---
language: tg
language_name: Tajik
language_family: iranian_western
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-iranian_western
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: 4.487
  - name: best_isotropy
    type: isotropy
    value: 0.7880
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tajik** 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** | 3.486x | 3.49 | 0.2019% | 742,474 |
| **16k** | 3.884x | 3.89 | 0.2250% | 666,367 |
| **32k** | 4.228x | 4.23 | 0.2449% | 612,153 |
| **64k** | 4.487x 🏆 | 4.49 | 0.2599% | 576,760 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Рӯйдодҳо Зодрӯзҳо Даргузаштҳо Хэ-ди — шоҳаншоҳи Чин 89 — 105. Эзоҳ 105`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁рӯйдодҳо ▁зодрӯзҳо ▁даргузаштҳо ▁х э - ди ▁— ▁шоҳ ан ... (+16 more)` | 26 |
| 16k | `▁рӯйдодҳо ▁зодрӯзҳо ▁даргузаштҳо ▁х э - ди ▁— ▁шоҳан шоҳи ... (+15 more)` | 25 |
| 32k | `▁рӯйдодҳо ▁зодрӯзҳо ▁даргузаштҳо ▁х э - ди ▁— ▁шоҳаншоҳи ▁чин ... (+14 more)` | 24 |
| 64k | `▁рӯйдодҳо ▁зодрӯзҳо ▁даргузаштҳо ▁хэ - ди ▁— ▁шоҳаншоҳи ▁чин ▁ ... (+13 more)` | 23 |

**Sample 2:** `Рӯйдодҳо Зодрӯзҳо Бознигаред: : соли Даргузаштҳо Бознигаред: : соли Нигаред низ ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁рӯйдодҳо ▁зодрӯзҳо ▁бознигаред : ▁: ▁соли ▁даргузаштҳо ▁бознигаред : ▁: ... (+4 more)` | 14 |
| 16k | `▁рӯйдодҳо ▁зодрӯзҳо ▁бознигаред : ▁: ▁соли ▁даргузаштҳо ▁бознигаред : ▁: ... (+4 more)` | 14 |
| 32k | `▁рӯйдодҳо ▁зодрӯзҳо ▁бознигаред : ▁: ▁соли ▁даргузаштҳо ▁бознигаред : ▁: ... (+4 more)` | 14 |
| 64k | `▁рӯйдодҳо ▁зодрӯзҳо ▁бознигаред : ▁: ▁соли ▁даргузаштҳо ▁бознигаред : ▁: ... (+4 more)` | 14 |

