---
language: tly
language_name: Talysh
language_family: iranian_western
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-iranian_western
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: 7.114
  - name: best_isotropy
    type: isotropy
    value: 0.4055
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Talysh** 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** | 7.016x | 7.11 | 0.0094% | 10,613 |
| **16k** | 7.056x | 7.15 | 0.0095% | 10,553 |
| **32k** | 7.087x | 7.18 | 0.0095% | 10,507 |
| **64k** | 7.114x 🏆 | 7.21 | 0.0096% | 10,466 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Taryx Hodison Movardəjon Mardəjon Idon, mərosimon ijən xysusijə ružon Səvonon ru...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁taryx ▁hodison ▁movardəjon ▁mardəjon ▁idon , ▁mərosimon ▁ijən ▁xysusijə ▁ružon ... (+2 more)` | 12 |
| 16k | `▁taryx ▁hodison ▁movardəjon ▁mardəjon ▁idon , ▁mərosimon ▁ijən ▁xysusijə ▁ružon ... (+2 more)` | 12 |
| 32k | `▁taryx ▁hodison ▁movardəjon ▁mardəjon ▁idon , ▁mərosimon ▁ijən ▁xysusijə ▁ružon ... (+2 more)` | 12 |
| 64k | `▁taryx ▁hodison ▁movardəjon ▁mardəjon ▁idon , ▁mərosimon ▁ijən ▁xysusijə ▁ružon ... (+2 more)` | 12 |

**Sample 2:** `Tárix Hodisaon Movardəyon Mardon İdon, mərosimon iyən xısusiya rúžon İstinodon`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tárix ▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁mərosimon ▁iyən ▁xısusiya ▁rúžon ... (+1 more)` | 11 |
| 16k | `▁tárix ▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁mərosimon ▁iyən ▁xısusiya ▁rúžon ... (+1 more)` | 11 |
| 32k | `▁tárix ▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁mərosimon ▁iyən ▁xısusiya ▁rúžon ... (+1 more)` | 11 |
| 64k | `▁tárix ▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁mərosimon ▁iyən ▁xısusiya ▁rúžon ... (+1 more)` | 11 |

**Sample 3:** `Hodisaon Movardəyon Mardon İdon, marásimon iyən xısusiya rúžon İstinodon`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁marásimon ▁iyən ▁xısusiya ▁rúžon ▁İstinodon` | 10 |
| 16k | `▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁marásimon ▁iyən ▁xısusiya ▁rúžon ▁İstinodon` | 10 |
| 32k | `▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁marásimon ▁iyən ▁xısusiya ▁rúžon ▁İstinodon` | 10 |
| 64k | `▁hodisaon ▁movardəyon ▁mardon ▁İdon , ▁marásimon ▁iyən ▁xısusiya ▁rúžon ▁İstinodon` | 10 |


