---
language: frr
language_name: Northern Frisian
language_family: germanic_west_anglofrisian
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_west_anglofrisian
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: 3.953
  - name: best_isotropy
    type: isotropy
    value: 0.8602
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

# Northern Frisian - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Northern Frisian** 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** | 3.042x | 3.05 | 0.0093% | 289,663 |
| **16k** | 3.385x | 3.39 | 0.0104% | 260,327 |
| **32k** | 3.690x | 3.69 | 0.0113% | 238,796 |
| **64k** | 3.953x 🏆 | 3.96 | 0.0121% | 222,923 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Wat menst dü? R - di buksteew R - det formeltiaken för di elektrisk wederstant u...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wat ▁menst ▁dü ? ▁r ▁- ▁di ▁buksteew ▁r ▁- ... (+27 more)` | 37 |
| 16k | `▁wat ▁menst ▁dü ? ▁r ▁- ▁di ▁buksteew ▁r ▁- ... (+25 more)` | 35 |
| 32k | `▁wat ▁menst ▁dü ? ▁r ▁- ▁di ▁buksteew ▁r ▁- ... (+22 more)` | 32 |
| 64k | `▁wat ▁menst ▁dü ? ▁r ▁- ▁di ▁buksteew ▁r ▁- ... (+22 more)` | 32 |

**Sample 2:** `Wat menst dü? Ponkt (Geometrii) Ponkt (Skrafttiaken) Ponkt (Spal)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wat ▁menst ▁dü ? ▁ponkt ▁( ge omet rii ) ... (+10 more)` | 20 |
| 16k | `▁wat ▁menst ▁dü ? ▁ponkt ▁( ge ometrii ) ▁ponkt ... (+9 more)` | 19 |
| 32k | `▁wat ▁menst ▁dü ? ▁ponkt ▁( ge ometrii ) ▁ponkt ... (+9 more)` | 19 |
| 64k | `▁wat ▁menst ▁dü ? ▁ponkt ▁( geometrii ) ▁ponkt ▁( ... (+7 more)` | 17 |

