README.md

---
language: fo
language_name: Faroese
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: 4.421
  - name: best_isotropy
    type: isotropy
    value: 0.8701
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Faroese** 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** | 3.578x | 3.58 | 0.0475% | 501,416 |
| **16k** | 3.909x | 3.91 | 0.0518% | 459,065 |
| **32k** | 4.191x | 4.19 | 0.0556% | 428,081 |
| **64k** | 4.421x 🏆 | 4.42 | 0.0586% | 405,872 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Nagano er ein býur á oynni Honshu í Japan. Í vóru OL-veturleikirnir í býnum. Áví...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁n ag ano ▁er ▁ein ▁býur ▁á ▁oynni ▁hon sh ... (+35 more)` | 45 |
| 16k | `▁nag ano ▁er ▁ein ▁býur ▁á ▁oynni ▁hon sh u ... (+34 more)` | 44 |
| 32k | `▁nag ano ▁er ▁ein ▁býur ▁á ▁oynni ▁hon shu ▁í ... (+29 more)` | 39 |
| 64k | `▁nag ano ▁er ▁ein ▁býur ▁á ▁oynni ▁honshu ▁í ▁japan ... (+28 more)` | 38 |

**Sample 2:** `Eslöv er ein býur í Eslövs kommunu í Skåne län í Svøríki. Býurin hevur umleið 17...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁e sl öv ▁er ▁ein ▁býur ▁í ▁e sl öv ... (+25 more)` | 35 |
| 16k | `▁e slöv ▁er ▁ein ▁býur ▁í ▁e slöv s ▁kommunu ... (+23 more)` | 33 |
| 32k | `▁eslöv ▁er ▁ein ▁býur ▁í ▁eslöv s ▁kommunu ▁í ▁skåne ... (+21 more)` | 31 |
| 64k | `▁eslöv ▁er ▁ein ▁býur ▁í ▁eslövs ▁kommunu ▁í ▁skåne ▁län ... (+20 more)` | 30 |

**Sample 3:** `Langeskov kommuna (danskt: Langeskov kommune), er ein kommuna í Fyns Amt í Danma...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lang e skov ▁kommuna ▁( danskt : ▁lang e skov ... (+28 more)` | 38 |
| 16k | `▁lang e skov ▁kommuna ▁( danskt : ▁lang e skov ... (+27 more)` | 37 |
| 32k | `▁lange skov ▁kommuna ▁( danskt : ▁lange skov ▁kommune ), ... (+24 more)` | 34 |
| 64k | `▁langeskov ▁kommuna ▁( danskt : ▁langeskov ▁kommune ), ▁er ▁ein ... (+21 more)` | 31 |


### Key Findings

- **Best Compression:** 64k achieves 4.421x compression
- **Lowest UNK Rate:** 8k with 0.0475% 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 | 19,074 | 14.22 | 52,510 | 11.9% | 30.1% |
| **2-gram** | Subword | 358 🏆 | 8.49 | 4,371 | 60.3% | 98.7% |
| **3-gram** | Word | 30,965 | 14.92 | 64,802 | 8.8% | 23.6% |
| **3-gram** | Subword | 3,173 | 11.63 | 35,149 | 21.7% | 64.3% |
| **4-gram** | Word | 56,491 | 15.79 | 107,657 | 6.7% | 19.4% |
| **4-gram** | Subword | 18,109 | 14.14 | 189,262 | 10.5% | 34.3% |
| **5-gram** | Word | 37,176 | 15.18 | 74,269 | 7.8% | 23.2% |
| **5-gram** | Subword | 64,574 | 15.98 | 496,959 | 6.5% | 21.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `f kr` | 17,129 |
| 2 | `árini f` | 6,533 |
| 3 | `er ein` | 5,079 |
| 4 | `í føroyum` | 4,019 |
| 5 | `øld f` | 2,454 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `árini f kr` | 6,533 |
| 2 | `øld f kr` | 2,454 |
| 3 | `hendingar føðingar andlát` | 751 |
| 4 | `ein kommuna í` | 656 |
| 5 | `ið byrjaði á` | 638 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ið byrjaði á einum` | 636 |
| 2 | `er ein kommuna í` | 621 |
| 3 | `f kr hendingar føðingar` | 548 |
| 4 | `kr hendingar føðingar andlát` | 534 |
| 5 | `er ein býur í` | 521 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `f kr hendingar føðingar andlát` | 534 |
| 2 | `føðingar andlát øld f kr` | 497 |
| 3 | `hendingar føðingar andlát øld f` | 495 |
| 4 | `kr hendingar føðingar andlát øld` | 493 |
| 5 | `kalendaranum eitt vanligt ár ið` | 476 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `r _` | 290,904 |
| 2 | `i n` | 229,266 |
| 3 | `a r` | 218,692 |
| 4 | `_ s` | 209,679 |
| 5 | `a n` | 183,340 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ í _` | 94,332 |
| 2 | `u r _` | 93,257 |
| 3 | `u m _` | 92,289 |
| 4 | `a r _` | 73,100 |
| 5 | `i ð _` | 65,495 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ o g _` | 65,054 |
| 2 | `_ e r _` | 33,635 |
| 3 | `_ a t _` | 28,671 |
| 4 | `n u m _` | 27,682 |
| 5 | `i n i _` | 26,628 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s u m _` | 22,835 |
| 2 | `_ v i ð _` | 20,464 |
| 3 | `_ t i l _` | 20,113 |
| 4 | `_ f . k r` | 17,103 |
| 5 | `f . k r .` | 17,094 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 358
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~21% 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 | 0.8217 | 1.767 | 5.75 | 176,129 | 17.8% |
| **1** | Subword | 0.8858 | 1.848 | 6.33 | 2,058 | 11.4% |
| **2** | Word | 0.2659 | 1.202 | 1.65 | 1,010,213 | 73.4% |
| **2** | Subword | 0.8361 | 1.785 | 5.38 | 13,016 | 16.4% |
| **3** | Word | 0.0884 | 1.063 | 1.15 | 1,662,607 | 91.2% |
| **3** | Subword | 0.8358 | 1.785 | 4.43 | 69,978 | 16.4% |
| **4** | Word | 0.0297 🏆 | 1.021 | 1.04 | 1,896,454 | 97.0% |
| **4** | Subword | 0.7103 | 1.636 | 3.08 | 309,872 | 29.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `í í høvuðsstaðarregión danmarkar var forkvinna á youtube com dýrd harrans deyður 30 sesongin av olju`
2. `og eru 1 4 5 97 265 maleisia myanmar aung san marino italskt tónaskald d 28`
3. `er amerikanskur sjónleikari og tann 44 minuttir útgávudato 14 f pearl bailey and stonehenge var tað`

