README.md

---
language: sm
language_name: Samoan
language_family: austronesian_polynesian
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_polynesian
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: 3.699
  - name: best_isotropy
    type: isotropy
    value: 0.2278
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Samoan** 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** | 3.479x | 3.48 | 0.3471% | 262,440 |
| **16k** | 3.631x | 3.63 | 0.3622% | 251,487 |
| **32k** | 3.699x 🏆 | 3.70 | 0.3691% | 246,822 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Faleu o le motu i Samoa e tu i le va o Upolu ma Savai'i. E 354 tagata e nonofo i...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁faleu ▁o ▁le ▁motu ▁i ▁samoa ▁e ▁tu ▁i ▁le ... (+18 more)` | 28 |
| 16k | `▁faleu ▁o ▁le ▁motu ▁i ▁samoa ▁e ▁tu ▁i ▁le ... (+18 more)` | 28 |
| 32k | `▁faleu ▁o ▁le ▁motu ▁i ▁samoa ▁e ▁tu ▁i ▁le ... (+18 more)` | 28 |

**Sample 2:** `'O Porirua, 'o se pitonu'u o Ueligitone, e tū i le itū i mātū o Ueligitone. 'O l...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁' o ▁po rirua , ▁' o ▁se ▁pitonu ' ... (+35 more)` | 45 |
| 16k | `▁' o ▁porirua , ▁' o ▁se ▁pitonu ' u ... (+33 more)` | 43 |
| 32k | `▁' o ▁porirua , ▁' o ▁se ▁pitonu ' u ... (+33 more)` | 43 |

**Sample 3:** `Gagana Urdu o le igoa o se tasi o gagana sili e tautalagia i Asia i Saute. o se ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gagana ▁u rd u ▁o ▁le ▁igoa ▁o ▁se ▁tasi ... (+19 more)` | 29 |
| 16k | `▁gagana ▁urdu ▁o ▁le ▁igoa ▁o ▁se ▁tasi ▁o ▁gagana ... (+17 more)` | 27 |
| 32k | `▁gagana ▁urdu ▁o ▁le ▁igoa ▁o ▁se ▁tasi ▁o ▁gagana ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 32k achieves 3.699x compression
- **Lowest UNK Rate:** 8k with 0.3471% 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 | 1,420 | 10.47 | 5,447 | 34.7% | 69.5% |
| **2-gram** | Subword | 148 🏆 | 7.21 | 1,516 | 82.0% | 99.6% |
| **3-gram** | Word | 4,688 | 12.19 | 9,293 | 16.7% | 49.5% |
| **3-gram** | Subword | 941 | 9.88 | 9,076 | 43.7% | 85.0% |
| **4-gram** | Word | 8,012 | 12.97 | 14,168 | 15.4% | 36.7% |
| **4-gram** | Subword | 3,888 | 11.92 | 32,524 | 25.1% | 60.3% |
| **5-gram** | Word | 5,147 | 12.33 | 8,822 | 19.7% | 40.7% |
| **5-gram** | Subword | 9,558 | 13.22 | 54,942 | 16.3% | 44.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o le` | 9,077 |
| 2 | `i le` | 5,656 |
| 3 | `ma le` | 1,981 |
| 4 | `o se` | 1,645 |
| 5 | `ai le` | 934 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `le itu i` | 323 |
| 2 | `i totonu o` | 318 |
| 3 | `le tele o` | 314 |
| 4 | `i le itu` | 292 |
| 5 | `i le taimi` | 261 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i le itu i` | 270 |
| 2 | `i totonu o le` | 162 |
| 3 | `i luga o le` | 161 |
| 4 | `i le taimi o` | 148 |
| 5 | `ina ua mavae le` | 144 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i le taimi o le` | 117 |
| 2 | `le fuainumera o roma e` | 109 |
| 3 | `ma le numera i luma` | 109 |
| 4 | `i le fuainumera o roma` | 109 |
| 5 | `numera ina ua mavae le` | 109 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 53,637 |
| 2 | `e _` | 43,766 |
| 3 | `_ l` | 34,339 |
| 4 | `l e` | 32,460 |
| 5 | `i _` | 31,222 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e` | 26,576 |
| 2 | `l e _` | 26,204 |
| 3 | `_ o _` | 19,315 |
| 4 | `_ m a` | 14,321 |
| 5 | `o _ l` | 11,791 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e _` | 23,778 |
| 2 | `o _ l e` | 10,327 |
| 3 | `_ o _ l` | 10,137 |
| 4 | `i _ l e` | 8,107 |
| 5 | `a _ o _` | 6,868 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o _ l e _` | 9,763 |
| 2 | `_ o _ l e` | 8,925 |
| 3 | `i _ l e _` | 7,577 |
| 4 | `_ i _ l e` | 5,715 |
| 5 | `a _ l e _` | 4,253 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 148
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~44% 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 | 0.7561 | 1.689 | 4.50 | 15,898 | 24.4% |
| **1** | Subword | 0.7846 | 1.723 | 5.33 | 833 | 21.5% |
| **2** | Word | 0.3231 | 1.251 | 1.84 | 71,107 | 67.7% |
| **2** | Subword | 0.8391 | 1.789 | 4.50 | 4,437 | 16.1% |
| **3** | Word | 0.1599 | 1.117 | 1.31 | 130,468 | 84.0% |
| **3** | Subword | 0.7319 | 1.661 | 3.20 | 19,925 | 26.8% |
| **4** | Word | 0.0696 🏆 | 1.049 | 1.11 | 170,247 | 93.0% |
| **4** | Subword | 0.4868 | 1.401 | 2.10 | 63,588 | 51.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `le fasi vaega aai tagata saina iunite setete o le taimi lona tino o se tamaoaiga`
2. `o le ʻulu taumamao pick the pacific ma talitonuga i le tausaga e mafai ona tagata`
3. `i comoros ma aganu u ma o se tasi pe nautele e sumpini ma agafesootai faasalalauga`

