README.md

---
language: lt
language_name: Lithuanian
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: 4.757
  - name: best_isotropy
    type: isotropy
    value: 0.8202
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-14
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lithuanian** 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** | 3.661x | 3.66 | 0.1102% | 2,105,079 |
| **16k** | 4.090x | 4.09 | 0.1231% | 1,884,341 |
| **32k** | 4.453x | 4.45 | 0.1340% | 1,730,520 |
| **64k** | 4.757x 🏆 | 4.76 | 0.1431% | 1,620,062 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Vilkonys – kaimas Panevėžio rajono savivaldybėje, 2 km nuo Raguvos. Gyventojai Š...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁vilk on ys ▁– ▁kaimas ▁panevėžio ▁rajono ▁savivaldybėje , ▁ ... (+11 more)` | 21 |
| 16k | `▁vilk onys ▁– ▁kaimas ▁panevėžio ▁rajono ▁savivaldybėje , ▁ 2 ... (+10 more)` | 20 |
| 32k | `▁vilk onys ▁– ▁kaimas ▁panevėžio ▁rajono ▁savivaldybėje , ▁ 2 ... (+9 more)` | 19 |
| 64k | `▁vilk onys ▁– ▁kaimas ▁panevėžio ▁rajono ▁savivaldybėje , ▁ 2 ... (+9 more)` | 19 |

**Sample 2:** `Džufros savivaldybė () – Libijos savivaldybė šalies centrinėje dalyje, Sacharos ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁dž u f ros ▁savivaldybė ▁() ▁– ▁lib ijos ▁savivaldybė ... (+18 more)` | 28 |
| 16k | `▁dž uf ros ▁savivaldybė ▁() ▁– ▁lib ijos ▁savivaldybė ▁šalies ... (+15 more)` | 25 |
| 32k | `▁dž uf ros ▁savivaldybė ▁() ▁– ▁libijos ▁savivaldybė ▁šalies ▁centrinėje ... (+12 more)` | 22 |
| 64k | `▁dž uf ros ▁savivaldybė ▁() ▁– ▁libijos ▁savivaldybė ▁šalies ▁centrinėje ... (+12 more)` | 22 |

**Sample 3:** `Dūdoriškiai – viensėdis Biržų rajono savivaldybėje, 6 km į vakarus nuo Pabiržės....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁dū do rišk iai ▁– ▁viensėdis ▁biržų ▁rajono ▁savivaldybėje , ... (+15 more)` | 25 |
| 16k | `▁dū do rišk iai ▁– ▁viensėdis ▁biržų ▁rajono ▁savivaldybėje , ... (+15 more)` | 25 |
| 32k | `▁dū do rišk iai ▁– ▁viensėdis ▁biržų ▁rajono ▁savivaldybėje , ... (+15 more)` | 25 |
| 64k | `▁dū do riškiai ▁– ▁viensėdis ▁biržų ▁rajono ▁savivaldybėje , ▁ ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.757x compression
- **Lowest UNK Rate:** 8k with 0.1102% 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 | 196,143 | 17.58 | 951,489 | 6.6% | 16.9% |
| **2-gram** | Subword | 347 🏆 | 8.44 | 16,291 | 61.2% | 98.5% |
| **3-gram** | Word | 370,705 | 18.50 | 1,291,283 | 4.1% | 12.0% |
| **3-gram** | Subword | 3,304 | 11.69 | 131,904 | 20.0% | 64.1% |
| **4-gram** | Word | 774,264 | 19.56 | 2,157,224 | 3.3% | 9.4% |
| **4-gram** | Subword | 21,025 | 14.36 | 755,683 | 8.5% | 31.1% |
| **5-gram** | Word | 702,338 | 19.42 | 1,649,947 | 3.1% | 8.5% |
| **5-gram** | Subword | 92,546 | 16.50 | 2,569,308 | 4.6% | 17.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nuo m` | 80,598 |
| 2 | `taip pat` | 61,102 |
| 3 | `m m` | 49,221 |
| 4 | `km į` | 40,737 |
| 5 | `g m` | 39,476 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `rajono savivaldybės gyvenvietės` | 21,760 |
| 2 | `šaltiniai rajono savivaldybės` | 18,042 |
| 3 | `gyventojai šaltiniai rajono` | 15,946 |
| 4 | `pr m e` | 15,933 |
| 5 | `0 0 0` | 11,090 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `šaltiniai rajono savivaldybės gyvenvietės` | 17,791 |
| 2 | `gyventojai šaltiniai rajono savivaldybės` | 15,570 |
| 3 | `m pr m e` | 9,199 |
| 4 | `0 0 0 0` | 6,658 |
| 5 | `į šiaurės rytus nuo` | 6,349 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `gyventojai šaltiniai rajono savivaldybės gyvenvietės` | 15,554 |
| 2 | `km į šiaurės rytus nuo` | 5,574 |
| 3 | `km į šiaurės vakarus nuo` | 4,918 |
| 4 | `0 0 0 0 0` | 4,143 |
| 5 | `general information about the player` | 2,888 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s _` | 8,108,761 |
| 2 | `o _` | 4,732,529 |
| 3 | `i n` | 4,492,534 |
| 4 | `. _` | 4,477,090 |
| 5 | `a s` | 3,925,055 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o s _` | 2,303,630 |
| 2 | `a s _` | 2,033,580 |
| 3 | `_ p a` | 1,580,889 |
| 4 | `i n i` | 1,432,110 |
| 5 | `a i _` | 1,247,013 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m . _` | 1,006,887 |
| 2 | `_ i r _` | 1,000,574 |
| 3 | `i j o s` | 645,380 |
| 4 | `j o s _` | 630,230 |
| 5 | `t a s _` | 487,967 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i j o s _` | 560,980 |
| 2 | `. _ m . _` | 345,387 |
| 3 | `b u v o _` | 340,153 |
| 4 | `_ b u v o` | 328,906 |
| 5 | `l i e t u` | 311,837 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 347
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~17% 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 | 1.0333 | 2.047 | 10.88 | 1,497,676 | 0.0% |
| **1** | Subword | 1.0306 | 2.043 | 6.87 | 9,691 | 0.0% |
| **2** | Word | 0.2905 | 1.223 | 1.79 | 16,264,065 | 71.0% |
| **2** | Subword | 0.6783 | 1.600 | 4.61 | 66,441 | 32.2% |
| **3** | Word | 0.0931 | 1.067 | 1.18 | 29,101,762 | 90.7% |
| **3** | Subword | 0.7377 | 1.667 | 4.28 | 306,205 | 26.2% |
| **4** | Word | 0.0375 🏆 | 1.026 | 1.06 | 34,194,540 | 96.3% |
| **4** | Subword | 0.7065 | 1.632 | 3.54 | 1,310,778 | 29.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `m m new york reprint der lehre von trips as ratas paskutinis vicekaralius vėliau tiškevičiaus logois...`
2. `ir žagarės vidurinės mokyklos patalpose aušros pradžios rokas beliukevičius g m rugpjūtį jo sūnų dže...`
3. `buvo prilyginti taip pat deltuvos žemė šiose pareigose g m atvyko į pasaulio lietuvių tarybos narių`

