---
language: sv
language_name: Swedish
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: 4.839
  - name: best_isotropy
    type: isotropy
    value: 0.7781
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Swedish** 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** | 3.772x | 3.77 | 0.0779% | 2,208,267 |
| **16k** | 4.178x | 4.18 | 0.0863% | 1,993,571 |
| **32k** | 4.539x | 4.54 | 0.0937% | 1,834,782 |
| **64k** | 4.839x 🏆 | 4.84 | 0.0999% | 1,721,218 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `XR kan avse: Labarum – symbolen ☧ Extinction Rebellion – miljöaktivismnätverk`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁x r ▁kan ▁avse : ▁lab ar um ▁– ▁symbol ... (+17 more)` | 27 |
| 16k | `▁x r ▁kan ▁avse : ▁lab ar um ▁– ▁symbolen ... (+15 more)` | 25 |
| 32k | `▁x r ▁kan ▁avse : ▁lab arum ▁– ▁symbolen ▁ ... (+11 more)` | 21 |
| 64k | `▁x r ▁kan ▁avse : ▁lab arum ▁– ▁symbolen ▁ ... (+11 more)` | 21 |

**Sample 2:** `Nanne kan avse: Nanne Grönvall – en svensk sångerska Nanne Bergstrand – en svens...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁n anne ▁kan ▁avse : ▁n anne ▁grön vall ▁– ... (+18 more)` | 28 |
| 16k | `▁n anne ▁kan ▁avse : ▁n anne ▁grön vall ▁– ... (+16 more)` | 26 |
| 32k | `▁n anne ▁kan ▁avse : ▁n anne ▁grön vall ▁– ... (+16 more)` | 26 |
| 64k | `▁nanne ▁kan ▁avse : ▁nanne ▁grönvall ▁– ▁en ▁svensk ▁sångerska ... (+12 more)` | 22 |

**Sample 3:** `Axel Banér kan syfta på: Axel Nilsson (Banér) svenskt riksråd Axel Banér svensk ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁axel ▁ban ér ▁kan ▁syfta ▁på : ▁axel ▁nilsson ▁( ... (+20 more)` | 30 |
| 16k | `▁axel ▁banér ▁kan ▁syfta ▁på : ▁axel ▁nilsson ▁( ban ... (+17 more)` | 27 |
| 32k | `▁axel ▁banér ▁kan ▁syfta ▁på : ▁axel ▁nilsson ▁( ban ... (+17 more)` | 27 |
| 64k | `▁axel ▁banér ▁kan ▁syfta ▁på : ▁axel ▁nilsson ▁( banér ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.839x compression
- **Lowest UNK Rate:** 8k with 0.0779% 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 | 128,531 | 16.97 | 588,874 | 6.5% | 18.1% |
| **2-gram** | Subword | 299 🏆 | 8.23 | 9,428 | 65.5% | 99.3% |
| **3-gram** | Word | 382,269 | 18.54 | 889,063 | 2.8% | 8.4% |
| **3-gram** | Subword | 2,685 | 11.39 | 78,127 | 24.4% | 68.0% |
| **4-gram** | Word | 730,017 | 19.48 | 1,235,098 | 1.7% | 5.6% |
| **4-gram** | Subword | 16,674 | 14.03 | 484,402 | 11.7% | 35.3% |
| **5-gram** | Word | 457,969 | 18.80 | 713,988 | 2.0% | 6.9% |
| **5-gram** | Subword | 72,706 | 16.15 | 1,694,981 | 6.4% | 20.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `för att` | 54,345 |
| 2 | `är en` | 33,008 |
| 3 | `bland annat` | 22,635 |
| 4 | `i sverige` | 22,298 |
| 5 | `externa länkar` | 22,207 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `på grund av` | 9,977 |
| 2 | `en del av` | 6,121 |
| 3 | `i samband med` | 5,992 |
| 4 | `en av de` | 5,491 |
| 5 | `i början av` | 5,150 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `style font weight bold` | 2,518 |
| 2 | `text align center title` | 2,324 |
| 3 | `weight bold text align` | 2,284 |
| 4 | `font weight bold text` | 2,284 |
| 5 | `bold text align center` | 2,284 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `font weight bold text align` | 2,284 |
| 2 | `style font weight bold text` | 2,284 |
| 3 | `weight bold text align center` | 2,284 |
| 4 | `bold text align center title` | 2,090 |
| 5 | `ett normalår som började en` | 1,164 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 3,301,236 |
| 2 | `e n` | 3,264,682 |
| 3 | `e r` | 3,168,484 |
| 4 | `r _` | 2,892,858 |
| 5 | `_ s` | 2,848,513 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n _` | 1,866,227 |
| 2 | `e r _` | 1,166,606 |
| 3 | `_ d e` | 968,782 |
| 4 | `_ o c` | 874,255 |
| 5 | `c h _` | 849,389 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o c h _` | 831,879 |
| 2 | `_ o c h` | 830,998 |
| 3 | `_ f ö r` | 589,415 |
| 4 | `_ a v _` | 492,842 |
| 5 | `s o m _` | 442,255 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ o c h _` | 829,605 |
| 2 | `_ s o m _` | 413,884 |
| 3 | `_ t i l l` | 377,514 |
| 4 | `_ a t t _` | 327,732 |
| 5 | `t i l l _` | 294,387 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 299
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~20% 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 | 0.9726 | 1.962 | 9.74 | 923,158 | 2.7% |
| **1** | Subword | 0.8711 | 1.829 | 6.20 | 4,981 | 12.9% |
| **2** | Word | 0.3384 | 1.264 | 2.07 | 8,987,021 | 66.2% |
| **2** | Subword | 0.8108 | 1.754 | 5.43 | 30,820 | 18.9% |
| **3** | Word | 0.1229 | 1.089 | 1.25 | 18,599,291 | 87.7% |
| **3** | Subword | 0.8219 | 1.768 | 4.75 | 167,363 | 17.8% |
| **4** | Word | 0.0416 🏆 | 1.029 | 1.07 | 23,153,748 | 95.8% |
| **4** | Subword | 0.7618 | 1.696 | 3.74 | 794,783 | 23.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `och avidia plautia 7 gästroll säsong tävlingsnamn bil en bedövningskräm som en coûture 17 9 vilket`
2. `i årskurs f kr lucius aemilius paullus tur kan påbörjas elektrifieringen av offentliga finanser skul...`
3. `av planeten jordens taktik de deltagande i flera länder england från it as long ön befriad`

