---
language: os
language_name: Ossetic
language_family: iranian_eastern
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-iranian_eastern
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: 3.901
  - name: best_isotropy
    type: isotropy
    value: 0.7990
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ossetic** 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** | 3.279x | 3.29 | 0.2317% | 140,728 |
| **16k** | 3.535x | 3.54 | 0.2497% | 130,553 |
| **32k** | 3.746x | 3.75 | 0.2646% | 123,211 |
| **64k** | 3.901x 🏆 | 3.91 | 0.2756% | 118,301 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Тахъазты Фидар. Дыгурон-уырыссаг дзырдуат — Аланыстон, (, ) — хуыз.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁тахъазты ▁фидар . ▁дыгурон - уырыссаг ▁дзырдуат ▁— ▁аланыстон , ... (+5 more)` | 15 |
| 16k | `▁тахъазты ▁фидар . ▁дыгурон - уырыссаг ▁дзырдуат ▁— ▁аланыстон , ... (+5 more)` | 15 |
| 32k | `▁тахъазты ▁фидар . ▁дыгурон - уырыссаг ▁дзырдуат ▁— ▁аланыстон , ... (+5 more)` | 15 |
| 64k | `▁тахъазты ▁фидар . ▁дыгурон - уырыссаг ▁дзырдуат ▁— ▁аланыстон , ... (+5 more)` | 15 |

**Sample 2:** `дон у Ирыстоны, рахиз Цагъаты Анастасия. Ирыстоны топоними. хай. Ирыстоны`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁дон ▁у ▁ирыстоны , ▁рахиз ▁цагъаты ▁анастасия . ▁ирыстоны ▁топоними ... (+4 more)` | 14 |
| 16k | `▁дон ▁у ▁ирыстоны , ▁рахиз ▁цагъаты ▁анастасия . ▁ирыстоны ▁топоними ... (+4 more)` | 14 |
| 32k | `▁дон ▁у ▁ирыстоны , ▁рахиз ▁цагъаты ▁анастасия . ▁ирыстоны ▁топоними ... (+4 more)` | 14 |
| 64k | `▁дон ▁у ▁ирыстоны , ▁рахиз ▁цагъаты ▁анастасия . ▁ирыстоны ▁топоними ... (+4 more)` | 14 |

**Sample 3:** `ХуыбарцЦагаева А. Дз. Топонимия Северной Осетии — Владикавказ: Ир, — с. 623. у н...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁хуы бар ццаг аева ▁а . ▁дз . ▁топонимия ▁северной ... (+24 more)` | 34 |
| 16k | `▁хуы бар ццаг аева ▁а . ▁дз . ▁топонимия ▁северной ... (+24 more)` | 34 |
| 32k | `▁хуы бар ццаг аева ▁а . ▁дз . ▁топонимия ▁северной ... (+23 more)` | 33 |
| 64k | `▁хуы бар ццаг аева ▁а . ▁дз . ▁топонимия ▁северной ... (+22 more)` | 32 |


