---
language: xal
language_name: Kalmyk
language_family: mongolic
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-mongolic
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: 3.639
  - name: best_isotropy
    type: isotropy
    value: 0.1174
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kalmyk** 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** | 3.145x | 3.16 | 0.5768% | 91,534 |
| **16k** | 3.407x | 3.42 | 0.6248% | 84,511 |
| **32k** | 3.639x 🏆 | 3.65 | 0.6673% | 79,119 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Бар сарин 11 григорин литд 345-гч (немсн җил болхла, 346-гч) җилин өдр болҗана. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁бар ▁сарин ▁ 1 1 ▁григорин ▁литд ▁ 3 4 ... (+34 more)` | 44 |
| 16k | `▁бар ▁сарин ▁ 1 1 ▁григорин ▁литд ▁ 3 4 ... (+34 more)` | 44 |
| 32k | `▁бар ▁сарин ▁ 1 1 ▁григорин ▁литд ▁ 3 4 ... (+34 more)` | 44 |

**Sample 2:** `Үсын теҗәлтенер (лат. Mammalia, ) — зоота, әмде төргеч, үстә көкүлдүг аңгудин ян...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁үсын ▁теҗәл тенер ▁( лат . ▁mammal ia , ▁) ... (+29 more)` | 39 |
| 16k | `▁үсын ▁теҗәлтенер ▁( лат . ▁mammalia , ▁) ▁— ▁зоота ... (+21 more)` | 31 |
| 32k | `▁үсын ▁теҗәлтенер ▁( лат . ▁mammalia , ▁) ▁— ▁зоота ... (+19 more)` | 29 |

**Sample 3:** `Цимлянск — Орсин Ниицәнә хотол балһсн. Ростова төгәлң. Ростов-на-Дону 236 киломе...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ц им л янск ▁— ▁орсин ▁ниицәнә ▁хотол ▁балһсн . ... (+16 more)` | 26 |
| 16k | `▁цимлянск ▁— ▁орсин ▁ниицәнә ▁хотол ▁балһсн . ▁ростова ▁төгәлң . ... (+13 more)` | 23 |
| 32k | `▁цимлянск ▁— ▁орсин ▁ниицәнә ▁хотол ▁балһсн . ▁ростова ▁төгәлң . ... (+13 more)` | 23 |


### Key Findings

- **Best Compression:** 32k achieves 3.639x compression
- **Lowest UNK Rate:** 8k with 0.5768% 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 | 365 🏆 | 8.51 | 947 | 61.0% | 100.0% |
| **2-gram** | Subword | 527 | 9.04 | 2,101 | 48.1% | 96.3% |
| **3-gram** | Word | 386 | 8.59 | 1,166 | 60.2% | 97.8% |
| **3-gram** | Subword | 3,159 | 11.63 | 12,446 | 21.8% | 63.5% |
| **4-gram** | Word | 581 | 9.18 | 2,282 | 53.6% | 87.8% |
| **4-gram** | Subword | 8,459 | 13.05 | 34,726 | 14.3% | 47.4% |
| **5-gram** | Word | 552 | 9.11 | 2,011 | 52.9% | 88.2% |
| **5-gram** | Subword | 10,799 | 13.40 | 42,887 | 13.1% | 45.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `шин җил` | 368 |
| 2 | `өдр болҗана` | 367 |
| 3 | `җилин өдр` | 367 |
| 4 | `җил күртл` | 366 |
| 5 | `григорин литд` | 366 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `җилин өдр болҗана` | 365 |
| 2 | `өдр болҗана шин` | 365 |
| 3 | `болҗана шин җил` | 364 |
| 4 | `немсн җил болхла` | 364 |
| 5 | `шин җил күртл` | 364 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `җилин өдр болҗана шин` | 365 |
| 2 | `өдр болҗана шин җил` | 364 |
| 3 | `болҗана шин җил күртл` | 363 |
| 4 | `гч җилин өдр болҗана` | 361 |
| 5 | `өдрмүд улдв йовдлмуд байруд` | 359 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `җилин өдр болҗана шин җил` | 364 |
| 2 | `өдр болҗана шин җил күртл` | 363 |
| 3 | `гч җилин өдр болҗана шин` | 361 |
| 4 | `өдрмүд улдв йовдлмуд байруд төрсн` | 358 |
| 5 | `улдв йовдлмуд байруд төрсн әмтн` | 358 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _` | 13,316 |
| 2 | `_ б` | 7,702 |
| 3 | `. _` | 6,970 |
| 4 | `и н` | 6,283 |
| 5 | `_ т` | 4,777 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `и н _` | 4,804 |
| 2 | `_ б о` | 2,339 |
| 3 | `б о л` | 2,207 |
| 4 | `_ җ и` | 2,083 |
| 5 | `җ и л` | 2,057 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ б о л` | 2,198 |
| 2 | `_ җ и л` | 2,036 |
| 3 | `_ б ә ә` | 1,180 |
| 4 | `н _ җ и` | 1,112 |
| 5 | `р и н _` | 1,078 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `н _ җ и л` | 1,102 |
| 2 | `_ з а а л` | 879 |
| 3 | `_ б о л җ` | 819 |
| 4 | `җ а н а .` | 799 |
| 5 | `_ ә м т н` | 797 |


