README.md

---
language: stq
language_name: Saterland Frisian
language_family: germanic_west_continental
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_continental
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: 3.853
  - name: best_isotropy
    type: isotropy
    value: 0.8013
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Saterland 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** | 3.193x | 3.20 | 0.5017% | 475,389 |
| **16k** | 3.446x | 3.45 | 0.5415% | 440,474 |
| **32k** | 3.679x | 3.68 | 0.5780% | 412,601 |
| **64k** | 3.853x 🏆 | 3.86 | 0.6055% | 393,914 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Gladsaxe Kommune is ne Kommune in ju Region Hovedstaden (deeniske Haudstäädregio...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁g lad sa xe ▁kommune ▁is ▁ne ▁kommune ▁in ▁ju ... (+26 more)` | 36 |
| 16k | `▁g lad sa xe ▁kommune ▁is ▁ne ▁kommune ▁in ▁ju ... (+22 more)` | 32 |
| 32k | `▁glad saxe ▁kommune ▁is ▁ne ▁kommune ▁in ▁ju ▁region ▁hovedstaden ... (+19 more)` | 29 |
| 64k | `▁gladsaxe ▁kommune ▁is ▁ne ▁kommune ▁in ▁ju ▁region ▁hovedstaden ▁( ... (+18 more)` | 28 |

**Sample 2:** `Pfaffenhofen an der Ilm is n Loundkring in dät düütske Buundeslound Bayern.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁p f af fen hof en ▁an ▁der ▁il m ... (+9 more)` | 19 |
| 16k | `▁pf affen hofen ▁an ▁der ▁il m ▁is ▁n ▁loundkring ... (+6 more)` | 16 |
| 32k | `▁pf affen hofen ▁an ▁der ▁ilm ▁is ▁n ▁loundkring ▁in ... (+5 more)` | 15 |
| 64k | `▁pfaffen hofen ▁an ▁der ▁ilm ▁is ▁n ▁loundkring ▁in ▁dät ... (+4 more)` | 14 |

**Sample 3:** `Fulda is n Loundkring in dät düütske Buundeslound Hessen.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ful da ▁is ▁n ▁loundkring ▁in ▁dät ▁düütske ▁buundeslound ▁hessen ... (+1 more)` | 11 |
| 16k | `▁fulda ▁is ▁n ▁loundkring ▁in ▁dät ▁düütske ▁buundeslound ▁hessen .` | 10 |
| 32k | `▁fulda ▁is ▁n ▁loundkring ▁in ▁dät ▁düütske ▁buundeslound ▁hessen .` | 10 |
| 64k | `▁fulda ▁is ▁n ▁loundkring ▁in ▁dät ▁düütske ▁buundeslound ▁hessen .` | 10 |


### Key Findings

- **Best Compression:** 64k achieves 3.853x compression
- **Lowest UNK Rate:** 8k with 0.5017% 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 | 6,044 | 12.56 | 16,081 | 19.7% | 45.7% |
| **2-gram** | Subword | 293 🏆 | 8.19 | 2,943 | 65.3% | 99.1% |
| **3-gram** | Word | 10,287 | 13.33 | 19,008 | 13.8% | 33.8% |
| **3-gram** | Subword | 2,400 | 11.23 | 21,778 | 26.5% | 70.4% |
| **4-gram** | Word | 29,669 | 14.86 | 45,315 | 8.7% | 19.7% |
| **4-gram** | Subword | 12,622 | 13.62 | 105,664 | 13.6% | 39.4% |
| **5-gram** | Word | 24,877 | 14.60 | 35,946 | 9.0% | 19.4% |
| **5-gram** | Subword | 39,312 | 15.26 | 231,740 | 8.2% | 25.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `fon ju` | 3,773 |
| 2 | `in ju` | 2,873 |
| 3 | `in dät` | 2,568 |
| 4 | `fon do` | 2,539 |
| 5 | `fon dän` | 1,901 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k β 100` | 541 |
| 2 | `in do niederlounde` | 493 |
| 3 | `ne meente in` | 439 |
| 4 | `un deer woonje` | 431 |
| 5 | `km un deer` | 429 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `km un deer woonje` | 426 |
| 2 | `ne meente in ju` | 414 |
| 3 | `is ne meente in` | 378 |
| 4 | `häd ne fläche fon` | 293 |
| 5 | `in dät düütske buundeslound` | 275 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `is ne meente in ju` | 359 |
| 2 | `ne meente in ju provints` | 269 |
| 3 | `ju meenteferwaltenge et häd ne` | 268 |
| 4 | `et häd ne fläche fon` | 268 |
| 5 | `fon ju meenteferwaltenge et häd` | 267 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 134,784 |
| 2 | `e _` | 118,096 |
| 3 | `e r` | 90,971 |
| 4 | `e n` | 90,798 |
| 5 | `_ d` | 76,474 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n _` | 38,276 |
| 2 | `_ f o` | 30,501 |
| 3 | `_ d ä` | 29,063 |
| 4 | `o n _` | 27,605 |
| 5 | `e r _` | 25,671 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ f o n` | 22,642 |
| 2 | `f o n _` | 22,312 |
| 3 | `_ j u _` | 21,043 |
| 4 | `d ä t _` | 20,655 |
| 5 | `_ d ä t` | 19,559 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ f o n _` | 21,808 |
| 2 | `_ d ä t _` | 19,421 |
| 3 | `l o u n d` | 8,645 |
| 4 | `n _ j u _` | 8,338 |
| 5 | `_ d ä n _` | 8,296 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 293
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.7314 | 1.660 | 4.57 | 79,075 | 26.9% |
| **1** | Subword | 1.0897 | 2.128 | 8.47 | 863 | 0.0% |
| **2** | Word | 0.2396 | 1.181 | 1.56 | 359,652 | 76.0% |
| **2** | Subword | 0.9968 | 1.996 | 5.88 | 7,299 | 0.3% |
| **3** | Word | 0.0775 | 1.055 | 1.12 | 559,203 | 92.3% |
| **3** | Subword | 0.8500 | 1.802 | 4.12 | 42,885 | 15.0% |
| **4** | Word | 0.0252 🏆 | 1.018 | 1.04 | 623,968 | 97.5% |
| **4** | Subword | 0.6551 | 1.575 | 2.66 | 176,559 | 34.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `fon situatione uut düütsklound ju sonaamde liga is dät konzil fon elektrizität n grootsten nutsen fo...`
2. `ju pestolle dät religiöse un 30 s k β 3 periplasmatisken ruum in doo sunt dät`
3. `dät noch nutsen fon ju provinz outränd dät floaks ounbaued hääd 153 ferseerde een griesbruun un`

