README.md

---
language: kbd
language_name: Kabardian
language_family: caucasian_northwest
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-caucasian_northwest
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: 4.542
  - name: best_isotropy
    type: isotropy
    value: 0.6517
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kabardian** 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** | 3.541x | 3.54 | 0.1767% | 352,078 |
| **16k** | 3.908x | 3.91 | 0.1950% | 319,043 |
| **32k** | 4.190x | 4.19 | 0.2091% | 297,527 |
| **64k** | 4.542x 🏆 | 4.55 | 0.2266% | 274,517 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Публий Овидий Назон (, 43 гъатхэпэм и 20, Сулмо — 17-18, Томис) — Урым империэм ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁п убл ий ▁о в ид ий ▁н аз он ... (+31 more)` | 41 |
| 16k | `▁публ ий ▁о в ид ий ▁наз он ▁(, ▁ ... (+29 more)` | 39 |
| 32k | `▁публий ▁о в идий ▁назон ▁(, ▁ 4 3 ▁гъатхэпэм ... (+26 more)` | 36 |
| 64k | `▁публий ▁овидий ▁назон ▁(, ▁ 4 3 ▁гъатхэпэм ▁и ▁ ... (+21 more)` | 31 |

**Sample 2:** `Адэипс () — Урысейм хэт Къэбэрдей-Балъкъэрым и щӀыпӀэм хэж псыщ Шэджэмым хэлъадэ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁адэ и пс ▁() ▁— ▁урысейм ▁хэт ▁къэбэрдей - балъкъэрым ... (+22 more)` | 32 |
| 16k | `▁адэ и пс ▁() ▁— ▁урысейм ▁хэт ▁къэбэрдей - балъкъэрым ... (+22 more)` | 32 |
| 32k | `▁адэ и пс ▁() ▁— ▁урысейм ▁хэт ▁къэбэрдей - балъкъэрым ... (+21 more)` | 31 |
| 64k | `▁адэипс ▁() ▁— ▁урысейм ▁хэт ▁къэбэрдей - балъкъэрым ▁и ▁щӏыпӏэм ... (+19 more)` | 29 |

**Sample 3:** `Шонэпс () — Урысейм хэт Къэрэшей-Шэрджэсым и щӀыпӀэм хэж псыщ Псыжъым хэлъадэу, ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ш онэ пс ▁() ▁— ▁урысейм ▁хэт ▁къэрэшей - шэрджэсым ... (+23 more)` | 33 |
| 16k | `▁ш онэ пс ▁() ▁— ▁урысейм ▁хэт ▁къэрэшей - шэрджэсым ... (+23 more)` | 33 |
| 32k | `▁ш онэ пс ▁() ▁— ▁урысейм ▁хэт ▁къэрэшей - шэрджэсым ... (+23 more)` | 33 |
| 64k | `▁шонэпс ▁() ▁— ▁урысейм ▁хэт ▁къэрэшей - шэрджэсым ▁и ▁щӏыпӏэм ... (+21 more)` | 31 |


