---
language: mt
language_name: Maltese
language_family: semitic_maltese
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-semitic_maltese
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: 4.089
  - name: best_isotropy
    type: isotropy
    value: 0.8419
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Maltese** 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** | 3.321x | 3.32 | 0.0374% | 1,583,826 |
| **16k** | 3.646x | 3.65 | 0.0411% | 1,442,511 |
| **32k** | 3.912x | 3.91 | 0.0441% | 1,344,286 |
| **64k** | 4.089x 🏆 | 4.09 | 0.0461% | 1,286,257 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Il-Festival tal-Eurovision kien it-62 edizzjoni ta' dan il-konkors u sar fil-bel...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁il - festival ▁tal - eurovision ▁kien ▁it - 6 ... (+25 more)` | 35 |
| 16k | `▁il - festival ▁tal - eurovision ▁kien ▁it - 6 ... (+25 more)` | 35 |
| 32k | `▁il - festival ▁tal - eurovision ▁kien ▁it - 6 ... (+25 more)` | 35 |
| 64k | `▁il - festival ▁tal - eurovision ▁kien ▁it - 6 ... (+25 more)` | 35 |

**Sample 2:** `Andrew Danylyszyn huwa eks-plejer tal-futbol u kowċ Ingliż. Bħalissa huwa jikkow...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁andrew ▁dan yl ys z yn ▁huwa ▁eks - plejer ... (+25 more)` | 35 |
| 16k | `▁andrew ▁dan yl ys z yn ▁huwa ▁eks - plejer ... (+24 more)` | 34 |
| 32k | `▁andrew ▁dan yl ys z yn ▁huwa ▁eks - plejer ... (+23 more)` | 33 |
| 64k | `▁andrew ▁dan yl ysz yn ▁huwa ▁eks - plejer ▁tal ... (+21 more)` | 31 |

**Sample 3:** `Caravaggio jista' jirreferi għal: Michelangelo Merisi da Caravaggio Polidoro da ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cara va g gio ▁jista ' ▁jirreferi ▁għal : ▁michel ... (+23 more)` | 33 |
| 16k | `▁cara va g gio ▁jista ' ▁jirreferi ▁għal : ▁michel ... (+22 more)` | 32 |
| 32k | `▁caravaggio ▁jista ' ▁jirreferi ▁għal : ▁michelangelo ▁mer isi ▁da ... (+9 more)` | 19 |
| 64k | `▁caravaggio ▁jista ' ▁jirreferi ▁għal : ▁michelangelo ▁merisi ▁da ▁caravaggio ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.089x compression
- **Lowest UNK Rate:** 8k with 0.0374% 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 | 49,202 | 15.59 | 189,449 | 7.9% | 23.6% |
| **2-gram** | Subword | 336 🏆 | 8.39 | 7,623 | 61.6% | 98.8% |
| **3-gram** | Word | 123,630 | 16.92 | 301,660 | 4.6% | 14.5% |
| **3-gram** | Subword | 2,929 | 11.52 | 55,069 | 23.9% | 65.1% |
| **4-gram** | Word | 209,692 | 17.68 | 441,539 | 5.1% | 13.5% |
| **4-gram** | Subword | 15,896 | 13.96 | 296,209 | 12.8% | 36.1% |
| **5-gram** | Word | 120,331 | 16.88 | 273,504 | 7.7% | 18.9% |
| **5-gram** | Subword | 56,702 | 15.79 | 862,182 | 8.0% | 23.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u l` | 39,353 |
| 2 | `li l` | 11,839 |
| 3 | `l ewwel` | 11,433 |
| 4 | `wirt dinji` | 8,996 |
| 5 | `ta wirt` | 8,725 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ta wirt dinji` | 8,587 |
| 2 | `sit ta wirt` | 4,041 |
| 3 | `wirt dinji tal` | 3,950 |
| 4 | `dinji tal unesco` | 3,793 |
| 5 | `biċċa l kbira` | 3,256 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sit ta wirt dinji` | 3,999 |
| 2 | `wirt dinji tal unesco` | 3,787 |
| 3 | `ta wirt dinji tal` | 3,751 |
| 4 | `siti ta wirt dinji` | 1,925 |
| 5 | `bħala sit ta wirt` | 1,675 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ta wirt dinji tal unesco` | 3,590 |
| 2 | `sit ta wirt dinji tal` | 2,398 |
| 3 | `bħala sit ta wirt dinji` | 1,671 |
| 4 | `siti ta wirt dinji tal` | 1,346 |
| 5 | `tal għażla tal unesco il` | 1,189 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t a` | 1,047,242 |
| 2 | `a _` | 1,023,851 |
| 3 | `l -` | 940,231 |
| 4 | `_ t` | 895,636 |
| 5 | `i _` | 849,324 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t a` | 674,251 |
| 2 | `t a l` | 280,698 |
| 3 | `i l -` | 272,166 |
| 4 | `a l -` | 270,242 |
| 5 | `l i _` | 269,230 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t a l` | 253,253 |
| 2 | `t a l -` | 248,468 |
| 3 | `t a ' _` | 230,227 |
| 4 | `_ t a '` | 225,523 |
| 5 | `_ i l -` | 179,478 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t a l -` | 248,166 |
| 2 | `_ t a ' _` | 225,229 |
| 3 | `z z j o n` | 113,258 |
| 4 | `z j o n i` | 93,893 |
| 5 | `j o n i _` | 81,419 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 336
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.9877 | 1.983 | 8.75 | 269,738 | 1.2% |
| **1** | Subword | 0.9806 | 1.973 | 6.28 | 3,872 | 1.9% |
| **2** | Word | 0.3921 | 1.312 | 2.17 | 2,357,628 | 60.8% |
| **2** | Subword | 0.8075 | 1.750 | 4.95 | 24,320 | 19.3% |
| **3** | Word | 0.1480 | 1.108 | 1.29 | 5,116,125 | 85.2% |
| **3** | Subword | 0.7607 | 1.694 | 4.18 | 120,346 | 23.9% |
| **4** | Word | 0.0521 🏆 | 1.037 | 1.08 | 6,574,732 | 94.8% |
| **4** | Subword | 0.6872 | 1.610 | 3.21 | 502,959 | 31.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ta fuq allmusic irlandiżi rebħu l ammont totali ta mckenzie referenzi fl aħħar paġna ġdida imsejħa`
2. `l politika u l art billi jintlaqgħu għadd ta żjara tar relegazzjoni unuri konsekuttivi mill puntdivi...`
3. `tal lava fil muntanji il kumpless tal ikel u franza ħolqa tat tmexxija biex toqtol 1`

