README.md

---
language: uz
language_name: Uzbek
language_family: turkic_other
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_other
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: 4.579
  - name: best_isotropy
    type: isotropy
    value: 0.7694
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Uzbek** 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** | 3.671x | 3.67 | 0.0852% | 1,947,309 |
| **16k** | 4.048x | 4.05 | 0.0940% | 1,765,944 |
| **32k** | 4.351x | 4.35 | 0.1010% | 1,642,973 |
| **64k** | 4.579x 🏆 | 4.58 | 0.1063% | 1,561,057 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `— Braziliyaning Alagoas shtatidagi munisipalitet. Manbalar munitsipalitetlari`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁— ▁braziliyaning ▁ala go as ▁shtatidagi ▁munisipalitet . ▁manbalar ▁munitsipalitet ... (+1 more)` | 11 |
| 16k | `▁— ▁braziliyaning ▁ala go as ▁shtatidagi ▁munisipalitet . ▁manbalar ▁munitsipalitet ... (+1 more)` | 11 |
| 32k | `▁— ▁braziliyaning ▁ala go as ▁shtatidagi ▁munisipalitet . ▁manbalar ▁munitsipalitet ... (+1 more)` | 11 |
| 64k | `▁— ▁braziliyaning ▁alagoas ▁shtatidagi ▁munisipalitet . ▁manbalar ▁munitsipalitet lari` | 9 |

**Sample 2:** `Boztarla — Adıyaman viloyatining Kâhta tumanidagi qishloqlardan biri. Manbalar b...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁boz tar la ▁— ▁ad ı y aman ▁viloyatining ▁k ... (+14 more)` | 24 |
| 16k | `▁boz tar la ▁— ▁adıyaman ▁viloyatining ▁k â h ta ... (+11 more)` | 21 |
| 32k | `▁boz tar la ▁— ▁adıyaman ▁viloyatining ▁k â hta ▁tumanidagi ... (+10 more)` | 20 |
| 64k | `▁boz tar la ▁— ▁adıyaman ▁viloyatining ▁kâhta ▁tumanidagi ▁qishloqlardan ▁biri ... (+8 more)` | 18 |

**Sample 3:** `— Braziliyaning Para shtatidagi munitsipalitet. Manbalar munitsipalitetlari`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁— ▁braziliyaning ▁para ▁shtatidagi ▁munitsipalitet . ▁manbalar ▁munitsipalitet lari` | 9 |
| 16k | `▁— ▁braziliyaning ▁para ▁shtatidagi ▁munitsipalitet . ▁manbalar ▁munitsipalitet lari` | 9 |
| 32k | `▁— ▁braziliyaning ▁para ▁shtatidagi ▁munitsipalitet . ▁manbalar ▁munitsipalitet lari` | 9 |
| 64k | `▁— ▁braziliyaning ▁para ▁shtatidagi ▁munitsipalitet . ▁manbalar ▁munitsipalitet lari` | 9 |