### Key Findings

- **Best Compression:** 64k achieves 3.901x compression
- **Lowest UNK Rate:** 8k with 0.2317% 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 | 3,788 | 11.89 | 11,541 | 24.3% | 55.4% |
| **2-gram** | Subword | 406 🏆 | 8.67 | 3,916 | 57.9% | 97.2% |
| **3-gram** | Word | 2,985 | 11.54 | 11,245 | 29.5% | 61.0% |
| **3-gram** | Subword | 3,147 | 11.62 | 27,926 | 23.4% | 65.1% |
| **4-gram** | Word | 4,436 | 12.12 | 19,787 | 27.9% | 56.3% |
| **4-gram** | Subword | 13,689 | 13.74 | 117,148 | 13.3% | 40.0% |
| **5-gram** | Word | 3,339 | 11.71 | 15,120 | 31.1% | 60.3% |
| **5-gram** | Subword | 32,155 | 14.97 | 219,588 | 10.1% | 30.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `административон центр` | 3,450 |
| 2 | `хуссар ирыстоны` | 2,544 |
| 3 | `у сахар` | 2,437 |
| 4 | `з д` | 1,539 |
| 5 | `центр у` | 1,478 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `административон центр у` | 1,464 |
| 2 | `з д ирон` | 1,320 |
| 3 | `йæ административон центр` | 1,314 |
| 4 | `2 аг рауагъд` | 1,181 |
| 5 | `рауагъд цхинвал республика` | 1,177 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `йæ административон центр у` | 1,306 |
| 2 | `аг рауагъд цхинвал республика` | 1,177 |
| 3 | `ирон 2 аг рауагъд` | 1,177 |
| 4 | `2 аг рауагъд цхинвал` | 1,177 |
| 5 | `д ирон 2 аг` | 1,177 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `2 аг рауагъд цхинвал республика` | 1,177 |
| 2 | `ирон 2 аг рауагъд цхинвал` | 1,177 |
| 3 | `д ирон 2 аг рауагъд` | 1,177 |
| 4 | `з д ирон 2 аг` | 1,177 |
| 5 | `аг рауагъд цхинвал республика 372` | 1,167 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы _` | 115,086 |
| 2 | `о н` | 67,122 |
| 3 | `. _` | 57,323 |
| 4 | `с т` | 50,166 |
| 5 | `, _` | 48,007 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `о н _` | 33,294 |
| 2 | `т ы _` | 26,081 |
| 3 | `_ — _` | 23,993 |
| 4 | `_ æ м` | 20,395 |
| 5 | `æ м æ` | 20,225 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ æ м æ` | 20,051 |
| 2 | `æ м æ _` | 19,557 |
| 3 | `о н ы _` | 10,876 |
| 4 | `_ й æ _` | 10,577 |
| 5 | `с т о н` | 9,896 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ æ м æ _` | 19,383 |
| 2 | `ы с т о н` | 9,292 |
| 3 | `с т о н ы` | 8,183 |
| 4 | `_ а з ы _` | 7,933 |
| 5 | `р ы с т о` | 7,533 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 406
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.6700 | 1.591 | 4.34 | 68,503 | 33.0% |
| **1** | Subword | 1.2100 | 2.313 | 9.73 | 927 | 0.0% |
| **2** | Word | 0.2070 | 1.154 | 1.45 | 292,738 | 79.3% |
| **2** | Subword | 1.1075 | 2.155 | 6.21 | 9,001 | 0.0% |
| **3** | Word | 0.0537 | 1.038 | 1.09 | 416,198 | 94.6% |
| **3** | Subword | 0.8368 | 1.786 | 3.82 | 55,801 | 16.3% |
| **4** | Word | 0.0178 🏆 | 1.012 | 1.03 | 443,373 | 98.2% |
| **4** | Subword | 0.5695 | 1.484 | 2.37 | 212,713 | 43.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `æмæ xviii та сæ арараты хох ирыстоны ацыдис райгуырдысты мамсыраты темырболат турчы сахар конгойы ко...`
2. `у сахар свердловсчы сергийы чызг куы сты 10 48 кандемир kandemir 31 матчы дæр ныззаууат азы`
3. `йæ административон центр у индонезийы амалхъомады архайын амарыныл йæ линник æмæ дæр кодтой æмæ дугт...`

**Context Size 2:**

1. `хуссар ирыстоны закъон ирон мыггагон ирон иууон номхыгъд сты ирон мыггаг æмæ уырым пага тотыкк абоны...`
2. `у сахар челябинсчы ис ашайы районы административон центр азы онг уыцы хуыдтой уыцы хонын байдыдтой у...`
3. `административон центр у сахар ис брабанты провинцийы административон центр аквитанийы`

**Context Size 3:**

1. `административон центр у чарльз таун вирджинийы`
2. `з д ирон 2 аг рауагъд цхинвал республика 372 с сты ирон мыггаг хъантемыраты алибег æмæ йæ династи`
3. `йæ административон центр у худжанд`

**Context Size 4:**

1. `йæ административон центр у нагасаки`
2. `аг рауагъд цхинвал республика 372 с ныхас сост р с кантемирова наукон ред джусойты нафи ир 263 ф сты`
3. `2 аг рауагъд цхинвал республика 372 с сты ирон мыггаг æмæ сты мыггаг уыд сæ дæр уыд чеселты комы`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_рд._уысистры_р_`
2. `ардтисовис.и)_лц`
3. `ы_ф_аданом_цин_с`