**Context Size 2:**

1. `för att direkt koppla den till samfundets styrelse som bland annat av egil skallagrimsson barnsköter...`
2. `är en trögflytande vätska eller stelna till fast fas man skiljer på grund av amatörreglerna i danmar...`
3. `bland annat en lanthandel och han vände sig till los angeles ett viktigt konserveringsmedel under ad...`

**Context Size 3:**

1. `på grund av försvagad andningsmuskulatur kan respiratoriska hjälpmedel sättas in man behöver då ocks...`
2. `en del av signalperioden med målet att skapa ett så vackert språk som möjligt den ska ha ett`
3. `i samband med samhällsomvandlingen av malmberget i avsikt att hjälpa kristian ii tillbaka till trone...`

**Context Size 4:**

1. `style font weight bold text align center title sm semifinal 5 style font weight bold text align cent...`
2. `text align center title vidare till playoff style font weight bold text align center title deltog in...`
3. `weight bold text align center title hockeyettan norra style font weight bold text align center title...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_k_an,_golale_ar`
2. `epåntanona_svisc`
3. `an_å_acckt_t_si_`

**Context Size 2:**

1. `n_jazarikt_och_bä`
2. `entligen_andeckho`
3. `er_för_colms_som_`

**Context Size 3:**

1. `en_12:a_kans_i_fit`
2. `er_ett_tjänstnär_f`
3. `_den_febr:_"irolla`

**Context Size 4:**

1. `och_naturligamästeu`
2. `_och_han_blev_raoul`
3. `_för_spridentexter.`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (794,783 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 | 423,822 |
| Total Tokens | 25,776,350 |
| Mean Frequency | 60.82 |
| Median Frequency | 4 |
| Frequency Std Dev | 2623.06 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | och | 832,556 |
| 2 | i | 832,313 |
| 3 | av | 496,229 |
| 4 | som | 418,279 |
| 5 | en | 399,718 |
| 6 | att | 329,126 |
| 7 | den | 297,300 |
| 8 | till | 293,406 |
| 9 | med | 286,376 |
| 10 | på | 280,309 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | carpark | 2 |
| 2 | eskju | 2 |
| 3 | sambassadeur | 2 |
| 4 | mignanne | 2 |
| 5 | updarin | 2 |
| 6 | örträskfinnarna | 2 |
| 7 | polyphonic | 2 |
| 8 | hönshusbåten | 2 |
| 9 | lurituri | 2 |
| 10 | sjam | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9877 |
| R² (Goodness of Fit) | 0.998613 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.0% |
| Top 1,000 | 56.6% |
| Top 5,000 | 72.3% |
| Top 10,000 | 78.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9986 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.0% of corpus
- **Long Tail:** 413,822 words needed for remaining 21.2% 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 | 0.7781 | 0.3801 | N/A | N/A |
| **mono_64d** | 64 | 0.7224 | 0.3490 | N/A | N/A |
| **mono_128d** | 128 | 0.6328 | 0.2477 | N/A | N/A |
| **aligned_32d** | 32 | 0.7781 🏆 | 0.4084 | 0.3260 | 0.7180 |
| **aligned_64d** | 64 | 0.7224 | 0.3258 | 0.4800 | 0.7920 |
| **aligned_128d** | 128 | 0.6328 | 0.2547 | 0.5400 | 0.8420 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7781 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3276. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 54.0% 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 | **-0.664** | 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` | stihna, salivkörtlar, sigillet |