### Key Findings

- **Best Compression:** 64k achieves 7.114x compression
- **Lowest UNK Rate:** 8k with 0.0094% 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 | 743 | 9.54 | 4,233 | 54.0% | 82.9% |
| **2-gram** | Subword | 342 🏆 | 8.42 | 2,791 | 61.8% | 98.0% |
| **3-gram** | Word | 856 | 9.74 | 5,805 | 52.1% | 82.2% |
| **3-gram** | Subword | 2,176 | 11.09 | 19,852 | 30.6% | 72.3% |
| **4-gram** | Word | 1,814 | 10.83 | 13,361 | 42.0% | 71.2% |
| **4-gram** | Subword | 6,982 | 12.77 | 74,256 | 21.8% | 54.1% |
| **5-gram** | Word | 1,902 | 10.89 | 11,754 | 38.9% | 70.4% |
| **5-gram** | Subword | 12,141 | 13.57 | 124,411 | 18.4% | 48.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ym avtomobili` | 4,526 |
| 2 | `šəhəronədə gyləje` | 3,397 |
| 3 | `rúžon i̇stinodon` | 1,820 |
| 4 | `xısusiya rúžon` | 1,820 |
| 5 | `hodisaon movardəyon` | 1,816 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `xısusiya rúžon i̇stinodon` | 1,820 |
| 2 | `hodisaon movardəyon mardon` | 1,788 |
| 3 | `movardəyon mardon i̇don` | 1,774 |
| 4 | `vadoəšone ym avtomobili` | 1,765 |
| 5 | `iyən xısusiya rúžon` | 1,714 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hodisaon movardəyon mardon i̇don` | 1,774 |
| 2 | `iyən xısusiya rúžon i̇stinodon` | 1,714 |
| 3 | `dehestanədə dije kom ironi` | 1,547 |
| 4 | `kom ironi gilan ostani` | 1,467 |
| 5 | `dije kom ironi gilan` | 1,398 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dehestanədə dije kom ironi gilan` | 1,398 |
| 2 | `dije kom ironi gilan ostani` | 1,398 |
| 3 | `i̇don mərosimon iyən xısusiya rúžon` | 1,344 |
| 4 | `mərosimon iyən xısusiya rúžon i̇stinodon` | 1,344 |
| 5 | `səvonon šəhristani žimon kardə vyron` | 1,332 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o n` | 70,792 |
| 2 | `ə _` | 52,913 |
| 3 | `n _` | 42,222 |
| 4 | `d ə` | 40,135 |
| 5 | `i _` | 34,998 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o n _` | 28,710 |
| 2 | `d ə _` | 22,125 |
| 3 | `ə d ə` | 21,448 |
| 4 | `e . _` | 16,068 |
| 5 | `a r d` | 12,522 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ə d ə _` | 17,621 |
| 2 | `n ə d ə` | 10,022 |
| 3 | `_ š ə h` | 8,534 |
| 4 | `t o m o` | 8,469 |
| 5 | `o b i l` | 8,462 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n ə d ə _` | 9,258 |
| 2 | `m o b i l` | 8,458 |
| 3 | `t o m o b` | 8,451 |
| 4 | `o m o b i` | 8,448 |
| 5 | `v t o m o` | 8,445 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 342
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~48% 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 | 0.6106 | 1.527 | 3.20 | 43,178 | 38.9% |
| **1** | Subword | 1.0896 | 2.128 | 8.57 | 771 | 0.0% |
| **2** | Word | 0.1424 | 1.104 | 1.26 | 136,913 | 85.8% |
| **2** | Subword | 1.0193 | 2.027 | 5.86 | 6,604 | 0.0% |
| **3** | Word | 0.0435 | 1.031 | 1.07 | 170,237 | 95.7% |
| **3** | Subword | 0.8163 | 1.761 | 3.58 | 38,701 | 18.4% |
| **4** | Word | 0.0232 🏆 | 1.016 | 1.04 | 179,970 | 97.7% |
| **4** | Subword | 0.5105 | 1.425 | 2.14 | 138,401 | 49.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `cy urusijəti cuvašija pajtaxte ym avtomobili soronə də vadoəšone ym avtomobili mercedes benz širkət ...`
2. `ym avtomobili almanijədə vadojdən ym avtomobili cinədə vadoəšone ym vərzyši ve kardedəbe italja še v...`
3. `səvonon avtomobilon istehsal kardə yn ruži ce amerikə materiki ijən xysusijə ružon səvonon ružon səv...`

**Context Size 2:**

1. `ym avtomobili soronədə vadoəšone ym avtomobili italijədə vadoəšone ym avtomobili soronə də vadoəšone...`
2. `šəhəronədə gyləje ym šəhər šahrud ru səpe vašte ijən peš žygo mehmondorəti ijən rəftori cošambə xatu...`
3. `xısusiya rúžon i̇stinodon als fiu vro roa rup af an ast ay ba bar bcl bg br`