**Sample 3:** `as det top-level-domain (TLD) faan Burundi. Luke uk diar`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁as ▁det ▁top - level - domain ▁( tld ) ... (+6 more)` | 16 |
| 16k | `▁as ▁det ▁top - level - domain ▁( tld ) ... (+6 more)` | 16 |
| 32k | `▁as ▁det ▁top - level - domain ▁( tld ) ... (+6 more)` | 16 |
| 64k | `▁as ▁det ▁top - level - domain ▁( tld ) ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 64k achieves 3.953x compression
- **Lowest UNK Rate:** 8k with 0.0093% 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 | 8,013 | 12.97 | 35,062 | 22.3% | 45.5% |
| **2-gram** | Subword | 383 🏆 | 8.58 | 7,011 | 59.6% | 97.8% |
| **3-gram** | Word | 12,833 | 13.65 | 47,461 | 17.8% | 39.0% |
| **3-gram** | Subword | 3,615 | 11.82 | 43,896 | 21.1% | 62.1% |
| **4-gram** | Word | 26,644 | 14.70 | 85,638 | 12.8% | 30.6% |
| **4-gram** | Subword | 21,148 | 14.37 | 210,827 | 11.8% | 34.3% |
| **5-gram** | Word | 25,713 | 14.65 | 69,952 | 11.4% | 28.7% |
| **5-gram** | Subword | 68,491 | 16.06 | 539,563 | 8.8% | 24.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `uun a` | 11,419 |
| 2 | `as en` | 9,278 |
| 3 | `uk diar` | 8,976 |
| 4 | `luke uk` | 8,822 |
| 5 | `faan a` | 7,893 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `luke uk diar` | 8,768 |
| 2 | `leit uun a` | 4,457 |
| 3 | `citypopulation de at` | 3,424 |
| 4 | `de at hoodsteed` | 3,371 |
| 5 | `at hoodsteed faan` | 2,526 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `citypopulation de at hoodsteed` | 3,370 |
| 2 | `de at hoodsteed faant` | 1,929 |
| 3 | `administrative division citypopulation de` | 1,819 |
| 4 | `luke uk diar uun` | 1,606 |
| 5 | `lidj administrative division citypopulation` | 1,454 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `citypopulation de at hoodsteed faant` | 1,929 |
| 2 | `lidj administrative division citypopulation de` | 1,454 |
| 3 | `division citypopulation de at hoodsteed` | 1,405 |
| 4 | `administrative division citypopulation de at` | 1,395 |
| 5 | `citypopulation de at hoodsteed faan` | 1,282 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 286,869 |
| 2 | `e n` | 196,071 |
| 3 | `t _` | 185,905 |
| 4 | `a n` | 172,458 |
| 5 | `_ a` | 153,980 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n _` | 105,520 |
| 2 | `a n _` | 77,330 |
| 3 | `u u n` | 55,150 |
| 4 | `a a n` | 54,694 |
| 5 | `_ d i` | 54,593 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ u u n` | 43,690 |
| 2 | `_ f a a` | 43,074 |
| 3 | `u u n _` | 42,913 |
| 4 | `f a a n` | 42,844 |
| 5 | `a a n _` | 32,819 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ f a a n` | 42,223 |
| 2 | `_ u u n _` | 36,000 |
| 3 | `f a a n _` | 31,557 |
| 4 | `_ d e t _` | 27,394 |
| 5 | `_ d i a r` | 18,519 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 383
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.6373 | 1.555 | 4.28 | 181,631 | 36.3% |
| **1** | Subword | 0.7998 | 1.741 | 5.45 | 4,452 | 20.0% |
| **2** | Word | 0.2130 | 1.159 | 1.48 | 775,133 | 78.7% |
| **2** | Subword | 0.7351 | 1.665 | 4.32 | 24,239 | 26.5% |
| **3** | Word | 0.0744 | 1.053 | 1.14 | 1,144,604 | 92.6% |
| **3** | Subword | 0.6972 | 1.621 | 3.60 | 104,619 | 30.3% |
| **4** | Word | 0.0329 🏆 | 1.023 | 1.06 | 1,289,490 | 96.7% |
| **4** | Subword | 0.6613 | 1.582 | 2.87 | 376,109 | 33.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `uun de at man tau twa futnuuten luke uk önslüten iin uun de geografii indialing faan`
2. `a cepheus ufkört del vallèscerdañola del rio mearim canela 2 villeurbanne luke uk bi t lun`
3. `faan aden uunt jen rochting haa en county as en sit en gemeen uun aasien uun`

**Context Size 2:**

1. `uun a maden faan det joseon köningrik uun korea störwen sturwen stürwen 12 febrewoore pribislaw i fü...`
2. `as en prowins uun a süüduast faan brüssel det hee 4 277 976 3 oblast wladimir sowjetunion`
3. `luke uk diar kwelen uun kronoberg`

**Context Size 3:**

1. `luke uk diar köninger an köninginen faan ingelun uun ingelun authority uun ingelun det ferwaltang sa...`
2. `leit uun a süüd faant lun det hee 4 466 800 lidj states agglomerations citypopulation de at hoodstee...`
3. `citypopulation de at hoodsteed faan t prowins det hee 13 042 lidj state in usa citypopulation de at`

**Context Size 4:**

1. `citypopulation de at hoodsteed faan t lun as port vila geografii a eilunen faan wanuaatuu ling auer ...`
2. `de at hoodsteed faant komuun as töreboda kwelen uun västra götaland`
3. `administrative division citypopulation de at hoodsteed faant prowins as guiyang geografii steeden dö...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_d,_bon_77_li:_(`
2. `en_daulit_das_31`
3. `an_538_den_fliju`

