README.md

---
language: fj
language_name: Fijian
language_family: austronesian_oceanic_other
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-austronesian_oceanic_other
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: 4.558
  - name: best_isotropy
    type: isotropy
    value: 0.3441
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Fijian** 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** | 4.221x | 4.23 | 0.2173% | 149,069 |
| **16k** | 4.473x | 4.48 | 0.2303% | 140,670 |
| **32k** | 4.558x 🏆 | 4.57 | 0.2348% | 138,019 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Shenzhen na siti mai Guagdog, Jaina. 10,78 milioni 'ei wilika kai (Jaina)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁shenz hen ▁na ▁siti ▁mai ▁gua g dog , ▁jaina ... (+15 more)` | 25 |
| 16k | `▁shenzhen ▁na ▁siti ▁mai ▁guagdog , ▁jaina . ▁ 1 ... (+12 more)` | 22 |
| 32k | `▁shenzhen ▁na ▁siti ▁mai ▁guagdog , ▁jaina . ▁ 1 ... (+12 more)` | 22 |

**Sample 2:** `Beijigi na Samoa Solomon Islands mai Jaina. (Jaina)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁beiji gi ▁na ▁samoa ▁solo mon ▁islands ▁mai ▁jaina . ... (+3 more)` | 13 |
| 16k | `▁beijigi ▁na ▁samoa ▁solomon ▁islands ▁mai ▁jaina . ▁( jaina ... (+1 more)` | 11 |
| 32k | `▁beijigi ▁na ▁samoa ▁solomon ▁islands ▁mai ▁jaina . ▁( jaina ... (+1 more)` | 11 |

**Sample 3:** `O Niukaseli ena Tyne () e dua na siti kei Vualiku Tokalau Igiladi. Sega ni veile...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁o ▁niukaseli ▁ena ▁ty ne ▁() ▁e ▁dua ▁na ▁siti ... (+16 more)` | 26 |
| 16k | `▁o ▁niukaseli ▁ena ▁tyne ▁() ▁e ▁dua ▁na ▁siti ▁kei ... (+15 more)` | 25 |
| 32k | `▁o ▁niukaseli ▁ena ▁tyne ▁() ▁e ▁dua ▁na ▁siti ▁kei ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 32k achieves 4.558x compression
- **Lowest UNK Rate:** 8k with 0.2173% 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 | 1,320 | 10.37 | 3,772 | 35.4% | 72.8% |
| **2-gram** | Subword | 135 🏆 | 7.08 | 1,021 | 82.8% | 100.0% |
| **3-gram** | Word | 2,319 | 11.18 | 5,139 | 26.7% | 58.4% |
| **3-gram** | Subword | 762 | 9.57 | 6,635 | 47.4% | 88.0% |
| **4-gram** | Word | 4,567 | 12.16 | 6,660 | 15.3% | 41.6% |
| **4-gram** | Subword | 2,839 | 11.47 | 23,852 | 29.5% | 65.9% |
| **5-gram** | Word | 2,249 | 11.14 | 2,889 | 17.2% | 54.1% |
| **5-gram** | Subword | 6,549 | 12.68 | 40,232 | 20.3% | 51.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dua na` | 2,793 |
| 2 | `e dua` | 1,910 |
| 3 | `kei na` | 1,768 |
| 4 | `na kena` | 1,059 |
| 5 | `mai na` | 875 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e dua na` | 1,710 |
| 2 | `me vaka na` | 432 |
| 3 | `ena dua na` | 337 |
| 4 | `e rawa ni` | 325 |
| 5 | `me baleta na` | 289 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kina e dua na` | 157 |
| 2 | `me vaka e dua` | 128 |
| 3 | `vaka e dua na` | 126 |
| 4 | `kei na dua na` | 94 |
| 5 | `dua vei ira na` | 94 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `me vaka e dua na` | 118 |
| 2 | `tiko kina e dua na` | 81 |
| 3 | `e tiko kina e dua` | 61 |
| 4 | `e dua vei ira na` | 61 |
| 5 | `e dua na vanua ni` | 30 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 58,970 |
| 2 | `i _` | 29,549 |
| 3 | `n a` | 29,239 |
| 4 | `_ n` | 27,570 |
| 5 | `k a` | 21,085 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n a _` | 27,144 |
| 2 | `_ n a` | 17,261 |
| 3 | `a _ n` | 13,306 |
| 4 | `a k a` | 12,166 |
| 5 | `n i _` | 10,459 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a _` | 16,868 |
| 2 | `_ n i _` | 9,009 |
| 3 | `v a k a` | 8,886 |
| 4 | `a _ n a` | 8,331 |
| 5 | `_ v a k` | 7,039 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ n a _` | 8,200 |
| 2 | `_ v a k a` | 6,983 |
| 3 | `i _ n a _` | 4,445 |
| 4 | `a _ n i _` | 4,282 |
| 5 | `_ e n a _` | 4,212 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 135
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~51% 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 | 0.7768 | 1.713 | 4.51 | 11,967 | 22.3% |
| **1** | Subword | 0.9522 | 1.935 | 6.63 | 397 | 4.8% |
| **2** | Word | 0.3443 | 1.270 | 1.87 | 53,271 | 65.6% |
| **2** | Subword | 0.9798 | 1.972 | 5.10 | 2,632 | 2.0% |
| **3** | Word | 0.1340 | 1.097 | 1.26 | 98,857 | 86.6% |
| **3** | Subword | 0.7901 | 1.729 | 3.31 | 13,399 | 21.0% |
| **4** | Word | 0.0539 🏆 | 1.038 | 1.08 | 123,164 | 94.6% |
| **4** | Subword | 0.5048 | 1.419 | 2.10 | 44,342 | 49.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `na veikau se kavu epinephelus macrospilos epinephelus howlandi epinephelus species ni rerevaka na ma...`
2. `ni percussion ni tauyavutaki ena dua na koro levu ni potukali puerto la voui karisito oqo`
3. `e kune ena rawa e dua na kawatamata kena vakayagataki me vaka axial 82 23 mi`

