README.md

---
language: sah
language_name: Yakut
language_family: turkic_siberian
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-turkic_siberian
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: 4.821
  - name: best_isotropy
    type: isotropy
    value: 0.8478
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Yakut** 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** | 3.680x | 3.68 | 0.1029% | 515,208 |
| **16k** | 4.119x | 4.12 | 0.1151% | 460,361 |
| **32k** | 4.506x | 4.51 | 0.1260% | 420,768 |
| **64k** | 4.821x 🏆 | 4.82 | 0.1347% | 393,326 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `мини Сантьяго () диэн Чиили киин уонна ордук улахан куората. Америка киин куорат...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁мини ▁сан т ья го ▁() ▁диэн ▁ч и или ... (+9 more)` | 19 |
| 16k | `▁мини ▁сан т ья го ▁() ▁диэн ▁чи или ▁киин ... (+8 more)` | 18 |
| 32k | `▁мини ▁сант ьяго ▁() ▁диэн ▁чиили ▁киин ▁уонна ▁ордук ▁улахан ... (+5 more)` | 15 |
| 64k | `▁мини ▁сантьяго ▁() ▁диэн ▁чиили ▁киин ▁уонна ▁ордук ▁улахан ▁куората ... (+4 more)` | 14 |

**Sample 2:** `Дабаан / Кобяйский вестник — Кэбээйи улууһун хаһыата. Бастакы нүөмэрэ сыллаахха ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁да баан ▁/ ▁к об яй ский ▁вест ник ▁— ... (+18 more)` | 28 |
| 16k | `▁дабаан ▁/ ▁коб яй ский ▁вест ник ▁— ▁кэбээйи ▁улууһун ... (+15 more)` | 25 |
| 32k | `▁дабаан ▁/ ▁кобяй ский ▁вестник ▁— ▁кэбээйи ▁улууһун ▁хаһыата . ... (+13 more)` | 23 |
| 64k | `▁дабаан ▁/ ▁кобяй ский ▁вестник ▁— ▁кэбээйи ▁улууһун ▁хаһыата . ... (+13 more)` | 23 |

**Sample 3:** `Алабама (Alabama) диэн АХШ соҕуруу штата (22-с). Олохтоохторун ахсаана 4.6 млн К...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ал аб ама ▁( al ab am a ) ▁диэн ... (+26 more)` | 36 |
| 16k | `▁ал аб ама ▁( al ab ama ) ▁диэн ▁ахш ... (+23 more)` | 33 |
| 32k | `▁алаб ама ▁( al ab ama ) ▁диэн ▁ахш ▁соҕуруу ... (+22 more)` | 32 |
| 64k | `▁алабама ▁( al ab ama ) ▁диэн ▁ахш ▁соҕуруу ▁штата ... (+20 more)` | 30 |