**Context Size 3:**

1. `hodisaon movardəyon mardon i̇don mərosimon iyən xısusiya rúžon i̇stinodon als fiu vro roa rup af an ...`
2. `movardəyon mardon i̇don marásimon iyən xısusiya rúžon i̇stinodon als fiu vro roa rup af an ast ay ba`
3. `vadoəšone ym avtomobili soronədə vadoəšone avtomobilon`

**Context Size 4:**

1. `hodisaon movardəyon mardon i̇don marásimon iyən xısusiya rúžon i̇stinodon als fiu vro roa rup af an ...`
2. `dehestanədə dije kom ironi gilan ostani rezvanšəhr šəhristani mijonə baxšədəj səvonon šəhristani žim...`
3. `kom ironi gilan ostani taleš šəhristani havigi baxšədəj səvonon šəhristani žimon kardə vyron`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_bijə_4_initijət`
2. `əbanestarišəding`
3. `omomon_əde)_aino`

**Context Size 2:**

1. `on_i̇stali_merissa`
2. `ə_maj_əhərismə_zi`
3. `n_ovidoəšǧul_di_i̇`

**Context Size 3:**

1. `on_votejdəbili_car`
2. `də_baxšədə_vadoəšo`
3. `ədə_figi_ceh-je_ni`

**Context Size 4:**

1. `ədə_diplom_—_hačči_`
2. `nədə_ənyvyštə_sori_`
3. `_šəhəronədə_isə,_a.`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (138,401 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 | 16,608 |
| Total Tokens | 296,552 |
| Mean Frequency | 17.86 |
| Median Frequency | 3 |
| Frequency Std Dev | 143.66 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | cy | 7,267 |
| 2 | səvonon | 6,324 |
| 3 | ym | 6,121 |
| 4 | avtomobili | 4,536 |
| 5 | bə | 4,007 |
| 6 | gyləje | 3,865 |
| 7 | šəhəronədə | 3,421 |
| 8 | šəhristani | 2,988 |
| 9 | byə | 2,185 |
| 10 | sorədə | 2,110 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | valehəkə | 2 |
| 2 | xyvəton | 2 |
| 3 | арх | 2 |
| 4 | ивинский | 2 |
| 5 | пустырник | 2 |
| 6 | румчерод | 2 |
| 7 | пушкина | 2 |
| 8 | lisejədə | 2 |
| 9 | tribunası | 2 |
| 10 | kolxozci | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0814 |
| R² (Goodness of Fit) | 0.995029 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 46.4% |
| Top 1,000 | 73.8% |
| Top 5,000 | 89.4% |
| Top 10,000 | 95.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9950 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 46.4% of corpus
- **Long Tail:** 6,608 words needed for remaining 4.5% 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 | 0.4055 🏆 | 0.4117 | N/A | N/A |
| **mono_64d** | 64 | 0.1008 | 0.4113 | N/A | N/A |
| **mono_128d** | 128 | 0.0122 | 0.4078 | N/A | N/A |
| **aligned_32d** | 32 | 0.4055 | 0.4071 | 0.0160 | 0.1580 |
| **aligned_64d** | 64 | 0.1008 | 0.4048 | 0.0220 | 0.2140 |
| **aligned_128d** | 128 | 0.0122 | 0.4015 | 0.0400 | 0.2100 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.4055 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4074. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.0% 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 | **0.454** | 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 |
|--------|----------|
| `-m` | mandže, məktəbon, motərizə |
| `-b` | bešin, bell, bəməl |
| `-s` | svtomobili, surgun, sute |
| `-k` | konnektikuti, kolxozi, kurs |
| `-d` | dovran, dəžə, dəbidə |
| `-t` | təbiətədə, təsəvvur, tehroni |
| `-a` | angivin, ailə, arktik |
| `-p` | pənohgorə, purəru, pedagog |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ə` | ətrofədə, pənohgorə, obə |
| `-n` | ruboijon, məktəbon, surgun |
| `-i` | caši, ənənəvi, svtomobili |
| `-də` | ətrofədə, midijədə, təbiətədə |
| `-on` | ruboijon, məktəbon, non |
| `-e` | mandže, sute, ukrajnavyže |
| `-a` | olja, octavia, ymružna |
| `-ti` | konnektikuti, fədokorəti, dyrozəti |

