---
language: pdc
language_name: Pennsylvania 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: 4.717
  - name: best_isotropy
    type: isotropy
    value: 0.3299
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Pennsylvania 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** | 3.880x | 3.89 | 0.0635% | 162,147 |
| **16k** | 4.243x | 4.25 | 0.0695% | 148,262 |
| **32k** | 4.544x | 4.55 | 0.0744% | 138,446 |
| **64k** | 4.717x 🏆 | 4.72 | 0.0772% | 133,367 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Almaluez is een Schtettel vun der Provinz Soria in der Automone Gmeeschaft vun C...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁al mal ue z ▁is ▁een ▁schtettel ▁vun ▁der ▁provinz ... (+18 more)` | 28 |
| 16k | `▁al mal ue z ▁is ▁een ▁schtettel ▁vun ▁der ▁provinz ... (+18 more)` | 28 |
| 32k | `▁al mal ue z ▁is ▁een ▁schtettel ▁vun ▁der ▁provinz ... (+18 more)` | 28 |
| 64k | `▁almaluez ▁is ▁een ▁schtettel ▁vun ▁der ▁provinz ▁soria ▁in ▁der ... (+15 more)` | 25 |

**Sample 2:** `Leacock iss en Schtettel in Leacock Taunschip, Lengeschder Kaundi, Pennsilfaani....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁leacock ▁iss ▁en ▁schtettel ▁in ▁leacock ▁taunschip , ▁lengeschder ▁kaundi ... (+7 more)` | 17 |
| 16k | `▁leacock ▁iss ▁en ▁schtettel ▁in ▁leacock ▁taunschip , ▁lengeschder ▁kaundi ... (+7 more)` | 17 |
| 32k | `▁leacock ▁iss ▁en ▁schtettel ▁in ▁leacock ▁taunschip , ▁lengeschder ▁kaundi ... (+7 more)` | 17 |
| 64k | `▁leacock ▁iss ▁en ▁schtettel ▁in ▁leacock ▁taunschip , ▁lengeschder ▁kaundi ... (+7 more)` | 17 |

**Sample 3:** `Aldealafuente is een Schtettel vun der Provinz Soria in der Automone Gmeeschaft ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁alde al af u ente ▁is ▁een ▁schtettel ▁vun ▁der ... (+19 more)` | 29 |
| 16k | `▁aldeal af u ente ▁is ▁een ▁schtettel ▁vun ▁der ▁provinz ... (+18 more)` | 28 |
| 32k | `▁aldealafu ente ▁is ▁een ▁schtettel ▁vun ▁der ▁provinz ▁soria ▁in ... (+16 more)` | 26 |
| 64k | `▁aldealafuente ▁is ▁een ▁schtettel ▁vun ▁der ▁provinz ▁soria ▁in ▁der ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.717x compression
- **Lowest UNK Rate:** 8k with 0.0635% 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 | 1,485 | 10.54 | 2,999 | 30.9% | 71.9% |
| **2-gram** | Subword | 275 🏆 | 8.10 | 1,611 | 67.1% | 99.4% |
| **3-gram** | Word | 1,485 | 10.54 | 3,202 | 32.7% | 70.5% |
| **3-gram** | Subword | 2,206 | 11.11 | 11,811 | 25.9% | 70.8% |
| **4-gram** | Word | 2,563 | 11.32 | 5,940 | 28.5% | 57.1% |
| **4-gram** | Subword | 10,502 | 13.36 | 48,090 | 14.0% | 40.8% |
| **5-gram** | Word | 1,806 | 10.82 | 4,400 | 33.1% | 63.1% |
| **5-gram** | Subword | 26,342 | 14.69 | 91,495 | 9.4% | 28.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `iss en` | 928 |
| 2 | `in der` | 558 |
| 3 | `vun der` | 501 |
| 4 | `unn schtedt` | 471 |
| 5 | `der provinz` | 368 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `vun der provinz` | 367 |
| 2 | `der provinz soria` | 363 |
| 3 | `unn schtedt in` | 257 |
| 4 | `castilla y león` | 185 |
| 5 | `in der automone` | 184 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `vun der provinz soria` | 363 |
| 2 | `in der automone gmeeschaft` | 184 |
| 3 | `der automone gmeeschaft vun` | 184 |
| 4 | `automone gmeeschaft vun castilla` | 184 |
| 5 | `gmeeschaft vun castilla y` | 184 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `gmeeschaft vun castilla y león` | 184 |
| 2 | `in der automone gmeeschaft vun` | 184 |
| 3 | `automone gmeeschaft vun castilla y` | 184 |
| 4 | `vun castilla y león schpaani` | 184 |
| 5 | `der automone gmeeschaft vun castilla` | 184 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c h` | 25,581 |
| 2 | `e r` | 25,413 |
| 3 | `e _` | 23,219 |
| 4 | `n _` | 22,368 |
| 5 | `r _` | 16,564 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s c h` | 15,636 |
| 2 | `e r _` | 13,206 |
| 3 | `_ d e` | 7,034 |
| 4 | `d e r` | 7,034 |
| 5 | `c h t` | 6,049 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `d e r _` | 5,686 |
| 2 | `_ s c h` | 4,818 |
| 3 | `s c h t` | 4,697 |
| 4 | `_ i n _` | 4,553 |
| 5 | `d i e _` | 3,905 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i e _` | 3,476 |
| 2 | `_ d e r _` | 3,339 |
| 3 | `_ v u n _` | 2,399 |
| 4 | `_ i s s _` | 2,345 |
| 5 | `_ s c h t` | 2,265 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 275
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.6516 | 1.571 | 3.63 | 28,179 | 34.8% |
| **1** | Subword | 1.2922 | 2.449 | 9.68 | 360 | 0.0% |
| **2** | Word | 0.1711 | 1.126 | 1.32 | 101,365 | 82.9% |
| **2** | Subword | 1.0992 | 2.142 | 6.28 | 3,480 | 0.0% |
| **3** | Word | 0.0466 | 1.033 | 1.07 | 132,478 | 95.3% |
| **3** | Subword | 0.8834 | 1.845 | 3.87 | 21,819 | 11.7% |
| **4** | Word | 0.0176 🏆 | 1.012 | 1.03 | 139,969 | 98.2% |
| **4** | Subword | 0.5973 | 1.513 | 2.38 | 84,388 | 40.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `in see fer dausende uff der christian gutknecht sei jo ah in denen end of traditional`
2. `der samuel j farmwald ihre felder breed of tears or lola lehman waar en annonymous gedicht`
3. `die geschwischter all so wie grick der grundsatz watt wie ken meh deitsche pokalsieger 2 stupid`