**Context Size 2:**

1. `dua na tabana ka rawa me wainimate igu ia e dau yaco na veikau na uca kei`
2. `e dua na vanua e vakavuna na vakayalo ni veika vulavula e dua na lali e tu`
3. `kei na vakayagataki vakalevu me maroroi tikoga na kisi kei galileo ena lomanibai oqo e sega ni`

**Context Size 3:**

1. `e dua na sikorere ena matavuvale artamidae e sa vakaiyacaga sara ki na vuqa na itutu taudaku ni`
2. `me vaka na ena vuku ni dredre ni kena vakamacalataki na veimataqali vakasama ni bibi e tiko na`
3. `ena dua na koniteina vakauyaya ni sega ni tiko manumanu nodra sui e tiko ena yanuyanu o vanua`

**Context Size 4:**

1. `kina e dua na balavu ni ivakatagedegede e 2 7 ki 3 1 na gauna na kena titobu na`
2. `me vaka e dua na vanua ni wai ka drodro yani ena dela ni qele se na boto wasawasa`
3. `vaka e dua na droini mai vei rembrandt e dua na bula vakailavo e dua na vanua e 28`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `aki)_nuy_me_dreg`
2. `_enataromau_sita`
3. `iva_da,_raluqope`

**Context Size 2:**

1. `a_oqo_takarauta_y`
2. `i_ena_na_na_ni_ca`
3. `na_me_tuidini_va_`

**Context Size 3:**

1. `na_raraiti_e_dua_k`
2. `_na_vakasir_franx_`
3. `a_na_uciwaseinamat`

**Context Size 4:**

1. `_na_veiwale_e_vura_`
2. `_ni_sa_vakarai_na_t`
3. `vakaya_na_kai._rist`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (44,342 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 | 5,184 |
| Total Tokens | 136,582 |
| Mean Frequency | 26.35 |
| Median Frequency | 3 |
| Frequency Std Dev | 317.63 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | na | 17,507 |
| 2 | ni | 9,047 |
| 3 | e | 7,598 |
| 4 | ena | 4,309 |
| 5 | kei | 3,339 |
| 6 | dua | 3,228 |
| 7 | me | 2,753 |
| 8 | ka | 2,414 |
| 9 | kena | 1,753 |
| 10 | mai | 1,556 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | pumona | 2 |
| 2 | ilatilati | 2 |
| 3 | cervix | 2 |
| 4 | movement | 2 |
| 5 | citations | 2 |
| 6 | translation | 2 |
| 7 | feminisimi | 2 |
| 8 | vakademografi | 2 |
| 9 | iceruniduka | 2 |
| 10 | balisi | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1690 |
| R² (Goodness of Fit) | 0.991059 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 63.9% |
| Top 1,000 | 88.2% |
| Top 5,000 | 99.7% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9911 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 63.9% of corpus
- **Long Tail:** -4,816 words needed for remaining 100.0% 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 | 0.3441 🏆 | 0.5376 | N/A | N/A |
| **mono_64d** | 64 | 0.0516 | 0.5508 | N/A | N/A |
| **mono_128d** | 128 | 0.0106 | 0.5737 | N/A | N/A |
| **aligned_32d** | 32 | 0.3441 | 0.5520 | 0.0100 | 0.1140 |
| **aligned_64d** | 64 | 0.0516 | 0.5538 | 0.0100 | 0.0700 |
| **aligned_128d** | 128 | 0.0106 | 0.5479 | 0.0100 | 0.0600 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.3441 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.5526. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.0% 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 | **0.058** | 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 |
|--------|----------|
| `-va` | vakavuniwai, vakabauti, vakasamataki |
| `-vak` | vakavuniwai, vakabauti, vakasamataki |
| `-vaka` | vakavuniwai, vakabauti, vakasamataki |
| `-ve` | veikau, veitokoni, veibasai |
| `-vei` | veikau, veitokoni, veibasai |
| `-ma` | malea, makawa, matasawa |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | ikoya, ijipita, república |
| `-i` | enijilisi, itaviqaravi, piqi |
| `-ki` | vakasamataki, vakayaloqaqataki, daramaki |
| `-aki` | vakasamataki, vakayaloqaqataki, daramaki |
| `-ka` | rawarataka, lifuka, taqomaka |
| `-taki` | vakasamataki, vakayaloqaqataki, yalataki |
| `-ni` | lesoni, sakini, nabavuni |
| `-aka` | rawarataka, taqomaka, marautaka |