**Context Size 2:**

1. `n_e_–_chöm_75_wai`
2. `en_dinj_sal_di_di`
3. `t_uk_wecholastell`

**Context Size 3:**

1. `en_regiuun_dialang`
2. `an_mølle,_city,_wa`
3. `uun_waast_._uun_de`

**Context Size 4:**

1. `_uun_det_uun_plaanj`
2. `_faan_det_wiar't_pr`
3. `uun_de_tonde“_wird_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (376,109 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 | 66,788 |
| Total Tokens | 1,624,166 |
| Mean Frequency | 24.32 |
| Median Frequency | 3 |
| Frequency Std Dev | 394.18 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | uun | 36,691 |
| 2 | a | 35,667 |
| 3 | faan | 32,983 |
| 4 | det | 29,888 |
| 5 | en | 29,725 |
| 6 | as | 28,692 |
| 7 | an | 21,444 |
| 8 | di | 19,350 |
| 9 | de | 18,079 |
| 10 | at | 17,888 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | gale | 2 |
| 2 | mesquite | 2 |
| 3 | uruguays | 2 |
| 4 | centésimos | 2 |
| 5 | lefgios | 2 |
| 6 | kythrea | 2 |
| 7 | yaşar | 2 |
| 8 | böyle | 2 |
| 9 | sanctorum | 2 |
| 10 | francs | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0507 |
| R² (Goodness of Fit) | 0.997825 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 40.1% |
| Top 1,000 | 64.7% |
| Top 5,000 | 80.0% |
| Top 10,000 | 86.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9978 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 40.1% of corpus
- **Long Tail:** 56,788 words needed for remaining 13.9% 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 | 0.8602 | 0.3383 | N/A | N/A |
| **mono_64d** | 64 | 0.8130 | 0.2806 | N/A | N/A |
| **mono_128d** | 128 | 0.6429 | 0.2451 | N/A | N/A |
| **aligned_32d** | 32 | 0.8602 🏆 | 0.3423 | 0.0720 | 0.3620 |
| **aligned_64d** | 64 | 0.8130 | 0.2874 | 0.1340 | 0.4960 |
| **aligned_128d** | 128 | 0.6429 | 0.2359 | 0.1840 | 0.5720 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8602 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2882. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 18.4% 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 | **0.189** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | beganfaan, jecheon, shen |
| `-en` | shen, sjineesen, āpfeelen |
| `-er` | mäfulger, altonaer, isomer |

### 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 |
|------|----------|------------------|----------|
| `ster` | 1.59x | 128 contexts | stern, oster, ester |
| `ulat` | 2.13x | 18 contexts | mulatta, annulata, maculata |
| `tion` | 1.98x | 20 contexts | tiong, aktion, nation |
| `unde` | 1.78x | 25 contexts | under, runde, lunde |
| `stri` | 1.51x | 41 contexts | strix, strid, strir |
| `istr` | 1.89x | 18 contexts | istra, istres, istria |
| `eede` | 1.56x | 34 contexts | eedel, leede, seede |
| `spri` | 1.93x | 16 contexts | sprit, sprian, spriin |
| `atio` | 1.96x | 15 contexts | nation, kation, elatior |
| `trik` | 2.23x | 9 contexts | trike, strik, trikala |
| `regi` | 1.68x | 19 contexts | regio, regie, regii |
| `coun` | 2.20x | 8 contexts | count, county, account |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| siamiilen | **`siamiil-en`** | 4.5 | `siamiil` |
| konsonanten | **`konsonant-en`** | 4.5 | `konsonant` |
| auernemen | **`auernem-en`** | 4.5 | `auernem` |
| öölebuumer | **`öölebuum-er`** | 4.5 | `öölebuum` |
| elektromotooren | **`elektromotoor-en`** | 4.5 | `elektromotoor` |
| werksteken | **`werkstek-en`** | 4.5 | `werkstek` |
| elefanten | **`elefant-en`** | 4.5 | `elefant` |
| französischen | **`französisch-en`** | 4.5 | `französisch` |
| delfiinen | **`delfiin-en`** | 4.5 | `delfiin` |
| plaantensköölen | **`plaantenskööl-en`** | 4.5 | `plaantenskööl` |
| stookruusen | **`stookruus-en`** | 4.5 | `stookruus` |
| tatarischen | **`tatarisch-en`** | 4.5 | `tatarisch` |
| protokolen | **`protokol-en`** | 4.5 | `protokol` |
| aptaanjen | **`aptaanj-en`** | 4.5 | `aptaanj` |
| asteroiiden | **`asteroiid-en`** | 4.5 | `asteroiid` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Northern Frisian 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 (3.95x) |
| N-gram | **2-gram** | Lowest perplexity (383) |
| Markov | **Context-4** | Highest predictability (96.7%) |
| 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 14:57:02*