README.md

---
language: is
language_name: Icelandic
language_family: germanic_north
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-germanic_north
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: 4.556
  - name: best_isotropy
    type: isotropy
    value: 0.8275
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Icelandic** 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** | 3.538x | 3.54 | 0.0547% | 1,307,527 |
| **16k** | 3.917x | 3.92 | 0.0605% | 1,181,053 |
| **32k** | 4.268x | 4.27 | 0.0660% | 1,083,827 |
| **64k** | 4.556x 🏆 | 4.56 | 0.0704% | 1,015,400 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ensími getur átt við: Ensím Íslensku hljómsveitina Ensími`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁en sí mi ▁getur ▁átt ▁við : ▁en sí m ... (+5 more)` | 15 |
| 16k | `▁ensí mi ▁getur ▁átt ▁við : ▁ensí m ▁íslensku ▁hljómsveitina ... (+2 more)` | 12 |
| 32k | `▁ensí mi ▁getur ▁átt ▁við : ▁ensím ▁íslensku ▁hljómsveitina ▁ensí ... (+1 more)` | 11 |
| 64k | `▁ensími ▁getur ▁átt ▁við : ▁ensím ▁íslensku ▁hljómsveitina ▁ensími` | 9 |

**Sample 2:** `Arís er íslenskt kvenmannsnafn. Dreifing á Íslandi Heimildir kvenmannsnöfn`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ar ís ▁er ▁íslenskt ▁kvenmannsnafn . ▁dreifing ▁á ▁íslandi ▁heimildir ... (+1 more)` | 11 |
| 16k | `▁ar ís ▁er ▁íslenskt ▁kvenmannsnafn . ▁dreifing ▁á ▁íslandi ▁heimildir ... (+1 more)` | 11 |
| 32k | `▁ar ís ▁er ▁íslenskt ▁kvenmannsnafn . ▁dreifing ▁á ▁íslandi ▁heimildir ... (+1 more)` | 11 |
| 64k | `▁ar ís ▁er ▁íslenskt ▁kvenmannsnafn . ▁dreifing ▁á ▁íslandi ▁heimildir ... (+1 more)` | 11 |

**Sample 3:** `Start-Up (Kóreska: 스타트업; Seutateueop) er suður-kóreskur sjónvarpsþáttur. sjónvar...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁st art - up ▁( kó re ska : ▁ ... (+18 more)` | 28 |
| 16k | `▁st art - up ▁( kóre ska : ▁ 스타트업 ... (+15 more)` | 25 |
| 32k | `▁start - up ▁( kóreska : ▁ 스타트업 ; ▁se ... (+13 more)` | 23 |
| 64k | `▁start - up ▁( kóreska : ▁ 스타트업 ; ▁se ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.556x compression
- **Lowest UNK Rate:** 8k with 0.0547% 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 | 76,323 | 16.22 | 290,201 | 7.5% | 20.3% |
| **2-gram** | Subword | 360 🏆 | 8.49 | 7,570 | 60.9% | 98.9% |
| **3-gram** | Word | 187,198 | 17.51 | 409,948 | 3.6% | 11.1% |
| **3-gram** | Subword | 3,285 | 11.68 | 62,993 | 21.8% | 63.7% |
| **4-gram** | Word | 412,107 | 18.65 | 661,434 | 2.3% | 6.9% |
| **4-gram** | Subword | 19,995 | 14.29 | 386,811 | 10.1% | 32.9% |
| **5-gram** | Word | 284,069 | 18.12 | 418,913 | 3.1% | 8.0% |
| **5-gram** | Subword | 84,371 | 16.36 | 1,264,141 | 5.6% | 18.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `til að` | 27,637 |
| 2 | `þar sem` | 24,592 |
| 3 | `á íslandi` | 18,253 |
| 4 | `því að` | 15,183 |
| 5 | `þess að` | 13,286 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `til þess að` | 8,156 |
| 2 | `með því að` | 4,654 |
| 3 | `þar sem hann` | 3,445 |
| 4 | `dreifing á íslandi` | 2,999 |
| 5 | `á íslandi heimildir` | 2,839 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dreifing á íslandi heimildir` | 2,780 |
| 2 | `kvenmannsnafn dreifing á íslandi` | 1,520 |
| 3 | `íslenskt kvenmannsnafn dreifing á` | 1,519 |
| 4 | `er íslenskt kvenmannsnafn dreifing` | 1,518 |
| 5 | `á íslandi heimildir kvenmannsnöfn` | 1,509 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `íslenskt kvenmannsnafn dreifing á íslandi` | 1,519 |
| 2 | `er íslenskt kvenmannsnafn dreifing á` | 1,518 |
| 3 | `dreifing á íslandi heimildir kvenmannsnöfn` | 1,509 |
| 4 | `kvenmannsnafn dreifing á íslandi heimildir` | 1,471 |
| 5 | `íslenskt karlmannsnafn dreifing á íslandi` | 1,309 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `r _` | 1,832,522 |
| 2 | `a r` | 1,368,870 |
| 3 | `_ s` | 1,362,774 |
| 4 | `i n` | 1,140,724 |
| 5 | `a _` | 1,027,671 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a r _` | 583,858 |
| 2 | `o g _` | 458,351 |
| 3 | `_ o g` | 457,248 |
| 4 | `u r _` | 447,514 |
| 5 | `_ í _` | 435,363 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ o g _` | 456,555 |
| 2 | `_ a ð _` | 255,398 |
| 3 | `s e m _` | 214,724 |
| 4 | `_ s e m` | 214,407 |
| 5 | `_ e r _` | 203,790 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s e m _` | 212,727 |
| 2 | `_ v a r _` | 160,455 |
| 3 | `_ t i l _` | 132,778 |
| 4 | `_ h a n n` | 91,569 |
| 5 | `_ v i ð _` | 89,262 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 360
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~19% 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 | 0.8991 | 1.865 | 7.58 | 645,450 | 10.1% |
| **1** | Subword | 0.8434 | 1.794 | 5.91 | 4,305 | 15.7% |
| **2** | Word | 0.3025 | 1.233 | 1.88 | 4,874,320 | 69.8% |
| **2** | Subword | 0.7898 | 1.729 | 5.23 | 25,387 | 21.0% |
| **3** | Word | 0.1108 | 1.080 | 1.21 | 9,119,459 | 88.9% |
| **3** | Subword | 0.8104 | 1.754 | 4.71 | 132,737 | 19.0% |
| **4** | Word | 0.0408 🏆 | 1.029 | 1.06 | 11,025,075 | 95.9% |
| **4** | Subword | 0.7484 | 1.680 | 3.57 | 624,878 | 25.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `og hentar vel stæðir og bornir fram sönnunargögn sem auðmjúkum manni sínum fyrir convention on train`
2. `í helgafellssveit akureyjar þar sem þau voru í skiftirækt hann var formaður utanríkismálanefndar um ...`
3. `á suður ítalíu ákvað hópurinn að ráða í þessu nafni sambandsins og er árlega sumarsýningu norræna`

