README.md

---
language: af
language_name: Afrikaans
language_family: germanic_west_anglofrisian
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_anglofrisian
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: 4.620
  - name: best_isotropy
    type: isotropy
    value: 0.6974
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Afrikaans** 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** | 3.748x | 3.75 | 0.0650% | 1,240,703 |
| **16k** | 4.108x | 4.11 | 0.0712% | 1,132,029 |
| **32k** | 4.402x | 4.40 | 0.0763% | 1,056,512 |
| **64k** | 4.620x 🏆 | 4.62 | 0.0801% | 1,006,543 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Electron is 'n industriële gebied in Johannesburg, Suid-Afrika. Verwysings van J...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁electr on ▁is ▁' n ▁industr iële ▁gebied ▁in ▁johannesburg ... (+8 more)` | 18 |
| 16k | `▁electr on ▁is ▁' n ▁industriële ▁gebied ▁in ▁johannesburg , ... (+7 more)` | 17 |
| 32k | `▁electr on ▁is ▁' n ▁industriële ▁gebied ▁in ▁johannesburg , ... (+7 more)` | 17 |
| 64k | `▁electron ▁is ▁' n ▁industriële ▁gebied ▁in ▁johannesburg , ▁suid ... (+6 more)` | 16 |

**Sample 2:** `Fig Tree Creek is 'n takrivier van die Kaaprivier in Mpumalanga in Suid-Afrika. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁fig ▁tree ▁c reek ▁is ▁' n ▁tak rivier ▁van ... (+22 more)` | 32 |
| 16k | `▁fig ▁tree ▁creek ▁is ▁' n ▁tak rivier ▁van ▁die ... (+20 more)` | 30 |
| 32k | `▁fig ▁tree ▁creek ▁is ▁' n ▁takrivier ▁van ▁die ▁kaap ... (+19 more)` | 29 |
| 64k | `▁fig ▁tree ▁creek ▁is ▁' n ▁takrivier ▁van ▁die ▁kaap ... (+19 more)` | 29 |

**Sample 3:** `Japan Nasionale Roete 390 is 'n nasionale snelweg in Japan. Verwysings paaie in ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁japan ▁nasionale ▁roete ▁ 3 9 0 ▁is ▁' n ... (+9 more)` | 19 |
| 16k | `▁japan ▁nasionale ▁roete ▁ 3 9 0 ▁is ▁' n ... (+9 more)` | 19 |
| 32k | `▁japan ▁nasionale ▁roete ▁ 3 9 0 ▁is ▁' n ... (+9 more)` | 19 |
| 64k | `▁japan ▁nasionale ▁roete ▁ 3 9 0 ▁is ▁' n ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 64k achieves 4.620x compression
- **Lowest UNK Rate:** 8k with 0.0650% 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 | 67,167 | 16.04 | 741,646 | 13.7% | 29.1% |
| **2-gram** | Subword | 253 🏆 | 7.98 | 13,611 | 69.5% | 99.3% |
| **3-gram** | Word | 295,297 | 18.17 | 1,507,746 | 5.8% | 16.9% |
| **3-gram** | Subword | 2,160 | 11.08 | 96,463 | 28.5% | 71.9% |
| **4-gram** | Word | 559,011 | 19.09 | 2,524,344 | 6.5% | 16.5% |
| **4-gram** | Subword | 12,656 | 13.63 | 532,733 | 15.0% | 40.0% |
| **5-gram** | Word | 326,109 | 18.31 | 1,744,378 | 9.4% | 21.4% |
| **5-gram** | Subword | 52,200 | 15.67 | 1,835,021 | 9.1% | 25.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `van die` | 511,917 |
| 2 | `in die` | 344,470 |
| 3 | `is n` | 115,009 |
| 4 | `en die` | 109,902 |
| 5 | `is die` | 91,555 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `van suid afrika` | 27,044 |
| 2 | `rolle in die` | 25,215 |
| 3 | `die 20ste eeu` | 24,473 |
| 4 | `van die 20ste` | 23,498 |
| 5 | `eksterne skakels in` | 22,336 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `van die 20ste eeu` | 23,435 |
| 2 | `manlike akteurs van die` | 20,400 |
| 3 | `rolle in die rolprente` | 19,639 |
| 4 | `van die 21ste eeu` | 15,805 |
| 5 | `plants of the world` | 14,447 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `bekend vir sy rolle in` | 13,780 |
| 2 | `vir sy rolle in die` | 13,771 |
| 3 | `akteurs van die 20ste eeu` | 12,560 |
| 4 | `manlike akteurs van die 20ste` | 12,536 |
| 5 | `plants of the world online` | 11,731 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 8,931,762 |
| 2 | `n _` | 5,874,572 |
| 3 | `i e` | 5,325,847 |
| 4 | `e r` | 4,823,982 |
| 5 | `_ d` | 4,520,196 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i e _` | 3,601,485 |
| 2 | `_ d i` | 3,186,521 |
| 3 | `d i e` | 3,062,960 |
| 4 | `a n _` | 1,896,257 |
| 5 | `e n _` | 1,548,169 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `d i e _` | 2,931,996 |
| 2 | `_ d i e` | 2,851,512 |
| 3 | `_ v a n` | 1,364,018 |
| 4 | `v a n _` | 1,348,393 |
| 5 | `n _ d i` | 1,174,871 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i e _` | 2,794,095 |
| 2 | `_ v a n _` | 1,320,773 |
| 3 | `n _ d i e` | 1,131,268 |
| 4 | `a n _ d i` | 628,822 |
| 5 | `v a n _ d` | 564,996 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 253
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.9424 | 1.922 | 9.98 | 888,057 | 5.8% |
| **1** | Subword | 1.0749 | 2.107 | 6.60 | 7,659 | 0.0% |
| **2** | Word | 0.3845 | 1.305 | 2.33 | 8,849,236 | 61.6% |
| **2** | Subword | 0.7312 | 1.660 | 4.61 | 50,492 | 26.9% |
| **3** | Word | 0.1708 | 1.126 | 1.40 | 20,626,048 | 82.9% |
| **3** | Subword | 0.7057 | 1.631 | 4.02 | 232,520 | 29.4% |
| **4** | Word | 0.0705 🏆 | 1.050 | 1.13 | 28,778,158 | 92.9% |
| **4** | Subword | 0.6912 | 1.615 | 3.50 | 934,149 | 30.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `die dr g mineur d ilse ná dié samewerking met 46 155 173 minute met ywer`
2. `van president trump het hierdie maniak nie voortsetting van die verbranding maak in die spesie is`
3. `in te veel van kaiserstuhl gebied rondom die farao self deur die nasionalistiese en geofiet wat`

