README.md

---
language: sq
language_name: Albanian
language_family: albanian
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-albanian
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: 4.622
  - name: best_isotropy
    type: isotropy
    value: 0.7903
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Albanian** 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** | 3.687x | 3.69 | 0.1022% | 1,633,568 |
| **16k** | 4.049x | 4.05 | 0.1123% | 1,487,544 |
| **32k** | 4.376x | 4.38 | 0.1213% | 1,376,347 |
| **64k** | 4.622x 🏆 | 4.62 | 0.1281% | 1,303,233 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `është vendbanim në Ish Republikën Jugosllave të Maqedonisë. në komunën e Novacës`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁është ▁vendbanim ▁në ▁ish ▁republikën ▁jugosllave ▁të ▁maqedonisë . ▁në ... (+5 more)` | 15 |
| 16k | `▁është ▁vendbanim ▁në ▁ish ▁republikën ▁jugosllave ▁të ▁maqedonisë . ▁në ... (+4 more)` | 14 |
| 32k | `▁është ▁vendbanim ▁në ▁ish ▁republikën ▁jugosllave ▁të ▁maqedonisë . ▁në ... (+4 more)` | 14 |
| 64k | `▁është ▁vendbanim ▁në ▁ish ▁republikën ▁jugosllave ▁të ▁maqedonisë . ▁në ... (+4 more)` | 14 |

**Sample 2:** `Mbi vitin 390 p.e.s.. Ngjarje Lindje Vdekje 390 p.e.s. p.e.s.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mbi ▁vitin ▁ 3 9 0 ▁p . e . ... (+21 more)` | 31 |
| 16k | `▁mbi ▁vitin ▁ 3 9 0 ▁p . e . ... (+21 more)` | 31 |
| 32k | `▁mbi ▁vitin ▁ 3 9 0 ▁p . e . ... (+21 more)` | 31 |
| 64k | `▁mbi ▁vitin ▁ 3 9 0 ▁p . e . ... (+21 more)` | 31 |

**Sample 3:** `Shqiponja Perandorake e Lindjes (Aquila heliaca) është një Shqiponjë e madhe mbr...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁shqip on ja ▁perandora ke ▁e ▁lindjes ▁( aqu ila ... (+20 more)` | 30 |
| 16k | `▁shqiponja ▁perandorake ▁e ▁lindjes ▁( aqu ila ▁he lia ca ... (+16 more)` | 26 |
| 32k | `▁shqiponja ▁perandorake ▁e ▁lindjes ▁( aqu ila ▁he lia ca ... (+15 more)` | 25 |
| 64k | `▁shqiponja ▁perandorake ▁e ▁lindjes ▁( aqu ila ▁he lia ca ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.622x compression
- **Lowest UNK Rate:** 8k with 0.1022% 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 | 103,585 | 16.66 | 735,922 | 8.7% | 21.6% |
| **2-gram** | Subword | 273 🏆 | 8.09 | 13,805 | 67.0% | 99.1% |
| **3-gram** | Word | 407,031 | 18.63 | 1,487,174 | 3.6% | 11.6% |
| **3-gram** | Subword | 2,395 | 11.23 | 109,546 | 26.0% | 70.6% |
| **4-gram** | Word | 1,138,059 | 20.12 | 2,670,902 | 2.8% | 7.3% |
| **4-gram** | Subword | 14,457 | 13.82 | 620,829 | 12.9% | 37.9% |
| **5-gram** | Word | 918,336 | 19.81 | 1,883,419 | 3.3% | 7.9% |
| **5-gram** | Subword | 61,644 | 15.91 | 2,032,514 | 7.3% | 23.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `për të` | 102,538 |
| 2 | `në vitin` | 94,038 |
| 3 | `e tij` | 91,198 |
| 4 | `është një` | 86,400 |
| 5 | `më të` | 65,002 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `lidhje të jashtme` | 34,104 |
| 2 | `për shkak të` | 15,607 |
| 3 | `e tij të` | 14,217 |
| 4 | `është një komunë` | 12,600 |
| 5 | `referime lidhje të` | 12,450 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referime lidhje të jashtme` | 12,389 |
| 2 | `është një komunë në` | 9,790 |
| 3 | `referimet lidhje të jashtme` | 8,703 |
| 4 | `për herë të parë` | 6,794 |
| 5 | `ka një popullsi prej` | 5,533 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `km referimet lidhje të jashtme` | 4,615 |
| 2 | `lidhje të jashtme informacion i` | 3,985 |
| 3 | `të jashtme informacion i përgjithshëm` | 3,984 |
| 4 | `informacion i përgjithshëm harta e` | 3,984 |
| 5 | `i përgjithshëm harta e kantonit` | 3,984 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ë _` | 7,800,858 |
| 2 | `e _` | 6,917,648 |
| 3 | `_ n` | 3,861,981 |
| 4 | `t ë` | 3,696,217 |
| 5 | `_ t` | 3,628,673 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t ë _` | 2,956,258 |
| 2 | `n ë _` | 2,160,628 |
| 3 | `_ t ë` | 2,148,124 |
| 4 | `_ e _` | 1,801,956 |
| 5 | `_ n ë` | 1,679,817 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t ë _` | 2,122,187 |
| 2 | `_ n ë _` | 1,575,702 |
| 3 | `d h e _` | 1,117,215 |
| 4 | `_ d h e` | 974,183 |
| 5 | `_ p ë r` | 960,414 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d h e _` | 966,499 |
| 2 | `_ n j ë _` | 630,318 |
| 3 | `e _ t ë _` | 584,704 |
| 4 | `_ p ë r _` | 452,162 |
| 5 | `_ n g a _` | 451,796 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 273
- **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 | 0.9594 | 1.945 | 9.98 | 960,080 | 4.1% |
| **1** | Subword | 1.0835 | 2.119 | 7.10 | 7,063 | 0.0% |
| **2** | Word | 0.3588 | 1.282 | 2.30 | 9,558,817 | 64.1% |
| **2** | Subword | 0.7555 | 1.688 | 4.95 | 50,088 | 24.4% |
| **3** | Word | 0.1576 | 1.115 | 1.37 | 21,934,967 | 84.2% |
| **3** | Subword | 0.7799 | 1.717 | 4.37 | 247,611 | 22.0% |
| **4** | Word | 0.0660 🏆 | 1.047 | 1.12 | 29,902,129 | 93.4% |
| **4** | Subword | 0.7135 | 1.640 | 3.50 | 1,082,029 | 28.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `të energjisë siq është i konsideroi gjithashtu edhe pak të dhe republika bosna në të cilat`
2. `e shkelte në indi i cili ia doli si zëvendës trajner të clintonit më shumë zbulime`
3. `në maduranthakam chennai shqip të jashtme html kultura e liqenit të njëjtin vit 5 vezë nga`