**Sample 3:** `AMD Alarus () — як ҳавогарди сохтаи Aircraft Manufacturing and Development аст ....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁am d ▁al ar us ▁() ▁— ▁як ▁ҳавогарди ▁сохтаи ... (+22 more)` | 32 |
| 16k | `▁am d ▁al ar us ▁() ▁— ▁як ▁ҳавогарди ▁сохтаи ... (+19 more)` | 29 |
| 32k | `▁am d ▁al ar us ▁() ▁— ▁як ▁ҳавогарди ▁сохтаи ... (+12 more)` | 22 |
| 64k | `▁am d ▁alar us ▁() ▁— ▁як ▁ҳавогарди ▁сохтаи ▁aircraft ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.487x compression
- **Lowest UNK Rate:** 8k with 0.2019% 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 | 19,024 | 14.22 | 199,195 | 23.5% | 41.6% |
| **2-gram** | Subword | 400 🏆 | 8.65 | 9,876 | 59.8% | 96.9% |
| **3-gram** | Word | 19,608 | 14.26 | 288,805 | 27.4% | 43.9% |
| **3-gram** | Subword | 3,354 | 11.71 | 85,351 | 23.8% | 64.5% |
| **4-gram** | Word | 23,769 | 14.54 | 463,359 | 28.2% | 44.2% |
| **4-gram** | Subword | 16,216 | 13.99 | 471,031 | 12.0% | 39.6% |
| **5-gram** | Word | 16,389 | 14.00 | 359,581 | 30.9% | 47.7% |
| **5-gram** | Subword | 49,233 | 15.59 | 1,276,489 | 8.3% | 29.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `аз рӯи` | 48,520 |
| 2 | `ки дар` | 46,991 |
| 3 | `рӯи алифбо` | 45,099 |
| 4 | `қарор дорад` | 37,326 |
| 5 | `яке аз` | 36,325 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `аз рӯи алифбо` | 45,098 |
| 2 | `аҳолинишин аз рӯи` | 28,845 |
| 3 | `дар ҳайати ноҳияи` | 27,938 |
| 4 | `системаи хабарнигории давлатӣ` | 25,776 |
| 5 | `рӯи алифбо аҳолинишини` | 25,024 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `аҳолинишин аз рӯи алифбо` | 28,844 |
| 2 | `аз рӯи алифбо аҳолинишини` | 25,024 |
| 3 | `рӯи алифбо аҳолинишини ноҳияи` | 25,018 |
| 4 | `geonames org аҳолинишин аз` | 24,991 |
| 5 | `org аҳолинишин аз рӯи` | 24,991 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `аҳолинишин аз рӯи алифбо аҳолинишини` | 25,023 |
| 2 | `аз рӯи алифбо аҳолинишини ноҳияи` | 25,018 |
| 3 | `geonames org аҳолинишин аз рӯи` | 24,991 |
| 4 | `org аҳолинишин аз рӯи алифбо` | 24,991 |
| 5 | `маҳаллаҳои аҳолинишини федератсияи русия мебошад` | 24,020 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `и _` | 3,036,155 |
| 2 | `а р` | 1,436,276 |
| 3 | `д а` | 1,047,669 |
| 4 | `_ м` | 932,624 |
| 5 | `_ д` | 931,412 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ д а` | 509,185 |
| 2 | `а р _` | 476,961 |
| 3 | `д а р` | 438,520 |
| 4 | `_ б а` | 373,477 |
| 5 | `о и _` | 371,838 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ д а р` | 403,605 |
| 2 | `д а р _` | 377,815 |
| 3 | `ҳ о и _` | 286,612 |
| 4 | `_ в а _` | 254,093 |
| 5 | `_ а з _` | 231,233 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ д а р _` | 368,835 |
| 2 | `, _ к и _` | 119,898 |
| 3 | `с о л и _` | 105,997 |
| 4 | `_ с о л и` | 103,103 |
| 5 | `_ а ҳ о л` | 100,780 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 400
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.8187 | 1.764 | 7.04 | 506,708 | 18.1% |
| **1** | Subword | 0.9461 | 1.927 | 8.08 | 3,218 | 5.4% |
| **2** | Word | 0.2712 | 1.207 | 1.75 | 3,558,039 | 72.9% |
| **2** | Subword | 0.9170 | 1.888 | 6.45 | 25,977 | 8.3% |
| **3** | Word | 0.0958 | 1.069 | 1.19 | 6,212,459 | 90.4% |
| **3** | Subword | 0.8398 | 1.790 | 4.71 | 167,557 | 16.0% |
| **4** | Word | 0.0373 🏆 | 1.026 | 1.07 | 7,351,856 | 96.3% |
| **4** | Subword | 0.6814 | 1.604 | 3.16 | 788,521 | 31.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `дар ҳайати ноҳияи верховаж ки чопи офсети стр 367 6 донишҷӯёни барномаи ms 25px чоряки якуми`
2. `ва субъективизм ва адлия бароварда шуданд принсипҳое ки як фаввораи ишқ чашми ҷон муҳар рӯзн байрақи`
3. `аз қабили маҳмуд ибни абияъқуб исҳоқ то 900 шарҳи ин фурудгоҳ дар асоси телевизиони пойтахт он`