**Context Size 2:**

1. `f kr 16 f kr hendingar føðingar andlát øld f kr 580 árini f kr hendingar føðingar`
2. `árini f kr árstal 152 f kr áratíggju 390 árini f kr 10 árini f kr 220`
3. `er ein kommuna í región suðurdanmark í danmark lærarastarvið gjørdist lívsstarv hansara var høvuðsat...`

**Context Size 3:**

1. `árini f kr 230 f kr 229 f kr 228 f kr 227 f kr 226 f kr`
2. `øld f kr áratíggju 490 árini 500 árini 510 árini 520 árini 530 árini 540 árini 550 árini`
3. `ein kommuna í gävleborgs län í svøríki bjuvs kommuna hevur 14 015 íbúgvar i riket län och kommuner`

**Context Size 4:**

1. `ið byrjaði á einum mánadegi hendingar 1 januar vestursámoa verður frælst ríki 8 november løgtingsval...`
2. `er ein kommuna í keypmannahavns amt í danmark høje taastrup kommuna hevur umleið 48 695 íbúgvar í da...`
3. `f kr hendingar føðingar andlát øld f kr`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_nangaterðrn_om.`
2. `apskand_úrim_160`
3. `rnörn_kl_býr_och`

**Context Size 2:**

1. `r_vilberðu_(svar_`
2. `iniziskur_sonakt_`
3. `ardin,_nast_hav_b`

**Context Size 3:**

1. `_í_dagføroyskilu,_`
2. `ur_í_føroyingur_tu`
3. `um_byrgdir_sonerha`

**Context Size 4:**

1. `_og_atli_bayern_lon`
2. `_er_m.a._í_nazithro`
3. `_at_náttúrutengdum_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (309,872 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 | 77,098 |
| Total Tokens | 2,107,707 |
| Mean Frequency | 27.34 |
| Median Frequency | 4 |
| Frequency Std Dev | 537.11 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | í | 96,564 |
| 2 | og | 65,210 |
| 3 | er | 34,690 |
| 4 | at | 28,863 |
| 5 | á | 26,503 |
| 6 | sum | 23,040 |
| 7 | av | 21,270 |
| 8 | við | 21,264 |
| 9 | f | 21,130 |
| 10 | til | 20,883 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | afgøres | 2 |
| 2 | semifinalerne | 2 |
| 3 | straffesparkskonkurrence | 2 |
| 4 | præmiepenge | 2 |
| 5 | udekampe | 2 |
| 6 | amerikanaranum | 2 |
| 7 | squibb | 2 |
| 8 | beregszásziová | 2 |
| 9 | brøðrarørslan | 2 |
| 10 | befg | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0122 |
| R² (Goodness of Fit) | 0.998602 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 38.1% |
| Top 1,000 | 61.0% |
| Top 5,000 | 77.8% |
| Top 10,000 | 84.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9986 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 38.1% of corpus
- **Long Tail:** 67,098 words needed for remaining 15.4% 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 | 0.8663 | 0.3394 | N/A | N/A |
| **mono_64d** | 64 | 0.8701 🏆 | 0.2508 | N/A | N/A |
| **mono_128d** | 128 | 0.8059 | 0.1852 | N/A | N/A |
| **aligned_32d** | 32 | 0.8663 | 0.3298 | 0.0720 | 0.3400 |
| **aligned_64d** | 64 | 0.8701 | 0.2499 | 0.1180 | 0.4260 |
| **aligned_128d** | 128 | 0.8059 | 0.1896 | 0.1760 | 0.5080 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.8701 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2574. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 17.6% 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 | **0.100** | 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 |
|--------|----------|