**Context Size 2:**

1. `van die eufraat te gaan om die lewe geroep om n nuwe uitgawe cambridge university press princeton`
2. `in die swartberge en die patrone diagonaal 2 4 brown bl 101 in suidoos asië panthera p`
3. `is n blouwit ster dit is egter vas gekant teen die middel van toenemende afvalligheid te volhard`

**Context Size 3:**

1. `rolle in die rolprente kitty foyle missile to the moon tour aangekondig n amptelike konserttoer met ...`
2. `van die 20ste eeu manlike akteurs van die 21ste eeu aktrises van die 21ste eeu manlike akteurs van`
3. `eksterne skakels in in manlike akteurs van die 20ste eeu manlike akteurs van die 20ste eeu aktrises ...`

**Context Size 4:**

1. `manlike akteurs van die 21ste eeu manlike akteurs van die 20ste eeu byna uitgeroei is die oorspronkl...`
2. `rolle in die rolprente batman the movie scream evelyn scream televisiereekse playhouse 90 frontier d...`
3. `plants of the world online van namibië van suid afrika van die tweede vryheidsoorlog die eerste is b...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_&_ligesagetiebe`
2. `e_n_dnore_drs_va`
3. `ie_wogerct_wache`

**Context Size 2:**

1. `e_van_gesede_wasc`
2. `n_baiensomenaar,_`
3. `ierk_ing_maaktors`

**Context Size 3:**

1. `ie_te_sies_die_in_`
2. `_die_redig_gebruit`
3. `die_alber_ds._hy_w`

**Context Size 4:**

1. `die_rolle_wêreld_en`
2. `_die_se_limitiek_di`
3. `_van_'n_albei_dat_h`


### 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 (934,149 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 | 404,957 |
| Total Tokens | 38,641,442 |
| Mean Frequency | 95.42 |
| Median Frequency | 4 |
| Frequency Std Dev | 6141.00 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | die | 2,844,119 |
| 2 | van | 1,325,435 |
| 3 | in | 1,115,990 |
| 4 | en | 1,052,538 |
| 5 | n | 806,584 |
| 6 | is | 768,312 |
| 7 | het | 648,164 |
| 8 | wat | 343,988 |
| 9 | the | 293,953 |
| 10 | op | 290,589 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | bajnokság | 2 |
| 2 | zalaegerszegi | 2 |
| 3 | akteurskategorieë | 2 |
| 4 | mullens | 2 |
| 5 | grafiekstruktuur | 2 |
| 6 | roostergrafieke | 2 |
| 7 | sokkerbekertitels | 2 |
| 8 | chalobah | 2 |
| 9 | sentrumverdediger | 2 |
| 10 | guðjohnsen | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0518 |
| R² (Goodness of Fit) | 0.995983 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 43.7% |
| Top 1,000 | 64.3% |
| Top 5,000 | 79.4% |
| Top 10,000 | 85.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9960 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 43.7% of corpus
- **Long Tail:** 394,957 words needed for remaining 15.0% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.6861 | 0.3709 | N/A | N/A |
| **mono_64d** | 64 | 0.6974 | 0.2860 | N/A | N/A |
| **mono_128d** | 128 | 0.6739 | 0.2351 | N/A | N/A |
| **aligned_32d** | 32 | 0.6861 | 0.3805 | 0.3500 | 0.6860 |
| **aligned_64d** | 64 | 0.6974 🏆 | 0.2901 | 0.5440 | 0.8400 |
| **aligned_128d** | 128 | 0.6739 | 0.2381 | 0.6160 | 0.8900 |