### Key Findings

- **Best Compression:** 64k achieves 4.821x compression
- **Lowest UNK Rate:** 8k with 0.1029% 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 | 33,576 | 15.04 | 87,387 | 8.4% | 25.1% |
| **2-gram** | Subword | 356 🏆 | 8.48 | 6,079 | 60.6% | 98.2% |
| **3-gram** | Word | 57,564 | 15.81 | 118,482 | 6.1% | 18.5% |
| **3-gram** | Subword | 2,820 | 11.46 | 50,098 | 23.1% | 68.5% |
| **4-gram** | Word | 209,016 | 17.67 | 319,912 | 3.4% | 9.6% |
| **4-gram** | Subword | 13,930 | 13.77 | 254,284 | 11.0% | 38.8% |
| **5-gram** | Word | 195,362 | 17.58 | 274,988 | 3.4% | 9.0% |
| **5-gram** | Subword | 45,556 | 15.48 | 629,633 | 6.5% | 24.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `өй санаа` | 4,417 |
| 2 | `өйө санаата` | 4,048 |
| 3 | `аан дойду` | 2,742 |
| 4 | `саха сирин` | 2,577 |
| 5 | `саха асср` | 2,460 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `өссө маны көр` | 1,889 |
| 2 | `республики саха якутия` | 1,390 |
| 3 | `каженкин и и` | 1,280 |
| 4 | `алпаабытынан сыллаахха төрөөбүттэр` | 1,114 |
| 5 | `туһаныллыбыт литература 1` | 1,107 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `туох барыта икки өрүттээх` | 876 |
| 2 | `информационный портал республики саха` | 861 |
| 3 | `портал республики саха якутия` | 860 |
| 4 | `барыта икки өрүттээх диэн` | 813 |
| 5 | `туһаныллыбыт литература 1 каженкин` | 665 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `информационный портал республики саха якутия` | 860 |
| 2 | `туох барыта икки өрүттээх диэн` | 813 |
| 3 | `литература 1 каженкин и и` | 657 |
| 4 | `туһаныллыбыт литература 1 каженкин и` | 657 |
| 5 | `официальный информационный портал республики саха` | 604 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _` | 619,303 |
| 2 | `а р` | 602,438 |
| 3 | `а _` | 471,311 |
| 4 | `_ с` | 433,862 |
| 5 | `т а` | 422,313 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `а н _` | 192,779 |
| 2 | `л а р` | 157,712 |
| 3 | `а р _` | 150,277 |
| 4 | `а р ы` | 145,884 |
| 5 | `а р а` | 133,944 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ б у о` | 58,557 |
| 2 | `_ с ы л` | 55,999 |
| 3 | `б у о л` | 55,036 |
| 4 | `л л а р` | 54,816 |
| 5 | `о н н а` | 54,239 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ б у о л` | 54,770 |
| 2 | `у о н н а` | 52,074 |
| 3 | `о н н а _` | 50,408 |
| 4 | `_ у о н н` | 50,389 |
| 5 | `_ д и э н` | 41,094 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 356
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.9050 | 1.873 | 6.88 | 263,617 | 9.5% |
| **1** | Subword | 0.8607 | 1.816 | 5.27 | 3,945 | 13.9% |
| **2** | Word | 0.2385 | 1.180 | 1.53 | 1,807,288 | 76.2% |
| **2** | Subword | 0.7585 | 1.692 | 5.05 | 20,757 | 24.1% |
| **3** | Word | 0.0759 | 1.054 | 1.12 | 2,761,887 | 92.4% |
| **3** | Subword | 0.7977 | 1.738 | 4.19 | 104,840 | 20.2% |
| **4** | Word | 0.0318 🏆 | 1.022 | 1.05 | 3,096,286 | 96.8% |
| **4** | Subword | 0.6406 | 1.559 | 2.84 | 439,294 | 35.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `уонна төрөппүт кыргыттара эбиттэр нуучча омуга олус судургу кытайдыы йиси диэн секта буоларын быһыыт...`
2. `диэн тыллааҕын ѳстѳѳҕүн сѳҕѳ махтайа көрдө иһиттэ сууйсуохха диэммин көрдөһө ааттаһа сылдьарга аналл...`
3. `киһи тас хаҕар абалык сир байҕал кытылыгар наарва анныгар кыргыһыыларга кыттыбыт улуу посольствотын ...`

**Context Size 2:**

1. `өй санаа тохтоппот дьонугар кубулуйаллар ол иһин арбита хас суруйдаҕын ахсын саҥаттан саҥа эр киһини...`
2. `өйө санаата кыра эрдэҕиттэн тугу оҥорорун быһааран сахалыы таҥара үөрэҕин нууччалар кэлиэхтэрин инни...`
3. `аан дойду иккис сэриитэ болгария киин куората уонна порта адьария өрөспүүбүлүкэтин киин куората этэ ...`

