README.md

---
language: ady
language_name: Adyghe
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: 4.197
  - name: best_isotropy
    type: isotropy
    value: 0.4880
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Adyghe** 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** | 3.406x | 3.41 | 0.1685% | 137,125 |
| **16k** | 3.759x | 3.76 | 0.1859% | 124,248 |
| **32k** | 4.197x 🏆 | 4.20 | 0.2076% | 111,273 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ермэлхэр — Кавказым ыкӏи дунаем тет лъэпкъ жъыдэдэмэ ащыщых. Армение`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ермэлхэр ▁— ▁кавказым ▁ыкӏи ▁дунаем ▁тет ▁лъэпкъ ▁жъыдэдэмэ ▁ащыщых . ... (+1 more)` | 11 |
| 16k | `▁ермэлхэр ▁— ▁кавказым ▁ыкӏи ▁дунаем ▁тет ▁лъэпкъ ▁жъыдэдэмэ ▁ащыщых . ... (+1 more)` | 11 |
| 32k | `▁ермэлхэр ▁— ▁кавказым ▁ыкӏи ▁дунаем ▁тет ▁лъэпкъ ▁жъыдэдэмэ ▁ащыщых . ... (+1 more)` | 11 |

**Sample 2:** `ТӀэшъу Светлан (УрысыбзэкӀэ: Светлана Тешева) Адыгэ журналист Адыгеим щыщ.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁тӏэ шъу ▁светлан ▁( урысыбзэкӏэ : ▁светлан а ▁те ше ... (+7 more)` | 17 |
| 16k | `▁тӏэ шъу ▁светлан ▁( урысыбзэкӏэ : ▁светлана ▁тешева ) ▁адыгэ ... (+4 more)` | 14 |
| 32k | `▁тӏэшъу ▁светлан ▁( урысыбзэкӏэ : ▁светлана ▁тешева ) ▁адыгэ ▁журналист ... (+3 more)` | 13 |

