README.md

---
language: pfl
language_name: Palatine German
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: 4.364
  - name: best_isotropy
    type: isotropy
    value: 0.6495
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Palatine German - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Palatine German** 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** | 3.530x | 3.53 | 0.2131% | 422,361 |
| **16k** | 3.824x | 3.83 | 0.2308% | 389,933 |
| **32k** | 4.130x | 4.13 | 0.2493% | 361,018 |
| **64k** | 4.364x 🏆 | 4.37 | 0.2634% | 341,693 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Trojany is en Ort im Pole mid 490 Oiwuhnern. Er liggt an Powiat Wołomiński, Woiw...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tro j any ▁is ▁en ▁ort ▁im ▁pole ▁mid ▁ ... (+36 more)` | 46 |
| 16k | `▁tro j any ▁is ▁en ▁ort ▁im ▁pole ▁mid ▁ ... (+33 more)` | 43 |
| 32k | `▁tro j any ▁is ▁en ▁ort ▁im ▁pole ▁mid ▁ ... (+29 more)` | 39 |
| 64k | `▁trojany ▁is ▁en ▁ort ▁im ▁pole ▁mid ▁ 4 9 ... (+22 more)` | 32 |

**Sample 2:** `Linux määnd Linux (Kernel), ein Betriebssysdemkern GNU/Linux, ein Betriebssysdem...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁linux ▁määnd ▁linux ▁( kern el ), ▁ein ▁betrieb ssy ... (+15 more)` | 25 |
| 16k | `▁linux ▁määnd ▁linux ▁( kernel ), ▁ein ▁betrieb ssy sd ... (+14 more)` | 24 |
| 32k | `▁linux ▁määnd ▁linux ▁( kernel ), ▁ein ▁betriebssy sdem kern ... (+10 more)` | 20 |
| 64k | `▁linux ▁määnd ▁linux ▁( kernel ), ▁ein ▁betriebssysdem kern ▁gnu ... (+8 more)` | 18 |

**Sample 3:** `D Tirkei (Türkisch: Türkiye) isch än Schdaad in Siedoschdeuropa un Asie. *`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁d ▁tir ke i ▁( t ür kisch : ▁tür ... (+13 more)` | 23 |
| 16k | `▁d ▁tirkei ▁( t ür kisch : ▁tür ki ye ... (+11 more)` | 21 |
| 32k | `▁d ▁tirkei ▁( türkisch : ▁tür ki ye ) ▁isch ... (+9 more)` | 19 |
| 64k | `▁d ▁tirkei ▁( türkisch : ▁türkiye ) ▁isch ▁än ▁schdaad ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 64k achieves 4.364x compression
- **Lowest UNK Rate:** 8k with 0.2131% 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 | 1,596 | 10.64 | 7,895 | 42.8% | 67.2% |
| **2-gram** | Subword | 299 🏆 | 8.22 | 2,272 | 64.5% | 99.1% |
| **3-gram** | Word | 749 | 9.55 | 6,606 | 57.5% | 78.8% |
| **3-gram** | Subword | 2,462 | 11.27 | 20,249 | 25.5% | 69.2% |
| **4-gram** | Word | 991 | 9.95 | 11,139 | 54.7% | 74.4% |
| **4-gram** | Subword | 12,442 | 13.60 | 97,333 | 14.2% | 41.4% |
| **5-gram** | Word | 718 | 9.49 | 8,011 | 58.2% | 78.9% |
| **5-gram** | Subword | 36,102 | 15.14 | 218,622 | 9.6% | 29.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `gheat zum` | 5,157 |
| 2 | `in de` | 3,099 |
| 3 | `vun de` | 1,953 |
| 4 | `im département` | 1,735 |
| 5 | `gemää im` | 1,725 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `franzesische gemää im` | 1,718 |
| 2 | `e franzesische gemää` | 1,718 |
| 3 | `in de rechion` | 1,717 |
| 4 | `gheat zum kommunalvaband` | 1,717 |
| 5 | `gemää im département` | 1,715 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e franzesische gemää im` | 1,716 |
| 2 | `d gemää gheat zum` | 1,714 |
| 3 | `franzesische gemää im département` | 1,713 |
| 4 | `gheat zum kommunalvaband bevelkerungsentwicklung` | 1,704 |
| 5 | `zum kommunalvaband bevelkerungsentwicklung johr` | 1,690 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e franzesische gemää im département` | 1,711 |
| 2 | `gheat zum kommunalvaband bevelkerungsentwicklung johr` | 1,690 |
| 3 | `in de rechion grand est` | 1,568 |
| 4 | `de rechion grand est bis` | 1,566 |
| 5 | `gemää gheat zum im arrondissement` | 1,554 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c h` | 112,146 |
| 2 | `e _` | 97,880 |
| 3 | `s c` | 81,174 |
| 4 | `_ d` | 64,393 |
| 5 | `e r` | 59,433 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s c h` | 80,747 |
| 2 | `i s c` | 34,260 |
| 3 | `d e _` | 29,075 |
| 4 | `c h _` | 28,932 |
| 5 | `_ d e` | 24,776 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i s c h` | 34,189 |
| 2 | `s c h d` | 19,362 |
| 3 | `s c h _` | 18,750 |
| 4 | `_ d e _` | 15,435 |
| 5 | `s c h e` | 13,396 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i s c h _` | 13,539 |
| 2 | `_ d i e _` | 10,434 |
| 3 | `_ v u n _` | 10,426 |
| 4 | `i s c h e` | 9,183 |
| 5 | `s c h e _` | 8,980 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 299
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.6525 | 1.572 | 3.88 | 87,418 | 34.8% |
| **1** | Subword | 1.6269 | 3.089 | 14.27 | 301 | 0.0% |
| **2** | Word | 0.1624 | 1.119 | 1.32 | 338,517 | 83.8% |
| **2** | Subword | 1.2631 | 2.400 | 7.86 | 4,289 | 0.0% |
| **3** | Word | 0.0398 | 1.028 | 1.06 | 447,210 | 96.0% |
| **3** | Subword | 0.9921 | 1.989 | 4.67 | 33,685 | 0.8% |
| **4** | Word | 0.0112 🏆 | 1.008 | 1.02 | 474,320 | 98.9% |
| **4** | Subword | 0.7156 | 1.642 | 2.82 | 157,397 | 28.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de wache 2 370 366 393 418 420 415 oiwohner es bezirksomt de draditionell dialekt de`
2. `die schaidl vun montbéliard gheat zum owerrhaialemannisch weblinks fußnote moselle in de rechion lot...`
3. `vun daitschlond eestraisch in de draditionell dialekt patois vun de lothringisch dialekt de rechion ...`

