---
language: kaa
language_name: Kara-Kalpak
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: 5.231
  - name: best_isotropy
    type: isotropy
    value: 0.8596
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Kara-Kalpak - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kara-Kalpak** 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** | 4.095x | 4.10 | 0.0535% | 1,035,724 |
| **16k** | 4.571x | 4.57 | 0.0597% | 927,895 |
| **32k** | 4.952x | 4.95 | 0.0647% | 856,500 |
| **64k** | 5.231x 🏆 | 5.23 | 0.0683% | 810,783 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Bobrovıtsâ () — Ukrainanıń Chernigov wálayatında jaylasqan qala. Bobrovıtsa rayo...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁bob r ov ıt s â ▁() ▁— ▁ukrain anıń ... (+29 more)` | 39 |
| 16k | `▁bob rov ıt s â ▁() ▁— ▁ukrainanıń ▁chern ig ... (+26 more)` | 36 |
| 32k | `▁bob rov ıt s â ▁() ▁— ▁ukrainanıń ▁chern ig ... (+26 more)` | 36 |
| 64k | `▁bobrovıt s â ▁() ▁— ▁ukrainanıń ▁chern ig ov ▁wálayatında ... (+22 more)` | 32 |

**Sample 2:** `— Qırǵızstannıń Osh wálayatı Úlken-Alay rayonındaǵı awıl. Úlken-Alay APJ quramın...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁— ▁qırǵızstannıń ▁osh ▁wálayatı ▁úlken - alay ▁rayonındaǵı ▁awıl . ... (+19 more)` | 29 |
| 16k | `▁— ▁qırǵızstannıń ▁osh ▁wálayatı ▁úlken - alay ▁rayonındaǵı ▁awıl . ... (+19 more)` | 29 |
| 32k | `▁— ▁qırǵızstannıń ▁osh ▁wálayatı ▁úlken - alay ▁rayonındaǵı ▁awıl . ... (+19 more)` | 29 |
| 64k | `▁— ▁qırǵızstannıń ▁osh ▁wálayatı ▁úlken - alay ▁rayonındaǵı ▁awıl . ... (+19 more)` | 29 |

