---
language: mk
language_name: Macedonian
language_family: slavic_south
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-slavic_south
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: 4.780
  - name: best_isotropy
    type: isotropy
    value: 0.7374
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Macedonian** 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** | 3.702x | 3.70 | 0.0702% | 2,405,262 |
| **16k** | 4.123x | 4.12 | 0.0782% | 2,159,772 |
| **32k** | 4.494x | 4.49 | 0.0852% | 1,981,404 |
| **64k** | 4.780x 🏆 | 4.78 | 0.0906% | 1,862,766 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `година во архитектурата содржи некои значајни настани. Настани во архитектурата ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+3 more)` | 13 |
| 16k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+3 more)` | 13 |
| 32k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+3 more)` | 13 |
| 64k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+3 more)` | 13 |

**Sample 2:** `година во архитектурата содржи некои значајни настани. Настани во архитектурата`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+1 more)` | 11 |
| 16k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+1 more)` | 11 |
| 32k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+1 more)` | 11 |
| 64k | `▁година ▁во ▁архитектурата ▁содржи ▁некои ▁значајни ▁настани . ▁настани ▁во ... (+1 more)` | 11 |

**Sample 3:** `31 мај — 151-иот ден во годината според грегоријанскиот календар (152-и во прест...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 3 1 ▁мај ▁— ▁ 1 5 1 - ... (+33 more)` | 43 |
| 16k | `▁ 3 1 ▁мај ▁— ▁ 1 5 1 - ... (+32 more)` | 42 |
| 32k | `▁ 3 1 ▁мај ▁— ▁ 1 5 1 - ... (+32 more)` | 42 |
| 64k | `▁ 3 1 ▁мај ▁— ▁ 1 5 1 - ... (+32 more)` | 42 |


### Key Findings

- **Best Compression:** 64k achieves 4.780x compression
- **Lowest UNK Rate:** 8k with 0.0702% 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 | 148,118 | 17.18 | 1,246,589 | 7.0% | 19.9% |
| **2-gram** | Subword | 310 🏆 | 8.28 | 17,556 | 66.9% | 98.2% |
| **3-gram** | Word | 382,752 | 18.55 | 2,398,097 | 4.7% | 17.5% |
| **3-gram** | Subword | 2,638 | 11.37 | 153,828 | 27.1% | 68.9% |
| **4-gram** | Word | 605,602 | 19.21 | 3,842,232 | 4.8% | 19.7% |
| **4-gram** | Subword | 15,114 | 13.88 | 929,390 | 13.0% | 37.7% |
| **5-gram** | Word | 281,875 | 18.10 | 2,561,910 | 6.9% | 27.5% |
| **5-gram** | Subword | 61,546 | 15.91 | 3,120,609 | 6.8% | 22.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `во година` | 270,904 |
| 2 | `да се` | 185,526 |
| 3 | `може да` | 82,758 |
| 4 | `исто така` | 74,629 |
| 5 | `година во` | 71,130 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `од страна на` | 47,837 |
| 2 | `п н е` | 45,911 |
| 3 | `за време на` | 45,528 |
| 4 | `во текот на` | 44,568 |
| 5 | `може да се` | 38,713 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `г п н е` | 26,767 |
| 2 | `во текот на и` | 13,167 |
| 3 | `година од страна на` | 13,039 |
| 4 | `база на податоци на` | 10,253 |
| 5 | `е вклучен и во` | 10,177 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `новиот општ каталог на длабоконебесни` | 10,166 |
| 2 | `општ каталог на длабоконебесни тела` | 10,166 |
| 3 | `тоа е вклучен и во` | 10,165 |
| 4 | `е вклучен и во други` | 10,165 |
| 5 | `вршено од повеќе истражувачи па` | 10,165 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 16,220,828 |
| 2 | `н а` | 9,755,201 |
| 3 | `о _` | 8,545,001 |
| 4 | `и _` | 8,299,189 |
| 5 | `_ н` | 7,088,266 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н а _` | 5,782,550 |
| 2 | `_ н а` | 5,471,722 |
| 3 | `_ в о` | 2,895,397 |
| 4 | `в о _` | 2,774,290 |
| 5 | `а т а` | 2,545,500 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ н а _` | 3,968,376 |
| 2 | `_ в о _` | 2,496,500 |
| 3 | `а т а _` | 2,159,054 |
| 4 | `и т е _` | 1,510,803 |
| 5 | `_ о д _` | 1,503,838 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _ н а _` | 1,123,156 |
| 2 | `_ г о д и` | 801,639 |
| 3 | `г о д и н` | 793,128 |
| 4 | `о д и н а` | 717,809 |
| 5 | `а _ в о _` | 641,767 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 310
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.9313 | 1.907 | 11.18 | 1,397,869 | 6.9% |
| **1** | Subword | 0.9537 | 1.937 | 6.98 | 8,643 | 4.6% |
| **2** | Word | 0.3725 | 1.295 | 2.41 | 15,610,954 | 62.7% |
| **2** | Subword | 0.7745 | 1.711 | 5.49 | 60,305 | 22.6% |
| **3** | Word | 0.1516 | 1.111 | 1.34 | 37,555,740 | 84.8% |
| **3** | Subword | 0.8197 | 1.765 | 4.77 | 330,722 | 18.0% |
| **4** | Word | 0.0598 🏆 | 1.042 | 1.11 | 50,433,239 | 94.0% |
| **4** | Subword | 0.7470 | 1.678 | 3.67 | 1,576,045 | 25.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `на минотаурот најстарото болничко лекување на електронот може да го ставаат во ноември се од овие`
2. `во г п н е независна држава за аварите да се случиле неколку минути по неколку`
3. `и надгледувајќи радикални реакции како и главен увозник skycom сад и во романија историјата како ugc`