### Key Findings

- **Best Compression:** 64k achieves 4.542x compression
- **Lowest UNK Rate:** 8k with 0.1767% 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 | 1,558 | 10.61 | 2,836 | 28.9% | 70.6% |
| **2-gram** | Subword | 394 🏆 | 8.62 | 2,782 | 58.6% | 97.2% |
| **3-gram** | Word | 1,116 | 10.12 | 2,525 | 37.0% | 74.5% |
| **3-gram** | Subword | 3,004 | 11.55 | 20,702 | 26.1% | 64.9% |
| **4-gram** | Word | 1,940 | 10.92 | 4,554 | 31.6% | 59.6% |
| **4-gram** | Subword | 13,210 | 13.69 | 77,181 | 13.2% | 39.7% |
| **5-gram** | Word | 1,471 | 10.52 | 3,389 | 34.1% | 65.4% |
| **5-gram** | Subword | 31,176 | 14.93 | 127,435 | 7.7% | 27.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `адыгэхэм я` | 416 |
| 2 | `я къуалэбзу` | 386 |
| 3 | `брат хьэсин` | 386 |
| 4 | `къуалэбзу щӏэныгъэр` | 386 |
| 5 | `тхылъхэр брат` | 299 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `адыгэхэм я къуалэбзу` | 386 |
| 2 | `я къуалэбзу щӏэныгъэр` | 386 |
| 3 | `тхылъхэр брат хьэсин` | 299 |
| 4 | `брат хьэсин адыгэхэм` | 299 |
| 5 | `хьэсин адыгэхэм я` | 299 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `адыгэхэм я къуалэбзу щӏэныгъэр` | 386 |
| 2 | `хьэсин адыгэхэм я къуалэбзу` | 299 |
| 3 | `брат хьэсин адыгэхэм я` | 299 |
| 4 | `тхылъхэр брат хьэсин адыгэхэм` | 299 |
| 5 | `я къуалэбзу щӏэныгъэр черкеск` | 211 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `хьэсин адыгэхэм я къуалэбзу щӏэныгъэр` | 299 |
| 2 | `брат хьэсин адыгэхэм я къуалэбзу` | 299 |
| 3 | `тхылъхэр брат хьэсин адыгэхэм я` | 299 |
| 4 | `адыгэхэм я къуалэбзу щӏэныгъэр черкеск` | 211 |
| 5 | `я къуалэбзу щӏэныгъэр черкеск къ` | 206 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `э _` | 32,580 |
| 2 | `м _` | 29,279 |
| 3 | `э м` | 26,549 |
| 4 | `э р` | 26,396 |
| 5 | `х э` | 25,875 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `э м _` | 16,638 |
| 2 | `_ к ъ` | 15,408 |
| 3 | `э р _` | 12,826 |
| 4 | `ъ у э` | 10,448 |
| 5 | `г ъ у` | 10,296 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `х э р _` | 6,565 |
| 2 | `г ъ у э` | 5,997 |
| 3 | `х э м _` | 5,976 |
| 4 | `м _ и _` | 4,974 |
| 5 | `э х э м` | 4,168 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ н э х ъ` | 3,022 |
| 2 | `ы г ъ у э` | 2,854 |
| 3 | `э х э р _` | 2,785 |
| 4 | `э х э м _` | 2,662 |
| 5 | `х э м _ я` | 2,645 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 394
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.5371 | 1.451 | 2.80 | 58,099 | 46.3% |
| **1** | Subword | 1.1013 | 2.145 | 8.35 | 788 | 0.0% |
| **2** | Word | 0.1119 | 1.081 | 1.19 | 162,358 | 88.8% |
| **2** | Subword | 1.0773 | 2.110 | 6.05 | 6,578 | 0.0% |
| **3** | Word | 0.0277 | 1.019 | 1.04 | 192,783 | 97.2% |
| **3** | Subword | 0.8756 | 1.835 | 3.66 | 39,780 | 12.4% |
| **4** | Word | 0.0099 🏆 | 1.007 | 1.01 | 199,396 | 99.0% |
| **4** | Subword | 0.5274 | 1.441 | 2.15 | 145,401 | 47.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `и нэхъыбэм къэрал хуит ящӏат адыгэ къуэджэхэм щыропсалъэ къаджищыр ашхаруа псалъэкӏэ йоджэ щопсэу ӏу...`
2. `я нэхъыбапӏэм административнэ сыхьэт чым пэщхъан адыгэ мазэцӏэхэр къипсэлъу къыгурыӏуэу ди лъэхъэнэм...`
3. `нэхъ ину щыт шъхьао хуэкӏэкӏыу къэрууфӏу итхьакӏумэхэр инкъым теплъэр нэхъыщхьэу хьэпщхупщ лъэпкъхэр...`

**Context Size 2:**

1. `адыгэхэм я къуалэбзу щӏэныгъэр черкесск гъ теплъэхэр лъэпкъхэр`
2. `къуалэбзу щӏэныгъэр черкеск къ гъ лъэпкъыр лъэпкъэгъухэр`
3. `брат хьэсин адыгэхэм я къуалэбзу щӏэныгъэр брат хьэсин черкесск гъ лъэпкъыр лъэпкъхэр`

**Context Size 3:**

1. `адыгэхэм я къуалэбзу щӏэныгъэр черкесск гъ теплъэхэр лъэпкъхэр`
2. `я къуалэбзу щӏэныгъэр черкеск къ гъ лъэпкъхэр лъэпкъыр`
3. `брат хьэсин адыгэхэм я къуалэбзу щӏэныгъэр черкесск гъ теплъэхэр хэкӏыгъуэхэр`