**Sample 3:** `— Qırǵızstannıń Batken wálayatı Qadamjay rayonındaǵı awıl. Awıl Maydan awıl okru...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁— ▁qırǵızstannıń ▁batken ▁wálayatı ▁qadamjay ▁rayonındaǵı ▁awıl . ▁awıl ▁maydan ... (+19 more)` | 29 |
| 16k | `▁— ▁qırǵızstannıń ▁batken ▁wálayatı ▁qadamjay ▁rayonındaǵı ▁awıl . ▁awıl ▁maydan ... (+19 more)` | 29 |
| 32k | `▁— ▁qırǵızstannıń ▁batken ▁wálayatı ▁qadamjay ▁rayonındaǵı ▁awıl . ▁awıl ▁maydan ... (+19 more)` | 29 |
| 64k | `▁— ▁qırǵızstannıń ▁batken ▁wálayatı ▁qadamjay ▁rayonındaǵı ▁awıl . ▁awıl ▁maydan ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 64k achieves 5.231x compression
- **Lowest UNK Rate:** 8k with 0.0535% 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 | 23,270 | 14.51 | 54,707 | 10.1% | 27.4% |
| **2-gram** | Subword | 339 🏆 | 8.41 | 4,784 | 62.1% | 98.8% |
| **3-gram** | Word | 20,253 | 14.31 | 46,477 | 13.1% | 28.7% |
| **3-gram** | Subword | 2,759 | 11.43 | 39,335 | 21.9% | 68.2% |
| **4-gram** | Word | 25,858 | 14.66 | 61,893 | 14.2% | 28.0% |
| **4-gram** | Subword | 13,674 | 13.74 | 197,359 | 11.1% | 37.3% |
| **5-gram** | Word | 14,234 | 13.80 | 37,066 | 17.5% | 35.1% |
| **5-gram** | Subword | 43,260 | 15.40 | 503,495 | 6.5% | 24.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sonday aq` | 3,034 |
| 2 | `menen birge` | 2,841 |
| 3 | `bolıp tabıladı` | 2,616 |
| 4 | `sırtqı siltemeler` | 2,295 |
| 5 | `bir neshe` | 2,269 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `derekler sırtqı siltemeler` | 1,685 |
| 2 | `légales geografiyası jer` | 1,398 |
| 3 | `adampopulations légales geografiyası` | 1,398 |
| 4 | `geografiyası jer maydanı` | 1,374 |
| 5 | `sonıń menen birge` | 1,344 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `adampopulations légales geografiyası jer` | 1,398 |
| 2 | `légales geografiyası jer maydanı` | 1,374 |
| 3 | `jaylasqan kommuna xalqı xalqı` | 1,319 |
| 4 | `sırtqı siltemeler departamenti kommunaları` | 1,319 |
| 5 | `derekler sırtqı siltemeler departamenti` | 1,318 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `adampopulations légales geografiyası jer maydanı` | 1,374 |
| 2 | `departamentinde jaylasqan kommuna xalqı xalqı` | 1,318 |
| 3 | `derekler sırtqı siltemeler departamenti kommunaları` | 1,318 |
| 4 | `km2 derekler sırtqı siltemeler departamenti` | 1,317 |
| 5 | `franciyanıń seine maritime departamentinde jaylasqan` | 707 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a r` | 340,214 |
| 2 | `l a` | 332,558 |
| 3 | `a n` | 303,317 |
| 4 | `n _` | 291,907 |
| 5 | `a _` | 281,704 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a r` | 145,814 |
| 2 | `a n _` | 91,773 |
| 3 | `l e r` | 91,522 |
| 4 | `i y a` | 90,612 |
| 5 | `_ h á` | 90,529 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ h á m` | 74,987 |
| 2 | `h á m _` | 73,954 |
| 3 | `l a r ı` | 52,831 |
| 4 | `ı n d a` | 52,080 |
| 5 | `l ı q _` | 47,017 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ h á m _` | 73,759 |
| 2 | `ı n d a _` | 37,981 |
| 3 | `a l ı q _` | 26,249 |
| 4 | `a d ı . _` | 25,896 |
| 5 | `e n e n _` | 25,107 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 339
- **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 | 0.9475 | 1.928 | 7.14 | 215,380 | 5.3% |
| **1** | Subword | 0.9483 | 1.930 | 8.43 | 1,371 | 5.2% |
| **2** | Word | 0.2249 | 1.169 | 1.49 | 1,535,314 | 77.5% |
| **2** | Subword | 1.0052 | 2.007 | 6.59 | 11,538 | 0.0% |
| **3** | Word | 0.0563 | 1.040 | 1.09 | 2,281,857 | 94.4% |
| **3** | Subword | 0.8603 | 1.815 | 4.43 | 75,969 | 14.0% |
| **4** | Word | 0.0154 🏆 | 1.011 | 1.02 | 2,476,994 | 98.5% |
| **4** | Subword | 0.6640 | 1.584 | 2.96 | 336,428 | 33.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `hám oqıw orınları la capital hám jazıwdı buyırıw sistemasınan wear os 1 1 sıyaqlı uluwmalıq yamasa`
2. `menen baylanıs kanalların usınǵan sorawları jiberiletuǵın reklamalardı alıp keledi generikler c php ...`
3. `ushın paydalanıladı óytkeni biraq bul kompilyatorǵa tán juwap beriw jolı qol menen qatnasqan hám mád...`

**Context Size 2:**

1. `sonday aq aldıńǵı qosıqlarınıń tariyxın izertley aladı internet protokolı 4 versiyası ipv4 ip adresi...`
2. `menen birge orınlanatuǵın programma kerek óytkeni ájiniyazǵa shekemgi qaraqalpaq shayırlarında bul f...`
3. `bolıp tabıladı bes juldız berip dosınıń mına sózlerin keltiredi windows api sonshelli keń tarqaldı b...`