**Context Size 2:**

1. `til að hjálpa til uppáhalds frasinn hans er einkum þekktur fyrir hlutverk sitt í davíð að hann`
2. `þar sem hann naut mikillar virðingar samtíðarmanna sinna hún var komin í millihýsil þá umbreytast eg...`
3. `því að þeir þorvaldur og andrea šušnjara lipeja tena 13 33 12 12 12 18 0 31`

**Context Size 3:**

1. `til þess að verða bandamaður michaels í fjórðu seríu er farið yfir launasjóðskenninguna og umfjöllun...`
2. `með því að stebbi finnur sig fastan á milli steins tóta og sleggju brúnó söguþráður kvikmyndir is le...`
3. `þar sem hann gerði voru ómerktar eins og venjan var áður núverandi ríkisstjórn er ráðuneyti kristrún...`

**Context Size 4:**

1. `dreifing á íslandi heimildir karlmannsnöfn millinöfn`
2. `kvenmannsnafn dreifing á íslandi heimildir karlmannsnöfn kvenmannsnöfn mannanöfn sem notuð eru sem s...`
3. `íslenskt kvenmannsnafn dreifing á íslandi heimildir karlmannsnöfn karlmannsnöfn karlmannsnöfn karlma...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_alanleft._sist_`
2. `a_að_mariða_hast`
3. `r_ng_g_18)._hafr`