**Context Size 2:**

1. `gheat zum un zum arrondissement geografie altviller licht vier kilometer im siedoschde vun de käwwer...`
2. `in de rechion grand est bis elsass d gemää gheat zum lorrain fußnote moselle`
3. `vun de kmg karl may gesellschaft ärforsch alle dengbare unnalaache un noch mä geschichtsträchtiche b...`

**Context Size 3:**

1. `franzesische gemää im département moselle in de rechion grand est bis elsass d gemää gheat zum im ar...`
2. `e franzesische gemää im département haut rhin owwaelsass in de rechion bourgogne franche comté bis r...`
3. `gheat zum kommunalvaband bevelkerungsentwicklung johr 354 1 608 1 544 1 819 1 835 dialekt de elsässi...`

**Context Size 4:**

1. `e franzesische gemää im département moselle in de rechion grand est bis elsass d gemää gheat zum im ...`
2. `d gemää gheat zum un zum arrondissement geografie oberhàgedàl licht 27 km vun mìlhüüse uf 473 m nn g...`
3. `franzesische gemää im département moselle in de rechion grand est bis elsass d gemää gheat zum im ar...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_opam_deammpeng'`
2. `e_oschanchbalier`
3. `ige_d_hord_strt_`

**Context Size 2:**

1. `chi_is_alziff_fie`
2. `e_ex_bels_daische`
3. `schnemand_hod,_we`

**Context Size 3:**

1. `schtur_derd_sitzen`
2. `ischazer_dur)_pol.`
3. `de_humorgassem_gra`

**Context Size 4:**

1. `isch_de_vum_kribdes`
2. `schdroffel_fronze_s`
3. `sch_am_straße/aden_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (157,397 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 | 31,612 |
| Total Tokens | 506,872 |
| Mean Frequency | 16.03 |
| Median Frequency | 3 |
| Frequency Std Dev | 185.36 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 15,844 |
| 2 | die | 10,693 |
| 3 | vun | 10,475 |
| 4 | im | 8,905 |
| 5 | in | 8,633 |
| 6 | zum | 7,441 |
| 7 | un | 7,392 |
| 8 | isch | 5,887 |
| 9 | gheat | 5,376 |
| 10 | unn | 4,121 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | atome | 2 |
| 2 | chomsky | 2 |
| 3 | pbk | 2 |
| 4 | zieschlschdää | 2 |
| 5 | middlb | 2 |
| 6 | owasadz | 2 |
| 7 | athena | 2 |
| 8 | volgsvasommlung | 2 |
| 9 | demosthenes | 2 |
| 10 | informale | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9887 |
| R² (Goodness of Fit) | 0.997009 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 42.8% |
| Top 1,000 | 65.6% |
| Top 5,000 | 81.2% |
| Top 10,000 | 88.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9970 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 42.8% of corpus
- **Long Tail:** 21,612 words needed for remaining 11.8% 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 | 0.6495 🏆 | 0.3590 | N/A | N/A |
| **mono_64d** | 64 | 0.2665 | 0.3523 | N/A | N/A |
| **mono_128d** | 128 | 0.0452 | 0.3632 | N/A | N/A |
| **aligned_32d** | 32 | 0.6495 | 0.3596 | 0.0320 | 0.1440 |
| **aligned_64d** | 64 | 0.2665 | 0.3544 | 0.0380 | 0.2340 |
| **aligned_128d** | 128 | 0.0452 | 0.3633 | 0.0500 | 0.2340 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6495 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3586. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.0% 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 | **1.639** | High formulaic/idiomatic 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 |
