---
language: de
language_name: German
language_family: germanic_west_continental
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - monolingual
  - family-germanic_west_continental
license: mit
library_name: wikilangs
pipeline_tag: feature-extraction
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: 4.386
  - name: best_isotropy
    type: isotropy
    value: 0.7104
  - name: vocabulary_size
    type: vocab
    value: 1000000
generated: 2025-12-30
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **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-gram)
- Markov chains (context of 1, 2, 3 and 4)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions
- 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. Summary & Recommendations](#6-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 3.507x | 3.49 | 0.1233% | 8,236,556 |
| **16k** | 3.844x | 3.82 | 0.1351% | 7,514,344 |
| **32k** | 4.144x | 4.12 | 0.1457% | 6,969,900 |
| **64k** | 4.386x 🏆 | 4.36 | 0.1541% | 6,586,435 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Sezemitz bzw. Sesemitz bezeichnet

 die Stadt Sezemice nad Loučnou, Tschechien
 ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁se z em itz ▁bzw . ▁s es em itz ... (+36 more)` | 46 |
| 16k | `▁se z em itz ▁bzw . ▁s es em itz ... (+33 more)` | 43 |
| 32k | `▁se zem itz ▁bzw . ▁ses em itz ▁bezeichnet ▁die ... (+27 more)` | 37 |
| 64k | `▁se zem itz ▁bzw . ▁ses em itz ▁bezeichnet ▁die ... (+26 more)` | 36 |

**Sample 2:** `Schillen ist der Name folgender Person:

 Ida Schillen (* 1956), deutsche Politi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sch illen ▁ist ▁der ▁name ▁folgender ▁person : ▁i da ... (+21 more)` | 31 |
| 16k | `▁sch illen ▁ist ▁der ▁name ▁folgender ▁person : ▁i da ... (+20 more)` | 30 |
| 32k | `▁sch illen ▁ist ▁der ▁name ▁folgender ▁person : ▁ida ▁sch ... (+19 more)` | 29 |
| 64k | `▁sch illen ▁ist ▁der ▁name ▁folgender ▁person : ▁ida ▁sch ... (+19 more)` | 29 |

**Sample 3:** `Băltăreți ist der Name mehrerer Orte in Rumänien:

 Băltăreți (Buzău), Dorf im K...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+47 more)` | 57 |
| 16k | `▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+45 more)` | 55 |
| 32k | `▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+45 more)` | 55 |
| 64k | `▁b ă lt ă re ț i ▁ist ▁der ▁name ... (+44 more)` | 54 |


### Key Findings

- **Best Compression:** 64k achieves 4.386x compression
- **Lowest UNK Rate:** 8k with 0.1233% 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 Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | 397,539 🏆 | 18.60 | 14,975,925 | 8.9% | 20.8% |
| **2-gram** | 330 🏆 | 8.37 | 56,875 | 63.2% | 98.5% |
| **3-gram** | 4,321,490 | 22.04 | 46,313,184 | 3.0% | 7.5% |
| **3-gram** | 3,011 | 11.56 | 458,754 | 25.3% | 66.1% |
| **4-gram** | 16,869,913 | 24.01 | 94,033,907 | 1.7% | 4.3% |
| **4-gram** | 18,869 | 14.20 | 3,362,393 | 12.7% | 36.5% |

### Top 5 N-grams by Size

**2-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kategorie :` | 6,792,008 |
| 2 | `) ,` | 4,653,717 |
| 3 | `in der` | 3,680,160 |
| 4 | `. die` | 3,639,368 |
| 5 | `, die` | 3,186,807 |

**3-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `, s .` | 2,005,174 |
| 2 | `) kategorie :` | 1,889,059 |
| 3 | `. in :` | 957,571 |
| 4 | `isbn 3 -` | 658,242 |
| 5 | `einzelnachweise kategorie :` | 655,352 |

**4-grams:**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `, isbn 3 -` | 601,963 |
| 2 | `, isbn 978 -` | 507,252 |
| 3 | `( hrsg . )` | 456,446 |
| 4 | `978 - 3 -` | 454,406 |
| 5 | `isbn 978 - 3` | 452,207 |


### Key Findings

- **Best Perplexity:** 2-gram with 330
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~37% of corpus
- **Recommendation:** 4-gram or 5-gram for best predictive performance

---
## 3. Markov Chain Evaluation

![Markov Entropy](visualizations/markov_entropy.png)

![Markov Branching](visualizations/markov_branching.png)

