---
language: bar
language_name: Bavarian
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: 4.003
  - name: best_isotropy
    type: isotropy
    value: 0.8432
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Bavarian** 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** | 3.167x | 3.17 | 0.0430% | 1,042,115 |
| **16k** | 3.477x | 3.48 | 0.0472% | 949,394 |
| **32k** | 3.753x | 3.75 | 0.0509% | 879,530 |
| **64k** | 4.003x 🏆 | 4.00 | 0.0543% | 824,531 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Forstern is a Gmoa im obaboarischn Landkroas Arrdeng. Im Netz Gemeinde Forstern ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁forst ern ▁is ▁a ▁gmoa ▁im ▁oba boarischn ▁landkroas ▁ar ... (+19 more)` | 29 |
| 16k | `▁forst ern ▁is ▁a ▁gmoa ▁im ▁obaboarischn ▁landkroas ▁arrdeng . ... (+15 more)` | 25 |
| 32k | `▁forst ern ▁is ▁a ▁gmoa ▁im ▁obaboarischn ▁landkroas ▁arrdeng . ... (+13 more)` | 23 |
| 64k | `▁forst ern ▁is ▁a ▁gmoa ▁im ▁obaboarischn ▁landkroas ▁arrdeng . ... (+12 more)` | 22 |

**Sample 2:** `Marlboro County. Obgruafa am 22. Feba is a County in South Carolina in da USA. B...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mar l boro ▁county . ▁obgruafa ▁am ▁ 2 2 ... (+18 more)` | 28 |
| 16k | `▁mar l boro ▁county . ▁obgruafa ▁am ▁ 2 2 ... (+18 more)` | 28 |
| 32k | `▁marl boro ▁county . ▁obgruafa ▁am ▁ 2 2 . ... (+17 more)` | 27 |
| 64k | `▁marlboro ▁county . ▁obgruafa ▁am ▁ 2 2 . ▁feba ... (+16 more)` | 26 |

**Sample 3:** `Hill County is a County in Montana in da USA. Beleg Im Netz in Montana`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁hill ▁county ▁is ▁a ▁county ▁in ▁montana ▁in ▁da ▁usa ... (+6 more)` | 16 |
| 16k | `▁hill ▁county ▁is ▁a ▁county ▁in ▁montana ▁in ▁da ▁usa ... (+6 more)` | 16 |
| 32k | `▁hill ▁county ▁is ▁a ▁county ▁in ▁montana ▁in ▁da ▁usa ... (+6 more)` | 16 |
| 64k | `▁hill ▁county ▁is ▁a ▁county ▁in ▁montana ▁in ▁da ▁usa ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 64k achieves 4.003x compression
- **Lowest UNK Rate:** 8k with 0.0430% 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 | 27,199 | 14.73 | 109,780 | 13.0% | 31.5% |
| **2-gram** | Subword | 361 🏆 | 8.50 | 7,796 | 60.7% | 98.3% |
| **3-gram** | Word | 40,782 | 15.32 | 128,747 | 12.7% | 26.6% |
| **3-gram** | Subword | 3,796 | 11.89 | 62,893 | 20.6% | 60.9% |
| **4-gram** | Word | 56,976 | 15.80 | 186,218 | 13.7% | 25.1% |
| **4-gram** | Subword | 27,410 | 14.74 | 362,482 | 9.1% | 28.4% |
| **5-gram** | Word | 38,882 | 15.25 | 130,277 | 15.7% | 28.0% |
| **5-gram** | Subword | 124,788 | 16.93 | 1,153,187 | 4.9% | 16.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `vo da` | 26,508 |
| 2 | `is a` | 22,819 |
| 3 | `in da` | 22,392 |
| 4 | `im netz` | 14,484 |
| 5 | `vo de` | 13,424 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `beleg im netz` | 3,530 |
| 2 | `in da usa` | 3,478 |
| 3 | `da beziak hod` | 2,393 |
| 4 | `im netz in` | 2,005 |
| 5 | `sitz vo da` | 1,888 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `beleg im netz in` | 1,575 |
| 2 | `da sitz vo da` | 1,482 |
| 3 | `is a county in` | 1,429 |
| 4 | `in da usa da` | 1,407 |
| 5 | `a katastralgmoa in da` | 1,387 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `flächn ausgwiesn gwesn ende woarn` | 1,385 |
| 2 | `hektar ois laundwiatschoftliche flächn gnutzt` | 1,385 |
| 3 | `forstwirtschaftli gnutzte flächn ausgwiesn gwesn` | 1,385 |
| 4 | `hektar sand ois forstwirtschaftli gnutzte` | 1,385 |
| 5 | `ois laundwiatschoftliche flächn gnutzt und` | 1,385 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 701,951 |
| 2 | `a _` | 667,528 |
| 3 | `c h` | 636,525 |
| 4 | `_ d` | 557,323 |
| 5 | `e _` | 479,658 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s c h` | 303,728 |
| 2 | `_ d e` | 253,515 |
| 3 | `_ d a` | 172,902 |
| 4 | `n d _` | 169,557 |
| 5 | `u n d` | 168,298 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a _` | 132,086 |
| 2 | `_ d e _` | 130,374 |
| 3 | `u n d _` | 127,939 |
| 4 | `_ u n d` | 119,950 |
| 5 | `i s c h` | 99,379 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ u n d _` | 118,720 |
| 2 | `_ v o _ d` | 44,559 |
| 3 | `_ i n _ d` | 37,539 |
| 4 | `i s c h e` | 33,643 |
| 5 | `_ d e s _` | 31,011 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 361
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~17% 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 | 0.7076 | 1.633 | 5.17 | 567,851 | 29.2% |
| **1** | Subword | 0.9427 | 1.922 | 6.61 | 3,387 | 5.7% |
| **2** | Word | 0.2111 | 1.158 | 1.52 | 2,930,161 | 78.9% |
| **2** | Subword | 0.9146 | 1.885 | 5.83 | 22,370 | 8.5% |
| **3** | Word | 0.0663 | 1.047 | 1.11 | 4,443,260 | 93.4% |
| **3** | Subword | 0.8673 | 1.824 | 4.66 | 130,496 | 13.3% |
| **4** | Word | 0.0224 🏆 | 1.016 | 1.04 | 4,937,652 | 97.8% |
| **4** | Subword | 0.7772 | 1.714 | 3.53 | 608,299 | 22.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de gepidn und bbö 178 bukit tinggi 72 canon triplex a 7 hz ws touro college`
2. `da effentlichn stroßn am 9 verletzter blick af de gebietskeapaschoftn in bayern gwen dem meearesspia...`
3. `und alfonso cuarón timothy j nö öbb infra öbb pv tullnerfelder bahn rengschbuach grünthal geografie ...`