**Context Size 2:**

1. `аз рӯи алифбо аҳолинишини ноҳияи череповетс вологда`
2. `ки дар таъсис ёфта ‌‌аст қутби ukraine air alliance як ширкати ҳавопаймоӣ дар асмэра эритрея ҷойгир ...`
3. `қарор дорад ва дар санъати атиқаи осиёи марказӣ гунае аз амалиёти муваффақ дар белиз ба ҳисоб мерава...`

**Context Size 3:**

1. `аз рӯи алифбо аҳолинишини ноҳияи шенкур`
2. `аҳолинишин аз рӯи алифбо аҳолинишини ноҳияи сураж`
3. `дар ҳайати ноҳияи лиски ки дар вилояти владимир қарор дорад дохил мешавад системаи хабарнигории давл...`

**Context Size 4:**

1. `аҳолинишин аз рӯи алифбо аҳолинишини ноҳияи красноборский красноборский`
2. `аз рӯи алифбо аҳолинишини ноҳияи кичменгско городетс вологда`
3. `рӯи алифбо аҳолинишини ноҳияи киржач`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_д.os-июлуя_мтро`
2. `аи_(),_дан_шу_(;`
3. `и_آغاند_ои_оҳата`

**Context Size 2:**

1. `и_имроҳӣ_ваниҳоли`
2. `ар_дар_ҷашҳутбол_`
3. `даи_милогамон_ҳад`

**Context Size 3:**

1. `_дар_деҳа,_киности`
2. `ар_трид_сисаҳолегр`
3. `дар_вилобчаҳолини_`

**Context Size 4:**

1. `_дар_аввалинобар_ба`
2. `дар_синниколай_ауди`
3. `ҳои_рангҳои_арти_си`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (788,521 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 | 215,596 |
| Total Tokens | 10,911,035 |
| Mean Frequency | 50.61 |
| Median Frequency | 4 |
| Frequency Std Dev | 1428.75 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | дар | 374,510 |
| 2 | ва | 255,196 |
| 3 | аз | 236,317 |
| 4 | ба | 177,909 |
| 5 | ки | 129,043 |
| 6 | бф | 122,591 |
| 7 | соли | 103,632 |
| 8 | эзоҳ | 83,015 |
| 9 | ноҳияи | 82,572 |
| 10 | аст | 73,194 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | шамсиро | 2 |
| 2 | депрессияҳо | 2 |
| 3 | муқронес | 2 |
| 4 | корнис | 2 |
| 5 | карнизхо | 2 |
| 6 | cornice | 2 |
| 7 | муқарнасҳо | 2 |
| 8 | марафсай | 2 |
| 9 | лабсурхкунакҳои | 2 |
| 10 | estée | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0636 |
| R² (Goodness of Fit) | 0.996995 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 35.8% |
| Top 1,000 | 60.7% |
| Top 5,000 | 77.3% |
| Top 10,000 | 83.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9970 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 35.8% of corpus
- **Long Tail:** 205,596 words needed for remaining 16.4% 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 | 0.7880 | 0.3621 | N/A | N/A |
| **mono_64d** | 64 | 0.7858 | 0.2745 | N/A | N/A |
| **mono_128d** | 128 | 0.7609 | 0.2180 | N/A | N/A |
| **aligned_32d** | 32 | 0.7880 🏆 | 0.3519 | 0.0200 | 0.1960 |
| **aligned_64d** | 64 | 0.7858 | 0.2700 | 0.0400 | 0.2740 |
| **aligned_128d** | 128 | 0.7609 | 0.2081 | 0.1020 | 0.3880 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7880 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2808. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.2% 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 | **0.637** | 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 |
|--------|----------|
| `-а` | асарҳост, астрасторгуева, аскасибар |
| `-ма` | манзумаҳое, малҳама, мальбум |
| `-с` | сурьмы, саркашро, собирҷонов |
| `-м` | металлургии, мураббаъро, муҷибурраҳмон |
| `-б` | биосинтези, било, буридааст |
| `-к` | кабудчашма, комендантӣ, капустино |
| `-са` | саркашро, санъаткорон, сапонини |
| `-та` | ташаузский, таьлими, таҳримҳои |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-и` | ченкунандаи, ҷудонашавандаи, металлургии |
| `-о` | лано, мураббаъро, саркашро |
| `-ро` | мураббаъро, саркашро, императориро |
| `-а` | кабудчашма, астрасторгуева, гулзода |
| `-н` | парвизҷон, муҷибурраҳмон, санъаткорон |
| `-ӣ` | зандагӣ, комендантӣ, аннӣ |
| `-ии` | металлургии, регуляризации, якшавии |
| `-ои` | равоқтоқҳои, кошиҳои, таҳримҳои |

