---
language: fy
language_name: Western 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: 4.585
  - name: best_isotropy
    type: isotropy
    value: 0.8266
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-09
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Western 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** | 3.696x | 3.70 | 0.0789% | 977,187 |
| **16k** | 4.052x | 4.05 | 0.0865% | 891,334 |
| **32k** | 4.350x | 4.35 | 0.0929% | 830,096 |
| **64k** | 4.585x 🏆 | 4.59 | 0.0979% | 787,685 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Samuel Maresius (Frankryk, wie û.o. heechlearaar oan de Universiteit fan Grins. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁samuel ▁mar es ius ▁( frank ryk , ▁wie ▁û ... (+26 more)` | 36 |
| 16k | `▁samuel ▁mar es ius ▁( frankryk , ▁wie ▁û . ... (+24 more)` | 34 |
| 32k | `▁samuel ▁mar es ius ▁( frankryk , ▁wie ▁û . ... (+21 more)` | 31 |
| 64k | `▁samuel ▁mar es ius ▁( frankryk , ▁wie ▁û . ... (+21 more)` | 31 |

**Sample 2:** `Zwijndrecht (Belgje) - in plak yn de Belgyske provinsje Antwerpen Zwijndrecht (N...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁zw ijn d recht ▁( bel gje ) ▁- ▁in ... (+23 more)` | 33 |
| 16k | `▁zw ijn d recht ▁( bel gje ) ▁- ▁in ... (+23 more)` | 33 |
| 32k | `▁zwijndrecht ▁( belgje ) ▁- ▁in ▁plak ▁yn ▁de ▁belgyske ... (+16 more)` | 26 |
| 64k | `▁zwijndrecht ▁( belgje ) ▁- ▁in ▁plak ▁yn ▁de ▁belgyske ... (+16 more)` | 26 |

**Sample 3:** `Foarfallen Berne Gangulfus, Frankysk hillige († 760) Ferstoarn iuw`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁foarfallen ▁berne ▁g ang ulf us , ▁frank ysk ▁hillige ... (+8 more)` | 18 |
| 16k | `▁foarfallen ▁berne ▁gang ulf us , ▁frank ysk ▁hillige ▁(† ... (+7 more)` | 17 |
| 32k | `▁foarfallen ▁berne ▁gang ulfus , ▁frankysk ▁hillige ▁(† ▁ 7 ... (+5 more)` | 15 |
| 64k | `▁foarfallen ▁berne ▁gangulfus , ▁frankysk ▁hillige ▁(† ▁ 7 6 ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 64k achieves 4.585x compression
- **Lowest UNK Rate:** 8k with 0.0789% 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 | 57,203 | 15.80 | 465,510 | 14.1% | 27.9% |
| **2-gram** | Subword | 266 🏆 | 8.05 | 8,299 | 66.8% | 99.3% |
| **3-gram** | Word | 299,808 | 18.19 | 933,282 | 3.2% | 10.5% |
| **3-gram** | Subword | 2,222 | 11.12 | 64,900 | 27.9% | 71.5% |
| **4-gram** | Word | 693,401 | 19.40 | 1,535,091 | 1.9% | 6.9% |
| **4-gram** | Subword | 13,001 | 13.67 | 386,948 | 14.2% | 40.4% |
| **5-gram** | Word | 545,201 | 19.06 | 1,044,881 | 1.9% | 7.3% |
| **5-gram** | Subword | 54,381 | 15.73 | 1,339,398 | 8.0% | 24.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `fan e` | 141,194 |
| 2 | `dy t` | 134,819 |
| 3 | `fan de` | 123,734 |
| 4 | `yn e` | 98,988 |
| 5 | `yn de` | 89,074 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dy t yn` | 12,335 |
| 2 | `dy t de` | 8,917 |
| 3 | `keppeling om utens` | 7,988 |
| 4 | `yn stoarn yn` | 7,907 |
| 5 | `berne yn stoarn` | 7,873 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `berne yn stoarn yn` | 7,871 |
| 2 | `f kr f kr` | 2,991 |
| 3 | `yn e feriene steaten` | 2,975 |
| 4 | `kr f kr f` | 2,776 |
| 5 | `yn e amerikaanske steat` | 2,575 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kr f kr f kr` | 2,776 |
| 2 | `f kr f kr f` | 2,776 |
| 3 | `om utens offisjele webside fan` | 2,314 |
| 4 | `keppelings om utens offisjele webside` | 2,291 |
| 5 | `yn e internet movie database` | 1,690 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 4,878,462 |
| 2 | `e _` | 4,610,980 |
| 3 | `e n` | 2,898,399 |
| 4 | `e r` | 2,688,468 |
| 5 | `t _` | 2,451,793 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n _` | 1,790,859 |
| 2 | `d e _` | 1,493,107 |
| 3 | `_ d e` | 1,370,256 |
| 4 | `a n _` | 1,211,042 |
| 5 | `_ f a` | 969,260 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 1,176,063 |
| 2 | `_ f a n` | 872,451 |
| 3 | `f a n _` | 862,725 |
| 4 | `_ y n _` | 734,798 |
| 5 | `_ i t _` | 642,514 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ f a n _` | 852,840 |
| 2 | `n _ d e _` | 356,953 |
| 3 | `n _ ' e _` | 267,813 |
| 4 | `n _ i t _` | 229,400 |
| 5 | `_ f o a r` | 216,531 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 266
- **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 | 0.9453 | 1.926 | 9.11 | 637,706 | 5.5% |
| **1** | Subword | 0.9583 | 1.943 | 7.11 | 3,156 | 4.2% |
| **2** | Word | 0.3681 | 1.291 | 2.23 | 5,803,614 | 63.2% |
| **2** | Subword | 0.9139 | 1.884 | 5.94 | 22,371 | 8.6% |
| **3** | Word | 0.1688 | 1.124 | 1.38 | 12,949,659 | 83.1% |
| **3** | Subword | 0.8088 | 1.752 | 4.68 | 132,865 | 19.1% |
| **4** | Word | 0.0712 🏆 | 1.051 | 1.12 | 17,845,307 | 92.9% |
| **4** | Subword | 0.7559 | 1.689 | 3.72 | 621,806 | 24.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de kroanein of aldekleaster wie net doopt op 1 35 5 6 cpn deasketten troch gerardus`
2. `fan út de gemeente sittard en driuwende boarplatfoarmen hefplatfoarm in kulturele sintra yn in dûnss...`
3. `yn dizze spoarline oanpast se 1 7 1 jannewaris heart hoewol t it lemma oer langere`

