---
language: lv
language_name: Latvian
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: 4.859
  - name: best_isotropy
    type: isotropy
    value: 0.8084
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Latvian** 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** | 3.645x | 3.65 | 0.1438% | 1,511,025 |
| **16k** | 4.088x | 4.09 | 0.1613% | 1,347,208 |
| **32k** | 4.505x | 4.51 | 0.1778% | 1,222,479 |
| **64k** | 4.859x 🏆 | 4.86 | 0.1917% | 1,133,428 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Vārniņas ir ciems Smiltenes novada Launkalnes pagastā. Atrodas pagasta dienvidau...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁vār n iņas ▁ir ▁ciems ▁smiltenes ▁novada ▁lau n kalnes ... (+17 more)` | 27 |
| 16k | `▁vār n iņas ▁ir ▁ciems ▁smiltenes ▁novada ▁laun kalnes ▁pagastā ... (+16 more)` | 26 |
| 32k | `▁vār n iņas ▁ir ▁ciems ▁smiltenes ▁novada ▁laun kalnes ▁pagastā ... (+16 more)` | 26 |
| 64k | `▁vārn iņas ▁ir ▁ciems ▁smiltenes ▁novada ▁launkalnes ▁pagastā . ▁atrodas ... (+14 more)` | 24 |

**Sample 2:** `Oknupe ir ciems Vīksnas pagastā, Balvu novadā. Atrodas 235 km attālumā no Rīgas....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ok nu pe ▁ir ▁ciems ▁v īks nas ▁pagastā , ... (+28 more)` | 38 |
| 16k | `▁ok nu pe ▁ir ▁ciems ▁vīks nas ▁pagastā , ▁balvu ... (+26 more)` | 36 |
| 32k | `▁ok nu pe ▁ir ▁ciems ▁vīksnas ▁pagastā , ▁balvu ▁novadā ... (+25 more)` | 35 |
| 64k | `▁ok nu pe ▁ir ▁ciems ▁vīksnas ▁pagastā , ▁balvu ▁novadā ... (+25 more)` | 35 |

**Sample 3:** `Luķes ir ciems Gulbenes novada Rankas pagastā. Atrodas pagasta ziemeļu daļā. Apd...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lu ķes ▁ir ▁ciems ▁gulbenes ▁novada ▁ran kas ▁pagastā . ... (+16 more)` | 26 |
| 16k | `▁lu ķes ▁ir ▁ciems ▁gulbenes ▁novada ▁ran kas ▁pagastā . ... (+16 more)` | 26 |
| 32k | `▁lu ķes ▁ir ▁ciems ▁gulbenes ▁novada ▁rankas ▁pagastā . ▁atrodas ... (+15 more)` | 25 |
| 64k | `▁lu ķes ▁ir ▁ciems ▁gulbenes ▁novada ▁rankas ▁pagastā . ▁atrodas ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.859x compression
- **Lowest UNK Rate:** 8k with 0.1438% 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 | 186,971 | 17.51 | 763,036 | 5.9% | 15.6% |
| **2-gram** | Subword | 377 🏆 | 8.56 | 13,410 | 58.1% | 98.3% |
| **3-gram** | Word | 376,228 | 18.52 | 1,082,562 | 4.6% | 11.0% |
| **3-gram** | Subword | 3,642 | 11.83 | 114,502 | 20.1% | 61.2% |
| **4-gram** | Word | 838,069 | 19.68 | 1,874,907 | 3.2% | 7.7% |
| **4-gram** | Subword | 22,176 | 14.44 | 679,251 | 9.2% | 30.8% |
| **5-gram** | Word | 716,017 | 19.45 | 1,422,304 | 3.0% | 7.4% |
| **5-gram** | Subword | 92,488 | 16.50 | 2,257,677 | 5.0% | 18.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ārējās saites` | 77,523 |
| 2 | `atsauces ārējās` | 46,856 |
| 3 | `kā arī` | 36,975 |
| 4 | `līdz gadam` | 31,268 |
| 5 | `gadā dzimušie` | 26,462 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `atsauces ārējās saites` | 46,815 |
| 2 | `no līdz gadam` | 19,254 |
| 3 | `ārējās saites gadā` | 14,728 |
| 4 | `saites gadā dzimušie` | 14,663 |
| 5 | `dzimušie gadā mirušie` | 9,849 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ārējās saites gadā dzimušie` | 14,640 |
| 2 | `gadā dzimušie gadā mirušie` | 8,825 |
| 3 | `atsauces ārējās saites gadā` | 7,950 |
| 4 | `gada vasaras olimpiskajās spēlēs` | 6,960 |
| 5 | `gada vasaras olimpisko spēļu` | 5,942 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `atsauces ārējās saites gadā dzimušie` | 7,930 |
| 2 | `gada vasaras olimpisko spēļu dalībnieki` | 4,199 |
| 3 | `ārējās saites gadā dzimušie gadā` | 3,572 |
| 4 | `saites gadā dzimušie gadā mirušie` | 3,570 |
| 5 | `atsauces ārējās saites gada filmas` | 3,413 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s _` | 7,415,857 |
| 2 | `a _` | 4,233,722 |
| 3 | `i e` | 3,834,903 |
| 4 | `a s` | 3,749,982 |
| 5 | `_ p` | 2,817,996 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a s _` | 2,663,220 |
| 2 | `i j a` | 1,092,354 |
| 3 | `_ g a` | 1,045,440 |
| 4 | `_ p a` | 969,042 |
| 5 | `e s _` | 927,955 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ u n _` | 832,357 |
| 2 | `_ g a d` | 790,192 |
| 3 | `j a s _` | 651,311 |
| 4 | `i j a s` | 601,430 |
| 5 | `_ i r _` | 445,858 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i j a s _` | 555,973 |
| 2 | `_ g a d a` | 327,759 |
| 3 | `_ g a d ā` | 311,319 |
| 4 | `g a d a _` | 289,208 |
| 5 | `s _ u n _` | 258,875 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 377
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~18% 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 | 1.0564 | 2.080 | 11.08 | 1,076,401 | 0.0% |
| **1** | Subword | 0.9798 | 1.972 | 6.86 | 5,866 | 2.0% |
| **2** | Word | 0.3096 | 1.239 | 1.86 | 11,904,580 | 69.0% |
| **2** | Subword | 0.8333 | 1.782 | 5.70 | 40,212 | 16.7% |
| **3** | Word | 0.1014 | 1.073 | 1.19 | 22,093,035 | 89.9% |
| **3** | Subword | 0.8282 | 1.775 | 4.78 | 229,319 | 17.2% |
| **4** | Word | 0.0411 🏆 | 1.029 | 1.07 | 26,247,285 | 95.9% |
| **4** | Subword | 0.7392 | 1.669 | 3.61 | 1,095,639 | 26.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `un atsauces ārējās saites gadā par bruņutanku divīziju tā barojas ar un ietērps bija andris bērziņš`
2. `ir piešķirta labākajam debitantam šo gleznu to šķietamo retumu novērojumi bija reperis 9 kārta sešpa...`
3. `no divām spāņu izcelsmes azerbaidžānas robežas dažkārt piedēvēto dzīvo krievijā kalugas 14 gadsimtā ...`

