---
language: olo
language_name: Livvi
language_family: uralic_finnic
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_finnic
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: 4.891
  - name: best_isotropy
    type: isotropy
    value: 0.6898
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Livvi** 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** | 3.676x | 3.68 | 0.1137% | 182,997 |
| **16k** | 4.132x | 4.14 | 0.1278% | 162,798 |
| **32k** | 4.545x | 4.55 | 0.1405% | 148,002 |
| **64k** | 4.891x 🏆 | 4.90 | 0.1512% | 137,524 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Midä rodih sinä vuon Ken rodihes sinä vuon Ken kuoli sinä vuon`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁midä ▁rodih ▁sinä ▁vuon ▁ken ▁rodihes ▁sinä ▁vuon ▁ken ▁kuoli ... (+2 more)` | 12 |
| 16k | `▁midä ▁rodih ▁sinä ▁vuon ▁ken ▁rodihes ▁sinä ▁vuon ▁ken ▁kuoli ... (+2 more)` | 12 |
| 32k | `▁midä ▁rodih ▁sinä ▁vuon ▁ken ▁rodihes ▁sinä ▁vuon ▁ken ▁kuoli ... (+2 more)` | 12 |
| 64k | `▁midä ▁rodih ▁sinä ▁vuon ▁ken ▁rodihes ▁sinä ▁vuon ▁ken ▁kuoli ... (+2 more)` | 12 |

**Sample 2:** `Merisinikorendo (Orthetrum cancellatum) on sinikorendoloin suguh kuului korendo.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mer is in ikor endo ▁( ort h etr um ... (+16 more)` | 26 |
| 16k | `▁meris in ikor endo ▁( orth etr um ▁c anc ... (+13 more)` | 23 |
| 32k | `▁meris inikorendo ▁( orth etr um ▁canc ell at um ... (+8 more)` | 18 |
| 64k | `▁merisinikorendo ▁( orthetrum ▁canc ell at um ) ▁on ▁sinikorendoloin ... (+4 more)` | 14 |

**Sample 3:** `Liečehtiedo on tiijollizen tiijon da praktiekallizien metodoin sistiemu, kudaman...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lieč eht iedo ▁on ▁tiij ollizen ▁tiijon ▁da ▁pr akt ... (+25 more)` | 35 |
| 16k | `▁lieč eht iedo ▁on ▁tiijollizen ▁tiijon ▁da ▁pr akt iek ... (+18 more)` | 28 |
| 32k | `▁liečeht iedo ▁on ▁tiijollizen ▁tiijon ▁da ▁praktiek allizien ▁met odoin ... (+14 more)` | 24 |
| 64k | `▁liečehtiedo ▁on ▁tiijollizen ▁tiijon ▁da ▁praktiek allizien ▁metodoin ▁sistiemu , ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.891x compression
- **Lowest UNK Rate:** 8k with 0.1137% 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 | 1,811 | 10.82 | 6,046 | 37.0% | 66.9% |
| **2-gram** | Subword | 316 🏆 | 8.30 | 2,510 | 62.6% | 98.9% |
| **3-gram** | Word | 1,998 | 10.96 | 7,436 | 36.9% | 64.5% |
| **3-gram** | Subword | 2,540 | 11.31 | 17,821 | 23.0% | 69.2% |
| **4-gram** | Word | 3,746 | 11.87 | 13,217 | 30.5% | 53.2% |
| **4-gram** | Subword | 11,661 | 13.51 | 76,149 | 12.6% | 40.3% |
| **5-gram** | Word | 3,362 | 11.72 | 10,586 | 29.5% | 54.3% |
| **5-gram** | Subword | 30,053 | 14.88 | 156,101 | 9.1% | 29.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `karjalan tazavallan` | 1,466 |
| 2 | `sinä vuon` | 1,390 |
| 3 | `pinduala on` | 1,196 |
| 4 | `on sijoitannuhes` | 1,182 |
| 5 | `sinä piän` | 1,095 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `järven pinduala on` | 866 |
| 2 | `järvi kudai on` | 858 |
| 3 | `sijoitannuhes karjalan tazavallan` | 856 |
| 4 | `on sijoitannuhes karjalan` | 855 |
| 5 | `kudai on sijoitannuhes` | 854 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `on sijoitannuhes karjalan tazavallan` | 852 |
| 2 | `kudai on sijoitannuhes karjalan` | 841 |
| 3 | `järvi kudai on sijoitannuhes` | 836 |
| 4 | `metrii korgiembi meren pindua` | 673 |
| 5 | `km järven pindu on` | 663 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kudai on sijoitannuhes karjalan tazavallan` | 841 |
| 2 | `järvi kudai on sijoitannuhes karjalan` | 829 |
| 3 | `kyläkunnan alovehel järven pinduala on` | 614 |
| 4 | `on järvi kudai on sijoitannuhes` | 586 |
| 5 | `rodih sinä vuon ken rodihes` | 449 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 79,897 |
| 2 | `_ k` | 51,186 |
| 3 | `a n` | 42,849 |
| 4 | `e n` | 40,303 |
| 5 | `i n` | 36,766 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n _` | 22,649 |
| 2 | `a n _` | 21,951 |
| 3 | `o n _` | 19,963 |
| 4 | `_ o n` | 15,790 |
| 5 | `n _ k` | 13,751 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ o n _` | 15,313 |
| 2 | `_ d a _` | 9,605 |
| 3 | `j ä r v` | 7,803 |
| 4 | `n _ p i` | 6,425 |
| 5 | `l a n _` | 6,288 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j ä r v e` | 5,611 |
| 2 | `k a r j a` | 5,267 |
| 3 | `a r j a l` | 5,260 |
| 4 | `r j a l a` | 5,139 |
| 5 | `_ k a r j` | 4,787 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 316
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.6069 | 1.523 | 3.28 | 65,772 | 39.3% |
| **1** | Subword | 1.2495 | 2.378 | 9.89 | 551 | 0.0% |
| **2** | Word | 0.1460 | 1.106 | 1.28 | 214,521 | 85.4% |
| **2** | Subword | 1.1250 | 2.181 | 6.23 | 5,449 | 0.0% |
| **3** | Word | 0.0462 | 1.033 | 1.08 | 272,135 | 95.4% |
| **3** | Subword | 0.8604 | 1.815 | 3.88 | 33,912 | 14.0% |
| **4** | Word | 0.0237 🏆 | 1.017 | 1.04 | 289,944 | 97.6% |
| **4** | Subword | 0.6016 | 1.517 | 2.47 | 131,456 | 39.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `on enzimäine on sijoitannuhes karjalan tazavallas kondupohjan piirin kylä on voimattomuksii l ubov t...`
2. `da ruadajien pos olku sumajärvi on 324 782 neliökilometrii vottovaara г янко музыканта переводан луа...`
3. `karjalan tazavallas kondupohjan piirin ven an keeli kiili maakeeli on vokali aa eä diftongas oa ua`