**Context Size 2:**

1. `u l uffiċċju meteoroloġiku tar renju unit isbn p 41 l italja u spanja għandhom wirt greco`
2. `li l bniedem jitħajjar jaqra iżjed ftit sentenzi biss huwa kkalkolat li l laħam kollu baqa fil`
3. `l ewwel debutt tiegħu huwa r raħal ingħatat isem matul il kors kollu tat taj mahal harvard`

**Context Size 3:**

1. `ta wirt dinji tal unesco u attwalment tinsab fil ġenb ta triq dom mintoff li jkun mid mediterranean`
2. `sit ta wirt dinji tal unesco fl 24 sessjoni tal kumitat tal wirt dinji tal unesco il kriterju`
3. `wirt dinji tal unesco u jħaddan fih bejn wieħed u ieħor 100 000 ettaru addizzjonali fl istess sena`

**Context Size 4:**

1. `sit ta wirt dinji ta importanza naturali globali il biċċa l kbira ta dawn għandhom il karatteristiċi...`
2. `wirt dinji tal unesco il valur universali straordinarju tas sit ġie rrikonoxxut abbażi ta kriterju w...`
3. `ta wirt dinji tal unesco minħabba l pożizzjoni interna tagħha évora hija waħda mill iżjed bliet impo...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_esiua_b'_jaħa,_`
2. `ase"ns-vedretape`
3. `ivogwgħad_fi_cr.`