**Context Size 2:**

1. `ы_мыгуый_æм_казон`
2. `он_(райгуырыстор,`
3. `._аслогонограты_а`

**Context Size 3:**

1. `он_дих_кодтой,_уым`
2. `ты_империйы_седерл`
3. `_—_458_с._истас_ко`

**Context Size 4:**

1. `æмæ_симиля»_«жизнью`
2. `_æмæ_георгийы_азы_2`
3. `оны_районы,_созыры_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (212,713 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 | 26,680 |
| Total Tokens | 558,043 |
| Mean Frequency | 20.92 |
| Median Frequency | 3 |
| Frequency Std Dev | 234.02 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | æмæ | 20,225 |
| 2 | у | 19,112 |
| 3 | йæ | 10,772 |
| 4 | азы | 9,341 |
| 5 | ирыстоны | 6,756 |
| 6 | ирон | 6,567 |
| 7 | сахар | 4,914 |
| 8 | ис | 4,518 |
| 9 | и | 4,222 |
| 10 | районы | 4,121 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | вазыгджындӕр | 2 |
| 2 | мардан | 2 |
| 3 | бернет | 2 |
| 4 | бастроп | 2 |
| 5 | ллано | 2 |
| 6 | мейсон | 2 |
| 7 | лампасас | 2 |
| 8 | накодочес | 2 |
| 9 | чирцъинайы | 2 |
| 10 | какета | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1191 |
| R² (Goodness of Fit) | 0.996097 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.2% |
| Top 1,000 | 70.4% |
| Top 5,000 | 86.6% |
| Top 10,000 | 92.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9961 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.2% of corpus
- **Long Tail:** 16,680 words needed for remaining 7.6% 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 | 0.7990 🏆 | 0.3569 | N/A | N/A |
| **mono_64d** | 64 | 0.5337 | 0.3206 | N/A | N/A |
| **mono_128d** | 128 | 0.1178 | 0.3107 | N/A | N/A |
| **aligned_32d** | 32 | 0.7990 | 0.3615 | 0.0140 | 0.1100 |
| **aligned_64d** | 64 | 0.5337 | 0.3182 | 0.0180 | 0.1460 |
| **aligned_128d** | 128 | 0.1178 | 0.3127 | 0.0540 | 0.2240 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7990 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3301. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.4% 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 | **1.006** | 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 |
|--------|----------|
| `-с` | сылгоймаджы, суарх, соня |
| `-а` | архипелаг, абалц, аллонты |
| `-к` | кларк, куры, кады |
| `-б` | биту, балаш, бидары |
| `-м` | медзилаборце, моисеев, мамытты |
| `-д` | джебетъа, дзау, дауыраты |
| `-т` | тырсыгом, трансильвани, тъилиана |
| `-ба` | балаш, бакусыны, батиста |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ы` | сылгоймаджы, рауайы, ратдзысты |
| `-н` | гурджаан, актуалон, оккупацион |
| `-йы` | рауайы, пиерийы, росариойы |
| `-ты` | ратдзысты, аллонты, африканерты |
| `-он` | актуалон, оккупацион, микрофинансон |
| `-и` | лариджани, эстели, трансильвани |
| `-а` | пирканмаа, джебетъа, сота |
| `-й` | владикавказский, калий, рафыстой |

### 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 |
|------|----------|------------------|----------|
| `дтой` | 2.00x | 22 contexts | радтой, ардтой, уыдтой |
| `ысты` | 1.84x | 25 contexts | ыстыр, фысты, мысты |
| `кодт` | 1.92x | 21 contexts | кодта, кодтой, кодтон |
| `ахар` | 1.92x | 20 contexts | сахар, махар, шахар |
| `дыст` | 1.94x | 18 contexts | цыдысты, уадысты, равдыст |
| `ыдис` | 1.90x | 17 contexts | уыдис, цыдис, ссыдис |
| `цент` | 1.89x | 17 contexts | центр, центы, центра |
| `райо` | 2.16x | 10 contexts | район, райони, районе |
| `гуыр` | 1.50x | 27 contexts | гуыры, гуырд, агуырд |
| `айон` | 1.83x | 14 contexts | хайон, район, райони |
| `истр` | 1.91x | 12 contexts | бистра, истрийы, министр |
| `ентр` | 2.07x | 8 contexts | центр, центра, центре |

### 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 |
|--------|--------|-----------|----------|
| `-к` | `-ы` | 203 words | конфедерацийы, кизилюрты |
| `-с` | `-ы` | 138 words | сконды, слесыры |
| `-б` | `-ы` | 126 words | банымайыны, бицъоты |
| `-а` | `-ы` | 118 words | алексейы, азары |
| `-м` | `-ы` | 112 words | малайзийы, муганы |
| `-д` | `-ы` | 105 words | димитровы, дзидзайы |
| `-т` | `-ы` | 100 words | тлаты, туркманчайы |
| `-г` | `-ы` | 97 words | гроднойы, габысаты |
| `-п` | `-ы` | 69 words | перуйы, парадоксы |
| `-к` | `-ты` | 64 words | кизилюрты, къониаты |

### 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 |
|------|-----------------|------------|------|
| музыканты | **`музыка-н-ты`** | 7.5 | `н` |
| комплексной | **`комплекс-н-ой`** | 7.5 | `н` |
| фыртыфырт | **`фыртыфы-р-т`** | 7.5 | `р` |
| бердзейнаг | **`бердзей-н-аг`** | 7.5 | `н` |
| беджызаты | **`беджыз-а-ты`** | 7.5 | `а` |
| административно | **`административ-н-о`** | 7.5 | `н` |
| чырыстонады | **`чырыстон-ад-ы`** | 6.0 | `чырыстон` |
| тырысатыл | **`тырыса-ты-л`** | 6.0 | `тырыса` |
| куыстадон | **`куыст-ад-он`** | 6.0 | `куыст` |
| кастилиаг | **`касти-ли-аг`** | 6.0 | `касти` |
| александрияйы | **`александр-ия-йы`** | 6.0 | `александр` |
| дзаумайыл | **`дзаума-йы-л`** | 6.0 | `дзаума` |
| рынчынтыл | **`рынчын-ты-л`** | 6.0 | `рынчын` |
| информационные | **`информацион-ны-е`** | 6.0 | `информацион` |
| сальвадораг | **`сальвадор-аг`** | 4.5 | `сальвадор` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ossetic 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 (3.90x) |
| N-gram | **2-gram** | Lowest perplexity (406) |
| Markov | **Context-4** | Highest predictability (98.2%) |
| 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: 2026-01-10 17:09:46*