---
language: tok
language_name: Toki Pona
language_family: constructed_auxlang
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-constructed_auxlang
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: 3.877
  - name: best_isotropy
    type: isotropy
    value: 0.6399
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

# Toki Pona - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Toki Pona** 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** | 3.658x | 3.66 | 0.3119% | 237,881 |
| **16k** | 3.744x | 3.75 | 0.3192% | 232,450 |
| **32k** | 3.840x | 3.84 | 0.3274% | 226,638 |
| **64k** | 3.877x 🏆 | 3.88 | 0.3306% | 224,433 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `li jan pi li sona mute lon ijo lili pi wan awen pi .`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁li ▁jan ▁pi ▁li ▁sona ▁mute ▁lon ▁ijo ▁lili ▁pi ... (+4 more)` | 14 |
| 16k | `▁li ▁jan ▁pi ▁li ▁sona ▁mute ▁lon ▁ijo ▁lili ▁pi ... (+4 more)` | 14 |
| 32k | `▁li ▁jan ▁pi ▁li ▁sona ▁mute ▁lon ▁ijo ▁lili ▁pi ... (+4 more)` | 14 |
| 64k | `▁li ▁jan ▁pi ▁li ▁sona ▁mute ▁lon ▁ijo ▁lili ▁pi ... (+4 more)` | 14 |

**Sample 2:** `luka jan li jo e . jan li ken pilin li ken tawa e ijo kepeken palisa luka. ona l...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁luka ▁jan ▁li ▁jo ▁e ▁. ▁jan ▁li ▁ken ▁pilin ... (+15 more)` | 25 |
| 16k | `▁luka ▁jan ▁li ▁jo ▁e ▁. ▁jan ▁li ▁ken ▁pilin ... (+15 more)` | 25 |
| 32k | `▁luka ▁jan ▁li ▁jo ▁e ▁. ▁jan ▁li ▁ken ▁pilin ... (+15 more)` | 25 |
| 64k | `▁luka ▁jan ▁li ▁jo ▁e ▁. ▁jan ▁li ▁ken ▁pilin ... (+15 more)` | 25 |

**Sample 3:** `thumb telo suli Kasipi anu telo suli Kasa li telo sike suli lon ma Elasija. ma E...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁thumb ▁telo ▁suli ▁kasi pi ▁anu ▁telo ▁suli ▁kasa ▁li ... (+21 more)` | 31 |
| 16k | `▁thumb ▁telo ▁suli ▁kasi pi ▁anu ▁telo ▁suli ▁kasa ▁li ... (+21 more)` | 31 |
| 32k | `▁thumb ▁telo ▁suli ▁kasipi ▁anu ▁telo ▁suli ▁kasa ▁li ▁telo ... (+20 more)` | 30 |
| 64k | `▁thumb ▁telo ▁suli ▁kasipi ▁anu ▁telo ▁suli ▁kasa ▁li ▁telo ... (+20 more)` | 30 |


