 1,363,432 |
| **32k** | 4.374x | 4.38 | 0.4891% | 1,246,440 |
| **64k** | 4.674x 🏆 | 4.68 | 0.5226% | 1,166,431 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Нортленд - (ҡитға исеме) лағы дәүләт. Иҫкәрмәләр Һылтанмалар`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁н орт лен д ▁- ▁( ҡит ға ▁исеме ) ... (+6 more)` | 16 |
| 16k | `▁н орт ленд ▁- ▁( ҡит ға ▁исеме ) ▁лағы ... (+4 more)` | 14 |
| 32k | `▁н орт ленд ▁- ▁( ҡитға ▁исеме ) ▁лағы ▁дәүләт ... (+3 more)` | 13 |
| 64k | `▁норт ленд ▁- ▁( ҡитға ▁исеме ) ▁лағы ▁дәүләт . ... (+2 more)` | 12 |

**Sample 2:** `Австралия — Көньяҡ ярымшарҙарҙа урынлашҡан дәүләт. Австралия (ҡитға) — Көнсығыш ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁австр алия ▁— ▁көньяҡ ▁ярым шар ҙарҙа ▁урынлашҡан ▁дәүләт . ... (+18 more)` | 28 |
| 16k | `▁австралия ▁— ▁көньяҡ ▁ярымшар ҙарҙа ▁урынлашҡан ▁дәүләт . ▁австралия ▁( ... (+13 more)` | 23 |
| 32k | `▁австралия ▁— ▁көньяҡ ▁ярымшар ҙарҙа ▁урынлашҡан ▁дәүләт . ▁австралия ▁( ... (+11 more)` | 21 |
| 64k | `▁австралия ▁— ▁көньяҡ ▁ярымшар ҙарҙа ▁урынлашҡан ▁дәүләт . ▁австралия ▁( ... (+11 more)` | 21 |

**Sample 3:** `йыл — йәкшәмбе көнөнән башланған йыл, кәбисә түгел. Ваҡиғалар Тыуғандар Вафат бу...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁йыл ▁— ▁й әк шәмбе ▁көнөнән ▁башланған ▁йыл , ▁кәбисә ... (+10 more)` | 20 |
| 16k | `▁йыл ▁— ▁йәкшәмбе ▁көнөнән ▁башланған ▁йыл , ▁кәбисә ▁түгел . ... (+8 more)` | 18 |
| 32k | `▁йыл ▁— ▁йәкшәмбе ▁көнөнән ▁башланған ▁йыл , ▁кәбисә ▁түгел . ... (+8 more)` | 18 |
| 64k | `▁йыл ▁— ▁йәкшәмбе ▁көнөнән ▁башланған ▁йыл , ▁кәбисә ▁түгел . ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.674x compression
- **Lowest UNK Rate:** 8k with 0.3982% 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 | 56,272 | 15.78 | 432,191 | 13.8% | 30.4% |
| **2-gram** | Subword | 488 🏆 | 8.93 | 13,737 | 52.3% | 96.8% |
| **3-gram** | Word | 53,798 | 15.72 | 562,854 | 18.1% | 34.8% |
| **3-gram** | Subword | 4,221 | 12.04 | 117,501 | 18.9% | 58.6% |
| **4-gram** | Word | 61,592 | 15.91 | 881,988 | 19.4% | 36.9% |
| **4-gram** | Subword | 21,484 | 14.39 | 685,600 | 10.3% | 33.2% |
| **5-gram** | Word | 37,893 | 15.21 | 658,444 | 21.5% | 41.3% |
| **5-gram** | Subword | 72,234 | 16.14 | 2,075,140 | 7.0% | 23.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `гө буйынса` | 60,195 |
| 2 | `һыу реестры` | 40,405 |
| 3 | `дәүләт һыу` | 40,403 |
| 4 | `йылға бассейны` | 40,327 |
| 5 | `рәсәй федерацияһы` | 37,239 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `һыу реестры мәғлүмәттәре` | 20,323 |
| 2 | `дәүләт һыу реестры` | 20,208 |
| 3 | `рәсәй дәүләт һыу` | 20,202 |
| 4 | `мәғлүмәттәре рәсәй дәүләт` | 20,170 |
| 5 | `реестры мәғлүмәттәре рәсәй` | 20,170 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `рәсәй дәүләт һыу реестры` | 20,195 |
| 2 | `реестры мәғлүмәттәре рәсәй дәүләт` | 20,170 |
| 3 | `мәғлүмәттәре рәсәй дәүләт һыу` | 20,170 |
| 4 | `һыу реестры мәғлүмәттәре рәсәй` | 20,167 |
| 5 | `дәүләт һыу реестрында һыу` | 20,160 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `реестры мәғлүмәттәре рәсәй дәүләт һыу` | 20,170 |
| 2 | `һыу реестры мәғлүмәттәре рәсәй дәүләт` | 20,167 |
| 3 | `мәғлүмәттәре рәсәй дәүләт һыу реестры` | 20,165 |
| 4 | `һыу реестрында һыу объектының коды` | 20,156 |
| 5 | `дәүләт һыу реестрында һыу объектының` | 20,156 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 2,391,231 |
| 2 | `а р` | 2,191,202 |
| 3 | `ы _` | 2,097,776 |
| 4 | `_ б` | 2,006,204 |
| 5 | `а н` | 1,864,458 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ й ы` | 754,633 |
| 2 | `й ы л` | 743,969 |
| 3 | `н д а` | 676,936 |
| 4 | `а н _` | 651,892 |
| 5 | `ы ң _` | 646,394 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ й ы л` | 707,090 |
| 2 | `ы н д а` | 467,625 |
| 3 | `_ һ ә м` | 441,510 |
| 4 | `һ ә м _` | 439,610 |
| 5 | `н д а _` | 408,202 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ һ ә м _` | 438,718 |
| 2 | `ы н д а _` | 353,882 |
| 3 | `_ й ы л д` | 323,522 |
| 4 | `й ы л ғ а` | 269,201 |
| 5 | `_ й ы л ғ` | 262,857 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 488
- **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 | 0.8991 | 1.865 | 8.98 | 912,874 | 10.1% |
| **1** | Subword | 0.9900 | 1.986 | 7.47 | 5,662 | 1.0% |
| **2** | Word | 0.2746 | 1.210 | 1.74 | 8,193,331 | 72.5% |
| **2** | Subword | 0.8598 | 1.815 | 5.90 | 42,271 | 14.0% |
| **3** | Word | 0.0885 | 1.063 | 1.17 | 14,249,949 | 91.1% |
| **3** | Subword | 0.8239 | 1.770 | 4.71 | 249,519 | 17.6% |
| **4** | Word | 0.0321 🏆 | 1.023 | 1.05 | 16,595,241 | 96.8% |
| **4** | Subword | 0.7025 | 1.627 | 3.37 | 1,174,607 | 29.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `һәм пәйғәмбәр аша ҡулға алалар диск ҡалын һуҙынҡылы ижеккә төшә көнбайыш конференцияһын әҙерләүҙә ул...`
2. `буйынса журналистар үҙҙәрен римляндар өсөн рәссам булараҡ игорь задорожный игорь а сатаров в н г сах...`
3. `һыу һәм төрлө биҙәгәндәр был блюдоның консистенцияһында исеменең типовой проект ҡаты алыштарҙа дошма...`