### Key Findings

- **Best Perplexity:** 2-gram (word) with 365
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~45% 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 | 0.4971 | 1.411 | 2.33 | 16,793 | 50.3% |
| **1** | Subword | 0.8848 | 1.847 | 5.67 | 990 | 11.5% |
| **2** | Word | 0.0907 | 1.065 | 1.18 | 38,734 | 90.9% |
| **2** | Subword | 0.8739 | 1.833 | 4.93 | 5,582 | 12.6% |
| **3** | Word | 0.0323 | 1.023 | 1.07 | 45,269 | 96.8% |
| **3** | Subword | 0.6900 | 1.613 | 2.79 | 27,441 | 31.0% |
| **4** | Word | 0.0186 🏆 | 1.013 | 1.05 | 48,120 | 98.1% |
| **4** | Subword | 0.3734 | 1.295 | 1.70 | 76,376 | 62.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `җил болхла 300 359 курсан билә заалт заалһуд официальный сайт городской администрации зах улс төр уг...`
2. `болҗана яһад гихлә күцәнә эн орн нутг һарһҗана ода чигн сольврмудт дурго әмтн өңгрсн әмтн өңгрсн`
3. `гч немсн җил инҗин лиҗ хальмг таңһачд девлет тілі медицихәнә шинҗәнә өөрдн келнд бәәсн адучнрин хамц...`

**Context Size 2:**

1. `шин җил күртл 122 өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз лит`
2. `җилин өдр болҗана шин җил күртл 286 өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз хальмг`
3. `өдр болҗана шин җил күртл 258 өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз лит`

**Context Size 3:**

1. `җилин өдр болҗана шин җил күртл 97 өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз лит`
2. `өдр болҗана шин җил күртл 250 өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз лит`
3. `өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз лит`

**Context Size 4:**

1. `җилин өдр болҗана шин җил күртл 195 өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз лит`
2. `өдр болҗана шин җил күртл 309 немсн җил болхла 310 гч җилин өдр болҗана шин җил күртл 107 өдрмүд`
3. `болҗана шин җил күртл 146 өдрмүд улдв йовдлмуд байруд төрсн әмтн өңгрсн әмтн янз лит`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_илһурелиетөөхое`
2. `несуд_боң._ачабо`
3. `аз._пехуша_җәң_*`

**Context Size 2:**

1. `н_нутн_бәәдлмудын`
2. `_биш_улус_тан,_—_`
3. `._100_курамьд_бол`

**Context Size 3:**

1. `ин_сайх_явуудольск`
2. `_болн-күмн_болн-кү`
3. `болсын_билә_энд_йи`

**Context Size 4:**

1. `_болхала_зогдр_җилд`
2. `_җилд_бәәнә._үлгүрл`
3. `_бәәдг_күүнә_то_10_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (76,376 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 | 5,702 |
| Total Tokens | 60,937 |
| Mean Frequency | 10.69 |
| Median Frequency | 3 |
| Frequency Std Dev | 41.92 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | җил | 788 |
| 2 | әмтн | 783 |
| 3 | болҗана | 774 |
| 4 | гч | 708 |
| 5 | җилд | 669 |
| 6 | билә | 616 |
| 7 | янз | 556 |
| 8 | өдр | 504 |
| 9 | җилин | 487 |
| 10 | балһсн | 481 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | занда | 2 |
| 2 | вокал | 2 |
| 3 | шугран | 2 |
| 4 | веран | 2 |
| 5 | белгородин | 2 |
| 6 | российск | 2 |
| 7 | геральдическ | 2 |
| 8 | решение | 2 |
| 9 | хувнь | 2 |
| 10 | зургдсн | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9603 |
| R² (Goodness of Fit) | 0.980684 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 44.4% |
| Top 1,000 | 76.2% |
| Top 5,000 | 97.7% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9807 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 44.4% of corpus
- **Long Tail:** -4,298 words needed for remaining 100.0% coverage