**Context Size 3:**

1. `derekler sırtqı siltemeler departamenti kommunaları`
2. `légales geografiyası jer maydanı 20 49 km2 derekler sırtqı siltemeler departamenti kommunaları`
3. `adampopulations légales geografiyası jer maydanı 19 09 km2 derekler sırtqı siltemeler departamenti k...`

**Context Size 4:**

1. `adampopulations légales geografiyası jer maydanı 14 37 km2 derekler sırtqı siltemeler departamenti k...`
2. `légales geografiyası jer maydanı 5 55 km2 derekler sırtqı siltemeler departamenti kommunaları`
3. `jaylasqan kommuna xalqı xalqı 2 635 adampopulations légales geografiyası jer maydanı 17 47 km2 derek...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_qın_ticenendaya`
2. `a_1460_deberoliy`
3. `idayamgi_—_p_tia`

**Context Size 2:**

1. `arın_dáwilladı_do`
2. `lar_twajları_dá_s`
3. `anlatınǵan_ionıń_`

**Context Size 3:**

1. `lar_bazlıq_derek,_`
2. `an_ashqada_basında`
3. `iyatlar_bolıwı_anı`

**Context Size 4:**

1. `_hám_ol_hası_qatnas`
2. `hám_g_sui_skepti_de`
3. `ında_kóterilgerisiw`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (336,428 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 | 94,344 |
| Total Tokens | 2,550,053 |
| Mean Frequency | 27.03 |
| Median Frequency | 4 |
| Frequency Std Dev | 320.88 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | hám | 74,114 |
| 2 | menen | 22,644 |
| 3 | ushın | 19,490 |
| 4 | bul | 18,802 |
| 5 | bir | 13,691 |
| 6 | ol | 12,270 |
| 7 | bolıp | 9,798 |
| 8 | yamasa | 8,778 |
| 9 | bolǵan | 8,505 |
| 10 | dep | 8,012 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | allaxabad | 2 |
| 2 | shaqapshasına | 2 |
| 3 | pondar | 2 |
| 4 | shechen | 2 |
| 5 | álimsultanov | 2 |
| 6 | alimsultanovtıń | 2 |
| 7 | xasavyurt | 2 |
| 8 | şebinkarahisar | 2 |
| 9 | 042 | 2 |
| 10 | i̇zel | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9824 |
| R² (Goodness of Fit) | 0.989215 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.4% |
| Top 1,000 | 49.2% |
| Top 5,000 | 71.8% |
| Top 10,000 | 80.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9892 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.4% of corpus
- **Long Tail:** 84,344 words needed for remaining 19.5% 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 | 0.8596 🏆 | 0.3821 | N/A | N/A |
| **mono_64d** | 64 | 0.8357 | 0.2373 | N/A | N/A |
| **mono_128d** | 128 | 0.8393 | 0.1678 | N/A | N/A |
| **aligned_32d** | 32 | 0.8596 | 0.3758 | 0.0640 | 0.2900 |
| **aligned_64d** | 64 | 0.8357 | 0.2292 | 0.1320 | 0.4080 |
| **aligned_128d** | 128 | 0.8393 | 0.1697 | 0.1560 | 0.4740 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8596 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2603. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 15.6% 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 | **0.422** | 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 |
|--------|----------|
| `-s` | sovxozı, sibirdiń, shakuriy |
| `-a` | arturo, adewir, aǵası |
| `-t` | toplaydı, talantın, túsiminiń |
| `-b` | besten, barri, bahalı |
| `-k` | komandiriniń, kaliforniyada, komponentleri |
| `-m` | mamanlıǵı, mellanox, materigin |
| `-ma` | mamanlıǵı, materigin, makbet |
| `-sh` | shakuriy, shıǵır, shtatı |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | dawamın, daǵdarısın, besten |
| `-a` | kaliforniyada, ıqlımına, evropaǵa |
| `-ı` | mamanlıǵı, toplaydı, sovxozı |
| `-ń` | komandiriniń, sibirdiń, oppengeymernıń |
| `-ıń` | oppengeymernıń, dárwazamanlardıń, klarustıń |
| `-i` | rsetti, komponentleri, xarakterlewshi |
| `-an` | aspan, gúmannan, saban |
| `-r` | populyar, ústinler, adewir |