**Context Size 2:**

1. `karjalan tazavallan mujejärven piirin lendieran kyläkundah kuului kylä sen kauti menöy ven an rajal ...`
2. `sinä vuon 28 sulakuudu fredrik i ruoččilaine kunigas ken kuoli sinä piän ken rodihes sinä vuon ken`
3. `pinduala on 616 km rahvahan lugumiäry on 387 489 196 v hengie 4 2 km järven pindu`

**Context Size 3:**

1. `järven pinduala on 1 1 km järvenpindu on 144 7 metrin korgevuol merenpinnalpäi järven lahtespäi vezi...`
2. `järvi kudai on sijoitannuhes karjalan tazavallan puudogan piirin krivcoin kyläkunnan alovehel järven...`
3. `sijoitannuhes karjalan tazavallan kemin piirin viäränkosken kyläkunnan alovehel järven pinduala on 2...`

**Context Size 4:**

1. `on sijoitannuhes karjalan tazavallan kalevalan piirin jyškyjärven kyläkunnan alovehel järven pindual...`
2. `kudai on sijoitannuhes karjalan tazavallan suojärven piirin alovehel järven pinduala on 1 2 km järve...`
3. `järvi kudai on sijoitannuhes karjalan tazavallan kalevalan piirin jyškyjärven kyläkunnan alovehele j...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_tervarie_gagiär`
2. `i_ramezi_kka_puu`
3. `al_hin_vvlielojo`

