---
language: pnt
language_name: Pontic
language_family: greek
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-greek
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: 3.670
  - name: best_isotropy
    type: isotropy
    value: 0.0523
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Pontic** 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** | 3.197x | 3.20 | 0.1329% | 100,820 |
| **16k** | 3.540x | 3.55 | 0.1472% | 91,057 |
| **32k** | 3.670x 🏆 | 3.68 | 0.1526% | 87,822 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Η Οσάκα εν πολιτεία σην Ιαπωνίαν. Οσήμερον εχ' πληθυσμόν 2.668.586 ανθρώπ.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁η ▁οσάκα ▁εν ▁πολιτεία ▁σην ▁ιαπωνίαν . ▁οσήμερον ▁εχ ' ... (+13 more)` | 23 |
| 16k | `▁η ▁οσάκα ▁εν ▁πολιτεία ▁σην ▁ιαπωνίαν . ▁οσήμερον ▁εχ ' ... (+13 more)` | 23 |
| 32k | `▁η ▁οσάκα ▁εν ▁πολιτεία ▁σην ▁ιαπωνίαν . ▁οσήμερον ▁εχ ' ... (+13 more)` | 23 |

**Sample 2:** `Ο Βόλος εν πόλην τρανή (τρανότερη της Μαγνησίας ούλης) παρά την θάλασσαν ασο κέν...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ο ▁βόλοσ ▁εν ▁πόλην ▁τραν ή ▁( τ ραν ότερη ... (+26 more)` | 36 |
| 16k | `▁ο ▁βόλοσ ▁εν ▁πόλην ▁τρανή ▁( τρανότερη ▁τησ ▁μαγνησίασ ▁ούλησ ... (+20 more)` | 30 |
| 32k | `▁ο ▁βόλοσ ▁εν ▁πόλην ▁τρανή ▁( τρανότερη ▁τησ ▁μαγνησίασ ▁ούλησ ... (+20 more)` | 30 |

**Sample 3:** `Η Λα Ροσέλ εν πολιτεία σην Γαλλίαν. Οσήμερον εχ' πληθυσμόν 74.998 ανθρώπ.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁η ▁λα ▁ρ οσ έλ ▁εν ▁πολιτεία ▁σην ▁γαλλίαν . ... (+13 more)` | 23 |
| 16k | `▁η ▁λα ▁ροσέλ ▁εν ▁πολιτεία ▁σην ▁γαλλίαν . ▁οσήμερον ▁εχ ... (+11 more)` | 21 |
| 32k | `▁η ▁λα ▁ροσέλ ▁εν ▁πολιτεία ▁σην ▁γαλλίαν . ▁οσήμερον ▁εχ ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 32k achieves 3.670x compression
- **Lowest UNK Rate:** 8k with 0.1329% 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 | 378 | 8.56 | 778 | 59.1% | 100.0% |
| **2-gram** | Subword | 411 | 8.68 | 1,785 | 57.2% | 97.4% |
| **3-gram** | Word | 302 🏆 | 8.24 | 829 | 68.5% | 100.0% |
| **3-gram** | Subword | 2,487 | 11.28 | 9,341 | 25.0% | 68.3% |
| **4-gram** | Word | 459 | 8.84 | 1,665 | 62.9% | 89.3% |
| **4-gram** | Subword | 7,482 | 12.87 | 24,840 | 13.4% | 46.9% |
| **5-gram** | Word | 321 | 8.33 | 1,188 | 70.5% | 96.3% |
| **5-gram** | Subword | 11,940 | 13.54 | 32,544 | 9.4% | 38.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `τη χρονίας` | 207 |
| 2 | `για να` | 153 |
| 3 | `το γρηγοριανόν` | 134 |
| 4 | `γρηγοριανόν ημερολόγιον` | 134 |
| 5 | `2 3` | 133 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `το γρηγοριανόν ημερολόγιον` | 133 |
| 2 | `2 3 4` | 132 |
| 3 | `15 16 17` | 131 |
| 4 | `17 18 19` | 131 |
| 5 | `9 10 11` | 131 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `25 26 27 28` | 131 |
| 2 | `9 10 11 12` | 131 |
| 3 | `10 11 12 13` | 131 |
| 4 | `3 4 5 6` | 131 |
| 5 | `11 12 13 14` | 131 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `8 9 10 11 12` | 131 |
| 2 | `10 11 12 13 14` | 131 |
| 3 | `11 12 13 14 15` | 131 |
| 4 | `12 13 14 15 16` | 131 |
| 5 | `13 14 15 16 17` | 131 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ν _` | 10,498 |
| 2 | `_ τ` | 7,042 |
| 3 | `α ν` | 5,192 |
| 4 | `α _` | 4,454 |
| 5 | `ς _` | 4,288 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ο ν _` | 2,539 |
| 2 | `α ν _` | 2,368 |
| 3 | `_ τ η` | 2,160 |
| 4 | `_ κ α` | 1,899 |
| 5 | `_ τ ο` | 1,888 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ τ η _` | 1,677 |
| 2 | `_ κ α ι` | 1,214 |
| 3 | `κ α ι _` | 1,179 |
| 4 | `_ τ ο _` | 1,174 |
| 5 | `_ ε ν _` | 752 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ κ α ι _` | 1,176 |
| 2 | `ν _ τ η _` | 594 |
| 3 | `_ χ ρ ο ν` | 536 |
| 4 | `ι κ ό ν _` | 527 |
| 5 | `χ ρ ο ν ί` | 523 |