**Context Size 2:**

1. `iss en fox der fux iss n sport wu mer mit der riepubliken paerdi gewebbgleecher`
2. `in der eastern panhandle unn aa zu danze fress mer mol en deitsch ballidischener er waar der`
3. `vun der provinz soria in der haal war en buh doch anner dings sin net schlimm fer`

**Context Size 3:**

1. `vun der provinz soria in der automone gmeeschaft vun castilla y león schpaani unn schtedt vun der pr...`
2. `unn schtedt in saarland`
3. `castilla y león schpaani unn schtedt vun der provinz soria in der automone gmeeschaft vun castilla y...`

**Context Size 4:**

1. `der automone gmeeschaft vun castilla y león schpaani unn schtedt vun der provinz soria in der automo...`
2. `vun castilla y león schpaani unn schtedt vun der provinz soria in der automone gmeeschaft vun castil...`
3. `gmeeschaft vun castilla y león schpaani unn schtedt vun der provinz soria in der automone gmeeschaft...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_s_cht_e,_iferge`
2. `erep_eieimererde`
3. `n_grerran,_nnter`

**Context Size 2:**

1. `chtehönnd_in,_der`
2. `ert_iner_enrich)_`
3. `e_laricarmwag_un_`

**Context Size 3:**

1. `schtary_in_penno_s`
2. `er_auder_dania_pa_`
3. `_de_spatribunn_kaz`

**Context Size 4:**

1. `der_drauskummer_sch`
2. `_schles_conestrain_`
3. `schtaert_in_uppe_sc`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (84,388 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 | 10,732 |
| Total Tokens | 149,432 |
| Mean Frequency | 13.92 |
| Median Frequency | 3 |
| Frequency Std Dev | 96.79 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | in | 4,681 |
| 2 | der | 3,786 |
| 3 | die | 3,773 |
| 4 | en | 2,612 |
| 5 | iss | 2,483 |
| 6 | vun | 2,435 |
| 7 | un | 1,871 |
| 8 | unn | 1,560 |
| 9 | hot | 1,279 |
| 10 | de | 1,270 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | tullio | 2 |
| 2 | giordana | 2 |
| 3 | treccani | 2 |
| 4 | fanta | 2 |
| 5 | schwammkuche | 2 |
| 6 | separatisten | 2 |
| 7 | ukrainische | 2 |
| 8 | konflikts | 2 |
| 9 | wöchentlich | 2 |
| 10 | basalinsulin | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0273 |
| R² (Goodness of Fit) | 0.991897 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 42.0% |
| Top 1,000 | 71.6% |
| Top 5,000 | 91.2% |
| Top 10,000 | 99.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9919 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 42.0% of corpus
- **Long Tail:** 732 words needed for remaining 1.0% 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 | 0.3299 | 0.4310 | N/A | N/A |
| **mono_64d** | 64 | 0.0803 | 0.4297 | N/A | N/A |
| **mono_128d** | 128 | 0.0119 | 0.4483 | N/A | N/A |
| **aligned_32d** | 32 | 0.3299 🏆 | 0.4273 | 0.0160 | 0.1480 |
| **aligned_64d** | 64 | 0.0803 | 0.4314 | 0.0380 | 0.1900 |
| **aligned_128d** | 128 | 0.0119 | 0.4354 | 0.0560 | 0.2520 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.3299 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4338. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.6% 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 | **1.205** | 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 |