**Context Size 2:**

1. `r_og_ver_er_þandu`
2. `ariðlaráðandurver`
3. `_skógismeigilsfæd`

**Context Size 3:**

1. `ar_bikarabbí_orian`
2. `og_heitimennda,_mi`
3. `_og_lankameríkur_a`

**Context Size 4:**

1. `_og_mannsson,_útgáf`
2. `_að_innarskógarþrúð`
3. `sem_juttum_mági_sig`


### 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 (624,878 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 | 287,581 |
| Total Tokens | 12,356,689 |
| Mean Frequency | 42.97 |
| Median Frequency | 4 |
| Frequency Std Dev | 1648.11 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | og | 457,899 |
| 2 | í | 437,515 |
| 3 | á | 265,620 |
| 4 | að | 256,592 |
| 5 | sem | 214,678 |
| 6 | er | 205,384 |
| 7 | var | 161,974 |
| 8 | til | 134,849 |
| 9 | við | 91,854 |
| 10 | af | 91,619 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 洞 | 2 |
| 2 | 리 | 2 |
| 3 | myeongjang | 2 |
| 4 | hitaþolnir | 2 |
| 5 | sløttum | 2 |
| 6 | noregslandi | 2 |
| 7 | triðja | 2 |
| 8 | beregszásziová | 2 |
| 9 | lúóa | 2 |
| 10 | keníumanna | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9806 |
| R² (Goodness of Fit) | 0.998336 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.0% |
| Top 1,000 | 56.0% |
| Top 5,000 | 71.7% |
| Top 10,000 | 78.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9983 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.0% of corpus
- **Long Tail:** 277,581 words needed for remaining 21.6% 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 | 0.8275 | 0.3448 | N/A | N/A |
| **mono_64d** | 64 | 0.7798 | 0.2809 | N/A | N/A |
| **mono_128d** | 128 | 0.7263 | 0.2042 | N/A | N/A |
| **aligned_32d** | 32 | 0.8275 🏆 | 0.3509 | 0.1760 | 0.5520 |
| **aligned_64d** | 64 | 0.7798 | 0.2744 | 0.3040 | 0.6540 |
| **aligned_128d** | 128 | 0.7263 | 0.2020 | 0.3960 | 0.6900 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8275 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2762. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 39.6% 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 | **-0.580** | 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` | skrúðsigling, safamýri, síuna |
| `-a` | alinu, alfarið, alvarlegar |
| `-b` | byrlaði, brahes, boðsundssveitar |
| `-h` | hænis, hryggsúlunnar, heimilisins |
| `-m` | markúsdóttur, mótmælendunum, málvísindamannsins |
| `-k` | kesiya, kóngsstaðadalur, kórónaveirufaraldurinn |
| `-ma` | markúsdóttur, maximine, masterpiece |
| `-t` | tyrrell, tannþráð, teypaða |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-r` | markúsdóttur, lágmarkar, boðsundssveitar |
| `-a` | röksemdafærsla, útrýma, síuna |
| `-i` | byrlaði, safamýri, pósthússtræti |
| `-n` | indverjinn, notodden, rodman |
| `-um` | mótmælendunum, gjaldmiðlakerfum, stöndum |
| `-ar` | lágmarkar, boðsundssveitar, hryggsúlunnar |
| `-ur` | markúsdóttur, ljóstvistur, kóngsstaðadalur |
| `-s` | brahes, hænis, ekkekrates |

### 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 |
|------|----------|------------------|----------|
| `sson` | 2.16x | 82 contexts | arsson, jesson, wesson |
| `nnar` | 1.68x | 96 contexts | ánnar, innar, unnar |
| `stjó` | 1.86x | 50 contexts | stjóra, stjórn, stjóri |
| `maðu` | 2.17x | 28 contexts | maður, ismaður, ármaður |
| `ngur` | 1.63x | 85 contexts | úngur, ungur, ingur |
| `ista` | 1.38x | 162 contexts | gista, istar, vista |
| `ngar` | 1.56x | 71 contexts | angar, ungar, ingar |
| `ndar` | 1.33x | 133 contexts | undar, andar, endar |
| `jórn` | 2.04x | 23 contexts | sjórn, stjórn, bjórnum |
| `egar` | 2.03x | 21 contexts | segar, vegar, þegar |
| `ndur` | 1.33x | 99 contexts | undur, endur, rindur |
| `ndir` | 1.41x | 70 contexts | endir, undir, randir |

### 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` | `-r` | 200 words | sjóðríkur, sérkennilegar |
| `-s` | `-i` | 158 words | stuttskífunni, seyði |
| `-s` | `-a` | 142 words | saxicola, shimada |
| `-h` | `-r` | 131 words | hugprýðinnar, hverfisveppur |
| `-s` | `-n` | 128 words | schliemann, sérútbúin |
| `-s` | `-m` | 92 words | söderström, sigruðum |
| `-s` | `-um` | 89 words | sigruðum, stráknum |
| `-h` | `-a` | 88 words | hálfbræðranna, helga |
| `-k` | `-r` | 87 words | kýlapestar, knapar |
| `-b` | `-r` | 83 words | bíldudalur, beaver |

### 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 |
|------|-----------------|------------|------|
| læknisins | **`læknis-i-ns`** | 7.5 | `i` |
| þrumuveðri | **`þrumuveð-r-i`** | 7.5 | `r` |
| ofbeldisfullra | **`ofbeldisfull-r-a`** | 7.5 | `r` |
| ketilbjörn | **`ketilbjö-r-n`** | 7.5 | `r` |
| meðlimina | **`meðlim-i-na`** | 7.5 | `i` |
| kambódíustjórn | **`kambódíustjó-r-n`** | 7.5 | `r` |
| óbreyttri | **`óbreytt-r-i`** | 7.5 | `r` |
| norðurodda | **`norðurod-d-a`** | 7.5 | `d` |
| jöhannsson | **`jöhanns-s-on`** | 7.5 | `s` |
| handelman | **`handelm-a-n`** | 7.5 | `a` |
| steypujárni | **`steypujá-r-ni`** | 7.5 | `r` |
| konuvísur | **`konuví-s-ur`** | 7.5 | `s` |
| heittemprað | **`heittempr-a-ð`** | 7.5 | `a` |
| sororculana | **`sororcu-la-na`** | 7.5 | `la` |
| hryggdýrum | **`hryggdý-r-um`** | 7.5 | `r` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Icelandic 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 (4.56x) |
| N-gram | **2-gram** | Lowest perplexity (360) |
| 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 06:06:11*