**Context Size 4:**

1. `адыгэхэм я къуалэбзу щӏэныгъэр черкеск къ гъ лъэпкъэгъухэр лъэпкъыр`
2. `брат хьэсин адыгэхэм я къуалэбзу щӏэныгъэр черкесск гъ хэкӏыгъуэхэр теплъэхэр`
3. `хьэсин адыгэхэм я къуалэбзу щӏэныгъэр черкеск къ гъ хэкӏыгъуэр лъэпкъхэр`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ргаууе_кӏыр_я_д`
2. `эр_зуэконгуэр_ɬʼ`
3. `ыхьэкӏыхъагу_сей`

**Context Size 2:**

1. `э_амазововой_идж_`
2. `м_нэм_щӏауэдардей`
3. `эм_щӏэубгъуэсилым`

**Context Size 3:**

1. `эм_и_литекӏэ,_абгъ`
2. `_къэошӏукӏэ_абы_ещ`
3. `эр_антар_иужь_кал_`

**Context Size 4:**

1. `хэр_и_нэхуаку,_налщ`
2. `хэм_я_нэхъ_инщ._апх`
3. `гъуэжь_лэчтхыгъэр_а`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (145,401 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 | 18,198 |
| Total Tokens | 179,236 |
| Mean Frequency | 9.85 |
| Median Frequency | 3 |
| Frequency Std Dev | 74.58 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | и | 8,299 |
| 2 | я | 3,463 |
| 3 | нэхъ | 1,395 |
| 4 | гъэм | 1,150 |
| 5 | хы | 930 |
| 6 | м | 915 |
| 7 | а | 847 |
| 8 | хэт | 669 |
| 9 | зы | 634 |
| 10 | км | 602 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | дэплъейр | 2 |
| 2 | хьэзыр | 2 |
| 3 | мэгурым | 2 |
| 4 | мывэр | 2 |
| 5 | уанэр | 2 |
| 6 | хабзэрэ | 2 |
| 7 | шыдым | 2 |
| 8 | зылъагъур | 2 |
| 9 | бзыпхъэ | 2 |
| 10 | куб | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9480 |
| R² (Goodness of Fit) | 0.991228 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 26.5% |
| Top 1,000 | 56.6% |
| Top 5,000 | 80.3% |
| Top 10,000 | 90.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9912 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 26.5% of corpus
- **Long Tail:** 8,198 words needed for remaining 9.5% 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 | 0.6517 | 0.3536 | N/A | N/A |
| **mono_64d** | 64 | 0.2166 | 0.3347 | N/A | N/A |
| **mono_128d** | 128 | 0.0438 | 0.3380 | N/A | N/A |
| **aligned_32d** | 32 | 0.6517 🏆 | 0.3583 | 0.0120 | 0.1220 |
| **aligned_64d** | 64 | 0.2166 | 0.3384 | 0.0260 | 0.1680 |
| **aligned_128d** | 128 | 0.0438 | 0.3433 | 0.0440 | 0.1920 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6517 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3444. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.4% 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 | **1.374** | 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 |
|--------|----------|
| `-къ` | къыкӏожыр, къупщхьэм, къакӏуэ |
| `-к` | куб, къыкӏожыр, къупщхьэм |
| `-п` | півострова, пурус, парку |
| `-а` | абгъуэр, атлантикэ, амазонэхэм |
| `-и` | икӏагъыр, ихахэм, иӏыгъыр |
| `-б` | бжыгъэри, бджэхьашъхьам, бзыр |
| `-зэ` | зэфӏэувэныгъэ, зэрщыту, зэхуакухэм |
| `-х` | хэхъурэ, хъыбарылъэ, хэтхэмрэ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-э` | хэхъурэ, хъыбарылъэ, убыхыбзэ |
| `-м` | щытехьэм, ихахэм, къупщхьэм |
| `-р` | икӏагъыр, абгъуэр, къыкӏожыр |
| `-эм` | щытехьэм, ихахэм, къупщхьэм |
| `-эр` | абгъуэр, гуэрэнхэр, ӏутхэр |
| `-у` | къимыгъану, хэтху, шху |
| `-ым` | ишхкъым, виетнамым, сыбырым |
| `-ӏэ` | ищӏагъымкӏэ, гъэмахуэкӏэ, бгъухэмкӏэ |