**Context Size 2:**

1. `гө буйынса сығарылыш 2 фаунаһы йылға мәғлүмәттәр буйынса аҙсылыҡтан император гвардияһы училищеһында...`
2. `һыу реестры мәғлүмәттәре рәсәй дәүләт һыу реестры мәғлүмәттәре рәсәй дәүләт һыу реестрында һыу объек...`
3. `дәүләт һыу реестры мәғлүмәттәре рәсәй дәүләт өлгөһөндәге диплом осоу аппараттарын ҡулланыуҙы көйләү ...`

**Context Size 3:**

1. `һыу реестры мәғлүмәттәре рәсәй дәүләт һыу реестры мәғлүмәте буйынса йылға двина печора һыу бассейны ...`
2. `дәүләт һыу реестры мәғлүмәте буйынса йылға двина печора һыу бассейны округында урынлашҡан һыу хужалы...`
3. `рәсәй дәүләт һыу реестры мәғлүмәте буйынса йылға кама һыу һаклағысы чусов сылвин ҡултығы һул ярына т...`

**Context Size 4:**

1. `рәсәй дәүләт һыу реестры мәғлүмәте буйынса йылға кама һыу бассейны округында урынлашҡан һыу хужалығы...`
2. `мәғлүмәттәре рәсәй дәүләт һыу реестры мәғлүмәте буйынса йылға көнбыйыш каспий һыу бассейны округында...`
3. `реестры мәғлүмәттәре рәсәй дәүләт һыу реестры мәғлүмәте буйынса йылға кама һыу бассейны округында ур...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_хрм_илға._—_брл`
2. `атемлашылларулең`
3. `ралүеүмәмка_ты_а`

