README.md

---
language: ce
language_name: Chechen
language_family: caucasian_northeast
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_northeast
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: 3.737
  - name: best_isotropy
    type: isotropy
    value: 0.8747
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Chechen** 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** | 2.792x | 2.80 | 0.9605% | 541,154 |
| **16k** | 3.113x | 3.12 | 1.0708% | 485,447 |
| **32k** | 3.423x | 3.43 | 1.1775% | 441,435 |
| **64k** | 3.737x 🏆 | 3.74 | 1.2855% | 404,354 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Бейца (Бихор) Бейца (Клуж) Бейца (Марамуреш) Бейца (Муреш) Бейца (Хунедоара) Бей...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁бей ца ▁( б их ор ) ▁бей ца ▁( ... (+30 more)` | 40 |
| 16k | `▁бей ца ▁( б ихор ) ▁бей ца ▁( к ... (+24 more)` | 34 |
| 32k | `▁бей ца ▁( бихор ) ▁бей ца ▁( клуж ) ... (+20 more)` | 30 |
| 64k | `▁бейца ▁( бихор ) ▁бейца ▁( клуж ) ▁бейца ▁( ... (+14 more)` | 24 |

**Sample 2:** `Киякты (Актобен область) Киякты (Мангистаунан область)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁к ия кт ы ▁( акт обен ▁область ) ▁к ... (+10 more)` | 20 |
| 16k | `▁к ия кты ▁( акт обен ▁область ) ▁к ия ... (+8 more)` | 18 |
| 32k | `▁кия кты ▁( актобен ▁область ) ▁кия кты ▁( ман ... (+3 more)` | 13 |
| 64k | `▁кия кты ▁( актобен ▁область ) ▁кия кты ▁( мангистаунан ... (+2 more)` | 12 |

**Sample 3:** `ХӀаджали (40° 14' N 47° 16' E), (Бардан кӀошт) ХӀаджали (40° 27' N 47° 05' E), (...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁хӏа дж али ▁( 4 0 ° ▁ 1 4 ... (+44 more)` | 54 |
| 16k | `▁хӏадж али ▁( 4 0 ° ▁ 1 4 ' ... (+42 more)` | 52 |
| 32k | `▁хӏадж али ▁( 4 0 ° ▁ 1 4 ' ... (+40 more)` | 50 |
| 64k | `▁хӏадж али ▁( 4 0 ° ▁ 1 4 ' ... (+40 more)` | 50 |


### Key Findings

- **Best Compression:** 64k achieves 3.737x compression
- **Lowest UNK Rate:** 8k with 0.9605% 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 | 3,390 | 11.73 | 113,212 | 22.9% | 62.3% |
| **2-gram** | Subword | 435 🏆 | 8.77 | 6,171 | 54.5% | 98.0% |
| **3-gram** | Word | 4,361 | 12.09 | 176,983 | 18.9% | 57.8% |
| **3-gram** | Subword | 2,517 | 11.30 | 59,082 | 23.1% | 68.3% |
| **4-gram** | Word | 5,357 | 12.39 | 387,928 | 16.4% | 55.1% |
| **4-gram** | Subword | 6,651 | 12.70 | 339,742 | 15.1% | 48.5% |
| **5-gram** | Word | 5,776 | 12.50 | 363,840 | 15.2% | 53.7% |
| **5-gram** | Subword | 11,240 | 13.46 | 966,556 | 12.7% | 40.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `нах беха` | 1,039,295 |
| 2 | `беха меттигаш` | 953,014 |
| 3 | `билгалдахарш хьажоргаш` | 387,484 |
| 4 | `климат кхузахь` | 314,080 |
| 5 | `кхузахь климат` | 293,860 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `нах беха меттигаш` | 952,977 |
| 2 | `климат кхузахь климат` | 274,749 |
| 3 | `кӏоштан нах беха` | 256,927 |
| 4 | `бахархой билгалдахарш хьажоргаш` | 156,557 |
| 5 | `ред а м` | 153,110 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `кӏоштан нах беха меттигаш` | 256,923 |
| 2 | `лелаш ду сахьтан аса` | 134,397 |
| 3 | `нийса лелаш ду сахьтан` | 134,397 |
| 4 | `сахьтан аса йу utc` | 133,768 |
| 5 | `ду сахьтан аса йу` | 133,768 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `нийса лелаш ду сахьтан аса` | 134,397 |
| 2 | `ду сахьтан аса йу utc` | 133,768 |
| 3 | `лелаш ду сахьтан аса йу` | 133,768 |
| 4 | `индексаш кӏоштан нах беха меттигаш` | 122,584 |
| 5 | `аьхка йовха хуьлу ткъа ӏа` | 113,661 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 10,875,281 |
| 2 | `. _` | 9,874,426 |
| 3 | `н _` | 8,151,111 |
| 4 | `а н` | 7,675,531 |
| 5 | `р а` | 6,751,030 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а н _` | 4,716,126 |
| 2 | `_ — _` | 2,941,993 |
| 3 | `р а _` | 2,306,576 |
| 4 | `а ш _` | 2,292,649 |
| 5 | `а х ь` | 2,054,431 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `т а н _` | 1,577,468 |
| 2 | `а х а р` | 1,505,060 |
| 3 | `а _ м е` | 1,193,821 |
| 4 | `а х ь _` | 1,177,180 |
| 5 | `_ м е т` | 1,177,138 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ м е т т` | 1,166,495 |
| 2 | `м е т т и` | 1,154,656 |
| 3 | `е т т и г` | 1,154,628 |
| 4 | `а _ м е т` | 1,067,312 |
| 5 | `_ н а х _` | 1,048,954 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 435
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~40% 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 | 0.6776 | 1.600 | 4.20 | 526,205 | 32.2% |
| **1** | Subword | 0.9453 | 1.926 | 9.06 | 1,550 | 5.5% |
| **2** | Word | 0.1950 | 1.145 | 1.49 | 2,194,953 | 80.5% |
| **2** | Subword | 0.9623 | 1.948 | 7.39 | 14,021 | 3.8% |
| **3** | Word | 0.0756 | 1.054 | 1.15 | 3,239,505 | 92.4% |
| **3** | Subword | 0.8389 | 1.789 | 4.99 | 103,540 | 16.1% |
| **4** | Word | 0.0367 🏆 | 1.026 | 1.08 | 3,672,181 | 96.3% |
| **4** | Subword | 0.7073 | 1.633 | 3.29 | 516,039 | 29.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `а зонехьклимат тверской области бахархойн дукхалла бахархойн дукхалла бахархойн дукхалла климат йу л...`
2. `нах беха меттигаш жудецан нах беха меттигаш штатан йукъахь дара кочими монки гуайкура перику индейн ...`
3. `беха меттигаш нах беха меттигаш нисйина нах беха меттигаш нисйина нах беха меттигаш кӏоштан индексаш...`