### 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 |
|------|----------|------------------|----------|
| `kard` | 1.60x | 45 contexts | karda, karde, kardə |
| `arde` | 1.41x | 65 contexts | marde, varde, ardeh |
| `onəd` | 1.46x | 52 contexts | lonədə, konədə, mionədə |
| `ardə` | 1.37x | 67 contexts | hardə, vardə, gardə |
| `vard` | 1.59x | 23 contexts | varde, vardə, edvard |
| `nədə` | 1.45x | 30 contexts | ənədə, çinədə, sinədə |
| `sijə` | 1.50x | 23 contexts | asijə, rusijə, asijəku |
| `rədə` | 1.38x | 24 contexts | arədə, šurədə, virədə |
| `omob` | 1.82x | 10 contexts | avtomobil, ávtomobil, svtomobili |
| `rist` | 1.88x | 9 contexts | bristol, xristian, kristian |
| `vono` | 1.39x | 18 contexts | vonon, cəvono, zyvono |
| `əjon` | 1.31x | 20 contexts | rəjon, cəjon, həjon |

### 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 |
|--------|--------|-----------|----------|
| `-m` | `-ə` | 121 words | myborizə, muhitədə |
| `-m` | `-i` | 77 words | müdiri, mandi |
| `-m` | `-n` | 76 words | məhrumijəton, mahnejin |
| `-s` | `-ə` | 72 words | səmavijə, sinifə |
| `-k` | `-ə` | 62 words | kucədə, koməndə |
| `-m` | `-də` | 59 words | muhitədə, məhəlonədə |
| `-h` | `-ə` | 59 words | hardəjnə, həzominə |
| `-d` | `-ə` | 58 words | doədə, devlətonədə |
| `-k` | `-n` | 55 words | kəvšənon, kəson |
| `-b` | `-ə` | 55 words | bəšmə, bəpəštə |

### 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 |
|------|-----------------|------------|------|
| namizədəti | **`namizə-də-ti`** | 7.5 | `də` |
| odəmonədəj | **`odəmonə-də-j`** | 7.5 | `də` |
| ostoroədə | **`ostoro-ə-də`** | 7.5 | `ə` |
| širkətədə | **`širkət-ə-də`** | 7.5 | `ə` |
| sərostəti | **`sərost-ə-ti`** | 7.5 | `ə` |
| hakimiyyətədə | **`hakimiyyət-ə-də`** | 7.5 | `ə` |
| sərkuonədə | **`sərkuon-ə-də`** | 7.5 | `ə` |
| nomerdəti | **`nomer-də-ti`** | 7.5 | `də` |
| təsərrufatədə | **`təsərrufat-ə-də`** | 7.5 | `ə` |
| nyǧyliədə | **`nyǧyli-ə-də`** | 7.5 | `ə` |
| isvecrədə | **`isvecr-ə-də`** | 7.5 | `ə` |
| nyvyšteədə | **`nyvyšte-ə-də`** | 7.5 | `ə` |
| materikiku | **`materik-i-ku`** | 7.5 | `i` |
| kuvejtədə | **`kuvejt-ə-də`** | 7.5 | `ə` |
| muhazirədə | **`muhazir-ə-də`** | 7.5 | `ə` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Talysh 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 (7.11x) |
| N-gram | **2-gram** | Lowest perplexity (342) |
| Markov | **Context-4** | Highest predictability (97.7%) |
| 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: 2026-01-11 01:10:11*