**Context Size 2:**

1. `fon ju eerste reflektion truch dissen phasenunnerskeed läskje do sik deer in dät fröie middeloaler f...`
2. `in ju provinz overijssel in do fereende stoaten fon amerikoa baalt sunt uk al eer n wrieuweluud`
3. `in dät noudelke top fon dän priester un skriftstaaler stuurwen 11 januoar maria chudnovsky israelisk...`

**Context Size 3:**

1. `k β 100 2 s 8 830 β 2 443 β n 0 β 100 β n 0`
2. `in do niederlounde dät gebiet fon ju meente is 115 18 km un deer woonje 71 176 moanskene`
3. `ne meente in ju provints utrecht in do niederlounde dongen is n sit fon ju meenteferwaltenge et häd`

**Context Size 4:**

1. `km un deer woonje moanskene wälle cbs en dal`
2. `ne meente in ju provinz gelderland in do niederlounde dät gebiet fon ju meente is in menaam uur stee...`
3. `is ne meente in ju provints suudhollound in do niederlounde oud beijerland waas n sit fon ju meentef...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_jun_wätesäsäss_`
2. `erht_s_iz"_ntt_(`
3. `n_akun_ot_u_arte`

**Context Size 2:**

1. `n_370_meetstouhfe`
2. `e_sowäd_ät_do_s/n`
3. `er_und._mi_sus_be`

**Context Size 3:**

1. `en_tsch_nit_ätters`
2. `_fon_wäch_broome_o`
3. `_dät_dät_die_moorp`

**Context Size 4:**

1. `_fon_chile,_do_bee_`
2. `fon_do_bedeelengsgr`
3. `_ju_lien._stuur_sun`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (176,559 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 | 33,645 |
| Total Tokens | 674,492 |
| Mean Frequency | 20.05 |
| Median Frequency | 3 |
| Frequency Std Dev | 289.08 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | fon | 22,092 |
| 2 | ju | 21,467 |
| 3 | dät | 19,882 |
| 4 | in | 19,036 |
| 5 | un | 16,143 |
| 6 | do | 14,444 |
| 7 | is | 9,102 |
| 8 | dän | 8,312 |
| 9 | n | 7,718 |
| 10 | die | 7,066 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | missionärswierk | 2 |
| 2 | qark | 2 |
| 3 | rwe | 2 |
| 4 | t4 | 2 |
| 5 | profeeten | 2 |
| 6 | uunheel | 2 |
| 7 | ientreeden | 2 |
| 8 | exilstied | 2 |
| 9 | perserköänich | 2 |
| 10 | exilierde | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0486 |
| R² (Goodness of Fit) | 0.998561 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 43.5% |
| Top 1,000 | 67.8% |
| Top 5,000 | 83.6% |
| Top 10,000 | 89.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9986 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 43.5% of corpus
- **Long Tail:** 23,645 words needed for remaining 10.2% 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 | 0.8013 | 0.3873 | N/A | N/A |
| **mono_64d** | 64 | 0.5138 | 0.3003 | N/A | N/A |
| **mono_128d** | 128 | 0.1305 | 0.2974 | N/A | N/A |
| **aligned_32d** | 32 | 0.8013 🏆 | 0.3735 | 0.0440 | 0.2480 |
| **aligned_64d** | 64 | 0.5138 | 0.3002 | 0.0800 | 0.3040 |
| **aligned_128d** | 128 | 0.1305 | 0.2977 | 0.1000 | 0.3940 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8013 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3261. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.0% 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 | **-0.228** | 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` | sprachatlas, sträite, seine |
