---
language: ltg
language_name: Latgalian
language_family: baltic
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-baltic
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: 5.184
  - name: best_isotropy
    type: isotropy
    value: 0.4321
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Latgalian** 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** | 3.845x | 3.85 | 0.1136% | 209,537 |
| **16k** | 4.349x | 4.35 | 0.1284% | 185,293 |
| **32k** | 4.833x | 4.84 | 0.1428% | 166,704 |
| **64k** | 5.184x 🏆 | 5.19 | 0.1531% | 155,441 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Hernmans von Baļke () beja pyrmais Livonejis ordyna magistris. Beja daguojumūs n...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁h ern mans ▁von ▁baļ ke ▁() ▁beja ▁pyrmais ▁livonejis ... (+19 more)` | 29 |
| 16k | `▁hern mans ▁von ▁baļ ke ▁() ▁beja ▁pyrmais ▁livonejis ▁ordyna ... (+17 more)` | 27 |
| 32k | `▁hern mans ▁von ▁baļke ▁() ▁beja ▁pyrmais ▁livonejis ▁ordyna ▁magistris ... (+15 more)` | 25 |
| 64k | `▁hernmans ▁von ▁baļke ▁() ▁beja ▁pyrmais ▁livonejis ▁ordyna ▁magistris . ... (+14 more)` | 24 |

**Sample 2:** `Tbilisi — Gruzejis golvysmīsts i pats leluokais mīsts.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁t b ilis i ▁— ▁gr uz ejis ▁golvysmīsts ▁i ... (+4 more)` | 14 |
| 16k | `▁t b ilis i ▁— ▁gruz ejis ▁golvysmīsts ▁i ▁pats ... (+3 more)` | 13 |
| 32k | `▁tbilisi ▁— ▁gruzejis ▁golvysmīsts ▁i ▁pats ▁leluokais ▁mīsts .` | 9 |
| 64k | `▁tbilisi ▁— ▁gruzejis ▁golvysmīsts ▁i ▁pats ▁leluokais ▁mīsts .` | 9 |

**Sample 3:** `Bygucs irā latgaļu tradicionalais gavieņa laika iedīņs nu sadukurātu buļbu, pupu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁by gu cs ▁irā ▁latgaļu ▁tradicionalais ▁gavieņa ▁laika ▁iedīņs ▁nu ... (+13 more)` | 23 |
| 16k | `▁bygucs ▁irā ▁latgaļu ▁tradicionalais ▁gavieņa ▁laika ▁iedīņs ▁nu ▁sad ukur ... (+9 more)` | 19 |
| 32k | `▁bygucs ▁irā ▁latgaļu ▁tradicionalais ▁gavieņa ▁laika ▁iedīņs ▁nu ▁sadukur ātu ... (+8 more)` | 18 |
| 64k | `▁bygucs ▁irā ▁latgaļu ▁tradicionalais ▁gavieņa ▁laika ▁iedīņs ▁nu ▁sadukurātu ▁buļbu ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 5.184x compression
- **Lowest UNK Rate:** 8k with 0.1136% 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 | 1,129 | 10.14 | 1,614 | 26.6% | 83.1% |
| **2-gram** | Subword | 359 🏆 | 8.49 | 1,848 | 58.3% | 98.7% |
| **3-gram** | Word | 1,202 | 10.23 | 1,863 | 29.0% | 79.0% |
| **3-gram** | Subword | 2,922 | 11.51 | 12,393 | 21.1% | 65.0% |
| **4-gram** | Word | 2,659 | 11.38 | 4,039 | 21.2% | 54.7% |
| **4-gram** | Subword | 12,757 | 13.64 | 46,485 | 11.1% | 36.0% |
| **5-gram** | Word | 2,091 | 11.03 | 3,145 | 23.8% | 59.7% |
| **5-gram** | Subword | 28,000 | 14.77 | 80,144 | 8.2% | 25.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nūruodis i` | 196 |
| 2 | `i olūti` | 196 |
| 3 | `nūvoda teritoriskais` | 159 |
| 4 | `teritoriskais padalīņs` | 157 |
| 5 | `pogosts irā` | 136 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nūruodis i olūti` | 196 |
| 2 | `nūvoda teritoriskais padalīņs` | 135 |
| 3 | `teritoriskais padalīņs vydzemē` | 83 |
| 4 | `padalīņs vydzemē pogosta` | 73 |
| 5 | `vydzemē pogosta centrys` | 71 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nūvoda teritoriskais padalīņs vydzemē` | 77 |
| 2 | `teritoriskais padalīņs vydzemē pogosta` | 73 |
| 3 | `padalīņs vydzemē pogosta centrys` | 71 |
| 4 | `pogosts tur rūbežu ar` | 50 |
| 5 | `a s preses nams` | 44 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nūvoda teritoriskais padalīņs vydzemē pogosta` | 73 |
| 2 | `teritoriskais padalīņs vydzemē pogosta centrys` | 71 |
| 3 | `pagasti enciklopēdija a s preses` | 42 |
| 4 | `latvijas pagasti enciklopēdija a s` | 42 |
| 5 | `a s preses nams rīga` | 42 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s _` | 26,697 |
| 2 | `a _` | 14,824 |
| 3 | `_ p` | 11,899 |
| 4 | `u _` | 11,109 |
| 5 | `u o` | 10,394 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `y s _` | 7,166 |
| 2 | `i s _` | 5,868 |
| 3 | `_ i _` | 3,658 |
| 4 | `s _ p` | 3,356 |
| 5 | `_ p a` | 3,202 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ p o g` | 2,252 |
| 2 | `g o s t` | 2,247 |
| 3 | `p o g o` | 2,246 |
| 4 | `o g o s` | 2,243 |
| 5 | `j i s _` | 2,080 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `p o g o s` | 2,242 |
| 2 | `o g o s t` | 2,242 |
| 3 | `_ p o g o` | 2,222 |
| 4 | `e j i s _` | 1,847 |
| 5 | `_ l a t g` | 1,295 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 359
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.5622 | 1.477 | 2.79 | 29,368 | 43.8% |
| **1** | Subword | 1.2575 | 2.391 | 10.03 | 386 | 0.0% |
| **2** | Word | 0.1160 | 1.084 | 1.18 | 81,444 | 88.4% |
| **2** | Subword | 1.1593 | 2.234 | 6.15 | 3,869 | 0.0% |
| **3** | Word | 0.0312 | 1.022 | 1.04 | 95,629 | 96.9% |
| **3** | Subword | 0.8465 | 1.798 | 3.54 | 23,778 | 15.3% |
| **4** | Word | 0.0149 🏆 | 1.010 | 1.02 | 99,029 | 98.5% |
| **4** | Subword | 0.5542 | 1.468 | 2.20 | 84,057 | 44.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i aļternativuos muzykys školā nu nazcik myudu iz zemi nūpierka lītovys i sagvuordus sovetu matematik...`
2. `nu 14 3 limbažu nūvoda teritoriskais padalīņs vydzemē kas tam normali izapiļdeit i snīgs izkreit dek...`
3. `irā latgaļu izdavumu izguoja pošā laikā pa cytam elementam atributu style stiļs 18 godu tyukstūšys r...`