**Context Size 2:**

1. `nuo m kursuoja trollino 15 ac šaltiniai miestai miestai apygardos apygardos vakarinius krantus skala...`
2. `taip pat katalikiškos pakraipos šv sebastijono atvaizdas andrėja mantenja mirė m balandžio 18 m bala...`
3. `m m gruodžio 11 d vilnius smuikininkas pedagogas vargonininkas chorvedys muzikos mokytojas lankydama...`

**Context Size 3:**

1. `šaltiniai rajono savivaldybės gyvenvietės miesto dalys`
2. `gyventojai šaltiniai rajono savivaldybės geležinkelio stotys kultūros vertybės geležinkelio stotys s...`
3. `pr m e galėjo būti knoso uostas įkūrimas dabartinį heraklioną 824 m įkūrė saracėnai išvaryti iš anda...`

**Context Size 4:**

1. `gyventojai šaltiniai rajono savivaldybės gyvenvietės kaimai aukštaitijos nacionaliniame parke kaimai`
2. `m pr m e jų indėlis į matematiką astronomiją ir mediciną būdamas 16 metų pagarsėjo išgydęs bucharos ...`
3. `0 0 0 0 0 0 0 1 0 4 1 1 0 ii grupė komandatšk rungt laim lyg`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_vičingauve_us_į`
2. `i_g_vilie_ją_aly`
3. `adiuvosłakaikari`

