README.md

---
language: kv
language_name: Komi
language_family: uralic_permian
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-uralic_permian
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: 4.057
  - name: best_isotropy
    type: isotropy
    value: 0.7808
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Komi** 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** | 3.121x | 3.13 | 0.1052% | 211,919 |
| **16k** | 3.570x | 3.58 | 0.1204% | 185,286 |
| **32k** | 3.866x | 3.87 | 0.1303% | 171,084 |
| **64k** | 4.057x 🏆 | 4.06 | 0.1368% | 163,039 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Сизимсё кӧкъямысдасӧд вояс - 781 восянь 790 воӧдз. Медыджыд лоӧмторъяс`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁сизим сё ▁кӧкъямыс дасӧд ▁вояс ▁- ▁ 7 8 1 ... (+9 more)` | 19 |
| 16k | `▁сизимсё ▁кӧкъямысдасӧд ▁вояс ▁- ▁ 7 8 1 ▁восянь ▁ ... (+7 more)` | 17 |
| 32k | `▁сизимсё ▁кӧкъямысдасӧд ▁вояс ▁- ▁ 7 8 1 ▁восянь ▁ ... (+7 more)` | 17 |
| 64k | `▁сизимсё ▁кӧкъямысдасӧд ▁вояс ▁- ▁ 7 8 1 ▁восянь ▁ ... (+7 more)` | 17 |

**Sample 2:** `451 Патиентия — тайӧ Шонді ылдӧсын астероид. Сылӧн ыджда — 224 км. Патиентия вос...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 4 5 1 ▁п ат и ент ия ▁— ... (+36 more)` | 46 |
| 16k | `▁ 4 5 1 ▁пат и ент ия ▁— ▁тайӧ ... (+32 more)` | 42 |
| 32k | `▁ 4 5 1 ▁пат и ентия ▁— ▁тайӧ ▁шонді ... (+26 more)` | 36 |
| 64k | `▁ 4 5 1 ▁патиентия ▁— ▁тайӧ ▁шонді ▁ылдӧсын ▁астероид ... (+22 more)` | 32 |