### Results

| Context | Avg Entropy | Perplexity | Branching Factor | Unique Contexts | Predictability |
|---------|-------------|------------|------------------|-----------------|----------------|
| **1** | 0.8229 | 1.769 | 11.84 | 11,563,865 | 17.7% |
| **1** | 0.3027 | 1.233 | 3.76 | 97,717 | 69.7% |
| **2** | 0.4537 | 1.370 | 3.19 | 136,857,243 | 54.6% |
| **2** | 0.4680 | 1.383 | 3.48 | 367,392 | 53.2% |
| **3** | 0.2356 | 1.177 | 1.69 | 435,861,393 | 76.4% |
| **3** | 0.6899 | 1.613 | 4.59 | 1,279,274 | 31.0% |
| **4** | 0.1157 🏆 | 1.084 | 1.25 | 735,113,439 | 88.4% |
| **4** | 0.7766 🏆 | 1.713 | 4.12 | 5,873,337 | 22.3% |

### Generated Text Samples

Below are text samples generated from each Markov chain model:

**Context Size 1:**

1. `. - richemont - hot 100 quadratkilometer , welche einflüsse wie beispielsweise in verbreitung ist ,`
2. `, s . nach 1945 - us navy siehe auch niklaas c2 und mühevollen aufbau befindlichen`
3. `der partei chinas größenwahn und kunstgewerbeschule zürich erschienenen faksimile “ ( landkreis gibt...`

**Context Size 2:**

1. `kategorie : autor kategorie : deutscher kategorie : mediziner ( 20 . rang schweizer cup und den`
2. `) , haselmusch ( pongau , salzburg u . a . glienke : die etwa drei weiher`
3. `in der die wache sowie geschätzt 7 , 5 – 6 ( 0 , 0554 6 +`

**Context Size 3:**

1. `, s . 296 widmete ihr die vehbi koç foundation contemporary art collection . the magazine of fantasy`
2. `) kategorie : wärmekennwert kategorie : messgröße ( abwasserbehandlung ) kategorie : träger der army...`
3. `. in : der tagesspiegel , 13 . juli 1267 , tochter von luigi vittorio bertarelli ( 1859`

**Context Size 4:**

1. `, isbn 3 - 930167 - 61 - 1 , s . 179 . untersuchungen und dokumentationen , die`
2. `, isbn 978 - 3 - 00 - 000367 - 7 . wilfried seeba ( für das landesmuseum oldenburg`
3. `( hrsg . ) : erwin piscator . das politische theater . ein kommentar . verlag schnell & steiner`


### Key Findings

- **Best Predictability:** Context-4 with 88.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (5,873,337 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 | 1,000,000 |
| Total Tokens | 970,645,273 |
| Mean Frequency | 970.65 |
| Median Frequency | 50 |
| Frequency Std Dev | 60089.51 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | der | 31,690,610 |
| 2 | und | 23,476,283 |
| 3 | die | 22,916,244 |
| 4 | in | 19,437,122 |
| 5 | von | 12,408,327 |
| 6 | im | 9,096,641 |
| 7 | des | 8,632,745 |
| 8 | den | 8,213,258 |
| 9 | mit | 7,476,726 |
| 10 | das | 6,990,663 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | flugzeugfertigung | 18 |
| 2 | erzgebirgsklinikum | 18 |
| 3 | kayoru | 18 |
| 4 | sumino | 18 |
| 5 | flüssigkeitskupplung | 18 |
| 6 | 02599 | 18 |
| 7 | purvaranga | 18 |
| 8 | piassava | 18 |
| 9 | domenick | 18 |
| 10 | artentstehung | 18 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0172 |
| R² (Goodness of Fit) | 0.998135 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 35.0% |
| Top 1,000 | 55.9% |
| Top 5,000 | 71.4% |
| Top 10,000 | 77.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9981 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 35.0% of corpus
- **Long Tail:** 990,000 words needed for remaining 22.4% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)

### Model Comparison

| Model | Vocab Size | Dimension | Avg Norm | Std Norm | Isotropy |
|-------|------------|-----------|----------|----------|----------|
| **mono_32d** | 4,270,148 | 32 | 3.020 | 0.882 | 0.7104 🏆 |
| **mono_64d** | 4,270,148 | 64 | 3.422 | 0.855 | 0.6896 |
| **mono_128d** | 4,270,148 | 128 | 3.801 | 0.852 | 0.6174 |
| **embeddings_enhanced** | 0 | 0 | 0.000 | 0.000 | 0.0000 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7104 (more uniform distribution)
- **Dimension Trade-off:** Higher dimensions capture more semantics but reduce isotropy
- **Vocabulary Coverage:** All models cover 4,270,148 words
- **Recommendation:** 100d for balanced semantic capture and efficiency

---
## 6. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **32k BPE** | Best compression (4.39x) with low UNK rate |
| N-gram | **5-gram** | Lowest perplexity (330) |
| Markov | **Context-4** | Highest predictability (88.4%) |
| 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},
  publisher = {HuggingFace},
  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)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2025-12-30 08:16:31*