**Sample 3:** `Ашрай - быслъымэнмэ къурмэным ыуж мэфэ гъэнэфагъэм щагъэжъорэ стырыпс. category`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁аш рай ▁- ▁быслъымэн мэ ▁къур мэным ▁ыуж ▁мэфэ ▁гъэнэф ... (+9 more)` | 19 |
| 16k | `▁аш рай ▁- ▁быслъымэн мэ ▁къурмэным ▁ыуж ▁мэфэ ▁гъэнэфагъэм ▁щагъэ ... (+4 more)` | 14 |
| 32k | `▁ашрай ▁- ▁быслъымэнмэ ▁къурмэным ▁ыуж ▁мэфэ ▁гъэнэфагъэм ▁щагъэжъорэ ▁стырыпс . ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 32k achieves 4.197x compression
- **Lowest UNK Rate:** 8k with 0.1685% 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 | 453 | 8.82 | 625 | 42.6% | 100.0% |
| **2-gram** | Subword | 407 🏆 | 8.67 | 2,126 | 56.6% | 97.3% |
| **3-gram** | Word | 759 | 9.57 | 977 | 31.6% | 100.0% |
| **3-gram** | Subword | 2,854 | 11.48 | 11,856 | 24.3% | 64.6% |
| **4-gram** | Word | 2,909 | 11.51 | 3,378 | 13.2% | 45.0% |
| **4-gram** | Subword | 10,911 | 13.41 | 36,062 | 12.4% | 39.2% |
| **5-gram** | Word | 2,658 | 11.38 | 2,950 | 12.2% | 45.6% |
| **5-gram** | Subword | 21,199 | 14.37 | 52,393 | 8.2% | 28.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `нэбгырэ млн` | 168 |
| 2 | `къехъу щэпсэу` | 104 |
| 3 | `м къехъу` | 89 |
| 4 | `дло м` | 87 |
| 5 | `адыгэ республикэм` | 80 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `м къехъу щэпсэу` | 76 |
| 2 | `къехъу щэпсэу хэгэгум` | 70 |
| 3 | `адыгэ республикэм и` | 46 |
| 4 | `дло м хахьэ` | 44 |
| 5 | `м хахьэ хэгъэгу` | 39 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `м къехъу щэпсэу хэгэгум` | 45 |
| 2 | `дло м хахьэ хэгъэгу` | 39 |
| 3 | `еуропэм хэт къэралыгъу къэлэ` | 23 |
| 4 | `америкэм ит къэралыгъу къэлэ` | 19 |
| 5 | `азием ит къэралыгъу къэлэ` | 18 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `км гъогу щыӏ къуаджэм ис` | 17 |
| 2 | `гъогу щыӏ къуаджэм ис цӏыфхэр` | 17 |
| 3 | `щыӏ къуаджэм ис цӏыфхэр илъэсхэм` | 17 |
| 4 | `къуаджэм ис цӏыфхэр илъэсхэм тетэу` | 17 |
| 5 | `ис цӏыфхэр илъэсхэм тетэу къуаджэм` | 17 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `г ъ` | 9,326 |
| 2 | `ъ э` | 9,249 |
| 3 | `э _` | 8,792 |
| 4 | `м _` | 7,740 |
| 5 | `э р` | 6,822 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `г ъ э` | 4,961 |
| 2 | `_ к ъ` | 4,140 |
| 3 | `э м _` | 3,581 |
| 4 | `ы г ъ` | 3,362 |
| 5 | `э р _` | 3,020 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы г ъ э` | 1,902 |
| 2 | `х э р _` | 1,448 |
| 3 | `а г ъ э` | 1,342 |
| 4 | `х э м _` | 1,303 |
| 5 | `_ к ъ э` | 1,289 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ а д ы г` | 1,062 |
| 2 | `а д ы г э` | 978 |
| 3 | `_ и л ъ э` | 670 |
| 4 | `д ы г э _` | 651 |
| 5 | `и л ъ э с` | 627 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 407
- **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 | 0.4341 | 1.351 | 2.09 | 22,655 | 56.6% |
| **1** | Subword | 1.4193 | 2.674 | 10.02 | 450 | 0.0% |
| **2** | Word | 0.0766 | 1.055 | 1.12 | 46,851 | 92.3% |
| **2** | Subword | 1.1376 | 2.200 | 5.57 | 4,503 | 0.0% |
| **3** | Word | 0.0248 | 1.017 | 1.04 | 51,794 | 97.5% |
| **3** | Subword | 0.7466 | 1.678 | 2.95 | 25,044 | 25.3% |
| **4** | Word | 0.0130 🏆 | 1.009 | 1.02 | 53,002 | 98.7% |
| **4** | Subword | 0.4264 | 1.344 | 1.85 | 73,859 | 57.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `и дгъэпсыфынущ адыгэ лъэпкъым и 29 м н ф ф ф ф х х х хъ`
2. `адыгэ хэхэсхэм ащыухъумэн ылъэкӏыгъ мыхъугъэ мышӏагъэхэр ыгу ит тарихъ лъапсэ иӏэу кӏэхьапӏэр ӏатау ...`
3. `м ахахьэ хэгъэгу тхьаматэр халед бахах географие еуропэм ыгу рихь римыхьмэ тетэу къуаджэм ис цӏыфхэр...`

**Context Size 2:**

1. `нэбгырэ млн 1 3 фэдиз ц1ыфэу дэс ау хьанэгъунэр ибгъэгъусэжьмэ млн 18 фэдиз мэхъу щыпсэухэрэм ромэ к...`
2. `къехъу щэпсэу я 67 норвегыбз дло м ахахьэ хэгъэгу эдгар ринкевичс къэрал тхьаматэр ульф кристерссон ...`
3. `м къехъу щэпсэу хэгэгум 1 240 192 км францыбзэ къэрал яйи бони хэгъэгу тхьаматэр халифа бен салман`

**Context Size 3:**

1. `м къехъу щэпсэу хэгэгум 147 570 км бенгалыбзэ дло м хахьэ хэгъэгу абдель азиз бутефлика къэрал тхьэм...`
2. `къехъу щэпсэу хэгэгум 140 800 км непали дло м хахьэ ез м хэхьанэу унашъо щыт ез м и`
3. `адыгэ республикэм и псыхъу а псыхъом пэблагъэу щыт къуажэ`