**Sample 3:** `Тюмень обласьт тайӧ регион Рочмуын. Видзӧдӧй тшӧтш Ханты-Вӧгул асвеськӧдлан кытш...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁т ю мен ь ▁обласьт ▁тайӧ ▁регион ▁рочмуын . ▁видзӧдӧй ... (+16 more)` | 26 |
| 16k | `▁тю мен ь ▁обласьт ▁тайӧ ▁регион ▁рочмуын . ▁видзӧдӧй ▁тшӧтш ... (+11 more)` | 21 |
| 32k | `▁тюмень ▁обласьт ▁тайӧ ▁регион ▁рочмуын . ▁видзӧдӧй ▁тшӧтш ▁ханты - ... (+9 more)` | 19 |
| 64k | `▁тюмень ▁обласьт ▁тайӧ ▁регион ▁рочмуын . ▁видзӧдӧй ▁тшӧтш ▁ханты - ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 64k achieves 4.057x compression
- **Lowest UNK Rate:** 8k with 0.1052% 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 | 4,415 | 12.11 | 14,094 | 22.1% | 55.9% |
| **2-gram** | Subword | 681 🏆 | 9.41 | 6,463 | 44.2% | 94.6% |
| **3-gram** | Word | 5,552 | 12.44 | 19,425 | 23.7% | 51.7% |
| **3-gram** | Subword | 5,657 | 12.47 | 40,644 | 16.0% | 51.0% |
| **4-gram** | Word | 8,996 | 13.14 | 34,620 | 23.6% | 45.0% |
| **4-gram** | Subword | 24,300 | 14.57 | 169,451 | 9.1% | 29.8% |
| **5-gram** | Word | 6,977 | 12.77 | 28,246 | 27.6% | 47.7% |
| **5-gram** | Subword | 55,081 | 15.75 | 319,260 | 6.7% | 22.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ӧд лун` | 2,382 |
| 2 | `республики коми` | 1,598 |
| 3 | `республика коми` | 1,394 |
| 4 | `сикт овмӧдчӧмин` | 1,392 |
| 5 | `коми республикаса` | 1,281 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `сыктывкар республика коми` | 1,059 |
| 2 | `республика коми энциклопедия` | 811 |
| 3 | `августа г издание` | 797 |
| 4 | `1 августа г` | 797 |
| 5 | `на 1 августа` | 797 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `1 августа г издание` | 797 |
| 2 | `на 1 августа г` | 797 |
| 3 | `и л где ты` | 717 |
| 4 | `жеребцов и л где` | 714 |
| 5 | `коми историко демографический справочник` | 704 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `на 1 августа г издание` | 797 |
| 2 | `жеребцов и л где ты` | 714 |
| 3 | `республики коми историко демографический справочник` | 704 |
| 4 | `пункты республики коми историко демографический` | 704 |
| 5 | `населенные пункты республики коми историко` | 703 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а _` | 76,965 |
| 2 | `. _` | 76,956 |
| 3 | `_ к` | 64,740 |
| 4 | `_ в` | 54,790 |
| 5 | `, _` | 52,769 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ к о` | 26,805 |
| 2 | `ы с ь` | 25,301 |
| 3 | `ъ я с` | 23,484 |
| 4 | `_ — _` | 22,691 |
| 5 | `_ в о` | 20,230 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ы с ь _` | 16,760 |
| 2 | `к о м и` | 15,656 |
| 3 | `_ к о м` | 15,118 |
| 4 | `ъ я с _` | 13,192 |
| 5 | `л ы с ь` | 12,862 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ к о м и` | 14,450 |
| 2 | `к о м и _` | 10,888 |
| 3 | `л ы с ь _` | 9,228 |
| 4 | `с ы к т ы` | 6,769 |
| 5 | `ы к т ы в` | 6,764 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 681
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.6233 | 1.540 | 3.71 | 115,439 | 37.7% |
| **1** | Subword | 0.4379 | 1.355 | 4.01 | 7,808 | 56.2% |
| **2** | Word | 0.1549 | 1.113 | 1.31 | 426,513 | 84.5% |
| **2** | Subword | 0.5508 | 1.465 | 3.55 | 31,340 | 44.9% |
| **3** | Word | 0.0585 | 1.041 | 1.11 | 556,965 | 94.2% |
| **3** | Subword | 0.5879 | 1.503 | 3.07 | 111,343 | 41.2% |
| **4** | Word | 0.0316 🏆 | 1.022 | 1.06 | 612,330 | 96.8% |
| **4** | Subword | 0.4947 | 1.409 | 2.22 | 341,894 | 50.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `коми пермяцко русский словарь грузинского языка ч ʧ сі чи ті vos сійӧ вӧлі лӧсьӧдавны каникуласигас`
2. `да 535 morinda phyllireoides sert austro caledon 49 м изд во 45 80 4 ньыль 5`
3. `сыктывкар коми республикаса почёта грамота коми литературы и муниципальное устройство республики ком...`

**Context Size 2:**

1. `ӧд лун коми кыв автономия панысьяс асшӧрлун шедӧдӧмын пайыс эм уналӧн кызьӧд воясӧ виз рочӧн княжпог...`
2. `республики коми историко демографический справочник сыктывкар история коми с древнейших времен до ко...`
3. `республика коми энциклопедия в 3 х тт емва да эжва юяс бокын но сикт грездъяс сикт сӧвет`

**Context Size 3:**

1. `сыктывкар республика коми административно территориальное деление на 1 августа г издание пятое сыкты...`
2. `республика коми энциклопедия сыктывкар т 1 3 ыстӧдъяс республикалӧн сиктъяс сикт грезд сикт овмӧдчӧм...`
3. `на 1 августа г издание шестое официальное гу тфи рк сыктывкар 278 с изьва мулӧн ин нимъяс топонимия`