**Context Size 2:**

1. `во година во полска и украина реката е 117 км2 дитмаршен 132 965 1 861 година пред`
2. `да се натпреварува водачи на земјата развојот на препарати за атрофичната кожа многу поширок опфат т...`
3. `може да има изразени оддавања на стронциум и алуминиум изопрооксиди соодветно првиот е анонимното ск...`

**Context Size 3:**

1. `од страна на данците кои се подолги од аксијалната пиридилна ga n врска со должини на страните а`
2. `за време на вечерата иван илич е веќе многу пијан кога линдорф влегува со пејачката стела и го`
3. `во текот на 367 и 368 исламска година настани 1 јануари ссср започнува со својата хуманитарна активн...`

**Context Size 4:**

1. `г п н е според продолжениот јулијански календар истата трае во текот на и година според асирскиот ка...`
2. `во текот на и година според асирскиот календар во којшто мерењето на времето започнува со 622 година...`
3. `година од страна на бугарските истражувачи генеричките лекови го формираат столбот на локалната екон...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_о_зна_скан_идо_`
2. `а._во_и_нина_н_с`
3. `ова_дичеме_на_ка`

**Context Size 2:**

1. `а_изенизвине_на_м`
2. `на_доне_перетски_`
3. `о_улигна_арларист`

**Context Size 3:**

1. `на_јанско-лисковек`
2. `_на_ост_попрата_же`
3. `_во_френ_каквиот_п`

**Context Size 4:**

1. `_на_чашките_заливор`
2. `_во_сличн_кривале_д`
3. `ата_долна_свињарски`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,576,045 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 | 629,840 |
| Total Tokens | 66,539,192 |
| Mean Frequency | 105.64 |
| Median Frequency | 4 |
| Frequency Std Dev | 7439.52 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | на | 3,984,194 |
| 2 | во | 2,517,366 |
| 3 | и | 2,001,305 |
| 4 | од | 1,514,717 |
| 5 | се | 1,235,287 |
| 6 | за | 987,031 |
| 7 | со | 823,175 |
| 8 | е | 782,070 |
| 9 | година | 672,383 |
| 10 | да | 610,844 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | калеуче | 2 |
| 2 | chiloé | 2 |
| 3 | преживениот | 2 |
| 4 | делевиш | 2 |
| 5 | platessoides | 2 |
| 6 | pleco | 2 |
| 7 | метарма | 2 |
| 8 | алалаона | 2 |
| 9 | octodecimguttata | 2 |
| 10 | домбасл | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9604 |
| R² (Goodness of Fit) | 0.996757 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 37.1% |
| Top 1,000 | 56.3% |
| Top 5,000 | 72.8% |
| Top 10,000 | 79.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9968 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 37.1% of corpus
- **Long Tail:** 619,840 words needed for remaining 20.2% 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 | 0.7374 | 0.3633 | N/A | N/A |
| **mono_64d** | 64 | 0.7024 | 0.2990 | N/A | N/A |
| **mono_128d** | 128 | 0.6203 | 0.2691 | N/A | N/A |
| **aligned_32d** | 32 | 0.7374 🏆 | 0.3635 | 0.1520 | 0.5340 |
| **aligned_64d** | 64 | 0.7024 | 0.2953 | 0.2380 | 0.6560 |
| **aligned_128d** | 128 | 0.6203 | 0.2655 | 0.3760 | 0.7180 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7374 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3093. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 37.6% 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 | **0.225** | 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` | стенливил, североисточен, салминен |
| `-ка` | кантрел, кач, католски |
| `-а` | аргас, азилантите, акнисте |
| `-ма` | мамуци, мажените, маринадата |
| `-по` | помориска, подјазичната, положат |
| `-к` | кантрел, кладошница, коинон |
| `-ко` | коинон, кошланд, копродукт |
| `-s` | sbordone, superluminal, stralsunder |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | душевина, електроника, пијаната |
| `-и` | издатоци, рудници, гликобелковини |
| `-е` | најневообичаените, субкултурните, царице |
| `-те` | најневообичаените, субкултурните, регистраторите |
| `-та` | пијаната, проверката, подјазичната |
| `-т` | еукариот, реверсот, меѓупарламентарниот |
| `-от` | еукариот, реверсот, меѓупарламентарниот |
| `-о` | витешкото, интимно, пароло |