|--------|----------|
| `-b` | but, batschdorf, bermont |
| `-s` | schdradegije, sorgt, schauschbielarin |
| `-g` | getötet, ganzes, grieche |
| `-ge` | getötet, gebredelde, geschischt |
| `-d` | diedesfelder, demag, dringge |
| `-a` | arie, angegliederd, aißerschde |
| `-h` | helmut, hawwn, heest |
| `-k` | kobuasch, kurpfälzischen, kommunalbolidig |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | arie, schdradegije, dringge |
| `-ch` | kobuasch, wissenschaftlich, dedisch |
| `-d` | caschdafeld, johrhunnerd, éfägd |
| `-h` | kobuasch, wissenschaftlich, dedisch |
| `-er` | diedesfelder, walther, über |
| `-he` | grieche, griesche, indraache |
| `-r` | wehr, diedesfelder, walther |
| `-n` | inschdiduzion, estimation, jedermann |

### 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 |
|------|----------|------------------|----------|
| `schd` | 1.54x | 480 contexts | schdä, schdr, äschd |
| `chde` | 1.71x | 154 contexts | achde, echde, äschde |
| `disc` | 1.67x | 81 contexts | disch, dischd, discht |
| `rsch` | 1.50x | 127 contexts | ersch, ärsch, aarsch |
| `scht` | 1.57x | 101 contexts | oscht, escht, sischt |
| `lisc` | 1.66x | 76 contexts | lisch, lische, lischd |
| `aisc` | 1.68x | 70 contexts | aisch, aischn, waisch |
| `scha` | 1.50x | 107 contexts | schad, ischa, schal |
| `chda` | 1.61x | 66 contexts | dochda, schdad, schdag |
| `schb` | 1.53x | 67 contexts | schbed, schbet, eschbe |
| `ersc` | 1.59x | 55 contexts | ersch, mersch, bersch |
| `gsch` | 1.49x | 68 contexts | gschid, gugsch, ängscht |

### 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` | 182 words | schdadtdeile, schreibmaschine |
| `-b` | `-e` | 137 words | bekannteschte, baigedrede |
| `-g` | `-e` | 124 words | geboore, ghaisse |
| `-a` | `-e` | 97 words | arweide, agduelle |
| `-g` | `-d` | 86 words | gfoldad, generalkonsulad |
| `-e` | `-e` | 84 words | erschte, einige |
| `-m` | `-e` | 76 words | mihlhause, massnohme |
| `-k` | `-e` | 74 words | koreanische, karte |
| `-b` | `-d` | 74 words | beowachd, bedeidend |
| `-g` | `-t` | 64 words | gewechselt, geghert |

### 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 |
|------|-----------------|------------|------|
| schwanheim | **`schwan-he-im`** | 7.5 | `he` |
| endschaidend | **`endschaid-e-nd`** | 7.5 | `e` |
| abgedrede | **`abgedr-e-de`** | 7.5 | `e` |
| schwobsheim | **`schwobs-he-im`** | 7.5 | `he` |
| grumbeere | **`grumbe-er-e`** | 7.5 | `er` |
| unnerscheid | **`unnersc-he-id`** | 7.5 | `he` |
| iwwerfiere | **`iwwerfi-er-e`** | 7.5 | `er` |
| grafendahn | **`grafenda-h-n`** | 7.5 | `h` |
| zunehmend | **`zunehm-e-nd`** | 7.5 | `e` |
| oigerischded | **`oigerischd-e-d`** | 7.5 | `e` |
| skanderbeg | **`skanderb-e-g`** | 7.5 | `e` |
| schdroofe | **`schdroo-f-e`** | 7.5 | `f` |
| schbaijara | **`schbaija-r-a`** | 7.5 | `r` |
| wahrschoints | **`wahrschoin-t-s`** | 7.5 | `t` |
| komblizierd | **`komblizi-er-d`** | 7.5 | `er` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Palatine German shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.36x) |
| N-gram | **2-gram** | Lowest perplexity (299) |
| Markov | **Context-4** | Highest predictability (98.9%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 17:45:35*