**Context Size 2:**

1. `o le numera i luma 13 i saint léonard de noblat mau faasino o isi taaloga lauiloa`
2. `i le i umi a ua o le atunuu i matu ma i ni tausaga o le`
3. `ma le pulega a siamani sa ina ua maeʻa ona faʻaleaogaina le tulafono lea na faʻatulagaina e`

**Context Size 3:**

1. `le itu i sasae ma vao mago i le ogatotonu ma le taufaaiuiuga o le na faatoilaloina malo`
2. `i totonu o fale gaosi mea manogi ma le fuala au e a ai iai tagata`
3. `le tele o malaga militeli i amazonia ma na latou manumalo i au peretania ma holani na faʻatutuina`

**Context Size 4:**

1. `i le itu i matu i le ina ua manumalo ia mehmet ali o le na toe faafoi mai`
2. `i totonu o le taimi μ 2σ ma le mea e le ai μ o le galuega taua ona`
3. `i luga o le koluse e pei o le us ma fa atau atu i lapopo a masani po`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_chale_mailaʻa,j`
2. `aau_me_akma_ta_l`
3. `ino._ma_ve_o'ita`

**Context Size 2:**

1. `a_se_181_mafa'i_f`
2. `e_kalosi_e_faʻalo`
3. `_le_pala,_e_mesei`

**Context Size 3:**

1. `_le_o_featrodriver`
2. `le_tusitu_o_luga_f`
3. `_o_le_upu_i_le_lal`

**Context Size 4:**

1. `_le_masani_ma_pi'i_`
2. `o_le_fa'atatau_e_om`
3. `_o_le_vaomalo_o_le_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (63,588 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 | 6,946 |
| Total Tokens | 205,396 |
| Mean Frequency | 29.57 |
| Median Frequency | 4 |
| Frequency Std Dev | 439.18 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | le | 23,989 |
| 2 | o | 21,093 |
| 3 | i | 12,188 |
| 4 | e | 7,623 |
| 5 | ma | 6,494 |
| 6 | ai | 3,240 |
| 7 | se | 2,986 |
| 8 | fa | 2,814 |
| 9 | a | 2,774 |
| 10 | na | 2,325 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | eisleben | 2 |
| 2 | magdeburg | 2 |
| 3 | halle | 2 |
| 4 | saale | 2 |
| 5 | 451 | 2 |
| 6 | komiunisi | 2 |
| 7 | stasi | 2 |
| 8 | henryk | 2 |
| 9 | dominiak | 2 |
| 10 | tychy | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1786 |
| R² (Goodness of Fit) | 0.991320 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 63.2% |
| Top 1,000 | 86.7% |
| Top 5,000 | 98.1% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9913 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 63.2% of corpus
- **Long Tail:** -3,054 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 | 0.2278 🏆 | 0.4650 | N/A | N/A |
| **mono_64d** | 64 | 0.0423 | 0.4640 | N/A | N/A |
| **mono_128d** | 128 | 0.0056 | 0.4667 | N/A | N/A |
| **aligned_32d** | 32 | 0.2278 | 0.4475 | 0.0180 | 0.1140 |
| **aligned_64d** | 64 | 0.0423 | 0.4740 | 0.0100 | 0.1280 |
| **aligned_128d** | 128 | 0.0056 | 0.4559 | 0.0100 | 0.1320 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.2278 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4622. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.8% 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 | **-0.073** | 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 |
|--------|----------|
| `-a` | aofaiga, antoine, amaloloina |
| `-t` | taunuu, tamaloloa, tioata |
| `-s` | sofia, saita, siaki |
| `-fa` | faautauta, faatumauina, faamatalaina |
| `-ma` | macon, mataʻafa, maui |
| `-m` | macon, mataʻafa, maui |
| `-f` | faautauta, fetolofi, fuga |
| `-p` | perth, pa, portuguese |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | faautauta, aofaiga, tamaloloa |
| `-na` | faatumauina, amaloloina, faamatalaina |
| `-i` | fetolofi, igilisi, siaki |
| `-ga` | aofaiga, fuga, aleaga |
| `-e` | antoine, portuguese, die |
| `-ia` | sofia, alapenia, omia |
| `-o` | faalagolago, fono, lafo |
| `-n` | macon, region, australien |

