---
language: da
language_name: Danish
language_family: germanic_north
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_north
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: 4.557
  - name: best_isotropy
    type: isotropy
    value: 0.7924
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-08
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Danish** 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** | 3.590x | 3.59 | 0.1227% | 1,644,330 |
| **16k** | 3.953x | 3.95 | 0.1351% | 1,493,346 |
| **32k** | 4.286x | 4.29 | 0.1465% | 1,377,449 |
| **64k** | 4.557x 🏆 | 4.56 | 0.1558% | 1,295,305 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ole Bornemann henviser til: Oluf Bornemann – dansk-norsk biskop Ole Bornemann (r...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ole ▁bor nem ann ▁henviser ▁til : ▁oluf ▁bor nem ... (+27 more)` | 37 |
| 16k | `▁ole ▁bor nemann ▁henviser ▁til : ▁oluf ▁bor nemann ▁– ... (+21 more)` | 31 |
| 32k | `▁ole ▁bor nemann ▁henviser ▁til : ▁oluf ▁bor nemann ▁– ... (+20 more)` | 30 |
| 64k | `▁ole ▁bornemann ▁henviser ▁til : ▁oluf ▁bornemann ▁– ▁dansk - ... (+16 more)` | 26 |

**Sample 2:** `18. April er en dansk dokumentarfilm fra instrueret af Poul Meyer. Eksterne henv...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)` | 21 |
| 16k | `▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)` | 21 |
| 32k | `▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)` | 21 |
| 64k | `▁ 1 8 . ▁april ▁er ▁en ▁dansk ▁dokumentarfilm ▁fra ... (+11 more)` | 21 |

**Sample 3:** `Takeshi Watanabe (født 10. september er en japansk fodboldspiller. Japans fodbol...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tak es hi ▁wat an ab e ▁( født ▁ ... (+12 more)` | 22 |
| 16k | `▁tak es hi ▁wat an abe ▁( født ▁ 1 ... (+11 more)` | 21 |
| 32k | `▁takes hi ▁wat an abe ▁( født ▁ 1 0 ... (+10 more)` | 20 |
| 64k | `▁takes hi ▁watanabe ▁( født ▁ 1 0 . ▁september ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.557x compression
- **Lowest UNK Rate:** 8k with 0.1227% 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 | 205,179 | 17.65 | 1,697,331 | 7.2% | 18.6% |
| **2-gram** | Subword | 291 🏆 | 8.19 | 16,676 | 66.5% | 99.0% |
| **3-gram** | Word | 930,238 | 19.83 | 3,294,874 | 2.7% | 7.8% |
| **3-gram** | Subword | 2,629 | 11.36 | 143,880 | 25.6% | 68.8% |
| **4-gram** | Word | 2,232,256 | 21.09 | 5,289,799 | 1.9% | 5.1% |
| **4-gram** | Subword | 16,827 | 14.04 | 898,389 | 12.2% | 36.9% |
| **5-gram** | Word | 1,710,284 | 20.71 | 3,467,271 | 1.9% | 5.4% |
| **5-gram** | Subword | 78,315 | 16.26 | 3,371,746 | 6.1% | 20.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `er en` | 214,430 |
| 2 | `eksterne henvisninger` | 158,401 |
| 3 | `til at` | 148,332 |
| 4 | `for at` | 127,680 |
| 5 | `i den` | 98,315 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referencer eksterne henvisninger` | 69,492 |
| 2 | `eksterne henvisninger fra` | 52,148 |
| 3 | `en del af` | 36,449 |
| 4 | `fra danmark fra` | 31,038 |
| 5 | `på grund af` | 24,747 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referencer eksterne henvisninger fra` | 31,041 |
| 2 | `fra danmark fra danmark` | 18,040 |
| 3 | `eksterne henvisninger fra danmark` | 13,653 |
| 4 | `eksterne henvisninger fra usa` | 10,607 |
| 5 | `eksterne henvisninger film fra` | 8,857 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referencer eksterne henvisninger fra danmark` | 8,198 |
| 2 | `referencer eksterne henvisninger fra usa` | 7,710 |
| 3 | `referencer eksterne henvisninger film fra` | 6,839 |
| 4 | `fra danmark fra danmark fra` | 6,792 |
| 5 | `eksterne henvisninger film fra fra` | 6,671 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e r` | 14,686,017 |
| 2 | `e _` | 12,413,595 |
| 3 | `e n` | 11,692,715 |
| 4 | `d e` | 11,106,628 |
| 5 | `r _` | 9,958,657 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e r _` | 6,591,787 |
| 2 | `e n _` | 5,761,673 |
| 3 | `_ d e` | 4,088,356 |
| 4 | `e t _` | 3,830,236 |
| 5 | `_ i _` | 3,324,144 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ o g _` | 2,559,398 |
| 2 | `_ f o r` | 1,851,842 |
| 3 | `_ a f _` | 1,698,296 |
| 4 | `d e n _` | 1,598,615 |
| 5 | `_ t i l` | 1,395,426 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t i l _` | 1,111,382 |
| 2 | `_ d e n _` | 1,013,475 |
| 3 | `_ s o m _` | 926,452 |
| 4 | `_ f r a _` | 883,398 |
| 5 | `_ f o r _` | 860,091 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 291
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~21% 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 | 0.9282 | 1.903 | 11.03 | 2,011,765 | 7.2% |
| **1** | Subword | 1.1734 | 2.255 | 7.58 | 8,958 | 0.0% |
| **2** | Word | 0.3698 | 1.292 | 2.34 | 22,156,805 | 63.0% |
| **2** | Subword | 0.6816 | 1.604 | 4.74 | 67,792 | 31.8% |
| **3** | Word | 0.1562 | 1.114 | 1.36 | 51,659,329 | 84.4% |
| **3** | Subword | 0.7837 | 1.722 | 4.70 | 321,234 | 21.6% |
| **4** | Word | 0.0627 🏆 | 1.044 | 1.11 | 69,884,622 | 93.7% |
| **4** | Subword | 0.7511 | 1.683 | 3.88 | 1,508,279 | 24.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i sverige bernadotte en tidligere premierminister vladimír vašíček tjekkisk eller med langt de flest...`
2. `og kortlagte dertil uhensigtsmæssige reaktionsmønstre på denne slags rum som et individuelt hold fra...`
3. `af det eneste gang i lælehe lunden og shimonoseki afstod unionen og sydlige ishav og egyptiske`