### 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 |
|------|----------|------------------|----------|
| `уваа` | 2.43x | 85 contexts | уваат, чуваа, жуваат |
| `увањ` | 2.04x | 160 contexts | лување, рување, чување |
| `увал` | 2.00x | 172 contexts | увала, јувал, дувал |
| `ијат` | 1.76x | 300 contexts | лијат, хијат, ријат |
| `ички` | 1.82x | 235 contexts | кички, нички, лички |
| `кедо` | 2.77x | 33 contexts | македо, алкедо, македон |
| `ањет` | 2.27x | 71 contexts | рањето, вањето, кањете |
| `нски` | 1.58x | 402 contexts | ронски, менски, ренски |
| `анск` | 1.34x | 935 contexts | канск, анска, данск |
| `иски` | 1.56x | 353 contexts | киски, тиски, писки |
| `инск` | 1.39x | 722 contexts | пинск, инско, минск |
| `онск` | 1.41x | 510 contexts | ронски, јонско, шонски |

### 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 |
|--------|--------|-----------|----------|
| `-п` | `-а` | 118 words | пресбикуза, пентесилеја |
| `-с` | `-а` | 108 words | самбра, скаса |
| `-п` | `-и` | 79 words | повелбени, пољани |
| `-п` | `-е` | 76 words | питите, поиде |
| `-к` | `-а` | 74 words | клитика, куиксама |
| `-с` | `-и` | 70 words | сукотаи, сапрофитии |
| `-с` | `-е` | 67 words | служите, софите |
| `-по` | `-а` | 66 words | поситна, почесна |
| `-а` | `-а` | 64 words | адарсана, аеторема |
| `-б` | `-а` | 62 words | безлисна, бозонската |

### 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 |
|------|-----------------|------------|------|
| клинетите | **`клинет-и-те`** | 7.5 | `и` |
| карантанците | **`карантанц-и-те`** | 7.5 | `и` |
| ҫемҫелӗхпалли | **`ҫемҫелӗхпал-л-и`** | 7.5 | `л` |
| кедровата | **`кедров-а-та`** | 7.5 | `а` |
| тркачката | **`тркач-ка-та`** | 7.5 | `ка` |
| пантотенат | **`пантотен-а-т`** | 7.5 | `а` |
| наранџито | **`наранџ-и-то`** | 7.5 | `и` |
| епросартан | **`епросар-та-н`** | 7.5 | `та` |
| стивенсовиот | **`стивенсов-и-от`** | 7.5 | `и` |
| организирано | **`организир-а-но`** | 7.5 | `а` |
| евроазијците | **`евроазијц-и-те`** | 7.5 | `и` |
| епистазата | **`епистаз-а-та`** | 7.5 | `а` |
| страдачите | **`страдач-и-те`** | 7.5 | `и` |
| поштарината | **`поштарин-а-та`** | 7.5 | `а` |
| дебатирано | **`дебатир-а-но`** | 7.5 | `а` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Macedonian shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.78x) |
| N-gram | **2-gram** | Lowest perplexity (310) |
| Markov | **Context-4** | Highest predictability (94.0%) |
| 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 18:37:02*