|--------|----------|
| `-s` | six, snake, saints |
| `-b` | bocuk, beyoncé, bisness |
| `-g` | gedicht, gebet, gegend |
| `-a` | alburtis, aguilera, abendlied |
| `-d` | daughters, deceased, dinger |
| `-m` | mens, moregets, mast |
| `-ge` | gedicht, gebet, gegend |
| `-h` | howard, hancock, heute |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | fiere, floradale, pennsilfaanische |
| `-er` | peter, wuediger, rer |
| `-t` | gedicht, percent, lambert |
| `-r` | peter, wuediger, rer |
| `-n` | stahn, lein, begann |
| `-s` | alburtis, wordpress, krääs |
| `-ch` | pennsylvaanisch, heinrich, touch |
| `-h` | turkish, pennsylvaanisch, heinrich |

### 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 |
|------|----------|------------------|----------|
| `scht` | 1.54x | 109 contexts | oscht, uscht, ischt |
| `chte` | 1.69x | 45 contexts | schteh, oschte, rechte |
| `nner` | 1.68x | 36 contexts | anner, inner, enner |
| `schd` | 1.52x | 41 contexts | erschd, oschde, feschd |
| `dder` | 1.71x | 25 contexts | odder, adder, udder |
| `esch` | 1.50x | 35 contexts | oesch, wesch, bescht |
| `tsch` | 1.51x | 34 contexts | tschuun, fritsch, deitsch |
| `lich` | 1.60x | 22 contexts | licht, lichter, seelich |
| `chta` | 1.59x | 21 contexts | schtae, schtaar, schtaab |
| `rsch` | 1.48x | 24 contexts | ersch, erschd, dorsch |
| `schi` | 1.40x | 27 contexts | dschim, schild, raschi |
| `chde` | 1.47x | 22 contexts | wichde, rechde, oschde |

### 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` | 128 words | settele, seele |
| `-g` | `-t` | 119 words | garret, gidget |
| `-g` | `-e` | 96 words | gedrosche, goodville |
| `-s` | `-r` | 91 words | seiner, schilder |
| `-s` | `-er` | 82 words | seiner, schilder |
| `-b` | `-e` | 73 words | blumme, berichte |
| `-s` | `-n` | 71 words | southern, stadion |
| `-s` | `-t` | 71 words | sippschaft, schtimmt |
| `-a` | `-e` | 62 words | age, australie |
| `-s` | `-s` | 58 words | swiss, situations |

### 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 |
|------|-----------------|------------|------|
| northeast | **`northea-s-t`** | 7.5 | `s` |
| southeast | **`southea-s-t`** | 7.5 | `s` |
| anschließend | **`anschließ-e-nd`** | 7.5 | `e` |
| ausgeruget | **`ausgerug-e-t`** | 7.5 | `e` |
| grankheet | **`grank-he-et`** | 7.5 | `he` |
| ertheiltet | **`ertheilt-e-t`** | 7.5 | `e` |
| otterness | **`otterne-s-s`** | 7.5 | `s` |
| historisch | **`histori-s-ch`** | 7.5 | `s` |
| mitglider | **`mitgli-d-er`** | 7.5 | `d` |
| kocherthalern | **`kocherthal-er-n`** | 6.0 | `kocherthal` |
| traditionell | **`tradition-el-l`** | 6.0 | `tradition` |
| foreigners | **`foreign-er-s`** | 6.0 | `foreign` |
| greeschde | **`greeschd-e`** | 4.5 | `greeschd` |
| interests | **`interest-s`** | 4.5 | `interest` |
| christians | **`christian-s`** | 4.5 | `christian` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Pennsylvania 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 (4.72x) |
| N-gram | **2-gram** | Lowest perplexity (275) |
| Markov | **Context-4** | Highest predictability (98.2%) |
| 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 17:39:48*