### 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 |
|------|----------|------------------|----------|
| `atak` | 1.45x | 18 contexts | mataka, vuataka, muataka |
| `akat` | 1.41x | 18 contexts | jakata, vakatui, vakatau |
| `kata` | 1.34x | 15 contexts | jakata, vakatau, vakatani |
| `itak` | 1.41x | 12 contexts | nuitaki, beitaki, kuitaki |
| `akar` | 1.34x | 12 contexts | vakaro, jakarta, vakarua |
| `veiv` | 1.45x | 9 contexts | veivala, veivola, veivula |
| `eiva` | 1.50x | 8 contexts | veivala, teivaka, teivaki |
| `akav` | 1.36x | 10 contexts | cakava, vakavo, rakavi |
| `akac` | 1.47x | 8 contexts | vakaca, vakacava, vakacegu |
| `ivak` | 1.43x | 8 contexts | teivaka, teivaki, ivakaro |
| `amat` | 1.46x | 7 contexts | tamata, squamata, matamata |
| `kara` | 1.40x | 7 contexts | karamu, ankara, vakarau |

### 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 |
|--------|--------|-----------|----------|
| `-va` | `-i` | 199 words | vakaoqori, vakaduri |
| `-va` | `-a` | 186 words | vakatubura, vakawasoma |
| `-ve` | `-i` | 126 words | veitiki, veitauni |
| `-va` | `-ki` | 79 words | vakaituvakitaki, vakarerevaki |
| `-va` | `-aki` | 75 words | vakaituvakitaki, vakarerevaki |
| `-va` | `-taki` | 70 words | vakaituvakitaki, vakamatautaki |
| `-va` | `-ka` | 58 words | vakatayaloyalotaka, vakasamataka |
| `-ve` | `-ki` | 52 words | veitiki, veiwalitaki |
| `-ve` | `-aki` | 48 words | veiwalitaki, veivakabulabulataki |
| `-ve` | `-a` | 45 words | vekita, venezuela |

### 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 |
|------|-----------------|------------|------|
| veivosakitaki | **`vei-vosa-ki-taki`** | 7.5 | `vosa` |
| vakaikuritaki | **`vaka-ikuri-taki`** | 6.0 | `ikuri` |
| veivosaki | **`vei-vosa-ki`** | 6.0 | `vosa` |
| vakatikina | **`vaka-tiki-na`** | 6.0 | `tiki` |
| vakabulabulataki | **`vaka-bulabula-taki`** | 6.0 | `bulabula` |
| vakatututaki | **`vaka-tutu-taki`** | 6.0 | `tutu` |
| vakasucuna | **`vaka-sucu-na`** | 6.0 | `sucu` |
| veiyasana | **`vei-yasa-na`** | 6.0 | `yasa` |
| vakagalalataki | **`vaka-galala-taki`** | 6.0 | `galala` |
| vakalewena | **`vaka-lewe-na`** | 6.0 | `lewe` |
| vakawaicalataki | **`vaka-waicala-taki`** | 6.0 | `waicala` |
| vakaduiduitaki | **`vaka-duidui-taki`** | 6.0 | `duidui` |
| vakadodonutaki | **`vaka-dodonu-taki`** | 6.0 | `dodonu` |
| veitinani | **`vei-tina-ni`** | 6.0 | `tina` |
| veitacini | **`vei-taci-ni`** | 6.0 | `taci` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Fijian 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 | **32k BPE** | Best compression (4.56x) |
| N-gram | **2-gram** | Lowest perplexity (135) |
| Markov | **Context-4** | Highest predictability (94.6%) |
| 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: 2026-01-04 14:43:20*