**Context Size 2:**

1. `tal-la_mifonizzjo`
2. `a_miopprobid-diet`
3. `l-bien_minhom_min`

**Context Size 3:**

1. `_tat-tqarra_ċent_u`
2. `tal-parpecil_")._b`
3. `il-għolja_s-seklud`

**Context Size 4:**

1. `_tal-lingwi_li_arma`
2. `tal-kiri_u_għall-ko`
3. `ta'_ġunju_ta'_torri`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (502,959 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 | 126,099 |
| Total Tokens | 7,639,629 |
| Mean Frequency | 60.58 |
| Median Frequency | 4 |
| Frequency Std Dev | 1684.27 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ta | 269,773 |
| 2 | l | 253,566 |
| 3 | tal | 248,940 |
| 4 | u | 226,218 |
| 5 | il | 198,043 |
| 6 | li | 147,076 |
| 7 | fil | 69,002 |
| 8 | f | 59,879 |
| 9 | mill | 52,554 |
| 10 | minn | 46,510 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | deliberately | 2 |
| 2 | plantations | 2 |
| 3 | tied | 2 |
| 4 | upwards | 2 |
| 5 | interred | 2 |
| 6 | glyph | 2 |
| 7 | coated | 2 |
| 8 | wrdc | 2 |
| 9 | vgh | 2 |
| 10 | kamila | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0760 |
| R² (Goodness of Fit) | 0.994751 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 38.9% |
| Top 1,000 | 64.3% |
| Top 5,000 | 81.5% |
| Top 10,000 | 87.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9948 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 38.9% of corpus
- **Long Tail:** 116,099 words needed for remaining 12.4% 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 | 0.8419 🏆 | 0.3444 | N/A | N/A |
| **mono_64d** | 64 | 0.7823 | 0.2641 | N/A | N/A |
| **mono_128d** | 128 | 0.7758 | 0.1839 | N/A | N/A |
| **aligned_32d** | 32 | 0.8419 | 0.3430 | 0.2100 | 0.5540 |
| **aligned_64d** | 64 | 0.7823 | 0.2631 | 0.3120 | 0.6740 |
| **aligned_128d** | 128 | 0.7758 | 0.1776 | 0.3460 | 0.7300 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8419 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2627. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 34.6% 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 | **-0.191** | 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` | sottoġeneri, sneijder, silobate |
| `-a` | accessed, asiana, artística |
| `-m` | maranci, mga, millstream |
| `-t` | tavira, taljanizzat, tsuga |
| `-ma` | maranci, maximilians, mauk |
| `-b` | bivio, brusino, boundary |
| `-k` | kumgang, kategorizzati, kordofan |
| `-p` | puritana, portas, pika |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | intensifika, tavira, mga |
| `-i` | maranci, ġenożi, sottoġeneri |
| `-s` | willans, vliers, chords |
| `-t` | taljanizzat, demgħat, akwedott |
| `-e` | genere, grosse, silobate |
| `-n` | geneugden, merian, alison |
| `-u` | jwessgħu, ahau, jintemmu |
| `-ti` | hiradoraggruppamenti, kategorizzati, osservanti |

### 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 |
|------|----------|------------------|----------|
| `iegħ` | 1.99x | 101 contexts | siegħ, biegħ, qiegħ |
| `niji` | 2.52x | 28 contexts | anijima, garniji, unijiet |
| `ijie` | 2.11x | 43 contexts | ijiem, hijiex, zijiet |
| `enti` | 1.57x | 154 contexts | menti, venti, renti |
| `ment` | 1.64x | 111 contexts | menti, lment, mento |
| `azzj` | 1.97x | 47 contexts | grazzji, nazzjon, spazzju |
| `nali` | 1.98x | 43 contexts | renali, kanali, penali |
| `enet` | 1.92x | 42 contexts | zenet, tenet, genet |
| `zjon` | 1.95x | 39 contexts | zjoni, unzjoni, porzjon |
| `onij` | 2.66x | 12 contexts | ironija, tonijiet, baronija |
| `atur` | 1.57x | 73 contexts | matur, natur, batur |
| `rali` | 1.79x | 38 contexts | ralik, orali, urali |

### 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 |
|--------|--------|-----------|----------|
| `-i` | `-a` | 116 words | istadtamhofħolqa, ikkonċentrata |
| `-m` | `-a` | 109 words | massalia, mgeżwra |
| `-i` | `-i` | 97 words | ikkunsmati, informattivi |
| `-p` | `-a` | 97 words | pema, pea |
| `-t` | `-a` | 94 words | titicaca, traviata |
| `-s` | `-i` | 91 words | sansoni, sjesti |
| `-k` | `-i` | 91 words | kardjovaskulari, kondutturi |
| `-p` | `-i` | 89 words | pohnpei, pendenti |
| `-k` | `-a` | 83 words | kbarħolqa, karozzerija |
| `-a` | `-a` | 78 words | agenda, akuta |

### 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 |
|------|-----------------|------------|------|
| probsthain | **`probsth-a-in`** | 7.5 | `a` |
| drammatiku | **`dramma-ti-ku`** | 7.5 | `ti` |
| ppressata | **`ppress-a-ta`** | 7.5 | `a` |
| kristianstad | **`kristians-ta-d`** | 7.5 | `ta` |
| koumenalis | **`koumen-al-is`** | 7.5 | `al` |
| humanities | **`humani-ti-es`** | 7.5 | `ti` |
| bniedemħolqa | **`bniedemħo-l-qa`** | 7.5 | `l` |
| walpurgis | **`walpurg-i-s`** | 7.5 | `i` |
| xewwikija | **`xewwik-i-ja`** | 7.5 | `i` |
| tropiklai | **`tropikl-a-i`** | 7.5 | `a` |
| urbanisation | **`urbanisa-ti-on`** | 7.5 | `ti` |
| conflicts | **`conflic-t-s`** | 7.5 | `t` |
| cantharus | **`canth-ar-us`** | 7.5 | `ar` |
| aristotli | **`aristo-t-li`** | 7.5 | `t` |
| widstrand | **`widstra-n-d`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Maltese 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 (4.09x) |
| N-gram | **2-gram** | Lowest perplexity (336) |
| Markov | **Context-4** | Highest predictability (94.8%) |
| 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 13:37:56*