**Context Size 3:**

1. `өссө маны көр социалистическай үлэ геройдарын тиһигэ саха сирэ быһаарыылар сигэлэр герои страны влад...`
2. `республики саха якутия усть алданский улус саха сирин нэһилиэктэрэ мэҥэ хаҥалас улууһа асср культура...`
3. `каженкин и и үлэ олох үөрэҕэ дьокуускай упк три 100 с 3 каженкин и и үрүҥ айыы буолуу`

**Context Size 4:**

1. `туох барыта икки өрүттээх диэн быһаараллара чуолкайдыыр киһи оҥорор бары быһыылара икки аҥы хайысхал...`
2. `информационный портал республики саха якутия мегино кангаласский улус саха сирин нэһилиэктэрэ сунтаа...`
3. `портал республики саха якутия перезахоронение анемподиста ивановича софронова алампа быһаарыылар алп...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_дисы_ттатыналэл`
2. `ааҕон_соинихсуль`
3. `рбыр._бурэ_ыыллл`

**Context Size 2:**

1. `н_бииртын_тиин_до`
2. `ар_диэстэ_миэттэт`
3. `а_сыыллар_туорини`

**Context Size 3:**

1. `ан_мҕа_ыыппа_таһар`
2. `ларыстыбакка_суннь`
3. `ар_өлбүтэн_бара,_б`

**Context Size 4:**

1. `_буола_1_млн_(ордуг`
2. `_сылдьар_экономичес`
3. `буолан_ытык_кэмҥэ_э`


### 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 (439,294 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 | 122,274 |
| Total Tokens | 3,622,506 |
| Mean Frequency | 29.63 |
| Median Frequency | 4 |
| Frequency Std Dev | 324.35 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | уонна | 50,320 |
| 2 | диэн | 40,412 |
| 3 | киһи | 29,647 |
| 4 | с | 25,150 |
| 5 | саха | 23,654 |
| 6 | бу | 20,603 |
| 7 | ол | 16,185 |
| 8 | сыллаахха | 16,147 |
| 9 | да | 13,610 |
| 10 | и | 13,282 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | харайыахха | 2 |
| 2 | гат | 2 |
| 3 | ингредиен | 2 |
| 4 | arc | 2 |
| 5 | raiders | 2 |
| 6 | таҥханан | 2 |
| 7 | иһиллээһинэ | 2 |
| 8 | таҥхалаан | 2 |
| 9 | биилэнэн | 2 |
| 10 | өргөстөнөн | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0285 |
| R² (Goodness of Fit) | 0.988986 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.4% |
| Top 1,000 | 51.2% |
| Top 5,000 | 72.5% |
| Top 10,000 | 80.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9890 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.4% of corpus
- **Long Tail:** 112,274 words needed for remaining 19.6% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.8478 🏆 | 0.3334 | N/A | N/A |
| **mono_64d** | 64 | 0.8398 | 0.2581 | N/A | N/A |
| **mono_128d** | 128 | 0.8362 | 0.1900 | N/A | N/A |
| **aligned_32d** | 32 | 0.8478 | 0.3244 | 0.0260 | 0.1780 |
| **aligned_64d** | 64 | 0.8398 | 0.2655 | 0.0420 | 0.2160 |
| **aligned_128d** | 128 | 0.8362 | 0.1911 | 0.0880 | 0.2900 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8478 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2604. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.8% 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 | **-0.628** | Low formulaic 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` | сабаҕалааһыннар, сирдьит, сүөлгэ |
| `-к` | кучевой, квинтети, көрдөнүллэр |
| `-т` | тиийинэрэ, тапсан, телеханааллар |
| `-б` | бэрээдэктэниини, барарга, бинтиэпкэни |
| `-а` | аппарат, антонивка, академияны |
| `-м` | майгыламмыт, модьуунунан, метохияны |
| `-д` | дуоһуйар, дьалыҥ, дириэктэрин |
| `-ма` | майгыламмыт, маалдьаҕарыгар, мавзолейыттан |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | өлбүттэрбитин, тапсан, йорктан |
| `-а` | оонньообута, оркестрга, суохха |
| `-р` | сабаҕалааһыннар, дуоһуйар, көрдөнүллэр |
| `-ар` | сабаҕалааһыннар, дуоһуйар, категорияларыгар |
| `-ан` | тапсан, йорктан, хаайыллыан |
| `-ын` | утарарын, программаларын, крайкомын |
| `-ы` | академияны, метохияны, рестораны |
| `-э` | тиийинэрэ, сүөлгэ, үүннэрдэ |