**Context Size 2:**

1. `nūruodis i olūti viesture sadraudzeiba nūruodis i olūti janina kūrseite anna stafecka latgola volūda...`
2. `nūvoda teritoriskais padalīņs vydzemē i latgolā kai golvonuo europys areala dīnavydu rūbežā napalelā...`
3. `teritoriskais padalīņs vydzemē pogosta centrys skuki pleiki nauļāni gromyki auguļova jonini zeimeigi...`

**Context Size 3:**

1. `nūvoda teritoriskais padalīņs vydzemē kas sasadora 3 pogostim brenguļu kauguru i trykuotys pogosta`
2. `nūruodis i olūti teiklavītys raudive anas platyrhynchos raudive`
3. `teritoriskais padalīņs vydzemē pogosta centrys galgovska nūruodis teiklavītys galgovskys pogosts guļ...`

**Context Size 4:**

1. `nūvoda teritoriskais padalīņs vydzemē pogosta centrys burtinīks nūruodis teiklavītys burtinīka pogos...`
2. `teritoriskais padalīņs vydzemē pogosta centrys vylpulka nūruodis`
3. `padalīņs vydzemē pogosta centrys jaunlaicine nūruodis`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pe_kra,_da_pā._`
2. `aitui_nacylūdicā`
3. `s_iaieists_bogot`