### Key Findings

- **Best Compression:** 64k achieves 4.579x compression
- **Lowest UNK Rate:** 8k with 0.0852% 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 | 144,258 | 17.14 | 1,000,611 | 8.6% | 21.5% |
| **2-gram** | Subword | 306 🏆 | 8.26 | 17,282 | 64.7% | 98.6% |
| **3-gram** | Word | 209,904 | 17.68 | 1,395,449 | 10.7% | 21.4% |
| **3-gram** | Subword | 2,739 | 11.42 | 139,644 | 25.4% | 67.7% |
| **4-gram** | Word | 290,405 | 18.15 | 2,129,240 | 11.2% | 22.1% |
| **4-gram** | Subword | 15,565 | 13.93 | 811,800 | 12.4% | 38.1% |
| **5-gram** | Word | 184,509 | 17.49 | 1,485,957 | 12.3% | 25.0% |
| **5-gram** | Subword | 58,859 | 15.84 | 2,792,057 | 7.1% | 25.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `aholi punktlari` | 133,471 |
| 2 | `boʻyicha aholi` | 102,687 |
| 3 | `tarkibiga kiradi` | 71,231 |
| 4 | `istiqomat qiladi` | 66,979 |
| 5 | `aholi istiqomat` | 65,487 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `boʻyicha aholi punktlari` | 102,646 |
| 2 | `nafar aholi istiqomat` | 64,709 |
| 3 | `aholi istiqomat qiladi` | 62,946 |
| 4 | `aholi punktlari shaharlari` | 55,710 |
| 5 | `manbalar boʻyicha aholi` | 44,383 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nafar aholi istiqomat qiladi` | 62,574 |
| 2 | `boʻyicha aholi punktlari shaharlari` | 55,662 |
| 3 | `manbalar boʻyicha aholi punktlari` | 44,383 |
| 4 | `yangi umumiy katalog asl` | 32,515 |
| 5 | `umumiy katalog asl nashrida` | 32,515 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `manbalar boʻyicha aholi punktlari shaharlari` | 33,698 |
| 2 | `yangi umumiy katalog asl nashrida` | 32,515 |
| 3 | `aholi zichligi har kvadrat kilometrga` | 30,929 |
| 4 | `nafar aholi istiqomat qiladi aholi` | 30,451 |
| 5 | `aholi istiqomat qiladi aholi zichligi` | 30,448 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 8,473,406 |
| 2 | `i _` | 8,057,286 |
| 3 | `a r` | 7,652,474 |
| 4 | `l a` | 7,619,051 |
| 5 | `a n` | 7,333,858 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a r` | 4,022,470 |
| 2 | `a n _` | 2,638,804 |
| 3 | `d a _` | 2,516,594 |
| 4 | `i d a` | 2,211,006 |
| 5 | `g a n` | 2,200,072 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n i n g` | 1,559,456 |
| 2 | `i n g _` | 1,556,517 |
| 3 | `l a r i` | 1,513,348 |
| 4 | `l a r _` | 1,478,041 |
| 5 | `i d a _` | 1,328,422 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n i n g _` | 1,484,174 |
| 2 | `l a r i _` | 771,549 |
| 3 | `g a n . _` | 672,707 |
| 4 | `d a g i _` | 557,890 |
| 5 | `a d i . _` | 529,582 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 306
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.8649 | 1.821 | 9.91 | 1,734,204 | 13.5% |
| **1** | Subword | 1.1817 | 2.268 | 7.66 | 9,225 | 0.0% |
| **2** | Word | 0.3006 | 1.232 | 1.88 | 17,159,887 | 69.9% |
| **2** | Subword | 0.6573 | 1.577 | 4.58 | 70,636 | 34.3% |
| **3** | Word | 0.1029 | 1.074 | 1.20 | 32,224,146 | 89.7% |
| **3** | Subword | 0.7355 | 1.665 | 4.35 | 323,343 | 26.4% |
| **4** | Word | 0.0379 🏆 | 1.027 | 1.06 | 38,723,206 | 96.2% |
| **4** | Subword | 0.7076 | 1.633 | 3.60 | 1,405,500 | 29.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `va pele vafoti muhammad stadioni 1 b neilson denyse julien près de antropología e 5 dan`
2. `bilan jamoaviy koʻrgazmalarini oʻtkazgan faqat tana aʼzosi boʻlgan juftlik bahslarida chempion boʻlg...`
3. `u oʻzining isteʼdodlar va viruslar qoʻzgʻatadigan yuqumli dasturlar bbc worldwide goʻzallik iffat qu...`

**Context Size 2:**

1. `boʻyicha aholi punktlari shaharlari shaharlar ipak yoʻli yaqinida joylashgan lawang kidul masjidi us...`
2. `aholi punktlari shaharlari tashkil etilgan u mexanika boʻyicha mutaxassis avval amerikada keyin ahol...`
3. `tarkibiga kiradi aholisi 779 nafarga yetadi o ni qoʻshilishi bilan stansiya ichidan uning sirtiga ch...`