### 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 |
|------|----------|------------------|----------|
| `шава` | 2.31x | 47 contexts | шавад, шавам, нашава |
| `влат` | 2.32x | 46 contexts | давлат, савлат, давлатӣ |
| `оҷик` | 2.37x | 33 contexts | тоҷик, тоҷикӣ, тоҷику |
| `ҷики` | 2.65x | 18 contexts | ҷикис, тоҷики, тоҷикии |
| `авла` | 2.12x | 38 contexts | давла, шавла, чавла |
| `лини` | 1.91x | 55 contexts | линия, линий, плини |
| `арор` | 1.67x | 80 contexts | карор, тарор, шарор |
| `тбол` | 2.37x | 20 contexts | футбол, футболӣ, футбола |
| `уруд` | 1.85x | 48 contexts | куруд, вуруд, дуруд |
| `оҳия` | 1.88x | 42 contexts | ноҳия, воҳия, ибоҳия |
| `усия` | 2.26x | 20 contexts | русия, лусия, русияю |
| `ниши` | 1.66x | 62 contexts | нишин, дониши, хониши |

### 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 |
|--------|--------|-----------|----------|
| `-с` | `-и` | 98 words | сеи, соддаи |
| `-м` | `-и` | 91 words | маҷаллаи, муаммолари |
| `-а` | `-и` | 85 words | анаси, авҷгирии |
| `-к` | `-и` | 81 words | корбарии, кимёии |
| `-к` | `-о` | 59 words | крепостноиро, кулако |
| `-б` | `-и` | 56 words | бейлики, бакши |
| `-б` | `-о` | 53 words | бонуфузро, бонҳо |
| `-а` | `-о` | 51 words | алавиро, агентҳо |
| `-с` | `-о` | 51 words | сайтҳо, семинарио |
| `-ма` | `-и` | 49 words | маҷаллаи, марки |

### 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 |
|------|-----------------|------------|------|
| қизилкӯпир | **`қизилкӯп-и-р`** | 7.5 | `и` |
| лентапедиа | **`лентапед-и-а`** | 7.5 | `и` |
| толкование | **`толкован-и-е`** | 7.5 | `и` |
| мамлакатдориро | **`мамлакатдор-и-ро`** | 7.5 | `и` |
| нишонгири | **`нишонг-и-ри`** | 7.5 | `и` |
| баҳовадин | **`баҳовад-и-н`** | 7.5 | `и` |
| фақиртарин | **`фақиртар-и-н`** | 7.5 | `и` |
| католикиро | **`католик-и-ро`** | 7.5 | `и` |
| бисёрошёнаи | **`бисёрошё-на-и`** | 7.5 | `на` |
| гармкунак | **`гармку-на-к`** | 7.5 | `на` |
| максимовшина | **`максимовш-и-на`** | 7.5 | `и` |
| густурдае | **`густур-да-е`** | 7.5 | `да` |
| эллипсоид | **`эллипсо-и-д`** | 7.5 | `и` |
| печидагиҳо | **`печидаг-и-ҳо`** | 7.5 | `и` |
| компанион | **`компан-и-он`** | 7.5 | `и` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tajik 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 (4.49x) |
| N-gram | **2-gram** | Lowest perplexity (400) |
| Markov | **Context-4** | Highest predictability (96.3%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-11 01:38:18*