**Context Size 2:**

1. `ārējās saites photographs of yamashita last words nr 99 miley cyrus dziesmu saraksts visu dziesmu mū...`
2. `atsauces ārējās saites kārļa blūma mājas gusevā kaļiņingradas apgabals krievijā bērnību aizvadījis l...`
3. `kā arī 24 šaha olimpiāde 2 galdiņš anna zatonskiha 3 galdiņš hiroko maeda japāna 6 no kopējās`

**Context Size 3:**

1. `atsauces ārējās saites salas okeāna salas okeāna salas okeāna salas sala un makdonalda salas daba vi...`
2. `no līdz gadam četras reizes pēc kārtas spēja kāpt uz goda pjedestāla pk posmā izcīnīja pokļukā ieņem...`
3. `ārējās saites gadā dzimušie futbolisti izlases futbolisti barcelona spēlētāji braga spēlētāji gada f...`

**Context Size 4:**

1. `ārējās saites gadā dzimušie dzimušie dziedātāji dziedātāji dzejnieki komponisti aktieri kas nosodīja...`
2. `gadā dzimušie gadā mirušie valodā rakstošie dzimušie filozofi`
3. `atsauces ārējās saites gadā dzimušie gadā mirušie šahisti dzimušie rakstnieki`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ga_—_v_tā_viero`
2. `ai_šas_pējeilstr`
3. `iskairbonsilieģe`