**Context Size 2:**

1. `нах беха меттигаш нах беха меттигаш лаха калифорни штатан йукъахь йу бахархой билгалдахарш литератур...`
2. `беха меттигаш воеводаллин нах беха меттигаш нисйина нах беха меттигаш нисйина нах беха меттигаш нах ...`
3. `билгалдахарш хьажоргаш спас деменскан кӏошт калугин областан спас деменскан кӏоштара дӏатесна эвла б...`

**Context Size 3:**

1. `нах беха меттигаш кӏоштан нах беха меттигаш штатан нах беха меттигаш штатан нах беха меттигаш штатан...`
2. `климат кхузахь климат йу лаьттайуккъера хӏордан барамехь йекъа а йовха ӏа шийла ца хуьйлат а галкина...`
3. `кӏоштан нах беха меттигаш штатан нах беха меттигаш нах беха меттигаш нисйина нах беха меттигаш нисйи...`

**Context Size 4:**

1. `лелаш ду сахьтан аса йу utc 3 билгалдахарш хьажоргаш устьян кӏоштан индексаш кӏоштан нах беха меттиг...`
2. `нийса лелаш ду сахьтан аса йу utc 3 билгалдахарш хьажоргаш приморскан кӏоштан индексаш областан прим...`
3. `ду сахьтан аса йу utc 7 билгалдахарш мохк`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_йаду_—_н_бще_вх`
2. `анташ_гахахарха_`
3. `нцалальталарклус`