**Context Size 4:**

1. `1 августа г издание шестое официальное гу тфи рк сыктывкар 278 с сикт грезд сикт овмӧдчӧмин грездъяс...`
2. `на 1 августа г издание пятое сыктывкар республика коми энциклопедия в 3 тт сыктывкар ыстӧдъяс вылыс ...`
3. `и л где ты живешь населенные пункты республики коми историко демографический справочник сыктывкар ис...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ктыджӧйисечмико`
2. `алломахъя_млазат`
3. `сопаын_кило_жез_`

**Context Size 2:**

1. `а_талӧны_jʊ_23932`
2. `._спублавканбур_о`
3. `_кмын_шойдъяслаын`

**Context Size 3:**

1. `_кокнижнӧй_уджаліс`
2. `ысьясӧ_сьыс_—_пемӧ`
3. `_—_коми_сарина_тэ_`

**Context Size 4:**

1. `ысь_18-ӧд_лун_лои_п`
2. `коми_музейӧн»,_арав`
3. `_комияса_кыв_(tod._`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (341,894 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 | 41,073 |
| Total Tokens | 725,042 |
| Mean Frequency | 17.65 |
| Median Frequency | 3 |
| Frequency Std Dev | 140.79 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | коми | 13,968 |
| 2 | да | 11,866 |
| 3 | сыктывкар | 5,358 |
| 4 | и | 5,043 |
| 5 | а | 4,697 |
| 6 | ӧд | 4,292 |
| 7 | тӧлысь | 4,290 |
| 8 | в | 4,031 |
| 9 | лун | 4,030 |
| 10 | сикт | 3,821 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | былины | 2 |
| 2 | символыс | 2 |
| 3 | палуоя | 2 |
| 4 | байтэрек | 2 |
| 5 | кухмо | 2 |
| 6 | хэнкок | 2 |
| 7 | тычы | 2 |
| 8 | идеал | 2 |
| 9 | университетъясысь | 2 |
| 10 | елюенэ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0595 |
| R² (Goodness of Fit) | 0.993095 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 26.6% |
| Top 1,000 | 59.7% |
| Top 5,000 | 79.2% |
| Top 10,000 | 86.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9931 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 26.6% of corpus
- **Long Tail:** 31,073 words needed for remaining 13.3% 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 | 0.7808 | 0.3587 | N/A | N/A |
| **mono_64d** | 64 | 0.5590 | 0.3120 | N/A | N/A |
| **mono_128d** | 128 | 0.1539 | 0.3129 | N/A | N/A |
| **aligned_32d** | 32 | 0.7808 🏆 | 0.3525 | 0.0260 | 0.1300 |
| **aligned_64d** | 64 | 0.5590 | 0.3133 | 0.0460 | 0.1960 |
| **aligned_128d** | 128 | 0.1539 | 0.3018 | 0.0580 | 0.2120 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7808 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3252. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.8% 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 | **1.101** | 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 |
|--------|----------|
| `-к` | калипсо, как, куратовалысь |
| `-с` | сартас, связь, сапёрнӧй |
| `-п` | пещераа, пансигӧн, партияӧн |
| `-в` | волывлӧма, вичӧн, выльног |
| `-м` | мыжы, медасьлісны, мирон |
| `-т` | турьев, тышкасьӧмлӧн, таын |
| `-ко` | комсь, колльӧдӧны, корӧмаӧсь |
| `-s` | semperflorens, scabrifolia, sz |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | айясыслӧн, вичӧн, пансигӧн |
| `-а` | волывлӧма, жанетта, пещераа |
| `-с` | сартас, бӧраныс, гӧгӧрсьыс |
| `-a` | trullifolia, dresslerara, carinilabia |
| `-ӧн` | айясыслӧн, вичӧн, пансигӧн |
| `-ь` | куратовалысь, связь, ль |
| `-яс` | квенъяс, войтыръяс, геологъяс |
| `-сь` | куратовалысь, комсь, лӧсьӧдӧмлысь |