**Context Size 4:**

1. `м къехъу щэпсэу хэгэгум чӏырэу иӏэр 322 460 км бзэшъхьаӏэхэр францыбзэ къэрал лӏышъхьэр алассан уатт...`
2. `дло м хахьэ хэгъэгу султанэу кабоос бин саид аль саид хэгъэгу тхьаматэр фахд бин махьмуд географие а...`
3. `еуропэм хэт къэралыгъу къэлэ тирана нэбгырэ млн 3 м къехъу щэпсэу хэгэгум 9 984 670 км я 2 англыбзэ`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_шхажъырэм_ащтем`
2. `эгекъэсхэ_ари_пч`
3. `ыгу,_цинащырыхэ_`

**Context Size 2:**

1. `гъэпсыр_зэрэ_ӏуад`
2. `ъэп_ву_адыгъэхьын`
3. `э_зыгэ_ж_дангьэ_т`

**Context Size 3:**

1. `гъэкъхэр,_кӏэ,_гум`
2. `_къэралыгъэдунэжъы`
3. `эм_и_–_зэрал_нэхэр`

**Context Size 4:**

1. `ыгъэ_гъэмрэ_приручи`
2. `хэр_бжъэдыгъуапэ_зэ`
3. `агъэхьан_хуейщ,_ахэ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (73,859 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 | 7,120 |
| Total Tokens | 45,308 |
| Mean Frequency | 6.36 |
| Median Frequency | 3 |
| Frequency Std Dev | 22.08 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | и | 999 |
| 2 | адыгэ | 660 |
| 3 | м | 508 |
| 4 | илъэсым | 406 |
| 5 | ащ | 391 |
| 6 | я | 320 |
| 7 | ары | 274 |
| 8 | а | 257 |
| 9 | нэбгырэ | 250 |
| 10 | е | 223 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | muzea | 2 |
| 2 | britishpedia | 2 |
| 3 | encyklopedia | 2 |
| 4 | osobistości | 2 |
| 5 | rzeczypospolitej | 2 |
| 6 | polskiej | 2 |
| 7 | bph | 2 |
| 8 | british | 2 |
| 9 | publishing | 2 |
| 10 | ltd | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.7863 |
| R² (Goodness of Fit) | 0.977814 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 28.8% |
| Top 1,000 | 60.5% |
| Top 5,000 | 90.6% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9778 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 28.8% of corpus
- **Long Tail:** -2,880 words needed for remaining 100.0% 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 | 0.4880 | 0.4410 | N/A | N/A |
| **mono_64d** | 64 | 0.2186 | 0.3951 | N/A | N/A |
| **mono_128d** | 128 | 0.0372 | 0.3901 | N/A | N/A |
| **aligned_32d** | 32 | 0.4880 🏆 | 0.4477 | 0.0460 | 0.3851 |
| **aligned_64d** | 64 | 0.2186 | 0.3901 | 0.2011 | 0.7701 |
| **aligned_128d** | 128 | 0.0372 | 0.3927 | 0.2759 | 0.8103 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.4880 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4094. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 27.6% 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 | **0.610** | 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` | къчр, къэлэшъо, къо |
| `-зэ` | зэрэхъугъэхэм, зэфэшъхьаф, зэхигъэуцогъэгъэ |
| `-къы` | къыӏуагъ, къыщыфэфедэщтхэу, къыгъэуцугъэ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-э` | литературоведческэ, уиджыбэ, лъымрэ |
| `-м` | заповедникым, хъуагъэм, ипэм |
| `-р` | тхэныр, хунгариер, къчр |
| `-эр` | алъытэщтыгъэр, тхыбзэр, ылъэгъурэр |
| `-эм` | хъуагъэм, ипэм, псалъэжьхэм |
| `-эу` | цӏэу, дэлъэу, щысэу |
| `-хэр` | тыркухэр, ежьхэр, ахэр |
| `-рэ` | лъымрэ, цӏэмрэ, зыфиӏорэ |