**Context Size 2:**

1. `për të kuptuar fuqinë e fjalëve dhe shprehjeve të pastra ishin të lirë nuk është e pasur`
2. `në vitin si regjisor aktor dhe çmimin kombëtar azem shkreli shkrimtar shqiptarë akademik i tipit gjy...`
3. `e tij hidrogjenin dhe squfuri nuk mund të jenë në gjendje të zhvendoste kryeqytetin e tyre los`

**Context Size 3:**

1. `lidhje të jashtme insee quinson`
2. `për shkak të papunësisë është dukshëm negativ efekti i dytë që ra nga kategoria në nivel ndërkombëta...`
3. `e tij të ardhshme ilenia betti më të cilën pati një djalë me nofkën candlewick i cili do`

**Context Size 4:**

1. `referime lidhje të jashtme profili tek chelseafc com profili tek goal com andrea ranocchia tek uefa ...`
2. `është një komunë në spanjë e vendosur në qarkun alt urgell të provincës lleida në katalonia ponts ka...`
3. `referimet lidhje të jashtme insee saint didier sur chalaronne është një komunë franceze e cila ndodh...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_2,_uamjë_nsisia`
2. `e_dmurë,_prornda`
3. `isha_prare_j_pës`

**Context Size 2:**

1. `ë_mun)._fulë_lojë`
2. `e_çdoi_nger_me_pu`
3. `_njepsemejatë_lat`

**Context Size 3:**

1. `të_zbulloges_të_ep`
2. `në_mundin_e_munim,`
3. `_të_tij_ca._shtu_n`

**Context Size 4:**

1. `_të_pjesë_egjimi_që`
2. `_në_qartësisht_për_`
3. `dhe_filmin_e_fsk-së`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,082,029 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 | 445,748 |
| Total Tokens | 37,825,256 |
| Mean Frequency | 84.86 |
| Median Frequency | 4 |
| Frequency Std Dev | 5646.34 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | të | 2,156,535 |
| 2 | e | 1,823,346 |
| 3 | në | 1,592,899 |
| 4 | dhe | 973,190 |
| 5 | i | 901,212 |
| 6 | një | 639,479 |
| 7 | me | 483,719 |
| 8 | për | 456,456 |
| 9 | nga | 456,107 |
| 10 | është | 317,914 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | hofbräu | 2 |
| 2 | steckerlfisch | 2 |
| 3 | 0i | 2 |
| 4 | 0tendë | 2 |
| 5 | guglhupf | 2 |
| 6 | wildmoser | 2 |
| 7 | zynq | 2 |
| 8 | systemc | 2 |
| 9 | ogrenci | 2 |
| 10 | memik | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9377 |
| R² (Goodness of Fit) | 0.997109 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.4% |
| Top 1,000 | 58.5% |
| Top 5,000 | 73.7% |
| Top 10,000 | 80.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9971 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.4% of corpus
- **Long Tail:** 435,748 words needed for remaining 19.6% 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 | 0.7903 🏆 | 0.3749 | N/A | N/A |
| **mono_64d** | 64 | 0.7310 | 0.2949 | N/A | N/A |
| **mono_128d** | 128 | 0.6419 | 0.2452 | N/A | N/A |
| **aligned_32d** | 32 | 0.7903 | 0.3890 | 0.2580 | 0.6680 |
| **aligned_64d** | 64 | 0.7310 | 0.2993 | 0.4940 | 0.8400 |
| **aligned_128d** | 128 | 0.6419 | 0.2548 | 0.6120 | 0.8980 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7903 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3097. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 61.2% 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 | **-0.661** | 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` | stroheim, shestani, shenjtëoren |