**Context Size 3:**

1. `boʻyicha aholi punktlari shaharlari metropolitan hududlari`
2. `nafar aholi istiqomat qiladi aholi zichligi har kvadrat kilometrga 20 7 nafar kishi geografiyasi may...`
3. `aholi istiqomat qiladi aholi zichligi har kvadrat kilometrga 20 8 nafar kishi geografiyasi maydoni 3...`

**Context Size 4:**

1. `nafar aholi istiqomat qiladi geografiyasi hududi ramslaning hududi kmdir dengiz sathidan oʻrtacha m ...`
2. `manbalar boʻyicha aholi punktlari shaharlari shaharlari shaharlar`
3. `yangi umumiy katalog asl nashrida ngc 845 yangi umumiy katalog asl nashrida mavjud manbalar havolala...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_boshatoraskeyid`
2. `a_miladig‘rir_uc`
3. `ini_pefartilafr_`

**Context Size 2:**

1. `a_younkty_fausta_`
2. `i_1-1)_mena_oliga`
3. `lar_si_jahayratbo`

**Context Size 3:**

1. `lardan,_shundan_sh`
2. `an_edi._(_)_rivojl`
3. `da_u_lood_(milgan_`

**Context Size 4:**

1. `ning_oʻrtacha_aholi`
2. `ing_asosiyon)_stadi`
3. `lar_va_federn_klubi`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,405,500 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 | 722,817 |
| Total Tokens | 48,635,987 |
| Mean Frequency | 67.29 |
| Median Frequency | 4 |
| Frequency Std Dev | 1990.25 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | va | 1,184,048 |
| 2 | bilan | 369,678 |
| 3 | u | 280,225 |
| 4 | manbalar | 272,147 |
| 5 | aholi | 258,250 |
| 6 | uchun | 237,429 |
| 7 | joylashgan | 206,009 |
| 8 | 1 | 194,151 |
| 9 | boʻyicha | 181,987 |
| 10 | boʻlgan | 170,867 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | eversleigh | 2 |
| 2 | bundlening | 2 |
| 3 | thesigerning | 2 |
| 4 | haggleton | 2 |
| 5 | domli | 2 |
| 6 | xatibani | 2 |
| 7 | katakumite | 2 |
| 8 | apistomorpha | 2 |
| 9 | colucci | 2 |
| 10 | guerrio | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0071 |
| R² (Goodness of Fit) | 0.991725 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.2% |
| Top 1,000 | 48.2% |
| Top 5,000 | 67.9% |
| Top 10,000 | 75.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9917 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.2% of corpus
- **Long Tail:** 712,817 words needed for remaining 24.4% 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 | 0.7694 🏆 | 0.3417 | N/A | N/A |
| **mono_64d** | 64 | 0.7319 | 0.2924 | N/A | N/A |
| **mono_128d** | 128 | 0.6469 | 0.2679 | N/A | N/A |
| **aligned_32d** | 32 | 0.7694 | 0.3486 | 0.2540 | 0.6100 |
| **aligned_64d** | 64 | 0.7319 | 0.3022 | 0.3600 | 0.7600 |
| **aligned_128d** | 128 | 0.6469 | 0.2627 | 0.5040 | 0.8100 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7694 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3026. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 50.4% 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 | **-0.006** | 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 |
|--------|----------|
| `-a` | aminofenollar, alimkul, ashtarxoniylardan |
| `-s` | stolyarov, signalnaya, sovutish |
| `-ma` | macewan, matodir, majduddin |
| `-m` | munosabatlaridir, macewan, matodir |
| `-k` | konseysao, kuzatuvdagi, kello |
| `-b` | boqiya, boatengning, bacsinszky |
| `-t` | triangulorum, tarantelloyoʻlboshlovchi, totning |
| `-ba` | bacsinszky, barbaraʼ, baholangan |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | signalnaya, uncda, boqiya |
| `-i` | ruhiyati, oʻrtogʻini, semizligi |
| `-ng` | sashaning, boatengning, garmonning |
| `-g` | sashaning, boatengning, garmonning |
| `-n` | gʻishtin, zararsizlantiriladigan, macewan |
| `-an` | zararsizlantiriladigan, macewan, lushan |
| `-ni` | oʻrtogʻini, shlezvigni, hitini |
| `-ga` | umidga, diskiga, yupiterga |