**Context Size 2:**

1. `n_dah._yhterii._–`
2. `_kajua_se_supuoli`
3. `an_li_j_järvosten`

**Context Size 3:**

1. `en_prot_oli_volliž`
2. `an_km²,_valien_eri`
3. `on_da_tuurimilaine`

**Context Size 4:**

1. `_on_voi_ollah_päivi`
2. `_da_syöjy_toriansko`
3. `järvi_on_mugah_enim`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (131,456 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 | 23,754 |
| Total Tokens | 323,407 |
| Mean Frequency | 13.61 |
| Median Frequency | 3 |
| Frequency Std Dev | 137.09 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | on | 15,359 |
| 2 | da | 9,616 |
| 3 | karjalan | 3,323 |
| 4 | kudai | 2,669 |
| 5 | oli | 2,573 |
| 6 | sinä | 2,491 |
| 7 | se | 2,234 |
| 8 | km | 1,949 |
| 9 | järven | 1,937 |
| 10 | vuvvennu | 1,694 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | alovehella | 2 |
| 2 | kivijogi | 2 |
| 3 | hurstinesiivet | 2 |
| 4 | tankoin | 2 |
| 5 | kaunokirjallisuuden | 2 |
| 6 | kirjailijaliiton | 2 |
| 7 | viččajogi | 2 |
| 8 | viččajärvi | 2 |
| 9 | nuokkijärveh | 2 |
| 10 | crottetan | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0015 |
| R² (Goodness of Fit) | 0.996450 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 34.5% |
| Top 1,000 | 62.9% |
| Top 5,000 | 81.9% |
| Top 10,000 | 89.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9965 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 34.5% of corpus
- **Long Tail:** 13,754 words needed for remaining 10.1% 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 | 0.6898 | 0.3579 | N/A | N/A |
| **mono_64d** | 64 | 0.2488 | 0.3561 | N/A | N/A |
| **mono_128d** | 128 | 0.0385 | 0.3444 | N/A | N/A |
| **aligned_32d** | 32 | 0.6898 🏆 | 0.3597 | 0.0160 | 0.1400 |
| **aligned_64d** | 64 | 0.2488 | 0.3454 | 0.0300 | 0.2300 |
| **aligned_128d** | 128 | 0.0385 | 0.3507 | 0.0540 | 0.2620 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6898 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3524. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.4% 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 | **0.855** | 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 |
|--------|----------|
| `-k` | käyttämine, kuduo, käskys |
| `-s` | suojoki, suolattomas, sundsvall |
| `-p` | poliittizen, poikkevuksennu, pohjazii |
| `-m` | mauri, majakovskii, muan |
| `-t` | toinegi, tulenisku, tunnetuimat |
| `-a` | ajatus, azerbaidžuananke, atlantiekan |
| `-l` | lähte, luodehpuoles, laulava |
| `-ka` | kazahstananke, kaitajärven, kaukozen |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | filippinoin, jevroupan, poliittizen |
| `-i` | suojoki, toinegi, nimesgi |
| `-en` | poliittizen, kuulujien, šveitsarien |
| `-s` | jäičäs, ajatus, estimates |
| `-u` | vuodizennu, poikkevuksennu, ohjattu |
| `-an` | jevroupan, dunan, muan |
| `-h` | niih, jiännyh, käskiettih |
| `-e` | lähte, käyttämine, azerbaidžuananke |

### 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 |
|------|----------|------------------|----------|
| `järv` | 1.86x | 57 contexts | järvi, järves, järven |
| `jala` | 1.92x | 27 contexts | jalat, jalal, karjala |
| `ttih` | 2.02x | 22 contexts | ruuttih, ruattih, piettih |
| `ärve` | 1.92x | 17 contexts | ärven, järves, järven |
| `iiri` | 1.88x | 16 contexts | hiiri, piiri, piiril |
| `kiel` | 1.61x | 25 contexts | kiely, kieli, kieleh |
| `kirj` | 1.73x | 15 contexts | kirju, kirja, kirjah |
| `uvve` | 1.52x | 20 contexts | uvvel, uvves, uvvet |
| `piir` | 1.79x | 10 contexts | piiri, piiril, piirit |
| `rjal` | 1.72x | 10 contexts | karjal, karjalu, karjala |
| `pind` | 2.05x | 6 contexts | pindu, pindua, pindah |
| `indu` | 1.31x | 20 contexts | pindu, rindu, uindu |

### 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 |
|--------|--------|-----------|----------|
| `-k` | `-n` | 240 words | konsulan, klassifikatsien |
| `-p` | `-n` | 139 words | plankan, persienlahten |
| `-k` | `-i` | 124 words | kiändi, kirjoi |
| `-s` | `-n` | 120 words | suolusmäen, saiman |
| `-k` | `-h` | 117 words | käyttöh, korpijärveh |
| `-m` | `-n` | 109 words | modernismin, mjanmaran |
| `-k` | `-en` | 103 words | klassifikatsien, karibien |
| `-t` | `-n` | 98 words | tarton, tradition |
| `-p` | `-i` | 96 words | pahanluadii, piirrettylöi |
| `-k` | `-u` | 92 words | kandiduattu, kirjalližushistourikku |

### 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 |
|------|-----------------|------------|------|
| filosoufies | **`filosouf-i-es`** | 7.5 | `i` |
| tevollizuon | **`tevolliz-u-on`** | 7.5 | `u` |
| järvenalah | **`järven-al-ah`** | 7.5 | `al` |
| neitronat | **`neitro-n-at`** | 7.5 | `n` |
| sekretarinnu | **`sekretarin-n-u`** | 7.5 | `n` |
| ičepiänneh | **`ičepiän-n-eh`** | 7.5 | `n` |
| löydäjänny | **`löydäjän-n-y`** | 7.5 | `n` |
| loppienuh | **`loppien-u-h`** | 7.5 | `u` |
| suvialovehil | **`su-vi-alovehil`** | 7.5 | `alovehil` |
| kažirodukunnan | **`kažirodukun-n-an`** | 7.5 | `n` |
| tundietun | **`tundie-tu-n`** | 7.5 | `tu` |
| suojärvessah | **`suojärves-s-ah`** | 7.5 | `s` |
| kiännöksien | **`kiännöks-i-en`** | 7.5 | `i` |
| piälikönny | **`piälikön-n-y`** | 7.5 | `n` |
| kaivandukoneh | **`kaivanduko-n-eh`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Livvi 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 (4.89x) |
| N-gram | **2-gram** | Lowest perplexity (316) |
| Markov | **Context-4** | Highest predictability (97.6%) |
| 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 16:33:55*