| `-a` | audiovizualeve, aktroj, alsek |
| `-b` | bronislawa, bpmn, beige |
| `-ma` | matricën, matërialit, marie |
| `-m` | matricën, muskës, matërialit |
| `-k` | krille, kobuleti, kontemporane |
| `-p` | performuar, pile, protoshqipisht |
| `-d` | drogave, duanë, delk |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | krille, rriteshe, craniate |
| `-t` | lincolnit, protoshqipisht, waset |
| `-n` | nderrohen, njomen, shenjtëoren |
| `-a` | bronislawa, sphyrna, pawaia |
| `-s` | gronovius, objectives, sphenophalos |
| `-i` | kobuleti, shestani, sendai |
| `-it` | lincolnit, nishanit, abdulbasit |
| `-in` | xhemin, korpusin, kukumin |

### 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 |
|------|----------|------------------|----------|
| `etit` | 2.01x | 131 contexts | getit, letit, eetit |
| `itha` | 2.18x | 66 contexts | sitha, ithac, pitha |
| `ioni` | 1.65x | 233 contexts | pioni, rioni, ionic |
| `rish` | 1.58x | 273 contexts | irish, rrish, prish |
| `ësis` | 1.99x | 80 contexts | njësis, njësisë, malësis |
| `gjit` | 1.81x | 118 contexts | gjith, ngjit, gjita |
| `itet` | 1.68x | 129 contexts | pitet, mitet, hitet |
| `jith` | 2.00x | 58 contexts | gjith, gjithi, gjitho |
| `rejt` | 1.64x | 143 contexts | krejt, grejt, drejt |
| `htet` | 1.95x | 64 contexts | shtet, shtetë, shteto |
| `ptar` | 2.67x | 18 contexts | loptar, guptar, šiptar |
| `efer` | 1.70x | 80 contexts | sefer, refer, nefer |

### 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` | `-e` | 113 words | publicae, prokurorie |
| `-s` | `-e` | 98 words | sketerre, shokve |
| `-k` | `-t` | 89 words | konotacionet, kurtit |
| `-s` | `-n` | 86 words | sankirtan, seksizmin |
| `-p` | `-t` | 82 words | pleasant, pinet |
| `-p` | `-n` | 81 words | prathan, ponton |
| `-s` | `-a` | 76 words | soraya, shkreta |
| `-k` | `-i` | 74 words | klorifikimi, kopulimi |
| `-a` | `-e` | 72 words | akide, ayrshire |
| `-s` | `-s` | 70 words | sunexpress, saldues |

### 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 |
|------|-----------------|------------|------|
| asteriskët | **`asteris-k-ët`** | 7.5 | `k` |
| mbaheshin | **`mbahe-sh-in`** | 7.5 | `sh` |
| hugjenotë | **`hugjeno-t-ë`** | 7.5 | `t` |
| grassroots | **`grassroo-t-s`** | 7.5 | `t` |
| kalorësiakë | **`kalorësia-k-ë`** | 7.5 | `k` |
| kushëriren | **`kushëri-re-n`** | 7.5 | `re` |
| parameswara | **`paramesw-ar-a`** | 7.5 | `ar` |
| aliagatit | **`aliaga-t-it`** | 7.5 | `t` |
| koretisht | **`koreti-sh-t`** | 7.5 | `sh` |
| arimateas | **`arimate-a-s`** | 7.5 | `a` |
| firdeusin | **`firdeu-s-in`** | 7.5 | `s` |
| gjithëkund | **`gjithëku-n-d`** | 7.5 | `n` |
| producteurs | **`producteu-r-s`** | 7.5 | `r` |
| vetëvranë | **`vetëv-ra-në`** | 7.5 | `ra` |
| georgjane | **`georgja-n-e`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Albanian 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 (4.62x) |
| N-gram | **2-gram** | Lowest perplexity (273) |
| Markov | **Context-4** | Highest predictability (93.4%) |
| 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: 2026-01-11 00:57:18*