| `-b` | boarnburgum, bilged, bouksteewe |
| `-a` | ac, alblasserdam, armenien |
| `-m` | moorsproakich, moalerstiel, mussolini |
| `-k` | kuuden, katalog, kloai |
| `-t` | tiedtjuuginne, twäärshälgen, taiga |
| `-h` | harmen, hipposideridae, h166s |
| `-g` | galapagos, gnassingbe, ghulam |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | piktogramme, experience, hipposideridae |
| `-en` | kuuden, harmen, ummen |
| `-n` | kuuden, harmen, ummen |
| `-ke` | elektroniske, warnecke, bruunske |
| `-d` | bilged, višegrad, betjud |
| `-r` | μr, pèder, basketbaalspieler |
| `-er` | pèder, basketbaalspieler, brockmeyer |
| `-t` | kräkt, uurrakt, freesluut |

### 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 |
|------|----------|------------------|----------|
| `nner` | 1.80x | 67 contexts | ünner, unner, runner |
| `loun` | 1.86x | 51 contexts | lound, ölound, lounde |
| `chte` | 1.63x | 79 contexts | echte, achte, ächte |
| `ucht` | 1.79x | 52 contexts | lucht, sucht, tucht |
| `euwe` | 1.71x | 62 contexts | wieuwe, heeuwe, nieuwe |
| `unne` | 1.75x | 44 contexts | nunne, unner, unnen |
| `iske` | 1.64x | 52 contexts | niske, fiske, aiske |
| `iede` | 1.57x | 59 contexts | siede, ieder, tiede |
| `ound` | 1.58x | 53 contexts | lound, pound, sound |
| `iere` | 1.62x | 36 contexts | ieren, hiere, jiere |
| `ansk` | 1.90x | 18 contexts | dansk, fransk, moansk |
| `oans` | 1.78x | 22 contexts | moansk, moanske, spoansk |

### 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` | 209 words | spahnharrenstätte, senckenbergreihe |
| `-b` | `-e` | 173 words | behärskede, blekinge |
| `-s` | `-n` | 134 words | susan, skottisken |
| `-k` | `-e` | 121 words | kamperske, kurre |
| `-s` | `-en` | 114 words | skottisken, sammelengen |
| `-a` | `-e` | 109 words | autolaampe, angèle |
| `-m` | `-e` | 109 words | määlne, muugelke |
| `-b` | `-n` | 98 words | bitsken, bummen |
| `-t` | `-e` | 91 words | twintichste, technike |
| `-b` | `-en` | 84 words | bitsken, bummen |

### 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 |
|------|-----------------|------------|------|
| beanspröäkede | **`beanspröäk-e-de`** | 7.5 | `e` |
| franciszek | **`francisz-e-k`** | 7.5 | `e` |
| schwäbisch | **`schwäbi-s-ch`** | 7.5 | `s` |
| ästerweede | **`ästerwe-e-de`** | 7.5 | `e` |
| biləsuvar | **`biləsuv-a-r`** | 7.5 | `a` |
| ruhrgebiet | **`ruhrgebi-e-t`** | 7.5 | `e` |
| smiddeeges | **`smiddeeg-e-s`** | 7.5 | `e` |
| giganteus | **`gigant-e-us`** | 7.5 | `e` |
| iersentied | **`iersenti-e-d`** | 7.5 | `e` |
| ottenjann | **`ottenja-n-n`** | 7.5 | `n` |
| niederdeutsches | **`niederdeutsch-e-s`** | 7.5 | `e` |
| ferfoulgeden | **`ferfoulge-d-en`** | 7.5 | `d` |
| oarbaidet | **`oarbaid-e-t`** | 7.5 | `e` |
| truchmisked | **`truchmisk-e-d`** | 7.5 | `e` |
| committee | **`committ-e-e`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Saterland 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 (3.85x) |
| N-gram | **2-gram** | Lowest perplexity (293) |
| Markov | **Context-4** | Highest predictability (97.5%) |
| 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 22:49:08*