**Context Size 2:**

1. `vo da blaa oim aussa und entschdengan seine wichdigstn litararischn weak da voda vo da gmoa kirchham`
2. `is a kuaza a1 kuaza mit klima b launga und zwoa enklkinda da hoeneß uli z bad`
3. `in da katastralgmoa dobranberg zsammgrechnt 84 bauflächn mit 44 633 m und 58 gärten auf 135 526`

**Context Size 3:**

1. `in da usa beleg im netz in virginia`
2. `beleg im netz in missouri`
3. `da beziak hod 39 451 eihwohna da sitz vo da vawoitung is leoti da beziak hod 12 786`

**Context Size 4:**

1. `beleg im netz in nebraska`
2. `da sitz vo da kroasvawoitung vo oanign landkroas liegt außahoib vom landkroas oft in da namasgleichn...`
3. `is a county in wisconsin in da usa beleg im netz in der emilia romagna des europapreises`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_w.adaiwenieurio`
2. `a_lidovicröniser`
3. `e_hmbrkum_runís_`

**Context Size 2:**

1. `n_fc_rein_wieforo`
2. `a_da_oschofferkea`
3. `chr_koi'seybunds_`

**Context Size 3:**

1. `schburyan_no_san_d`
2. `_dem_scusdecentisc`
3. `_daument_in_und_zu`

**Context Size 4:**

1. `_da_letztn_de_ameri`
2. `_de_marekd_om_auf_1`
3. `und_botta_200+_maß_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (608,299 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 | 212,365 |
| Total Tokens | 5,339,853 |
| Mean Frequency | 25.14 |
| Median Frequency | 3 |
| Frequency Std Dev | 712.67 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 136,913 |
| 2 | da | 136,168 |
| 3 | und | 119,185 |
| 4 | in | 101,699 |
| 5 | a | 92,218 |
| 6 | vo | 91,584 |
| 7 | is | 86,664 |
| 8 | im | 70,677 |
| 9 | des | 33,854 |
| 10 | hod | 30,719 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mechanisches | 2 |
| 2 | stabilisierungssystem | 2 |
| 3 | voeffentlecht | 2 |
| 4 | innpuls | 2 |
| 5 | buagstej | 2 |
| 6 | nuwenburg | 2 |
| 7 | kulturweges | 2 |
| 8 | spessartprojektes | 2 |
| 9 | terrassnfermig | 2 |
| 10 | tuamhigi | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9730 |
| R² (Goodness of Fit) | 0.999444 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 34.1% |
| Top 1,000 | 55.0% |
| Top 5,000 | 70.0% |
| Top 10,000 | 76.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9994 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 34.1% of corpus
- **Long Tail:** 202,365 words needed for remaining 23.3% 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 | 0.8296 | 0.3402 | N/A | N/A |
| **mono_64d** | 64 | 0.8410 | 0.2581 | N/A | N/A |
| **mono_128d** | 128 | 0.8432 🏆 | 0.1737 | N/A | N/A |
| **aligned_32d** | 32 | 0.8296 | 0.3341 | 0.0920 | 0.3960 |
| **aligned_64d** | 64 | 0.8410 | 0.2543 | 0.1940 | 0.6020 |
| **aligned_128d** | 128 | 0.8432 | 0.1862 | 0.2860 | 0.6780 |