**Context Size 2:**

1. `s_kopiniai_važoda`
2. `o_bel_patvė_citas`
3. `ingotentrauliteli`

**Context Size 3:**

1. `os_karius_sodų_būt`
2. `as_ii_panų_siniais`
3. `_pastame_garalianč`

**Context Size 4:**

1. `_m._laipėdoje_yra_k`
2. `_ir_dvejų_žvaigždę_`
3. `ijos_karoliuojas,_a`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,310,778 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 | 719,992 |
| Total Tokens | 41,466,357 |
| Mean Frequency | 57.59 |
| Median Frequency | 4 |
| Frequency Std Dev | 2237.16 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | m | 1,249,293 |
| 2 | ir | 1,005,030 |
| 3 | buvo | 329,252 |
| 4 | į | 322,738 |
| 5 | nuo | 252,061 |
| 6 | d | 244,466 |
| 7 | iš | 222,420 |
| 8 | su | 217,987 |
| 9 | 1 | 212,417 |
| 10 | yra | 198,413 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | triumphal | 2 |
| 2 | sawano | 2 |
| 3 | taisen | 2 |
| 4 | iryu | 2 |
| 5 | nzk | 2 |
| 6 | lorensavo | 2 |
| 7 | gauchos | 2 |
| 8 | architekturze | 2 |
| 9 | sztuce | 2 |
| 10 | łubieński | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9393 |
| R² (Goodness of Fit) | 0.994466 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 23.0% |
| Top 1,000 | 44.0% |
| Top 5,000 | 62.7% |
| Top 10,000 | 70.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9945 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 23.0% of corpus
- **Long Tail:** 709,992 words needed for remaining 29.4% 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 | 0.8202 🏆 | 0.3473 | N/A | N/A |
| **mono_64d** | 64 | 0.8013 | 0.2803 | N/A | N/A |
| **mono_128d** | 128 | 0.7515 | 0.2219 | N/A | N/A |
| **aligned_32d** | 32 | 0.8202 | 0.3470 | 0.1200 | 0.4580 |
| **aligned_64d** | 64 | 0.8013 | 0.2841 | 0.3160 | 0.7180 |
| **aligned_128d** | 128 | 0.7515 | 0.2188 | 0.4260 | 0.7780 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8202 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2832. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 42.6% 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 | **-0.511** | 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` | stambinant, smutki, sanio |
| `-a` | abaujaus, atidėliojimą, antigono |
| `-ma` | maškė, maršruto, maceika |
| `-k` | kišenes, kaljan, khan |
| `-m` | maškė, mágica, mergystės |
| `-ka` | kaljan, kastilija, kalanti |
| `-p` | praktikuoti, partenopė, pajė |
| `-pa` | partenopė, pajė, paitensis |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | kišenes, goblets, hallas |
| `-as` | hallas, anamas, kuartas |
| `-i` | praktikuoti, smutki, trūki |
| `-is` | alramis, paitensis, refrakcinis |
| `-o` | antigono, sanio, sliesoraičio |
| `-e` | užantyje, geheimnisse, šturmane |
| `-a` | mágica, arhitektūra, susuka |
| `-ai` | antikomunistiniai, užkuriai, laurinavičiai |

### 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 |
|------|----------|------------------|----------|
| `inių` | 1.80x | 283 contexts | ainių, žinių, ninių |
| `etuv` | 2.37x | 59 contexts | betuvė, rietuvę, sietuvą |
| `yven` | 1.82x | 148 contexts | lyven, gyvenu, gyveną |
| `inim` | 1.53x | 306 contexts | minim, dinim, minime |
| `gyve` | 1.86x | 92 contexts | gyvenu, gyveną, gyvenc |
| `iaur` | 1.66x | 139 contexts | iauri, žiaurų, siaure |
| `tinė` | 1.34x | 421 contexts | etinė, matinė, vatinė |
| `ltin` | 1.42x | 229 contexts | altin, altino, baltin |
| `ausi` | 1.47x | 173 contexts | kausi, gausi, ausim |
| `tuvo` | 1.98x | 45 contexts | tuvos, tuvoje, bytuvo |
| `ajon` | 1.66x | 80 contexts | fajon, rajon, pajon |
| `ietu` | 1.54x | 104 contexts | vietu, kietu, lietu |

### 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` | 299 words | pingus, plėtotos |
| `-s` | `-s` | 261 words | slaugymas, statybiniais |
| `-k` | `-s` | 206 words | kreatininas, komarnicos |
| `-a` | `-s` | 202 words | ajagozas, apsukrus |
| `-b` | `-s` | 142 words | bubles, begėdis |
| `-d` | `-s` | 128 words | dramblys, džinhanas |
| `-p` | `-i` | 124 words | piktindamiesi, pirkiniui |
| `-m` | `-s` | 114 words | monofizitais, meniškais |
| `-s` | `-i` | 97 words | stasiūniečiai, segmentuojasi |
| `-s` | `-o` | 85 words | slomo, skaitytojo |

### 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 |
|------|-----------------|------------|------|
| stankiškiuose | **`stankiškiuo-s-e`** | 7.5 | `s` |
| pertekusi | **`perteku-s-i`** | 7.5 | `s` |
| ekranuose | **`ekranuo-s-e`** | 7.5 | `s` |
| bačkonyse | **`bačkony-s-e`** | 7.5 | `s` |
| ramonuose | **`ramonuo-s-e`** | 7.5 | `s` |
| komentaruose | **`komentaruo-s-e`** | 7.5 | `s` |
| hidnotrija | **`hidnotr-i-ja`** | 7.5 | `i` |
| šaudyklose | **`šaudyklo-s-e`** | 7.5 | `s` |
| nuomojosi | **`nuomojo-s-i`** | 7.5 | `s` |
| suvynioja | **`suvyni-o-ja`** | 7.5 | `o` |
| riboženkliai | **`riboženkl-i-ai`** | 7.5 | `i` |
| potvarkiuose | **`potvarkiuo-s-e`** | 7.5 | `s` |
| antigvosą | **`antigvo-s-ą`** | 7.5 | `s` |
| užutekiuose | **`užutekiuo-s-e`** | 7.5 | `s` |
| muitinėse | **`muitinė-s-e`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lithuanian 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 (4.76x) |
| N-gram | **2-gram** | Lowest perplexity (347) |
| Markov | **Context-4** | Highest predictability (96.3%) |
| 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: 2026-01-14 22:52:53*