### Key Findings

- **Best Compression:** 64k achieves 3.877x compression
- **Lowest UNK Rate:** 8k with 0.3119% 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 | 1,784 | 10.80 | 8,596 | 35.0% | 71.9% |
| **2-gram** | Subword | 173 🏆 | 7.44 | 3,590 | 80.8% | 98.6% |
| **3-gram** | Word | 9,356 | 13.19 | 26,212 | 15.8% | 40.7% |
| **3-gram** | Subword | 827 | 9.69 | 18,670 | 47.9% | 88.1% |
| **4-gram** | Word | 25,228 | 14.62 | 48,455 | 8.7% | 24.5% |
| **4-gram** | Subword | 2,554 | 11.32 | 53,488 | 30.6% | 73.0% |
| **5-gram** | Word | 22,731 | 14.47 | 33,862 | 7.1% | 21.0% |
| **5-gram** | Subword | 5,661 | 12.47 | 80,304 | 22.6% | 58.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ona li` | 8,041 |
| 2 | `pi ma` | 5,270 |
| 3 | `li lon` | 4,710 |
| 4 | `li kama` | 3,919 |
| 5 | `lon ma` | 3,858 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `la ona li` | 2,256 |
| 2 | `li jo e` | 2,192 |
| 3 | `tenpo sike nanpa` | 1,954 |
| 4 | `li pana e` | 1,213 |
| 5 | `li pali e` | 1,206 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tenpo sike nanpa la` | 920 |
| 2 | `li toki e ni` | 711 |
| 3 | `lon tenpo sike nanpa` | 681 |
| 4 | `ona li jo e` | 467 |
| 5 | `li lon poka pi` | 395 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tan lipu panton la o` | 310 |
| 2 | `ni li tan lipu panton` | 310 |
| 3 | `li tan lipu panton la` | 310 |
| 4 | `lipu panton la o lukin` | 308 |
| 5 | `li lon poka pi ma` | 271 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _` | 121,798 |
| 2 | `a _` | 110,798 |
| 3 | `_ l` | 95,333 |
| 4 | `n _` | 82,681 |
| 5 | `l i` | 79,391 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l i _` | 59,912 |
| 2 | `_ l i` | 52,409 |
| 3 | `m a _` | 35,268 |
| 4 | `a n _` | 30,697 |
| 5 | `_ p i` | 28,301 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l i _` | 43,280 |
| 2 | `_ m a _` | 22,649 |
| 3 | `_ p i _` | 22,047 |
| 4 | `j a n _` | 18,891 |
| 5 | `_ j a n` | 18,294 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ j a n _` | 17,670 |
| 2 | `a _ l i _` | 14,888 |
| 3 | `_ l o n _` | 13,719 |
| 4 | `t o k i _` | 11,203 |
| 5 | `_ o n a _` | 10,033 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 173
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~58% 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 | 0.1889 | 1.140 | 2.20 | 65,460 | 81.1% |
| **1** | Subword | 0.1801 | 1.133 | 2.48 | 25,715 | 82.0% |
| **2** | Word | 0.2377 | 1.179 | 1.82 | 143,545 | 76.2% |
| **2** | Subword | 0.1739 | 1.128 | 1.96 | 63,776 | 82.6% |
| **3** | Word | 0.2300 | 1.173 | 1.49 | 260,140 | 77.0% |
| **3** | Subword | 0.2523 | 1.191 | 1.88 | 124,781 | 74.8% |
| **4** | Word | 0.1262 🏆 | 1.091 | 1.21 | 385,658 | 87.4% |
| **4** | Subword | 0.2531 | 1.192 | 1.58 | 234,227 | 74.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `li suli alansi tenpo sike nanpa pini soweli tawa lupa telo lili la nimi pi jan`
2. `ma osuman utala suli pi ma palata li kama tan ona li tan ona li sama`
3. `pi telo kajolawe la jan alonola en nena mama ona ona lon sowikino li jo e`

**Context Size 2:**

1. `ona li nanpa lili li pana lukin e ilo utala wawa pi pali pi tenpo weka akesi`
2. `pi ma pilisin li kepeken toki inli nasin telo suli ni li lon anpa toki aja la`
3. `li lon mun ante nasin ni li kalama musi kepeken kalama b li ken luka e palisa`

**Context Size 3:**

1. `la ona li pana e wile ona tawa kulupu pi jan panko ona li utala lon kulupu ante`
2. `li jo e kalama pi toki alapi li jo e ante mute pi poka ali la ona li`
3. `tenpo sike nanpa la jan mase besenson li lawa e ale li lon li ken kama kon wawa`

**Context Size 4:**

1. `tenpo sike nanpa la kulupu talipan li weka e lawa epanja lon ma tomo kapite tenpo sike la utala`
2. `li toki e ni sina o tomo e ona ante ni li pali lili taso utala ma nanpa tu`
3. `lon tenpo sike nanpa tenpo poka la ilo pokalo ante en ilo kalama pi ilo pokalo ala li kama`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ja,_а_to_1259_p`
2. `akama_li"ki_mula`
3. `ike_matosupinuli`