### 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 |
|------|----------|------------------|----------|
| `лӧма` | 2.03x | 47 contexts | олӧма, вӧлӧма, кылӧма |
| `ӧдӧм` | 1.80x | 62 contexts | тӧдӧм, ӧлӧдӧм, ӧшӧдӧм |
| `ръяс` | 1.67x | 76 contexts | уръяс, юръяс, юӧръяс |
| `існы` | 2.08x | 23 contexts | юлісны, олісны, кулісны |
| `ӧлыс` | 2.30x | 15 contexts | тӧлыс, пӧлыс, йӧлыс |
| `ӧдъя` | 1.98x | 23 contexts | мӧдъяс, юкӧдъяс, инӧдъяс |
| `дъяс` | 1.62x | 39 contexts | садъяс, андъяс, видъяс |
| `въяс` | 1.62x | 38 contexts | увъяс, овъяс, левъяс |
| `отыр` | 1.91x | 21 contexts | котыр, котыра, котырӧ |
| `исто` | 2.02x | 15 contexts | истор, исток, истоки |
| `стор` | 1.89x | 16 contexts | истор, пастор, простор |
| `коты` | 1.93x | 15 contexts | котыр, котыра, котырӧ |

### 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` | `-н` | 88 words | кн, кипрушевлӧн |
| `-п` | `-н` | 70 words | предприятиеяслӧн, поэмаясын |
| `-к` | `-а` | 68 words | кипасалӧма, косьювомса |
| `-с` | `-н` | 64 words | семуковын, сборникъясын |
| `-к` | `-с` | 64 words | коммунистъяс, кыръясыс |
| `-с` | `-а` | 61 words | ставмирса, сорта |
| `-п` | `-а` | 61 words | пырӧма, пылаева |
| `-в` | `-н` | 60 words | вӧркутаын, войын |
| `-п` | `-с` | 58 words | примитіс, поэтъясӧс |
| `-в` | `-ы` | 58 words | восьтны, вуджны |

### 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 |
|------|-----------------|------------|------|
| странанас | **`страна-н-ас`** | 7.5 | `н` |
| парткомса | **`партко-м-са`** | 7.5 | `м` |
| скрипкаӧн | **`скрипк-а-ӧн`** | 7.5 | `а` |
| институтлысь | **`институт-лы-сь`** | 6.0 | `институт` |
| висьтавсьӧ | **`висьтав-сь-ӧ`** | 6.0 | `висьтав` |
| кальӧлысь | **`кальӧ-лы-сь`** | 6.0 | `кальӧ` |
| авторлысь | **`автор-лы-сь`** | 6.0 | `автор` |
| ветлысьяслы | **`ветлысь-яс-лы`** | 6.0 | `ветлысь` |
| войскаясӧн | **`войска-яс-ӧн`** | 6.0 | `войска` |
| абхазияын | **`абхаз-ия-ын`** | 6.0 | `абхаз` |
| национальносьт | **`национально-сь-т`** | 6.0 | `национально` |
| пемӧслысь | **`пемӧс-лы-сь`** | 6.0 | `пемӧс` |
| ӧтувтчӧмӧн | **`ӧтувтчӧм-ӧн`** | 4.5 | `ӧтувтчӧм` |
| пемӧсъясӧс | **`пе-мӧсъясӧс`** | 4.5 | `мӧсъясӧс` |
| балтикаса | **`балтика-са`** | 4.5 | `балтика` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Komi 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 (4.06x) |
| N-gram | **2-gram** | Lowest perplexity (681) |
| Markov | **Context-4** | Highest predictability (96.8%) |
| 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 08:51:50*