**Context Size 2:**

1. `а_хила_дуьлинецес`
2. `._у-фактябра_эххь`
3. `н_йоккъах_бехь_ст`

**Context Size 3:**

1. `ан_областан_сизал_`
2. `_—_январь_современ`
3. `ра_хьолехьажоргаш_`

**Context Size 4:**

1. `тан_асан_коммунан_х`
2. `ахарш_хьажоргаши_(д`
3. `а_меттигаш_коммунан`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (516,039 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 | 238,347 |
| Total Tokens | 67,032,110 |
| Mean Frequency | 281.24 |
| Median Frequency | 3 |
| Frequency Std Dev | 8160.67 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | а | 1,815,637 |
| 2 | нах | 1,049,193 |
| 3 | беха | 1,039,696 |
| 4 | меттигаш | 968,757 |
| 5 | йу | 814,157 |
| 6 | м | 798,557 |
| 7 | климат | 741,272 |
| 8 | в | 736,957 |
| 9 | билгалдахарш | 631,076 |
| 10 | с | 588,454 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | эмпачадо | 2 |
| 2 | энано | 2 |
| 3 | эскопетал | 2 |
| 4 | эскриторио | 2 |
| 5 | макариос | 2 |
| 6 | эроика | 2 |
| 7 | скирринг | 2 |
| 8 | зигуинчор | 2 |
| 9 | зигуиншор | 2 |
| 10 | люксембургхо | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.8633 |
| R² (Goodness of Fit) | 0.948539 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.8% |
| Top 1,000 | 83.4% |
| Top 5,000 | 96.8% |
| Top 10,000 | 97.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9485 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.8% of corpus
- **Long Tail:** 228,347 words needed for remaining 2.2% 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 | 0.8747 | 0.3629 | N/A | N/A |
| **mono_64d** | 64 | 0.8592 | 0.2868 | N/A | N/A |
| **mono_128d** | 128 | 0.7998 | 0.2691 | N/A | N/A |
| **aligned_32d** | 32 | 0.8747 🏆 | 0.3562 | 0.0120 | 0.0960 |
| **aligned_64d** | 64 | 0.8592 | 0.3007 | 0.0320 | 0.2180 |
| **aligned_128d** | 128 | 0.7998 | 0.2615 | 0.1100 | 0.3620 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8747 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3062. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 11.0% 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 | **0.335** | 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 |
|--------|----------|
| `-ка` | каркаусь, кассагумахи, кафка |
| `-ко` | костровскан, коховка, колумбехь |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-а` | ледара, жиховка, масленка |
| `-н` | галийн, кувшин, самодийн |
| `-о` | белшево, санторо, эрцо |
| `-ан` | тӏаьрсиган, менделеевскан, костровскан |
| `-во` | белшево, миллерово, горяново |
| `-ка` | жиховка, масленка, раковка |
| `-ово` | миллерово, горяново, атынаково |
| `-ки` | недниковски, новокубански, ибараки |

### 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 |
|------|----------|------------------|----------|
| `архо` | 2.00x | 121 contexts | архон, лархо, тархо |
| `исто` | 1.91x | 130 contexts | мисто, чисто, исток |
| `галд` | 2.88x | 16 contexts | галда, галдо, галдун |
| `ргаш` | 2.28x | 34 contexts | ургаш, воргаш, мургаш |
| `харх` | 2.14x | 41 contexts | йахарх, хархув, мухарх |
| `икин` | 1.84x | 62 contexts | викин, рикин, бикин |
| `халл` | 1.55x | 92 contexts | халле, халль, халла |
| `рхой` | 2.30x | 19 contexts | лархой, сурхой, ахархой |
| `лгал` | 2.36x | 17 contexts | билгал, билгало, билгала |
| `игаш` | 2.34x | 17 contexts | бигаш, цигаш, эхигаш |
| `етти` | 1.73x | 42 contexts | бетти, нетти, петтит |
| `ттиг` | 1.96x | 25 contexts | меттиг, гаттиг, ме́ттиг |

### 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 |
|--------|--------|-----------|----------|
| `-ко` | `-а` | 44 words | комната, колохта |
| `-ка` | `-о` | 40 words | кастелларо, карманково |
| `-ка` | `-а` | 38 words | казчана, кажа |
| `-ко` | `-о` | 35 words | корково, кощейково |
| `-ка` | `-н` | 27 words | кассон, капланецкан |
| `-ко` | `-н` | 23 words | конкистадоран, коюнлун |
| `-ко` | `-во` | 17 words | корково, кощейково |
| `-ка` | `-во` | 16 words | карманково, каптырево |
| `-ка` | `-ан` | 15 words | капланецкан, каштан |
| `-ко` | `-ан` | 13 words | конкистадоран, котован |

### 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 |
|------|-----------------|------------|------|
| евдокимовски | **`евдокимовс-ки`** | 4.5 | `евдокимовс` |
| заказникан | **`заказник-ан`** | 4.5 | `заказник` |
| череповецан | **`череповец-ан`** | 4.5 | `череповец` |
| господиново | **`господин-ово`** | 4.5 | `господин` |
| вайнахана | **`вайнаха-на`** | 4.5 | `вайнаха` |
| воротынскан | **`воротынск-ан`** | 4.5 | `воротынск` |
| кинофильман | **`кинофильм-ан`** | 4.5 | `кинофильм` |
| дийцаршна | **`дийцарш-на`** | 4.5 | `дийцарш` |
| театрашка | **`театраш-ка`** | 4.5 | `театраш` |
| федотован | **`федотов-ан`** | 4.5 | `федотов` |
| веселовка | **`веселов-ка`** | 4.5 | `веселов` |
| маядыково | **`маядык-ово`** | 4.5 | `маядык` |
| ходоровка | **`ходоров-ка`** | 4.5 | `ходоров` |
| новиковски | **`новиковс-ки`** | 4.5 | `новиковс` |
| меженашна | **`меженаш-на`** | 4.5 | `меженаш` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Chechen 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 (3.74x) |
| N-gram | **2-gram** | Lowest perplexity (435) |
| Markov | **Context-4** | Highest predictability (96.3%) |
| 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 20:55:32*