### Key Findings

- **Best Perplexity:** 3-gram (word) with 302
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~39% 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 | 0.4938 | 1.408 | 2.69 | 11,667 | 50.6% |
| **1** | Subword | 1.2400 | 2.362 | 8.79 | 439 | 0.0% |
| **2** | Word | 0.1458 | 1.106 | 1.25 | 31,022 | 85.4% |
| **2** | Subword | 1.0962 | 2.138 | 5.25 | 3,856 | 0.0% |
| **3** | Word | 0.0419 | 1.029 | 1.07 | 38,349 | 95.8% |
| **3** | Subword | 0.6896 | 1.613 | 2.67 | 20,216 | 31.0% |
| **4** | Word | 0.0219 🏆 | 1.015 | 1.04 | 40,551 | 97.8% |
| **4** | Subword | 0.3670 | 1.290 | 1.70 | 53,958 | 63.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `τη γαλλίαν οσήμερον εχ πληθυσμόν τη λέξην encyclopaedia αέτς άμον ντο εποίκαν χάταλα δίδυμα σα commo...`
2. `το ποτάμ λέχκουνταν doğu karadeniz dağları άμα ευρίσκουμε και φιλόλογον γιόχαν βόλφγκανγκ μπέριςς έβ...`
3. `και ο πληθυσμόν σα δυτικά πίσω σην πολωνίαν την ρώμην επέμνεν έναν συνεργασίαν ντο ευρίεται σο`

**Context Size 2:**

1. `για να τελούτεν η χρονία 363 ημέρας για να εγροικάτεν κι εσείς αούτο εν το γράψιμον το`
2. `τη χρονίας ίστε λεει μας το γρηγοριανόν ημερολόγιον επέμναν άλλα 360 ημέρας σο δίσεκτον τη χρονία ατ...`
3. `το γρηγοριανόν ημερολόγιον κι εχ 31 ημέρας σ αβούτον το κράτος έχεις ως επίσημον λαλίαν την καζακική...`

**Context Size 3:**

1. `το γρηγοριανόν ημερολόγιον επέμναν άλλα 348 ημέρας για να τελούτεν η χρονία ατά ντ εγένταν εγεννέθαν...`
2. `2 3 4 5 6 u 7 u 8 9 10 11 12 13 14 15 16 17`
3. `21 22 23 24 25 26 27 28 29 30 31 28 τρυγομηνά εν 301ον ημέρα τη χρονίας`

**Context Size 4:**

1. `10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28`
2. `25 26 27 28 29 30 31 η 1 τη καλανταρί εν 1ον ημέρα τη χρονίας άμον ντο λεει`
3. `19 20 21 22 23 24 25 26 27 28 29 30 31 η 7 τη καλανταρί εν 7ον`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_σ'_25_τοκ_σία):`
2. `αυν_ην_ουμβοξυρό`
3. `ν_η_ρίαι_δαιο_να`