### 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 |
|------|----------|------------------|----------|
| `ллэр` | 1.69x | 122 contexts | үллэр, иллэр, кэллэр |
| `ллар` | 1.49x | 220 contexts | ыллар, аллар, ууллар |
| `һаар` | 1.92x | 56 contexts | аһаары, таһаар, уһаара |
| `иллэ` | 1.54x | 141 contexts | иллэң, чиллэ, иллэҥ |
| `аары` | 1.48x | 170 contexts | баары, шаары, маары |
| `ыыла` | 1.47x | 158 contexts | мыыла, кыыла, сыыла |
| `ахха` | 1.83x | 57 contexts | дахха, тахха, аахха |
| `элэр` | 1.58x | 109 contexts | кэлэр, элэрэ, кэлэри |
| `ттар` | 1.47x | 140 contexts | ыттар, аттар, уттар |
| `ннар` | 1.47x | 125 contexts | раннар, ханнар, гуннар |
| `ылаа` | 1.42x | 128 contexts | тылаа, ылаат, тылаах |
| `үттэ` | 1.64x | 63 contexts | сүттэ, бүттэ, пүттэр |

### 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 |
|--------|--------|-----------|----------|
| `-с` | `-н` | 212 words | соморсун, саҥарарын |
| `-к` | `-н` | 204 words | күнүнэн, комсомолецтарын |
| `-б` | `-н` | 195 words | буһарарын, биллон |
| `-т` | `-н` | 194 words | тириэньэрдэрин, таһаарбыттарын |
| `-к` | `-р` | 141 words | кытаатыннарар, көлөлөөхтөр |
| `-к` | `-а` | 138 words | кронштадка, куурулла |
| `-с` | `-а` | 136 words | сфера, саҥардыллыбыттара |
| `-а` | `-а` | 129 words | арабтарга, айыаҕа |
| `-с` | `-р` | 128 words | сирбитигэр, сууттаммыттар |
| `-б` | `-р` | 110 words | босхолуур, бырааһынньыктыыллар |

### 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 |
|------|-----------------|------------|------|
| эттэхтэринэ | **`эттэхтэри-н-э`** | 7.5 | `н` |
| өйөөһүнүнэн | **`өйөөһүнү-н-эн`** | 7.5 | `н` |
| туттарбат | **`туттарб-а-т`** | 7.5 | `а` |
| фольклоре | **`фолькло-р-е`** | 7.5 | `р` |
| ассириецтары | **`ассириецт-ар-ы`** | 7.5 | `ар` |
| мазендеран | **`мазенде-р-ан`** | 7.5 | `р` |
| сүтүктэнэн | **`сүтүктэ-н-эн`** | 7.5 | `н` |
| миэтэрэнэн | **`миэтэрэ-н-эн`** | 7.5 | `н` |
| сулууспалаахтары | **`сулууспалаахт-ар-ы`** | 7.5 | `ар` |
| студентката | **`студентк-а-та`** | 7.5 | `а` |
| дуоспуруннаах | **`дуоспурунн-а-ах`** | 7.5 | `а` |
| репертуарнай | **`репертуар-н-ай`** | 7.5 | `н` |
| сымнаҕастарын | **`сымнаҕаст-ар-ын`** | 7.5 | `ар` |
| уоппуттарын | **`уоппутт-ар-ын`** | 7.5 | `ар` |
| моделлары | **`моделл-ар-ы`** | 7.5 | `ар` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Yakut 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 (4.82x) |
| N-gram | **2-gram** | Lowest perplexity (356) |
| 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 19:38:04*