**Context Size 2:**

1. `fan e grutte dobbe besuden teksas folrûn sa ûntstie stadichoan in paleis en de grutte sû oarloch`
2. `dy t har kearden tsjin e jierren de redaksje fan charles williams transposition and other poems adam`
3. `fan de stilste song er by tafal of rieden it is letterlik út de earste oerwinning helle`

**Context Size 3:**

1. `dy t yn drylts op 12 febrewaris har partner yn dit konkoers wie e de groot ek de`
2. `dy t de ferlerne gebieten wer werompakt en as ryksgoaen yn it dútske keizerryk under de weimarrepubl...`
3. `berne yn stoarn yn stoarn yn de 20e iuw waarden karakterisearre troch tige heech opmakke kapsels guo...`

**Context Size 4:**

1. `f kr f kr f kr f kr f kr f kr f kr sjoch ek iuwskema jierskema deiskema`
2. `yn e feriene steaten foar opskuor soarge troch him ta de drager fan ien fan harren films spile oare`
3. `kr f kr f kr f kr f kr f kr f kr f kr f kr f kr`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_wern_imkar_fomi`
2. `enoaaslat_utwêry`
3. `ndes_itrenjop_ve`

**Context Size 2:**

1. `n_om_wurde_rov_6e`
2. `e_ferden_utslânst`
3. `en_rettliblyk_wrâ`

**Context Size 3:**

1. `en_spedacht_troch_`
2. `de_tiation_yn_oar_`
3. `_de_âlderen_(*_-_l`

**Context Size 4:**

1. `_de_wer_de_lân_28_-`
2. `_fan_'e_lit_einige_`
3. `fan_de_mandy,_ornar`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (621,806 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 | 288,790 |
| Total Tokens | 22,743,254 |
| Mean Frequency | 78.75 |
| Median Frequency | 4 |
| Frequency Std Dev | 3957.81 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 1,204,486 |
| 2 | fan | 856,838 |
| 3 | yn | 766,114 |
| 4 | it | 650,720 |
| 5 | en | 563,600 |
| 6 | in | 518,256 |
| 7 | e | 325,741 |
| 8 | t | 279,402 |
| 9 | op | 222,427 |
| 10 | mei | 208,595 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | paleobiogeografy | 2 |
| 2 | palaios | 2 |
| 3 | afrotropis | 2 |
| 4 | antarktis | 2 |
| 5 | neärktis | 2 |
| 6 | neotropis | 2 |
| 7 | paleärktis | 2 |
| 8 | νέος | 2 |
| 9 | tropis | 2 |
| 10 | sahulplat | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0465 |
| R² (Goodness of Fit) | 0.997413 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 45.7% |
| Top 1,000 | 65.1% |
| Top 5,000 | 79.4% |
| Top 10,000 | 84.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9974 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 45.7% of corpus
- **Long Tail:** 278,790 words needed for remaining 15.1% 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 | 0.8266 | 0.3772 | N/A | N/A |
| **mono_64d** | 64 | 0.7657 | 0.3036 | N/A | N/A |
| **mono_128d** | 128 | 0.7103 | 0.2325 | N/A | N/A |
| **aligned_32d** | 32 | 0.8266 🏆 | 0.3840 | 0.2540 | 0.6200 |
| **aligned_64d** | 64 | 0.7657 | 0.3009 | 0.4000 | 0.7340 |
| **aligned_128d** | 128 | 0.7103 | 0.2303 | 0.4360 | 0.7600 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8266 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3048. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 43.6% 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 | **-0.699** | 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` | sâltmar, súdamerikaansk, stanwyck |
| `-a` | aue, ayanna, audiïnsjes |