**Context Size 2:**

1. `ν_απερ,_ο_γιαφέρα`
2. `_τηλεία_βικος_ατ'`
3. `αν_τη_μορί_|_4_5_`

**Context Size 3:**

1. `ον_ο_άλλα_20_21_22`
2. `αν_τη_βερολόγιον,_`
3. `_τη_ασίαν_η_χώρας_`

**Context Size 4:**

1. `_τη_χρονίαν_σην_και`
2. `_και_διαδικτυακήν_σ`
3. `και_κάτω_από_τιμόρ.`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (53,958 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 | 3,936 |
| Total Tokens | 45,584 |
| Mean Frequency | 11.58 |
| Median Frequency | 3 |
| Frequency Std Dev | 56.78 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | τη | 1,685 |
| 2 | το | 1,240 |
| 3 | και | 1,182 |
| 4 | η | 1,115 |
| 5 | ο | 813 |
| 6 | εν | 783 |
| 7 | τ | 746 |
| 8 | σα | 652 |
| 9 | τα | 572 |
| 10 | σο | 475 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | μπασάν | 2 |
| 2 | επάτησεν | 2 |
| 3 | υόρκην | 2 |
| 4 | τραγωδός | 2 |
| 5 | πρόσωπα | 2 |
| 6 | μούζικας | 2 |
| 7 | born | 2 |
| 8 | rolling | 2 |
| 9 | stone | 2 |
| 10 | δείχν | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9722 |
| R² (Goodness of Fit) | 0.971817 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 54.0% |
| Top 1,000 | 83.1% |
| Top 5,000 | 0.0% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9718 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 54.0% of corpus
- **Long Tail:** -6,064 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 | 0.0523 | 0.6492 | N/A | N/A |
| **mono_64d** | 64 | 0.0087 | 0.6629 | N/A | N/A |
| **mono_128d** | 128 | 0.0013 | 0.6851 | N/A | N/A |
| **aligned_32d** | 32 | 0.0523 🏆 | 0.6519 | 0.0429 | 0.3286 |
| **aligned_64d** | 64 | 0.0087 | 0.6348 | 0.0357 | 0.3571 |
| **aligned_128d** | 128 | 0.0013 | 0.6853 | 0.0500 | 0.4143 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.0523 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.6615. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.0% 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 | **1.493** | 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 |
|--------|----------|
| `-ε` | εύκρατο, εγκυκλοπαίδεια, εταιρία |
| `-α` | αλβανίας, αρχηγοί, αρχαία |
| `-κ` | κόκκινον, κοσμικοί, καλατσεύ |
| `-π` | πρώτον, περσικόν, προξενείον |
| `-σ` | συστέματα, σάββατον, συγκεκριμένα |
| `-κα` | καλατσεύ, κατάληξη, καζίνο |
| `-πα` | παπάδες, πατέρα, παράδειγμα |
| `-επ` | επιτροπή, εποίν, επίσης |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ν` | οποίον, έρτεν, τιράνων |
| `-ς` | χερσόνησος, αλβανίας, λέξεις |
| `-αν` | ρωμανίαν, ίαν, μάναν |
| `-α` | συστέματα, ρωμαίικα, εγκυκλοπαίδεια |
| `-ον` | οποίον, κόκκινον, πρώτον |
| `-ας` | αλβανίας, εργασίας, γαλλίας |
| `-όν` | περσικόν, σκανδιναβικόν, εθνικόν |
| `-ος` | χερσόνησος, τέλος, μύρος |

### 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 |
|------|----------|------------------|----------|
| `ικόν` | 1.32x | 17 contexts | υλικόν, εικόνα, ενικόν |
| `ματα` | 1.41x | 10 contexts | θέματα, βήματα, ρήματα |
| `εται` | 1.37x | 5 contexts | ψέεται, ίνεται, λύεται |

### 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 |
|--------|--------|-----------|----------|
| `-ε` | `-ν` | 127 words | εποίν, εγεννέθαν |
| `-α` | `-ν` | 79 words | αν, ασίαν |
| `-π` | `-ν` | 65 words | πρώτον, περσικόν |
| `-α` | `-ς` | 60 words | αλβανίας, αχουλής |
| `-κ` | `-ν` | 56 words | κόκκινον, κρύον |
| `-ε` | `-εν` | 54 words | εδέβεν, εφτάτεν |
| `-σ` | `-ν` | 49 words | σάββατον, σκανδιναβικόν |
| `-π` | `-ς` | 44 words | ποδοσφαιριστής, παπάδες |
| `-κ` | `-ς` | 41 words | καραμανλής, κερτς |
| `-ε` | `-αν` | 40 words | εγεννέθαν, επηρεάσταν |

### 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 |
|------|-----------------|------------|------|
| γράψιματα | **`γράψιμ-α-τα`** | 7.5 | `α` |
| εποίκενατα | **`εποίκεν-α-τα`** | 7.5 | `α` |
| λιθουανία | **`λιθου-αν-ία`** | 7.5 | `αν` |
| ανθρώπους | **`ανθρώπ-ου-ς`** | 6.0 | `ανθρώπ` |
| καλαντάρτς | **`καλαντάρτ-ς`** | 4.5 | `καλαντάρτ` |
| βιογραφικόν | **`βιογραφικό-ν`** | 4.5 | `βιογραφικό` |
| υπολογιστήν | **`υπολογιστή-ν`** | 4.5 | `υπολογιστή` |
| σημαντικόν | **`σημαντικό-ν`** | 4.5 | `σημαντικό` |
| καλομηνάς | **`καλομηνά-ς`** | 4.5 | `καλομηνά` |
| ξεχωριστόν | **`ξεχωριστό-ν`** | 4.5 | `ξεχωριστό` |
| περιοδικόν | **`περιοδικό-ν`** | 4.5 | `περιοδικό` |
| θεσσαλονίκης | **`θεσσαλονίκη-ς`** | 4.5 | `θεσσαλονίκη` |
| ερχίνεσεν | **`ερχίνεσε-ν`** | 4.5 | `ερχίνεσε` |
| συνορεύνε | **`συνορεύ-νε`** | 4.5 | `συνορεύ` |
| συνδέζμαι | **`συνδέζμ-αι`** | 4.5 | `συνδέζμ` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Pontic 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 (3.67x) |
| N-gram | **3-gram** | Lowest perplexity (302) |
| Markov | **Context-4** | Highest predictability (97.8%) |
| 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 18:08:17*