---
## 5. Word Embeddings Evaluation

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

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

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

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


### 5.1 Cross-Lingual Alignment

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

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


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.1174 🏆 | 0.4833 | N/A | N/A |
| **mono_64d** | 64 | 0.0176 | 0.4778 | N/A | N/A |
| **mono_128d** | 128 | 0.0022 | 0.4977 | N/A | N/A |
| **aligned_32d** | 32 | 0.1174 | 0.4950 | 0.0189 | 0.1483 |
| **aligned_64d** | 64 | 0.0176 | 0.4980 | 0.0252 | 0.1577 |
| **aligned_128d** | 128 | 0.0022 | 0.5085 | 0.0252 | 0.1451 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.1174 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4934. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 2.5% 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 | **0.960** | 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 |
|--------|----------|
| `-б` | буудян, барбадосин, большая |
| `-к` | кок, клинцы, кев |
| `-т` | терек, температура, тэре |
| `-х` | холбогдол, хүмүүс, храмы |
| `-с` | саранск, сууна, салават |
| `-а` | административті, априкин, амта |
| `-н` | ниитә, николаевск, нутугт |
| `-м` | модна, моңһол, масидин |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-н` | гөрнзин, априкин, җилдән |
| `-ин` | гөрнзин, априкин, масидин |
| `-а` | модна, сууна, индира |
| `-р` | залвар, бооцаһар, алдар |
| `-д` | дуудад, моңһлмуд, пролетармуд |
| `-ан` | холвалһан, олан, бооцан |
| `-к` | терек, саранск, кок |
| `-ск` | саранск, николаевск, краснослободск |

### 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 |
|------|----------|------------------|----------|
| `бичи` | 1.75x | 12 contexts | бичиг, бичих, бичиги |
| `горо` | 1.88x | 9 contexts | город, города, городе |
| `олһа` | 1.79x | 9 contexts | толһа, толһан, болһан |
| `алһс` | 1.83x | 8 contexts | балһсн, балһсан, балһсна |
| `парт` | 1.88x | 7 contexts | парти, парть, партии |
| `лһсн` | 1.83x | 6 contexts | балһсн, балһсна, балһснь |
| `толһ` | 1.82x | 6 contexts | толһа, толһан, толһас |
| `ород` | 1.88x | 5 contexts | город, города, городе |
| `балһ` | 1.83x | 5 contexts | балһсн, балһсан, балһсна |

### 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 |
|--------|--------|-----------|----------|
| `-б` | `-н` | 68 words | буудян, барбадосин |
| `-к` | `-н` | 41 words | киевийн, калион |
| `-т` | `-н` | 41 words | тәвдмн, трансцендентн |
| `-м` | `-н` | 33 words | масидин, медлин |
| `-б` | `-ин` | 31 words | барбадосин, балкармудин |
| `-х` | `-н` | 31 words | хальмгудын, холвалһан |
| `-а` | `-н` | 30 words | априкин, арһон |
| `-с` | `-н` | 30 words | салвадормудин, суданмудин |
| `-к` | `-ин` | 28 words | кергүдин, камерудин |
| `-н` | `-н` | 25 words | нутгийн, нэгэн |

### 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 |
|------|-----------------|------------|------|
| возрождения | **`возрожде-н-ия`** | 7.5 | `н` |
| холвалһана | **`холвалһа-н-а`** | 7.5 | `н` |
| федеративная | **`федератив-н-ая`** | 7.5 | `н` |
| карамчанд | **`карамча-н-д`** | 7.5 | `н` |
| партияның | **`партия-н-ың`** | 7.5 | `н` |
| закаменск | **`закаме-н-ск`** | 7.5 | `н` |
| государственн | **`государстве-н-н`** | 7.5 | `н` |
| суңһугдана | **`суңһугда-н-а`** | 7.5 | `н` |
| провинциясының | **`провинциясы-н-ың`** | 7.5 | `н` |
| лихтенштейна | **`лихтенштей-н-а`** | 7.5 | `н` |
| партиясының | **`партиясы-н-ың`** | 7.5 | `н` |
| апшеронск | **`апшеро-н-ск`** | 7.5 | `н` |
| депутатнар | **`депутат-н-ар`** | 7.5 | `н` |
| дагестана | **`дагеста-н-а`** | 7.5 | `н` |
| дуһарҗана | **`дуһарҗа-н-а`** | 7.5 | `н` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kalmyk shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **32k BPE** | Best compression (3.64x) |
| N-gram | **2-gram** | Lowest perplexity (365) |
| Markov | **Context-4** | Highest predictability (98.1%) |
| 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 04:51:14*