### Key Findings

- **Best Isotropy:** mono_128d with 0.8432 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2578. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 28.6% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.694** | 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 |
|--------|----------|
| `-sc` | scharmbeck, schitznvaein, schiaf |
| `-sch` | scharmbeck, schitznvaein, schiaf |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | şabran, unterwestern, weidesdn |
| `-en` | metallen, theologen, münzen |
| `-ng` | wondering, pisang, umwondlung |
| `-er` | gräberfelder, eichenauer, weydenhammer |
| `-ch` | hoierschbouch, weißabgleich, obergreutschach |
| `-ung` | umwondlung, auflösung, ausbroadung |

### 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 |
|------|----------|------------------|----------|
| `ster` | 2.00x | 209 contexts | aster, ester, stern |
| `schl` | 1.77x | 287 contexts | eschl, ischl, schlau |
| `schr` | 1.99x | 137 contexts | schrit, schrim, schreg |
| `gsch` | 1.77x | 181 contexts | gschai, gschdö, gschmo |
| `uach` | 1.99x | 99 contexts | buach, huach, suach |
| `itsc` | 2.19x | 64 contexts | gitsch, nitsch, kitsch |
| `icht` | 1.54x | 345 contexts | eicht, wicht, richt |
| `atio` | 2.26x | 45 contexts | ratio, natio, nation |
| `nisc` | 1.77x | 126 contexts | nisch, nischn, nischt |
| `reic` | 1.78x | 97 contexts | reich, reichd, reichl |
| `chof` | 2.07x | 50 contexts | schof, schoft, schofn |
| `tion` | 1.73x | 93 contexts | tione, aktion, notion |

### 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 |
|--------|--------|-----------|----------|
| `-sc` | `-n` | 52 words | schbondan, schbüün |
| `-sc` | `-er` | 16 words | schatzgräber, schweinsteiger |
| `-sc` | `-en` | 13 words | schlampen, screven |
| `-sc` | `-ng` | 11 words | schädlbedeckung, schraubvabindung |
| `-sc` | `-ch` | 10 words | scharlach, schbruch |
| `-sc` | `-ung` | 4 words | schädlbedeckung, schraubvabindung |

### 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 |
|------|-----------------|------------|------|
| schnitzen | **`sch-nitz-en`** | 6.0 | `nitz` |
| enthaltenen | **`enthalt-en-en`** | 6.0 | `enthalt` |
| schwensen | **`sch-wens-en`** | 6.0 | `wens` |
| herrnhausen | **`herrnhaus-en`** | 4.5 | `herrnhaus` |
| schrottenberg | **`sch-rottenberg`** | 4.5 | `rottenberg` |
| heaschafamülien | **`heaschafamüli-en`** | 4.5 | `heaschafamüli` |
| fawoitung | **`fawoit-ung`** | 4.5 | `fawoit` |
| regulären | **`regulär-en`** | 4.5 | `regulär` |
| leitmeritzer | **`leitmeritz-er`** | 4.5 | `leitmeritz` |
| jungfrauen | **`jungfrau-en`** | 4.5 | `jungfrau` |
| gespenster | **`gespenst-er`** | 4.5 | `gespenst` |
| dynastien | **`dynasti-en`** | 4.5 | `dynasti` |
| referenten | **`referent-en`** | 4.5 | `referent` |
| birkenhainer | **`birkenhain-er`** | 4.5 | `birkenhain` |
| rettersheimer | **`rettersheim-er`** | 4.5 | `rettersheim` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Bavarian 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 (4.00x) |
| N-gram | **2-gram** | Lowest perplexity (361) |
| Markov | **Context-4** | Highest predictability (97.8%) |
| 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: 2026-01-03 19:01:37*