**Context Size 2:**

1. `er en aristokrat fra oneglia på en figur på fordi de manglede stadig konkrete beviser det objekts`
2. `eksterne henvisninger fra nederlandene fra flandern og champagne fra reims til danmark og derpaa ble...`
3. `til at åbne sine egne retoriske færdigheder selvom de ikke mangler det umiddelbares friskhed inspira...`

**Context Size 3:**

1. `referencer eksterne henvisninger 05 i vejle i alt var omkring 100 000 lysår og en tykkelse af cirka`
2. `eksterne henvisninger fra mozambique fra maputo ved sommer ol mestre fra usa sølvmedaljevindere fra ...`
3. `en del af moskenes kommune i nordland fylke i norge med et underskud på godt én million kroner`

**Context Size 4:**

1. `referencer eksterne henvisninger fra storbritannien medaljevindere i gymnastik mestre fra grækenland...`
2. `fra danmark fra danmark af videnskabernes selskab i dansk biografisk leksikon fra danmark thomas 1 f...`
3. `eksterne henvisninger fra danmark film fra fra nordisk film dramafilm fra danmark instrueret af augu...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_het_i_ldshic._k`
2. `enoge_der_8.a_t.`
3. `rerliolin,_opon_`

**Context Size 2:**

1. `er_ers_kum._ten_e`
2. `e_asterdyra_et_fo`
3. `en_i_kitler_være_`

**Context Size 3:**

1. `er_randsbog_blev_p`
2. `en_i_han_ver_guldv`
3. `_det_af_daktat_og_`

**Context Size 4:**

1. `_og_kristia_schlesw`
2. `_forfattish_music_d`
3. `_af_storia_italiste`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,508,279 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 | 885,946 |
| Total Tokens | 86,775,295 |
| Mean Frequency | 97.95 |
| Median Frequency | 4 |
| Frequency Std Dev | 6460.78 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 3,396,891 |
| 2 | og | 2,568,581 |
| 3 | af | 1,716,528 |
| 4 | en | 1,361,402 |
| 5 | til | 1,134,702 |
| 6 | er | 1,086,363 |
| 7 | den | 1,040,601 |
| 8 | at | 980,457 |
| 9 | på | 948,450 |
| 10 | som | 939,070 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | elektronikinteresserede | 2 |
| 2 | sinoefloden | 2 |
| 3 | deathconsciousness | 2 |
| 4 | folkedanseforeninger | 2 |
| 5 | affranchi | 2 |
| 6 | superfilmen | 2 |
| 7 | kettletoft | 2 |
| 8 | sandays | 2 |
| 9 | crummack | 2 |
| 10 | rousays | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0001 |
| R² (Goodness of Fit) | 0.998027 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 38.2% |
| Top 1,000 | 58.1% |
| Top 5,000 | 73.3% |
| Top 10,000 | 79.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9980 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 38.2% of corpus
- **Long Tail:** 875,946 words needed for remaining 20.5% 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 | 0.7924 🏆 | 0.3816 | N/A | N/A |
| **mono_64d** | 64 | 0.7720 | 0.3058 | N/A | N/A |
| **mono_128d** | 128 | 0.7142 | 0.2314 | N/A | N/A |
| **aligned_32d** | 32 | 0.7924 | 0.3910 | 0.4140 | 0.7940 |
