README.md

---
language: no
language_name: Norwegian
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: 4.616
  - name: best_isotropy
    type: isotropy
    value: 0.7672
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-15
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Norwegian** 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** | 3.635x | 3.64 | 0.0399% | 2,710,690 |
| **16k** | 4.005x | 4.01 | 0.0440% | 2,459,935 |
| **32k** | 4.341x | 4.34 | 0.0477% | 2,269,700 |
| **64k** | 4.616x 🏆 | 4.62 | 0.0507% | 2,134,495 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Atacama eller Atakama kan ha flere betydninger: Atacamaørkenen – ørken i Chile A...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁at ac ama ▁eller ▁at ak ama ▁kan ▁ha ▁flere ... (+33 more)` | 43 |
| 16k | `▁at ac ama ▁eller ▁at ak ama ▁kan ▁ha ▁flere ... (+31 more)` | 41 |
| 32k | `▁at ac ama ▁eller ▁at ak ama ▁kan ▁ha ▁flere ... (+29 more)` | 39 |
| 64k | `▁at ac ama ▁eller ▁at ak ama ▁kan ▁ha ▁flere ... (+29 more)` | 39 |

**Sample 2:** `Monroe County er et fylke i den amerikanske delstaten Tennessee. Eksterne lenker...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mon ro e ▁county ▁er ▁et ▁fylke ▁i ▁den ▁amerikanske ... (+19 more)` | 29 |
| 16k | `▁mon roe ▁county ▁er ▁et ▁fylke ▁i ▁den ▁amerikanske ▁delstaten ... (+12 more)` | 22 |
| 32k | `▁monroe ▁county ▁er ▁et ▁fylke ▁i ▁den ▁amerikanske ▁delstaten ▁tennessee ... (+11 more)` | 21 |
| 64k | `▁monroe ▁county ▁er ▁et ▁fylke ▁i ▁den ▁amerikanske ▁delstaten ▁tennessee ... (+11 more)` | 21 |

**Sample 3:** `Koroljov kan vise til: Koroljov (by) – en by i Moskva oblast, Russland Sergej Ko...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kor ol j ov ▁kan ▁vise ▁til : ▁kor ol ... (+25 more)` | 35 |
| 16k | `▁kor ol jov ▁kan ▁vise ▁til : ▁kor ol jov ... (+20 more)` | 30 |
| 32k | `▁kor ol jov ▁kan ▁vise ▁til : ▁kor ol jov ... (+19 more)` | 29 |
| 64k | `▁kor ol jov ▁kan ▁vise ▁til : ▁kor ol jov ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 64k achieves 4.616x compression
- **Lowest UNK Rate:** 8k with 0.0399% 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 | 270,383 | 18.04 | 2,970,545 | 7.0% | 17.9% |
| **2-gram** | Subword | 296 🏆 | 8.21 | 30,863 | 66.1% | 99.0% |
| **3-gram** | Word | 1,285,855 | 20.29 | 6,366,112 | 3.4% | 8.5% |
| **3-gram** | Subword | 2,800 | 11.45 | 208,249 | 24.1% | 67.7% |
| **4-gram** | Word | 2,996,170 | 21.51 | 10,912,386 | 2.7% | 6.7% |
| **4-gram** | Subword | 18,923 | 14.21 | 1,234,998 | 11.1% | 34.9% |
| **5-gram** | Word | 2,303,329 | 21.14 | 7,869,992 | 2.9% | 7.4% |
| **5-gram** | Subword | 92,380 | 16.50 | 4,656,738 | 5.7% | 19.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `eksterne lenker` | 435,397 |
| 2 | `er en` | 432,099 |
| 3 | `sommer ol` | 283,606 |
| 4 | `referanser eksterne` | 277,093 |
| 5 | `under sommer` | 275,051 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `referanser eksterne lenker` | 277,015 |
| 2 | `under sommer ol` | 274,932 |
| 3 | `sommer ol under` | 106,745 |
| 4 | `ol under sommer` | 103,617 |
| 5 | `sommer ol i` | 65,471 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `under sommer ol under` | 106,680 |
| 2 | `ol under sommer ol` | 103,617 |
| 3 | `sommer ol under sommer` | 103,575 |
| 4 | `under sommer ol i` | 61,581 |
| 5 | `under sommer ol for` | 48,780 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sommer ol under sommer ol` | 103,575 |
| 2 | `under sommer ol under sommer` | 103,531 |
| 3 | `ol under sommer ol for` | 36,333 |
| 4 | `formelt beskrevet i formelt beskrevet` | 27,673 |
| 5 | `beskrevet i formelt beskrevet av` | 27,651 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e r` | 27,548,918 |
| 2 | `e n` | 22,490,846 |
| 3 | `e _` | 22,399,502 |
| 4 | `r _` | 18,922,644 |
| 5 | `n _` | 16,899,339 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e r _` | 12,200,885 |
| 2 | `e n _` | 10,670,318 |
| 3 | `_ i _` | 6,820,289 |
| 4 | `e t _` | 6,507,409 |
| 5 | `_ d e` | 5,931,351 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ o g _` | 4,595,611 |
| 2 | `_ f o r` | 3,343,084 |
| 3 | `_ a v _` | 2,759,889 |
| 4 | `_ s o m` | 2,745,498 |
| 5 | `_ t i l` | 2,488,067 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s o m _` | 2,381,655 |
| 2 | `_ t i l _` | 1,966,332 |
| 3 | `_ f o r _` | 1,856,984 |
| 4 | `_ m e d _` | 1,454,863 |
| 5 | `_ b l e _` | 1,454,774 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 296
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~19% 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 | 0.9170 | 1.888 | 11.03 | 3,288,766 | 8.3% |
| **1** | Subword | 1.4172 | 2.671 | 10.38 | 14,974 | 0.0% |
| **2** | Word | 0.3729 | 1.295 | 2.40 | 36,234,623 | 62.7% |
| **2** | Subword | 0.5610 | 1.475 | 3.64 | 155,200 | 43.9% |
| **3** | Word | 0.1666 | 1.122 | 1.39 | 86,777,316 | 83.3% |
| **3** | Subword | 0.6401 | 1.558 | 3.93 | 563,952 | 36.0% |
| **4** | Word | 0.0713 🏆 | 1.051 | 1.13 | 120,628,993 | 92.9% |
| **4** | Subword | 0.6848 | 1.607 | 3.69 | 2,214,293 | 31.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i nord i skjermkort til var sist i i black studioalbum culture palgrave s kardinal carlo`
2. `og etter alle akajere grekerne bakover rundede sider i london oxford university press kjempefesten i...`
3. `av turneringen for røa sentrum av kjøtt hue da som trykkbølger er i langrenn 15km classic`