**Context Size 2:**

1. `s_ku_seviņa_(par_`
2. `a_dreglerfespiesm`
3. `iempielleines_atk`

**Context Size 3:**

1. `as_(bhk),_for_de_r`
2. `ija_resstan"_tika/`
3. `_gada_slēdzirnaziņ`

**Context Size 4:**

1. `_un_šķērso_valdīts_`
2. `_gadā._iedalīt_pašr`
3. `jas_kultāti_pat_hom`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,095,639 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 | 525,941 |
| Total Tokens | 31,646,239 |
| Mean Frequency | 60.17 |
| Median Frequency | 4 |
| Frequency Std Dev | 1858.77 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | un | 837,232 |
| 2 | ir | 448,994 |
| 3 | no | 329,310 |
| 4 | ar | 312,526 |
| 5 | gadā | 311,069 |
| 6 | gada | 295,620 |
| 7 | par | 232,587 |
| 8 | bija | 182,230 |
| 9 | arī | 168,500 |
| 10 | 1 | 160,323 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | gesnēriju | 2 |
| 2 | oerst | 2 |
| 3 | feuillet | 2 |
| 4 | aizšauta | 2 |
| 5 | حمّص | 2 |
| 6 | saspaidot | 2 |
| 7 | levantiešu | 2 |
| 8 | bowsera | 2 |
| 9 | гайлите | 2 |
| 10 | kuckersiana | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9424 |
| R² (Goodness of Fit) | 0.995100 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 24.5% |
| Top 1,000 | 46.0% |
| Top 5,000 | 65.1% |
| Top 10,000 | 73.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9951 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 24.5% of corpus
- **Long Tail:** 515,941 words needed for remaining 26.9% 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 | 0.8084 🏆 | 0.3574 | N/A | N/A |
| **mono_64d** | 64 | 0.7789 | 0.2822 | N/A | N/A |
| **mono_128d** | 128 | 0.7122 | 0.2116 | N/A | N/A |
| **aligned_32d** | 32 | 0.8084 | 0.3676 | 0.1900 | 0.5080 |
| **aligned_64d** | 64 | 0.7789 | 0.2789 | 0.2640 | 0.6700 |
| **aligned_128d** | 128 | 0.7122 | 0.2124 | 0.3740 | 0.7500 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8084 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2850. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 37.4% 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 | **-0.593** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-s` | skatījumus, selēku, saucietis |
| `-a` | antwone, antociānus, atkritēju |
| `-k` | kemalisms, kuģu, korporatīvajām |
| `-ma` | makrofaunā, materiālzinātnes, maksillas |
| `-p` | peculiarities, pilsoņtiesību, pūpēžu |
| `-b` | beijing, blīvējumiem, bbva |
| `-m` | metālopera, makrofaunā, městec |
| `-d` | daiļkrāsotāja, džungļus, definēja |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | cuspidatus, skatījumus, informatics |
| `-a` | daiļkrāsotāja, leontīna, definēja |
| `-as` | lielsusējas, lentas, elektrizācijas |
| `-u` | ofenbergu, imulu, pilsoņtiesību |
| `-i` | šakarniai, zonai, oviši |
| `-m` | stūrētājam, korporatīvajām, reliktām |
| `-e` | antwone, zvirgzdupe, edamame |
| `-em` | blīvējumiem, frančiem, briesmoņiem |

### 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 |
|------|----------|------------------|----------|
| `pēlē` | 2.56x | 98 contexts | spēlē, spēlēj, spēlēt |
| `spēl` | 2.22x | 107 contexts | spēlē, spēlu, spēle |
| `akst` | 1.65x | 272 contexts | bakst, aksts, aksta |
| `veid` | 1.57x | 278 contexts | veidu, veida, veidi |
| `tisk` | 1.45x | 327 contexts | ētiskā, ētiska, ētiski |
| `dzīv` | 1.65x | 122 contexts | dzīve, dzīva, dzīvi |
| `tsau` | 2.39x | 25 contexts | atsauc, atsauce, atsauks |
| `iskā` | 1.55x | 134 contexts | diskā, riskā, ētiskā |
| `alst` | 1.49x | 144 contexts | valst, salst, aalst |
| `eido` | 1.58x | 108 contexts | eidos, feido, veido |
| `ācij` | 1.53x | 117 contexts | ācija, nācija, mācija |
| `ības` | 1.83x | 49 contexts | lības, rības, čības |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-s` | 248 words | skurass, schildts |
| `-p` | `-s` | 235 words | pogačarsričards, praxis |
| `-a` | `-s` | 210 words | aments, abdelazīzs |
| `-k` | `-s` | 172 words | krūzes, kodzas |
| `-b` | `-s` | 139 words | bekingemšīras, beringovskas |
| `-s` | `-a` | 112 words | skolvadība, sēretika |
| `-d` | `-s` | 111 words | dedalus, dauders |
| `-p` | `-a` | 100 words | pārraidija, patnema |
| `-k` | `-a` | 94 words | koldhārbora, kairiša |
| `-m` | `-s` | 92 words | mazjaudīgus, micromys |

### 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 |
|------|-----------------|------------|------|
| aprīlīdžeks | **`aprīlīdž-e-ks`** | 7.5 | `e` |
| trusēniem | **`trusēn-i-em`** | 7.5 | `i` |
| skābputras | **`skābput-ra-s`** | 7.5 | `ra` |
| pilsoniski | **`pilsoni-s-ki`** | 7.5 | `s` |
| asinssālim | **`asinssāl-i-m`** | 7.5 | `i` |
| gūstekņiem | **`gūstekņ-i-em`** | 7.5 | `i` |
| uzņēmīgiem | **`uzņēmīg-i-em`** | 7.5 | `i` |
| pieraduma | **`pieradu-m-a`** | 7.5 | `m` |
| prikumsku | **`prikum-s-ku`** | 7.5 | `s` |
| kērklīsas | **`kērklī-s-as`** | 7.5 | `s` |
| acantosis | **`acanto-s-is`** | 7.5 | `s` |
| miecēšana | **`miecēš-a-na`** | 7.5 | `a` |
| kapranoss | **`kaprano-s-s`** | 7.5 | `s` |
| veinštrāses | **`veinštrā-s-es`** | 7.5 | `s` |
| ūdenssuņiem | **`ūdenssuņ-i-em`** | 7.5 | `i` |

### 6.6 Linguistic Interpretation

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.86x) |
| N-gram | **2-gram** | Lowest perplexity (377) |
| Markov | **Context-4** | Highest predictability (95.9%) |
| 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 15:10:38*