| **aligned_64d** | 64 | 0.7720 | 0.3076 | 0.6360 | 0.9000 |
| **aligned_128d** | 128 | 0.7142 | 0.2447 | 0.7560 | 0.9480 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7924 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3104. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 75.6% 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 | **-0.739** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | uforfalskede, ledocarpaceae, hærgende |
| `-n` | fjerntogsperron, flexlinjen, industriudstillingen |
| `-s` | bialiks, epicurus, ratios |
| `-r` | bredevandsbakker, provinshertugdømmer, linseskyer |
| `-er` | bredevandsbakker, provinshertugdømmer, linseskyer |
| `-en` | flexlinjen, industriudstillingen, jordbundslæren |
| `-et` | affrikeret, polyarkiet, panserkorpset |
| `-ne` | heatene, beslutningsevne, skillingsviserne |

### 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 |
|------|----------|------------------|----------|
| `irke` | 2.09x | 181 contexts | birke, virke, dirke |
| `elig` | 1.65x | 256 contexts | helig, selig, zelig |
| `embe` | 2.00x | 89 contexts | tembe, rembe, embed |
| `nger` | 1.45x | 439 contexts | inger, enger, anger |
| `tisk` | 1.73x | 152 contexts | tiske, etisk, tiski |
| `ndel` | 1.42x | 393 contexts | andel, endel, ndele |
| `mber` | 1.52x | 264 contexts | imber, amber, ember |
| `nmar` | 1.77x | 85 contexts | anmary, enmark, donmar |
| `lsen` | 1.52x | 174 contexts | elsen, ólsen, olsen |
| `rste` | 1.33x | 307 contexts | erste, første, fyrste |
| `rden` | 1.38x | 227 contexts | erden, urden, arden |
| `oner` | 1.34x | 260 contexts | zoner, joner, loner |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| profeterne | **`prof-et-er-ne`** | 7.5 | `prof` |
| regierende | **`regi-er-en-de`** | 7.5 | `regi` |
| kunstkritikeres | **`kunstkritik-er-es`** | 6.0 | `kunstkritik` |
| buccaneer | **`bucca-ne-er`** | 6.0 | `bucca` |
| udvikleres | **`udvikl-er-es`** | 6.0 | `udvikl` |
| håndredskaberne | **`håndredskab-er-ne`** | 6.0 | `håndredskab` |
| bolværkerne | **`bolværk-er-ne`** | 6.0 | `bolværk` |
| autogenereret | **`autog-en-er-er-et`** | 6.0 | `autog` |
| fællesgraven | **`fællesgrav-en`** | 4.5 | `fællesgrav` |
| feltflyvepladser | **`feltflyveplads-er`** | 4.5 | `feltflyveplads` |
| sangtrioen | **`sangtrio-en`** | 4.5 | `sangtrio` |
| teknologiparken | **`teknologipark-en`** | 4.5 | `teknologipark` |
| finnmarken | **`finnmark-en`** | 4.5 | `finnmark` |
| patriarker | **`patriark-er`** | 4.5 | `patriark` |
| synonymordbogen | **`synonymordbog-en`** | 4.5 | `synonymordbog` |

### 6.6 Linguistic Interpretation

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.56x) |
| N-gram | **2-gram** | Lowest perplexity (291) |
| Markov | **Context-4** | Highest predictability (93.7%) |
| 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: 2026-01-08 09:40:43*