**Context Size 2:**

1. `er en bygd og en stedsplassering de lasala fernando exercise of social psychology of interpersonal r...`
2. `eksterne lenker fra russland vant han maratontittelen han tok sete i parlamentet og hvor de ligger n...`
3. `referanser eksterne lenker ungdommens passbåter inkludert familiebåt`

**Context Size 3:**

1. `referanser eksterne lenker fotballspillere fotballtrenere for sheffield united fc for middlesbrough ...`
2. `under sommer ol for marokko under sommer ol for brasil under sommer ol for ukraina under sommer ol`
3. `sommer ol under sommer ol under sommer ol for japan under sommer ol for storbritannia under sommer o...`

**Context Size 4:**

1. `under sommer ol under sommer ol medaljevinnere i fekting fra brno`
2. `sommer ol under sommer ol under sommer ol under sommer ol fra st petersburg i medaljevinnere i fotba...`
3. `ol under sommer ol fra kitchener i ontario under paralympiske vinterleker i salt lake city sammen me...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_alat_ut_hi_uked`
2. `ed_eiste_forkek.`
3. `r._mest_r_1:kkst`

**Context Size 2:**

1. `er_å_e39_(lychell`
2. `en_målørskold._ti`
3. `e_1:34_−_haelsent`

**Context Size 3:**

1. `er_hevelsene._etts`
2. `en_edingerπ_på_dve`
3. `_i_kun_det_for_å_o`

**Context Size 4:**

1. `_og_militær_sk_7._r`
2. `_for_omkrig_og_deri`
3. `_av_ei_begynne_seg_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,214,293 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 | 1,490,817 |
| Total Tokens | 165,713,306 |
| Mean Frequency | 111.16 |
| Median Frequency | 4 |
| Frequency Std Dev | 9324.61 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 6,998,391 |
| 2 | og | 4,610,581 |
| 3 | av | 2,777,264 |
| 4 | som | 2,403,719 |
| 5 | en | 2,260,501 |
| 6 | er | 2,015,901 |
| 7 | til | 1,991,863 |
| 8 | på | 1,902,653 |
| 9 | for | 1,878,752 |
| 10 | med | 1,483,151 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | diamantpål | 2 |
| 2 | diamantthomas | 2 |
| 3 | peppykalle | 2 |
| 4 | nilsenkong | 2 |
| 5 | versjonstallene | 2 |
| 6 | muoraš | 2 |
| 7 | weddemorten | 2 |
| 8 | meggrusomme | 2 |
| 9 | canadansk | 2 |
| 10 | humdingerøyvind | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0045 |
| R² (Goodness of Fit) | 0.998793 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 37.0% |
| Top 1,000 | 57.3% |
| Top 5,000 | 72.2% |
| Top 10,000 | 78.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9988 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 37.0% of corpus
- **Long Tail:** 1,480,817 words needed for remaining 21.7% 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 | 0.7672 🏆 | 0.3805 | N/A | N/A |
| **mono_64d** | 64 | 0.7454 | 0.2902 | N/A | N/A |
| **mono_128d** | 128 | 0.6845 | 0.2470 | N/A | N/A |
| **aligned_32d** | 32 | 0.7672 | 0.3729 | 0.4300 | 0.7940 |
| **aligned_64d** | 64 | 0.7454 | 0.3083 | 0.6320 | 0.8960 |
| **aligned_128d** | 128 | 0.6845 | 0.2340 | 0.7700 | 0.9520 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7672 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3055. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 77.0% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.618** | 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 |
|--------|----------|
| `-s` | separatistene, spindoktor, strengarrangementer |
| `-a` | airwaysnairobi, aschenbroedel, allerns |