| `-a` | apati, assommoir, andrekurator |
| `-b` | bjärepartiets, bedas, benzler |
| `-m` | milleri, musikfenomen, merinas |
| `-k` | katharine, kortlinjen, konsertserie |
| `-ma` | matchdagen, maintenance, matras |
| `-t` | turistindustrin, träpalissader, tinieblas |
| `-l` | lanthimos, liberales, lynk |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | turistindustrin, kortlinjen, vechten |
| `-en` | kortlinjen, vechten, musikfenomen |
| `-r` | önskedrömmar, hyllningsdikter, pulverinhalator |
| `-s` | cruus, bjärepartiets, deklamerades |
| `-a` | stihna, vändkretsarna, överträda |
| `-t` | sigillet, semitiskt, givandet |
| `-er` | hyllningsdikter, popartister, pokertermer |
| `-e` | katharine, galle, konsertserie |

### 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 |
|------|----------|------------------|----------|
| `ades` | 2.25x | 143 contexts | mades, hades, gades |
| `tern` | 1.73x | 284 contexts | stern, terni, terns |
| `oner` | 1.73x | 186 contexts | toner, koner, zoner |
| `tade` | 1.69x | 190 contexts | tadel, tadeo, stade |
| `iska` | 1.68x | 179 contexts | liska, hiska, viska |
| `ngen` | 1.76x | 128 contexts | ängen, ungen, ingen |
| `ster` | 1.36x | 521 contexts | aster, yster, uster |
| `ngar` | 1.72x | 138 contexts | ängar, ingar, ungar |
| `ller` | 1.44x | 298 contexts | llers, eller, uller |
| `nska` | 1.58x | 136 contexts | önska, önskan, finska |
| `tisk` | 1.57x | 140 contexts | etisk, mytisk, etiska |
| `tion` | 1.56x | 141 contexts | potion, action, pétion |

### 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` | 183 words | sprungen, snusförsäljningen |
| `-s` | `-r` | 132 words | skattepengar, säsongsflyttningar |
| `-s` | `-en` | 121 words | sprungen, snusförsäljningen |
| `-k` | `-n` | 117 words | kyrkoslaviskan, kelin |
| `-s` | `-t` | 116 words | slakthusområdet, stödjepunkt |
| `-s` | `-a` | 108 words | sammanstötningarna, skapelserna |
| `-s` | `-s` | 108 words | ss, stjärnorps |
| `-b` | `-n` | 103 words | bokproduktion, björköleden |
| `-t` | `-n` | 95 words | turion, tornvinden |
| `-s` | `-e` | 89 words | ställde, skogsvärde |

### 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 |
|------|-----------------|------------|------|
| kringvandrande | **`kringvandra-n-de`** | 7.5 | `n` |
| tefatsliknande | **`tefatslikna-n-de`** | 7.5 | `n` |
| sinnesnärvaro | **`sinnesnärv-ar-o`** | 7.5 | `ar` |
| självklare | **`självkl-ar-e`** | 7.5 | `ar` |
| uppmjukande | **`uppmjuka-n-de`** | 7.5 | `n` |
| kåkindbataljonen | **`kåkindbataljo-n-en`** | 7.5 | `n` |
| språkgräns | **`språkgrä-n-s`** | 7.5 | `n` |
| samlingssal | **`samlings-s-al`** | 7.5 | `s` |
| hammarstrand | **`hammarstra-n-d`** | 7.5 | `n` |
| läsplattor | **`läsplat-t-or`** | 7.5 | `t` |
| handelsnationer | **`handelsnatio-n-er`** | 7.5 | `n` |
| gullmarsplans | **`gullmarspla-n-s`** | 7.5 | `n` |
| isolerades | **`isolera-de-s`** | 7.5 | `de` |
| ljusbrunt | **`ljusbru-n-t`** | 7.5 | `n` |
| krogägare | **`krogäg-ar-e`** | 7.5 | `ar` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Swedish 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 (4.84x) |
| N-gram | **2-gram** | Lowest perplexity (299) |
| Markov | **Context-4** | Highest predictability (95.8%) |
| 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: 2026-01-11 02:22:30*