| `-st` | statsleiðararnar, stovnum, stillir |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-r` | roykir, kippur, rannsóknir |
| `-n` | hóttan, alden, tuin |
| `-um` | homrum, stovnum, sonevndum |
| `-ar` | statsleiðararnar, pilar, akrar |
| `-ur` | kippur, heindrikkur, tríkantur |
| `-in` | tuin, mentamálaráðharrin, undirsjóvartunnilin |
| `-num` | stovnum, skarninum, muslimunum |
| `-ir` | roykir, rannsóknir, stillir |

### 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 |
|------|----------|------------------|----------|
| `rini` | 2.22x | 35 contexts | árini, trini, irini |
| `ggja` | 1.63x | 94 contexts | eggja, oyggja, síggja |
| `ansk` | 1.64x | 88 contexts | mansk, dansk, fransk |
| `ndin` | 1.56x | 111 contexts | endin, andin, vandin |
| `nlei` | 1.99x | 36 contexts | gunleif, sunleif, finleif |
| `aður` | 1.95x | 30 contexts | jaður, maður, staður |
| `ngar` | 1.61x | 56 contexts | ongar, ingar, ungar |
| `ndur` | 1.59x | 56 contexts | undur, endur, óndur |
| `ikar` | 1.78x | 36 contexts | bikar, tikari, peikar |
| `ldur` | 1.69x | 43 contexts | aldur, eldur, baldur |
| `eldu` | 1.77x | 30 contexts | eldur, teldu, feldu |
| `nsku` | 1.81x | 27 contexts | ensku, enskur, finsku |

### 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 |
|--------|--------|-----------|----------|
| `-st` | `-r` | 34 words | studentaskúlanæmingar, stívur |
| `-st` | `-n` | 23 words | stormen, stundin |
| `-st` | `-um` | 17 words | studioalbum, strandgeiranum |
| `-st` | `-ar` | 12 words | studentaskúlanæmingar, stokkar |
| `-st` | `-ni` | 11 words | strandafjøllini, strandalondini |
| `-st` | `-ur` | 10 words | stívur, stórídnaður |
| `-st` | `-num` | 8 words | strandgeiranum, stættatinginum |
| `-st` | `-ir` | 7 words | steroidir, stættir |
| `-st` | `-ið` | 6 words | strandaøkið, stórbýarøkið |
| `-st` | `-in` | 5 words | stundin, stapin |

### 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 |
|------|-----------------|------------|------|
| prestagarðurin | **`prestagarð-ur-in`** | 6.0 | `prestagarð` |
| harðskapurin | **`harðskap-ur-in`** | 6.0 | `harðskap` |
| handverkarum | **`handverk-ar-um`** | 6.0 | `handverk` |
| mentanini | **`menta-ni-ni`** | 6.0 | `menta` |
| tjóðargarðurin | **`tjóðargarð-ur-in`** | 6.0 | `tjóðargarð` |
| krossfiskurin | **`krossfisk-ur-in`** | 6.0 | `krossfisk` |
| forstaðinum | **`forstaði-num`** | 4.5 | `forstaði` |
| fyrrapartin | **`fyrrapart-in`** | 4.5 | `fyrrapart` |
| landsløgum | **`landsløg-um`** | 4.5 | `landsløg` |
| suðuroyarmálið | **`suðuroyarmál-ið`** | 4.5 | `suðuroyarmál` |
| gongustjørnunum | **`gongustjørnu-num`** | 4.5 | `gongustjørnu` |
| sóknarprestin | **`sóknarprest-in`** | 4.5 | `sóknarprest` |
| fjórðingar | **`fjórðing-ar`** | 4.5 | `fjórðing` |
| lastbilar | **`lastbil-ar`** | 4.5 | `lastbil` |
| grundlógin | **`grundlóg-in`** | 4.5 | `grundlóg` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Faroese 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 (4.42x) |
| N-gram | **2-gram** | Lowest perplexity (358) |
| Markov | **Context-4** | Highest predictability (97.0%) |
| 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: 2026-01-04 14:57:33*