### Key Findings

- **Best Isotropy:** aligned_64d with 0.6974 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3001. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 61.6% 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 | **-0.147** | 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 |
|--------|----------|
| `-ma` | maanteorieë, markomgewing, mataiva |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | squeeze, summerside, tirolse |
| `-s` | repsyfers, sangkunstenaars, kananaskis |
| `-er` | shaffer, ondier, skilpadkewer |
| `-es` | langafstandroetes, treasuries, ferrities |
| `-ng` | enkelstring, markomgewing, erlösung |
| `-ing` | enkelstring, markomgewing, navorsingsbelangstelling |
| `-te` | sudete, heroute, afleweringsdienste |
| `-de` | summerside, geünieerde, uitgetrede |

### 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 |
|------|----------|------------------|----------|
| `pren` | 2.42x | 29 contexts | prens, prent, prend |
| `staa` | 1.70x | 98 contexts | staak, staas, staab |
| `ings` | 1.49x | 146 contexts | lings, wings, hings |
| `kend` | 1.58x | 95 contexts | kendo, kenda, kende |
| `eken` | 1.48x | 124 contexts | teken, deken, reken |
| `ebru` | 2.04x | 32 contexts | gebru, hebrus, cebrus |
| `erdi` | 1.58x | 85 contexts | ferdi, serdi, verdi |
| `brui` | 1.78x | 44 contexts | bruin, bruit, bruis |
| `elik` | 1.53x | 82 contexts | melik, elika, lelik |
| `aans` | 1.44x | 88 contexts | aansê, faans, maans |
| `ersk` | 1.32x | 109 contexts | koersk, perski, perske |
| `kste` | 1.42x | 71 contexts | ekster, dikste, rykste |

### 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 |
|--------|--------|-----------|----------|
| `-ma` | `-e` | 32 words | mapogsgrotte, malte |
| `-ma` | `-s` | 24 words | magnesiumlegerings, maatskappybestuurders |
| `-ma` | `-er` | 11 words | marineer, mansspeler |
| `-ma` | `-ng` | 5 words | maksimalisering, magsdeling |
| `-ma` | `-en` | 5 words | marten, maurren |
| `-ma` | `-te` | 4 words | mapogsgrotte, malte |
| `-ma` | `-se` | 4 words | majestueuse, manneristiese |
| `-ma` | `-es` | 4 words | maccabees, maykersfees |
| `-ma` | `-ing` | 3 words | maksimalisering, magsdeling |
| `-ma` | `-de` | 2 words | malahide, mansonbendelede |

### 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 |
|------|-----------------|------------|------|
| durangense | **`dura-ng-en-se`** | 7.5 | `dura` |
| bessinger | **`bess-ing-er`** | 6.0 | `bess` |
| selflaaiende | **`selflaai-en-de`** | 6.0 | `selflaai` |
| durlacher | **`durlach-er`** | 4.5 | `durlach` |
| emotionen | **`emotion-en`** | 4.5 | `emotion` |
| afgeperste | **`afgepers-te`** | 4.5 | `afgepers` |
| apostelen | **`apostel-en`** | 4.5 | `apostel` |
| kazachstanse | **`kazachstan-se`** | 4.5 | `kazachstan` |
| afgerolde | **`afgerol-de`** | 4.5 | `afgerol` |
| luggelanseerde | **`luggelan-se-er-de`** | 4.5 | `luggelan` |
| verveling | **`vervel-ing`** | 4.5 | `vervel` |
| biofiltrering | **`biofiltr-er-ing`** | 3.0 | `biofiltr` |
| gefasiliteer | **`gefasili-te-er`** | 3.0 | `gefasili` |
| palermosteen | **`palermos-te-en`** | 3.0 | `palermos` |
| trekmense | **`trekm-en-se`** | 3.0 | `trekm` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Afrikaans 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 (253) |
| 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: 2026-01-03 19:59:08*