### 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 |
|------|----------|------------------|----------|
| `lard` | 1.63x | 167 contexts | larda, lardı, alardı |
| `atla` | 1.64x | 122 contexts | atlas, atlan, atlar |
| `tler` | 1.65x | 98 contexts | etler, bitler, pátler |
| `asın` | 1.45x | 170 contexts | basın, pasın, tasın |
| `ardı` | 1.86x | 47 contexts | yardı, bardı, lardı |
| `ayla` | 1.45x | 107 contexts | layla, aylar, zayla |
| `shıl` | 1.74x | 47 contexts | aqshıl, shılım, oyshıl |
| `alıq` | 1.41x | 104 contexts | xalıq, salıq, balıq |
| `tuǵı` | 2.22x | 18 contexts | tuǵın, atatuǵın, ótetuǵın |
| `wshı` | 1.85x | 30 contexts | suwshı, oyıwshı, oqıwshı |
| `ciya` | 1.76x | 34 contexts | raciya, akciya, faciya |
| `ladı` | 1.61x | 47 contexts | aladı, oyladı, aqladı |

### 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` | 140 words | sozılıwǵa, samaveda |
| `-s` | `-n` | 123 words | sportın, sedan |
| `-a` | `-ı` | 109 words | alındı, aleksandriyalı |
| `-k` | `-i` | 104 words | kúndizgi, keńeytpeni |
| `-a` | `-n` | 97 words | ańlatpaytuǵının, australian |
| `-b` | `-n` | 95 words | báhárinen, baylanısıwınan |
| `-s` | `-ı` | 94 words | sırtqı, sawatlı |
| `-t` | `-ı` | 94 words | tartısıwlardı, tulı |
| `-t` | `-n` | 92 words | talqılaǵan, turatuǵının |
| `-a` | `-a` | 88 words | albina, auditoriyasına |

### 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 |
|------|-----------------|------------|------|
| vetnamnıń | **`vetnam-n-ıń`** | 7.5 | `n` |
| raketalardı | **`raketal-ar-dı`** | 7.5 | `ar` |
| bruklindaǵı | **`bruklin-da-ǵı`** | 7.5 | `da` |
| waqıyadan | **`waqıya-da-n`** | 7.5 | `da` |
| freymvorkları | **`freymvorkl-ar-ı`** | 7.5 | `ar` |
| galitsina | **`galitsi-n-a`** | 7.5 | `n` |
| futbolshılardı | **`futbolshıl-ar-dı`** | 7.5 | `ar` |
| kolonnası | **`kolon-na-sı`** | 7.5 | `na` |
| redaktorlarda | **`redaktorl-ar-da`** | 7.5 | `ar` |
| sanktgallendaǵı | **`sanktgallen-da-ǵı`** | 7.5 | `da` |
| abdujalil | **`abdujal-i-l`** | 7.5 | `i` |
| singlların | **`singll-ar-ın`** | 7.5 | `ar` |
| zanjibarda | **`zanjib-ar-da`** | 7.5 | `ar` |
| kóringenindey | **`kóringenin-de-y`** | 7.5 | `de` |
| nuqsanların | **`nuqsanl-ar-ın`** | 7.5 | `ar` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kara-Kalpak 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 (5.23x) |
| N-gram | **2-gram** | Lowest perplexity (339) |
| Markov | **Context-4** | Highest predictability (98.5%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-10 07:05:40*