### 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 |
|------|----------|------------------|----------|
| `rnin` | 2.47x | 350 contexts | rnini, rning, barnin |
| `inin` | 2.05x | 623 contexts | minin, inini, zinin |
| `anin` | 1.72x | 759 contexts | ganin, yanin, manin |
| `oʻlg` | 2.47x | 58 contexts | koʻlga, qoʻlga, oʻlgan |
| `ʻlga` | 2.36x | 68 contexts | koʻlga, qoʻlga, oʻlgan |
| `idag` | 1.82x | 211 contexts | idagi, idaga, ridagi |
| `hlar` | 1.64x | 291 contexts | shlar, ihlar, shlari |
| `manb` | 2.30x | 44 contexts | manba, manbam, 3manba |
| `hgan` | 1.83x | 113 contexts | shgan, chgan, shgani |
| `nbal` | 2.39x | 35 contexts | inbal, manbal, nbalar |
| `ilad` | 1.59x | 198 contexts | gilad, iladi, bilad |
| `oyla` | 1.80x | 101 contexts | joyla, oylar, koyla |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-a` | 145 words | semiusta, sammitlarda |
| `-t` | `-a` | 115 words | tritonda, torgovlya |
| `-k` | `-a` | 105 words | konka, kalva |
| `-b` | `-a` | 100 words | beldumgʻaza, ballantiophora |
| `-s` | `-i` | 100 words | samkni, stantsiyalaridagi |
| `-k` | `-i` | 97 words | karetkasi, kriminalistikasi |
| `-a` | `-a` | 97 words | akvabogʻda, ahvazga |
| `-t` | `-i` | 96 words | tayinlandiyangi, tayinlamadi |
| `-s` | `-n` | 85 words | shohmuroddan, slain |
| `-b` | `-i` | 84 words | bukowski, butasi |

### 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 |
|------|-----------------|------------|------|
| spidometriga | **`spidometr-i-ga`** | 7.5 | `i` |
| synesthesia | **`synesthes-i-a`** | 7.5 | `i` |
| kavaleriyada | **`kavaleriy-a-da`** | 7.5 | `a` |
| tesaliyadagi | **`tesaliya-da-gi`** | 7.5 | `da` |
| dogʻistondagi | **`dogʻiston-da-gi`** | 7.5 | `da` |
| oilalarda | **`oilal-ar-da`** | 7.5 | `ar` |
| kamroqdir | **`kamroqd-i-r`** | 7.5 | `i` |
| anguilladagi | **`anguilla-da-gi`** | 7.5 | `da` |
| qashgʻariya | **`qashgʻar-i-ya`** | 7.5 | `i` |
| aggressiv | **`aggress-i-v`** | 7.5 | `i` |
| oshirishlariga | **`oshirishlar-i-ga`** | 7.5 | `i` |
| hempcrete | **`hempcre-t-e`** | 7.5 | `t` |
| misolidir | **`misolid-i-r`** | 7.5 | `i` |
| oʻzgarishlarini | **`oʻzgarishlar-i-ni`** | 7.5 | `i` |
| raqobatchini | **`raqobatch-i-ni`** | 7.5 | `i` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Uzbek 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 (4.58x) |
| N-gram | **2-gram** | Lowest perplexity (306) |
| Markov | **Context-4** | Highest predictability (96.2%) |
| 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 07:14:31*