**Context Size 2:**

1. `а_ра_һуң_съ_идери`
2. `ар._энты_хайындат`
3. `ы_—_буягацияһальс`

**Context Size 3:**

1. `_йыл_17_дек_тип_ик`
2. `йылдығыштабыуат_ге`
3. `ндағы_мәғилми_хеҙм`

**Context Size 4:**

1. `_йылдан_булат_ҡулты`
2. `ындағы_ҡарағыҙ_барғ`
3. `_һәм_бөтә_советы,_п`


### 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 (1,174,607 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 | 390,661 |
| Total Tokens | 21,477,387 |
| Mean Frequency | 54.98 |
| Median Frequency | 4 |
| Frequency Std Dev | 1227.90 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | һәм | 441,701 |
| 2 | буйынса | 199,502 |
| 3 | һыу | 168,327 |
| 4 | менән | 154,212 |
| 5 | йылға | 141,020 |
| 6 | йылда | 136,113 |
| 7 | рәсәй | 107,301 |
| 8 | йыл | 96,991 |
| 9 | йылдың | 89,541 |
| 10 | бассейны | 87,464 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | совкомбанк | 2 |
| 2 | маркетплейстың | 2 |
| 3 | суларға | 2 |
| 4 | кишлак | 2 |
| 5 | пацанский | 2 |
| 6 | мунден | 2 |
| 7 | гертфордшир | 2 |
| 8 | кроуға | 2 |
| 9 | франклоу | 2 |
| 10 | алтынкүлдән | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0499 |
| R² (Goodness of Fit) | 0.992209 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 23.9% |
| Top 1,000 | 52.3% |
| Top 5,000 | 71.5% |
| Top 10,000 | 78.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9922 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 23.9% of corpus
- **Long Tail:** 380,661 words needed for remaining 21.4% 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 | 0.7605 | 0.3607 | N/A | N/A |
| **mono_64d** | 64 | 0.7711 🏆 | 0.2817 | N/A | N/A |
| **mono_128d** | 128 | 0.7589 | 0.2238 | N/A | N/A |
| **aligned_32d** | 32 | 0.7605 | 0.3651 | 0.0420 | 0.2620 |
| **aligned_64d** | 64 | 0.7711 | 0.2829 | 0.0820 | 0.3600 |
| **aligned_128d** | 128 | 0.7589 | 0.2231 | 0.1140 | 0.4340 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.7711 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2896. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 11.4% 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 | **0.762** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | менеджерҙарға, клиентела, пегаға |
| `-ың` | амфитеатрының, лединың, ғәлиәкбәровтың |
| `-ан` | ҡыҙылдарҙан, саутунан, сығылған |
| `-ар` | андекстар, имплантаттар, тартыуҙар |
| `-ға` | менеджерҙарға, пегаға, ҡалыуға |
| `-ның` | амфитеатрының, лединың, соустарының |
| `-на` | градина, ағзаһына, катилина |
| `-ов` | крестов, әбшәрипов, протезов |

### 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 |
|------|----------|------------------|----------|
| `ссей` | 3.12x | 29 contexts | шоссей, иессей, бассей |
| `олог` | 1.84x | 205 contexts | лолог, полог, молог |
| `әүлә` | 2.51x | 39 contexts | дәүлә, хәүлә, шәүлә |
| `ассе` | 2.28x | 57 contexts | массе, хассе, гассе |
| `шҡор` | 3.03x | 15 contexts | башҡор, башҡорт, башҡорд |
| `лған` | 1.54x | 230 contexts | ялған, ҡлған, алған |
| `арҙы` | 1.62x | 168 contexts | парҙы, сарҙы, барҙы |
| `арҙа` | 1.48x | 266 contexts | барҙа, арҙан, арҙат |
| `аһын` | 1.35x | 378 contexts | шаһын, анаһын, яһаһын |
| `ттар` | 1.37x | 344 contexts | аттар, юттар, ттары |
| `ылға` | 1.49x | 213 contexts | йылға, ҡылға, ылғал |
| `лдар` | 1.45x | 236 contexts | алдар, ялдар, улдар |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| александровна | **`александр-ов-на`** | 6.0 | `александр` |
| мессинаның | **`месси-на-ның`** | 6.0 | `месси` |
| салаватовна | **`салават-ов-на`** | 6.0 | `салават` |
| терракотанан | **`терракот-ан-ан`** | 6.0 | `терракот` |
| моденаның | **`моде-на-ның`** | 6.0 | `моде` |
| доломанов | **`долом-ан-ов`** | 6.0 | `долом` |
| склонениеһына | **`склонениеһы-на`** | 4.5 | `склонениеһы` |
| характеров | **`характер-ов`** | 4.5 | `характер` |
| ваҡытының | **`ваҡыты-ның`** | 4.5 | `ваҡыты` |
| кейекбайға | **`кейекбай-ға`** | 4.5 | `кейекбай` |
| фомичёваның | **`фомичёва-ның`** | 4.5 | `фомичёва` |
| никаноров | **`никанор-ов`** | 4.5 | `никанор` |
| терапияһынан | **`терапияһын-ан`** | 4.5 | `терапияһын` |
| телевидениеһынан | **`телевидениеһын-ан`** | 4.5 | `телевидениеһын` |
| сепаратизмына | **`сепаратизмы-на`** | 4.5 | `сепаратизмы` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Bashkir 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 (4.67x) |
| N-gram | **2-gram** | Lowest perplexity (488) |
| 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: 2026-01-03 20:08:48*