### 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 |
|------|----------|------------------|----------|
| `тыгъ` | 1.84x | 28 contexts | тыгъэ, тыгъу, итыгъ |
| `эпкъ` | 1.90x | 25 contexts | нэпкъ, тхэпкъ, лъэпкъ |
| `ъагъ` | 2.25x | 14 contexts | лъагъо, пчъагъ, пчъагъэ |
| `агъэ` | 1.63x | 39 contexts | благъэ, тхагъэ, пчагъэ |
| `дыгэ` | 2.03x | 14 contexts | адыгэ, адыгэу, адыгэм |
| `къуа` | 2.23x | 10 contexts | къуае, къуажэ, къуадж |
| `эхэр` | 1.72x | 20 contexts | бэхэр, дзэхэр, усэхэр |
| `ъхьэ` | 1.84x | 16 contexts | шъхьэ, пшъхьэ, шъхьэм |
| `псэу` | 1.70x | 20 contexts | упсэу, щэпсэу, щыпсэу |
| `шъхь` | 1.61x | 23 contexts | шъхьэ, пшъхьэ, шъхьэм |
| `ыгъо` | 1.66x | 19 contexts | цыгъо, мыгъо, цыгъор |
| `гъэх` | 1.79x | 14 contexts | багъэх, яӏагъэх, тхыгъэх |

### 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` | 94 words | къохьапӏэ, къыхаутыгъэ |
| `-къ` | `-р` | 64 words | къабзэр, къызэдыхэфэныр |
| `-къ` | `-м` | 56 words | къэралыгъуэм, къунетрэм |
| `-къ` | `-эр` | 52 words | къабзэр, къуаджэхэр |
| `-зэ` | `-р` | 43 words | зэреджэхэр, зэрар |
| `-зэ` | `-м` | 41 words | зэблэтхъуным, зэрагъэтэрэзыжьыгъэм |
| `-къ` | `-эм` | 36 words | къэралыгъуэм, къунетрэм |
| `-зэ` | `-эр` | 34 words | зэреджэхэр, зэпырыбгъэзэжьынхэр |
| `-къ` | `-эу` | 33 words | къыщегъэжьагъэу, къинэу |
| `-зэ` | `-э` | 31 words | зэкъотыныгъэ, зэралэжьырэ |

### 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 |
|------|-----------------|------------|------|
| республикэмрэ | **`республик-эм-рэ`** | 6.0 | `республик` |
| макъэхэмрэ | **`макъэ-хэм-рэ`** | 6.0 | `макъэ` |
| литературэмрэ | **`литератур-эм-рэ`** | 6.0 | `литератур` |
| благъохэмрэ | **`благъо-хэм-рэ`** | 6.0 | `благъо` |
| бзылъфыгъэмрэ | **`бзылъфыгъ-эм-рэ`** | 6.0 | `бзылъфыгъ` |
| литературэр | **`литератур-эр`** | 4.5 | `литератур` |
| диалектэу | **`диалект-эу`** | 4.5 | `диалект` |
| агъэфедэрэ | **`агъэфедэ-рэ`** | 4.5 | `агъэфедэ` |
| шъхьафитэу | **`шъхьафит-эу`** | 4.5 | `шъхьафит` |
| зыкъэзыӏэтыгъэм | **`зыкъэзыӏэтыгъ-эм`** | 4.5 | `зыкъэзыӏэтыгъ` |
| ишъхъэрэмрэ | **`ишъхъ-эр-эм-рэ`** | 4.5 | `ишъхъ` |
| адэмыехэр | **`адэмые-хэр`** | 4.5 | `адэмые` |
| зэкъоуцохэу | **`зэ-къ-оуцох-эу`** | 4.5 | `оуцох` |
| ыгузэгухэм | **`ыгузэгу-хэм`** | 4.5 | `ыгузэгу` |
| беслъэнейхэр | **`беслъэней-хэр`** | 4.5 | `беслъэней` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Adyghe 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 | **32k BPE** | Best compression (4.20x) |
| N-gram | **2-gram** | Lowest perplexity (407) |
| Markov | **Context-4** | Highest predictability (98.7%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-03 18:25:02*