### 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 |
|------|----------|------------------|----------|
| `ыгъэ` | 1.62x | 51 contexts | шыгъэ, тыгъэ, дыгъэ |
| `агъэ` | 1.71x | 40 contexts | уагъэ, дагъэ, дагъэр |
| `эпкъ` | 1.83x | 31 contexts | нэпкъ, жэпкъ, лэпкъ |
| `эхэм` | 1.49x | 68 contexts | жэхэм, пэхэм, дэхэм |
| `эхэр` | 1.57x | 54 contexts | фэхэр, нэхэр, сэхэр |
| `шъхь` | 1.63x | 35 contexts | шъхьэ, ишъхьэ, шъхьэм |
| `эгъу` | 1.46x | 52 contexts | жэгъу, нэгъу, мэгъу |
| `ыгъу` | 1.47x | 47 contexts | шыгъу, яӏыгъу, мыгъуэ |
| `ъэра` | 2.08x | 14 contexts | къэрал, гъэращ, гъэрауэ |
| `эхъу` | 1.41x | 43 contexts | мэхъу, нэхъу, мэхъур |
| `эхъы` | 1.71x | 21 contexts | нэхъыжъ, нэхъыжь, нэхъыбэ |
| `къым` | 1.44x | 34 contexts | пкъым, инкъым, ипкъым |

### 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 |
|--------|--------|-----------|----------|
| `-къ` | `-э` | 154 words | къашыргъэгъуабжэ, къамэ |
| `-къ` | `-р` | 105 words | къодор, къызэрагъэсэбэпыр |
| `-п` | `-э` | 95 words | плӏыуэ, псыӏуфэ |
| `-х` | `-э` | 94 words | хымрэ, хухуабжэ |
| `-п` | `-м` | 86 words | пэкъыухэм, прусиэм |
| `-къ` | `-м` | 84 words | къущхьэхэм, къуэхьэпӏэм |
| `-и` | `-э` | 80 words | испаныбзэкӏэ, ицӏэ |
| `-зэ` | `-э` | 80 words | зэмылӏаужыгъуэ, зэригъэунэхумкӏэ |
| `-къ` | `-у` | 80 words | къэлэлэху, къыгъану |
| `-т` | `-э` | 79 words | техуауэ, таукъуэ |

### 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 |
|------|-----------------|------------|------|
| здэпсомрэ | **`здэпсо-м-рэ`** | 7.5 | `м` |
| ухуэмеймэ | **`ухуэмей-м-э`** | 7.5 | `м` |
| ирихьэлӏэу | **`ирихьэл-ӏэ-у`** | 7.5 | `ӏэ` |
| мэзджэдщхьэтумэ | **`мэзджэдщхьэту-м-э`** | 7.5 | `м` |
| ягъэлъапӏэт | **`ягъэлъап-ӏэ-т`** | 7.5 | `ӏэ` |
| уругуаимрэ | **`уругуаи-м-рэ`** | 7.5 | `м` |
| щӏыӏэтыӏэщ | **`щӏыӏэты-ӏэ-щ`** | 7.5 | `ӏэ` |
| виетнамым | **`виетна-м-ым`** | 7.5 | `м` |
| шъхьафхэу | **`шъхьаф-хэ-у`** | 7.5 | `хэ` |
| абдежьхэм | **`абдежь-хэ-м`** | 7.5 | `хэ` |
| раджбаромэ | **`раджбаро-м-э`** | 7.5 | `м` |
| праягамрэ | **`праяга-м-рэ`** | 7.5 | `м` |
| къаукъазми | **`къаукъаз-м-и`** | 7.5 | `м` |
| цитоплазмэ | **`цитоплаз-м-э`** | 7.5 | `м` |
| цӏэрыӏуэт | **`цӏэрыӏу-э-т`** | 6.0 | `цӏэрыӏу` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kabardian 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 (4.54x) |
| N-gram | **2-gram** | Lowest perplexity (394) |
| Markov | **Context-4** | Highest predictability (99.0%) |
| 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 07:17:37*