| `-b` | baggeljen, bertken, bijlmermeer |
| `-k` | kleanmakkerssit, klazien, koloanisearre |
| `-ma` | maslup, mawr, maltesen |
| `-t` | tsjoch, trommelet, thessalonika |
| `-m` | maslup, mikroplestiks, museumkolleksje |
| `-be` | bertken, beblette, bevensen |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | aue, lânsearre, strange |
| `-en` | baggeljen, eksportearjen, bertken |
| `-n` | baggeljen, eksportearjen, bertken |
| `-s` | mikroplestiks, konkwistadores, myrtillus |
| `-er` | snuggerder, rossacher, wrakseler |
| `-r` | sâltmar, snuggerder, rossacher |
| `-t` | elektrisiteitsnet, ranft, kleanmakkerssit |
| `-ng` | minachting, 2kyung, stroomsteuring |

### 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 |
|------|----------|------------------|----------|
| `tter` | 1.65x | 304 contexts | atter, utter, etter |
| `nnen` | 1.64x | 135 contexts | onnen, annen, innen |
| `arre` | 1.50x | 211 contexts | oarre, farre, harre |
| `nder` | 1.33x | 419 contexts | ûnder, ender, únder |
| `erke` | 1.55x | 177 contexts | erken, erkel, ierke |
| `rden` | 1.61x | 145 contexts | arden, orden, erden |
| `chte` | 1.44x | 247 contexts | èchte, echte, achte |
| `aste` | 1.47x | 207 contexts | laste, paste, gaste |
| `asje` | 1.83x | 55 contexts | aasje, tasje, pasje |
| `joch` | 1.56x | 101 contexts | rjoch, jocht, sjoch |
| `urde` | 1.87x | 45 contexts | wurde, murde, burde |
| `nske` | 1.65x | 72 contexts | ynske, anske, munske |

### 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` | `-e` | 172 words | swiniastate, slokke |
| `-s` | `-n` | 164 words | sisyljen, sprektalen |
| `-s` | `-en` | 129 words | sisyljen, sprektalen |
| `-b` | `-n` | 118 words | bestriden, bistehûden |
| `-s` | `-s` | 113 words | söss, sebaldus |
| `-b` | `-e` | 97 words | buchverlage, bungle |
| `-k` | `-e` | 89 words | konvensjonele, kommee |
| `-k` | `-n` | 88 words | kaishakunin, konventuelen |
| `-a` | `-e` | 85 words | arsjitektuerskoalle, awardnominearreynternetbabe |
| `-p` | `-e` | 84 words | protohistoarje, psoolme |

### 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 |
|------|-----------------|------------|------|
| observeum | **`observ-e-um`** | 7.5 | `e` |
| karavanen | **`karava-n-en`** | 7.5 | `n` |
| yndustriegebiet | **`yndustriegebi-e-t`** | 7.5 | `e` |
| belenenses | **`belenens-e-s`** | 7.5 | `e` |
| constantina | **`constanti-n-a`** | 7.5 | `n` |
| trewantsjes | **`trewantsj-e-s`** | 7.5 | `e` |
| diktegroei | **`diktegro-e-i`** | 7.5 | `e` |
| moeremans | **`moerema-n-s`** | 7.5 | `n` |
| feangeniet | **`feangeni-e-t`** | 7.5 | `e` |
| nederrynsk | **`nederry-n-sk`** | 7.5 | `n` |
| diagnostiek | **`diagnosti-e-k`** | 7.5 | `e` |
| praelectiones | **`praelection-e-s`** | 7.5 | `e` |
| hulstreed | **`hulstre-e-d`** | 7.5 | `e` |
| suderseedunen | **`suderseedu-n-en`** | 7.5 | `n` |
| maskerdokes | **`maskerdok-e-s`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Western 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 (4.58x) |
| N-gram | **2-gram** | Lowest perplexity (266) |
| Markov | **Context-4** | Highest predictability (92.9%) |
| 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: 2026-01-09 23:41:39*