| `-m` | merl, monody, marmorverk |
| `-ma` | marmorverk, marelok, manducatio |
| `-b` | bizness, ballkastem, begrepsrealisme |
| `-k` | kunstnerorganisasjonene, kjønnscellen, kærlighedsoffer |
| `-t` | tekstilopplysningskontoret, tooluk, togtunnelene |
| `-e` | enigmencyrtus, eigeninnlemmet, ellia |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-en` | kjønnscellen, nanjinggaten, fjellutstikkeren |
| `-n` | gunman, kjønnscellen, nanjinggaten |
| `-e` | separatistene, lillefosse, begrepsrealisme |
| `-er` | førsteprinsipper, strengarrangementer, kærlighedsoffer |
| `-r` | førsteprinsipper, spindoktor, strengarrangementer |
| `-s` | phytomedicines, bizness, confections |
| `-t` | weeghconst, ferdigstillt, tekstilopplysningskontoret |
| `-et` | tekstilopplysningskontoret, slektshjemmet, klodset |

### 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 |
|------|----------|------------------|----------|
| `ndel` | 1.69x | 558 contexts | ndele, endel, andel |
| `embe` | 2.07x | 139 contexts | vembe, lembe, bembe |
| `irke` | 1.87x | 213 contexts | kirke, dirke, pirke |
| `lsen` | 1.72x | 240 contexts | olsen, elsen, alsen |
| `nger` | 1.40x | 608 contexts | enger, unger, inger |
| `rbei` | 1.99x | 84 contexts | arbei, garbei, arbeia |
| `nnen` | 1.58x | 257 contexts | ennen, unnen, onnen |
| `nser` | 1.60x | 217 contexts | inser, unser, ānser |
| `oner` | 1.49x | 300 contexts | moner, voner, joner |
| `nker` | 1.50x | 288 contexts | anker, inker, enker |
| `gger` | 1.49x | 289 contexts | igger, ogger, agger |
| `ngen` | 1.34x | 450 contexts | ungen, yngen, ongen |

### 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` | `-n` | 168 words | sentralkomitén, spillekarrieren |
| `-s` | `-e` | 159 words | soldatkeisere, solbergske |
| `-s` | `-r` | 124 words | sogneadministratorer, sester |
| `-s` | `-s` | 123 words | späths, substantivfrasens |
| `-s` | `-en` | 117 words | spillekarrieren, shippingavdelingen |
| `-s` | `-er` | 109 words | sogneadministratorer, sester |
| `-k` | `-n` | 103 words | knuten, klassikersesongen |
| `-b` | `-n` | 100 words | billigutgaven, belteplaten |
| `-b` | `-e` | 89 words | baudinière, bandbredde |
| `-s` | `-t` | 87 words | sanctificat, smalahovesleppet |

### 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 |
|------|-----------------|------------|------|
| stjernevind | **`stjernevi-n-d`** | 7.5 | `n` |
| tolkalina | **`tolkali-n-a`** | 7.5 | `n` |
| panikkfølelse | **`panikkfølel-s-e`** | 7.5 | `s` |
| nordurland | **`nordurla-n-d`** | 7.5 | `n` |
| toppstein | **`toppst-e-in`** | 7.5 | `e` |
| pollinatorer | **`pollinato-r-er`** | 7.5 | `r` |
| vuojatädno | **`vuojatäd-n-o`** | 7.5 | `n` |
| sanderscaren | **`sandersca-r-en`** | 7.5 | `r` |
| stølevann | **`støleva-n-n`** | 7.5 | `n` |
| utstrosset | **`utstros-s-et`** | 7.5 | `s` |
| samfunnslønn | **`samfunnslø-n-n`** | 7.5 | `n` |
| sluttattest | **`sluttatte-s-t`** | 7.5 | `s` |
| georgantas | **`georgan-ta-s`** | 7.5 | `ta` |
| creontiades | **`creontiad-e-s`** | 7.5 | `e` |
| trastorno | **`trastor-n-o`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Norwegian 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 (4.62x) |
| N-gram | **2-gram** | Lowest perplexity (296) |
| Markov | **Context-4** | Highest predictability (92.9%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-16 03:53:26*