### 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 |
|------|----------|------------------|----------|
| `faat` | 1.79x | 10 contexts | faatoa, faatau, faatonu |
| `usia` | 1.48x | 15 contexts | lusia, fusia, tusia |
| `aata` | 1.78x | 9 contexts | alaata, faatau, faatasi |
| `alol` | 1.56x | 11 contexts | malolo, malole, palolo |
| `atas` | 1.46x | 13 contexts | atasi, atasia, atassi |
| `amat` | 1.36x | 14 contexts | amata, tamato, mamate |
| `loga` | 1.51x | 10 contexts | iloga, aloga, pologa |
| `aʻat` | 1.86x | 6 contexts | faʻatau, faʻatasi, faʻatusa |
| `atal` | 1.30x | 15 contexts | atali, matala, atalii |
| `faas` | 1.65x | 7 contexts | faasee, faasao, faasoa |
| `tion` | 1.54x | 8 contexts | action, station, section |
| `mafa` | 1.56x | 7 contexts | mafai, mafaia, mamafa |

### 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 |
|--------|--------|-----------|----------|
| `-fa` | `-a` | 323 words | faautauta, faatumauina |
| `-a` | `-a` | 202 words | aofaiga, amaloloina |
| `-t` | `-a` | 140 words | tamaloloa, tioata |
| `-fa` | `-na` | 128 words | faatumauina, faamatalaina |
| `-fa` | `-ga` | 104 words | faʻasinomaga, faʻauʻuga |
| `-s` | `-a` | 70 words | sofia, saita |
| `-a` | `-na` | 67 words | amaloloina, aolaolaina |
| `-fa` | `-i` | 61 words | faafetaui, faamaoti |
| `-f` | `-a` | 61 words | faautauta, fuga |
| `-ma` | `-a` | 60 words | mataʻafa, manatuaina |

### 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 |
|------|-----------------|------------|------|
| faatapulaa | **`faatapul-a-a`** | 7.5 | `a` |
| mulimulitai | **`mulimuli-ta-i`** | 7.5 | `ta` |
| television | **`televis-i-on`** | 7.5 | `i` |
| atinaeina | **`atinae-i-na`** | 7.5 | `i` |
| faatulaga | **`fa-a-tulaga`** | 7.5 | `tulaga` |
| faʻamoemoeina | **`faʻamoemoe-i-na`** | 7.5 | `i` |
| faataunuuina | **`faataunuu-i-na`** | 7.5 | `i` |
| felagolagomai | **`felagolagom-a-i`** | 7.5 | `a` |
| mataituina | **`mataitu-i-na`** | 7.5 | `i` |
| faatosina | **`faato-si-na`** | 7.5 | `si` |
| faaitulagi | **`fa-a-itulagi`** | 7.5 | `itulagi` |
| limasefulu | **`li-ma-sefulu`** | 7.5 | `sefulu` |
| faʻatulaga | **`faʻatul-a-ga`** | 7.5 | `a` |
| fonotatalo | **`fonotat-a-lo`** | 7.5 | `a` |
| vaʻavaʻaia | **`vaʻavaʻ-a-ia`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Samoan 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 (3.70x) |
| N-gram | **2-gram** | Lowest perplexity (148) |
| Markov | **Context-4** | Highest predictability (93.0%) |
| 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: 2026-01-10 21:21:35*