**Context Size 2:**

1. `s_pojs._dasdīņs_c`
2. `a_i_linacānu_īlī_`
3. `_pošonoja_iseito_`

**Context Size 3:**

1. `ys_planamsa_punkti`
2. `is_austrumā._nūvod`
3. `_i_medņovysova_dor`

**Context Size 4:**

1. `_pogostā_dzeiguo_pa`
2. `gostā,_gods_canadā_`
3. `pogostu_pogosts_var`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (84,057 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 | 10,308 |
| Total Tokens | 93,904 |
| Mean Frequency | 9.11 |
| Median Frequency | 3 |
| Frequency Std Dev | 48.87 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 3,760 |
| 2 | nu | 1,224 |
| 3 | pogosts | 1,012 |
| 4 | irā | 958 |
| 5 | ar | 789 |
| 6 | godā | 708 |
| 7 | nūvoda | 575 |
| 8 | a | 505 |
| 9 | pogosta | 483 |
| 10 | kai | 466 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | said | 2 |
| 2 | little | 2 |
| 3 | baby | 2 |
| 4 | hide | 2 |
| 5 | much | 2 |
| 6 | see | 2 |
| 7 | izjemūt | 2 |
| 8 | way | 2 |
| 9 | garden | 2 |
| 10 | drupys | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9146 |
| R² (Goodness of Fit) | 0.986958 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 30.0% |
| Top 1,000 | 62.1% |
| Top 5,000 | 87.4% |
| Top 10,000 | 99.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9870 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 30.0% of corpus
- **Long Tail:** 308 words needed for remaining 0.7% 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 | 0.4321 🏆 | 0.4107 | N/A | N/A |
| **mono_64d** | 64 | 0.1003 | 0.4086 | N/A | N/A |
| **mono_128d** | 128 | 0.0125 | 0.4060 | N/A | N/A |
| **aligned_32d** | 32 | 0.4321 | 0.4131 | 0.0160 | 0.1700 |
| **aligned_64d** | 64 | 0.1003 | 0.3974 | 0.0420 | 0.2080 |
| **aligned_128d** | 128 | 0.0125 | 0.3946 | 0.0780 | 0.2380 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.4321 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4051. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 7.8% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **1.350** | 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 |
|--------|----------|
| `-s` | senegals, sataisūt, svātuo |
| `-p` | pasauktys, point, pamat |
| `-k` | kryšānu, koru, kleštoru |
| `-a` | atlaidys, american, aleksandris |
| `-m` | magma, muzykā, musulmoni |
| `-v` | vītolvys, vosor, vacupē |
| `-d` | dolaru, dekters, desmarest |
| `-l` | lels, lūkūt, likvidātuo |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | atlaidys, lels, uralensis |
| `-a` | opera, magma, garuma |
| `-u` | kryšānu, dolaru, koru |
| `-ys` | atlaidys, pasauktys, sardzeibys |
| `-is` | uralensis, rusifikacejis, aleksandris |
| `-i` | cierkvi, rogi, sīvīti |
| `-ja` | antologija, sarja, pasaruodeja |
| `-ā` | taidā, muzykā, okā |

### 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 |
|------|----------|------------------|----------|
| `ejis` | 1.65x | 30 contexts | mejis, bejis, siejis |
| `stei` | 1.50x | 30 contexts | vaļstei, raksteit, raksteis |
| `olūd` | 2.03x | 9 contexts | volūdu, volūda, volūdā |
| `skai` | 1.45x | 23 contexts | skaitu, skaitā, skaits |
| `zeiv` | 1.65x | 14 contexts | dzeiv, dzeivo, dzeive |
| `volū` | 2.03x | 8 contexts | volūdu, volūda, volūdā |
| `atga` | 2.00x | 8 contexts | latgali, latgale, latgaļu |
| `dzei` | 1.44x | 19 contexts | dzeiv, dzeivo, dzeive |
| `eiby` | 1.76x | 10 contexts | vīneibys, vareibys, ticeibys |
| `teib` | 1.59x | 13 contexts | tauteibu, plateibu, kusteiba |
| `ūvod` | 1.90x | 8 contexts | nūvoda, nūvodā, nūvodu |
| `nūvo` | 1.90x | 8 contexts | nūvoda, nūvodā, nūvodu |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-s` | 264 words | pošleluos, pyrmškolys |
| `-s` | `-s` | 246 words | sacapums, saroksts |
| `-a` | `-s` | 196 words | astis, auss |
| `-v` | `-s` | 178 words | vydtautyskūs, vydslaikūs |
| `-d` | `-s` | 146 words | doktoranturys, dīnavydlatgolys |
| `-k` | `-s` | 146 words | katuoleibys, kusteibys |
| `-p` | `-a` | 145 words | pebraļa, pabeigta |
| `-m` | `-s` | 118 words | maratons, mežūtnis |
| `-l` | `-s` | 113 words | laikvuords, lingvists |
| `-s` | `-a` | 111 words | sloveneja, statusa |

### 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 |
|------|-----------------|------------|------|
| izacēluse | **`izacēlu-s-e`** | 7.5 | `s` |
| bengalensis | **`bengalen-s-is`** | 7.5 | `s` |
| publiciejuse | **`publicieju-s-e`** | 7.5 | `s` |
| buoreņtīsa | **`buoreņtī-s-a`** | 7.5 | `s` |
| afrikaans | **`afrika-a-ns`** | 7.5 | `a` |
| literārajā | **`literār-a-jā`** | 7.5 | `a` |
| frameless | **`framele-s-s`** | 7.5 | `s` |
| izacāluse | **`izacālu-s-e`** | 7.5 | `s` |
| hondurass | **`hondura-s-s`** | 7.5 | `s` |
| phillipsi | **`phillip-s-i`** | 7.5 | `s` |
| izslyvušajā | **`izslyvuš-a-jā`** | 7.5 | `a` |
| golvonais | **`golvon-a-is`** | 7.5 | `a` |
| desmarest | **`desmare-s-t`** | 7.5 | `s` |
| atsaroduse | **`atsarodu-s-e`** | 7.5 | `s` |
| rūkroksti | **`rūkrok-s-ti`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Latgalian 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 (5.18x) |
| N-gram | **2-gram** | Lowest perplexity (359) |
| Markov | **Context-4** | Highest predictability (98.5%) |
| 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 11:25:06*