**Context Size 2:**

1. `i_janu_ma_ma_li_p`
2. `a_sin:_ma_tomolig`
3. `_lawili_ma_alin_l`

**Context Size 3:**

1. `li_konsun._jan_jak`
2. `_lipu_konnanpa_waw`
3. `ma_ona._toki_la,_l`

**Context Size 4:**

1. `_li_pi_musi_suli_ma`
2. `_ma_pi_tosi._tenpo_`
3. `_pi_mani_tawa_jan_l`


### Key Findings

- **Best Predictability:** Context-4 (word) with 87.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (234,227 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 | 8,403 |
| Total Tokens | 501,701 |
| Mean Frequency | 59.70 |
| Median Frequency | 3 |
| Frequency Std Dev | 806.61 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | li | 44,539 |
| 2 | ma | 23,946 |
| 3 | pi | 22,102 |
| 4 | jan | 18,961 |
| 5 | e | 18,959 |
| 6 | lon | 15,067 |
| 7 | la | 13,426 |
| 8 | ona | 12,375 |
| 9 | toki | 11,308 |
| 10 | ni | 10,869 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | insensi | 2 |
| 2 | sowe | 2 |
| 3 | kokusi | 2 |
| 4 | kalakowan | 2 |
| 5 | joyce | 2 |
| 6 | paleotti | 2 |
| 7 | puwi | 2 |
| 8 | mansuko | 2 |
| 9 | mapalen | 2 |
| 10 | pamilika | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1358 |
| R² (Goodness of Fit) | 0.948458 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 84.0% |
| Top 1,000 | 95.0% |
| Top 5,000 | 98.6% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9485 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 84.0% of corpus
- **Long Tail:** -1,597 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 | 0.6399 🏆 | 0.3743 | N/A | N/A |
| **mono_64d** | 64 | 0.3162 | 0.3433 | N/A | N/A |
| **mono_128d** | 128 | 0.0458 | 0.3341 | N/A | N/A |
| **aligned_32d** | 32 | 0.6399 | 0.3702 | 0.0300 | 0.1700 |
| **aligned_64d** | 64 | 0.3162 | 0.3389 | 0.0440 | 0.1820 |
| **aligned_128d** | 128 | 0.0458 | 0.3383 | 0.0860 | 0.2240 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6399 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3498. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.6% 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 | **-0.638** | 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` | sakata, sukokala, susana |
| `-p` | pita, piko, pilanowa |
| `-a` | azərbaycanlı, aqui, akutu |
| `-t` | tuson, tumu, tiktok |
| `-k` | kanesika, khalsa, kaponala |
| `-m` | martini, monde, musicanticum |
| `-l` | lakuna, loekito, lija |
| `-n` | netunu, nws, nu |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | ejupoja, kanesika, pita |
| `-n` | tuson, ān, kilokan |
| `-i` | martini, wedi, aqui |
| `-e` | giuseppe, monde, ee |
| `-o` | 1ilo, piko, loekito |
| `-u` | ru, akutu, tumu |
| `-an` | kilokan, pusan, lilan |
| `-ja` | ejupoja, lija, pewija |

### 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 |
|------|----------|------------------|----------|
| `tenp` | 2.12x | 9 contexts | tenpi, tenpo, nitenpo |
| `nanp` | 1.96x | 5 contexts | nanpa, tunanpa, nanpajan |
| `enpo` | 2.15x | 4 contexts | tenpo, penpo, nitenpo |

### 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 |
|--------|--------|-----------|----------|
| `-k` | `-a` | 74 words | kanesika, khalsa |
| `-s` | `-a` | 63 words | sakata, sukokala |
| `-p` | `-a` | 62 words | pita, pilanowa |
| `-s` | `-n` | 59 words | sonun, sunokulupusitelen |
| `-a` | `-a` | 53 words | alapama, antasika |
| `-p` | `-n` | 46 words | pusan, polijan |
| `-k` | `-n` | 44 words | kilokan, kann |
| `-k` | `-i` | 41 words | koseli, kalali |
| `-m` | `-a` | 36 words | mila, maka |
| `-l` | `-a` | 32 words | lakuna, lija |

### 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 |
|------|-----------------|------------|------|
| romanoslipu | **`romanos-li-pu`** | 7.5 | `li` |
| lilikalama | **`li-li-kalama`** | 7.5 | `kalama` |
| mesijawiki | **`mesija-wi-ki`** | 7.5 | `wi` |
| nijonnimi | **`nijon-ni-mi`** | 7.5 | `ni` |
| sonalinja | **`so-na-linja`** | 7.5 | `linja` |
| tawalinja | **`ta-wa-linja`** | 7.5 | `linja` |
| nanpasike | **`nanpa-si-ke`** | 7.5 | `si` |
| castellano | **`castell-an-o`** | 7.5 | `an` |
| insijenapoli | **`insijena-po-li`** | 7.5 | `po` |
| mamasitelen | **`ma-ma-sitelen`** | 7.5 | `sitelen` |
| lasinatoki | **`lasina-to-ki`** | 7.5 | `to` |
| pinikepeke | **`pi-ni-kepeke`** | 7.5 | `kepeke` |
| europanto | **`europ-an-to`** | 7.5 | `an` |
| kalalinuna | **`kalalinu-n-a`** | 7.5 | `n` |
| monsipoka | **`monsi-po-ka`** | 7.5 | `po` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Toki Pona 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 (3.88x) |
| N-gram | **2-gram** | Lowest perplexity (173) |
| Markov | **Context-4** | Highest predictability (87.4%) |
| 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 01:32:14*