README.md

---
language: io
language_name: Ido
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: 4.198
  - name: best_isotropy
    type: isotropy
    value: 0.7983
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ido** 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** | 3.502x | 3.50 | 0.1398% | 1,043,846 |
| **16k** | 3.779x | 3.78 | 0.1508% | 967,447 |
| **32k** | 4.003x | 4.00 | 0.1597% | 913,354 |
| **64k** | 4.198x 🏆 | 4.20 | 0.1675% | 870,791 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Surabaya esas urbo en Indonezia. Segun statistiki dil yaro ol havis habitanti. L...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁su ra ba ya ▁esas ▁urbo ▁en ▁indonezia . ▁segun ... (+22 more)` | 32 |
| 16k | `▁sura ba ya ▁esas ▁urbo ▁en ▁indonezia . ▁segun ▁statistiki ... (+21 more)` | 31 |
| 32k | `▁sura ba ya ▁esas ▁urbo ▁en ▁indonezia . ▁segun ▁statistiki ... (+21 more)` | 31 |
| 64k | `▁sura baya ▁esas ▁urbo ▁en ▁indonezia . ▁segun ▁statistiki ▁dil ... (+20 more)` | 30 |

**Sample 2:** `Alessandro Algardi (n. ye la 27ma di novembro til la 10ma di junio esis Italiana...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁al es sand ro ▁algar di ▁( n . ▁ye ... (+25 more)` | 35 |
| 16k | `▁alessandro ▁algar di ▁( n . ▁ye ▁la ▁ 2 ... (+20 more)` | 30 |
| 32k | `▁alessandro ▁algar di ▁( n . ▁ye ▁la ▁ 2 ... (+20 more)` | 30 |
| 64k | `▁alessandro ▁algardi ▁( n . ▁ye ▁la ▁ 2 7 ... (+19 more)` | 29 |

**Sample 3:** `127 aK <--> 125 aK / 2ma yarcento aK Eventi Naski Morti Demetrius 2ma, rejo di S...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 1 2 7 ▁ak ▁<--> ▁ 1 2 5 ... (+26 more)` | 36 |
| 16k | `▁ 1 2 7 ▁ak ▁<--> ▁ 1 2 5 ... (+26 more)` | 36 |
| 32k | `▁ 1 2 7 ▁ak ▁<--> ▁ 1 2 5 ... (+24 more)` | 34 |
| 64k | `▁ 1 2 7 ▁ak ▁<--> ▁ 1 2 5 ... (+22 more)` | 32 |


### Key Findings

- **Best Compression:** 64k achieves 4.198x compression
- **Lowest UNK Rate:** 8k with 0.1398% 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 | 6,638 | 12.70 | 110,517 | 24.1% | 59.4% |
| **2-gram** | Subword | 268 🏆 | 8.07 | 6,097 | 67.9% | 99.3% |
| **3-gram** | Word | 11,261 | 13.46 | 195,686 | 21.4% | 52.5% |
| **3-gram** | Subword | 1,922 | 10.91 | 41,403 | 28.8% | 75.7% |
| **4-gram** | Word | 22,731 | 14.47 | 409,855 | 19.3% | 45.9% |
| **4-gram** | Subword | 8,112 | 12.99 | 211,688 | 16.0% | 50.4% |
| **5-gram** | Word | 26,396 | 14.69 | 378,626 | 19.1% | 42.8% |
| **5-gram** | Subword | 22,092 | 14.43 | 608,475 | 11.3% | 38.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `la mezvalora` | 36,791 |
| 2 | `en la` | 36,605 |
| 3 | `de la` | 33,305 |
| 4 | `o pluse` | 25,103 |
| 5 | `yari o` | 24,921 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `yari o pluse` | 24,876 |
| 2 | `65 yari o` | 18,786 |
| 3 | `min kam 18` | 18,694 |
| 4 | `kam 18 yari` | 18,691 |
| 5 | `la mezvalora revenuo` | 18,348 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `65 yari o pluse` | 18,782 |
| 2 | `min kam 18 yari` | 18,690 |
| 3 | `evante min kam 18` | 18,058 |
| 4 | `evante 65 yari o` | 17,999 |
| 5 | `la demografiala kontado di` | 13,448 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `evante min kam 18 yari` | 18,055 |
| 2 | `evante 65 yari o pluse` | 17,995 |
| 3 | `segun la demografiala kontado di` | 13,417 |
| 4 | `vivis sub la povreso lineo` | 11,202 |
| 5 | `esas plene lektebla en ido` | 11,081 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 1,248,693 |
| 2 | `o _` | 1,110,924 |
| 3 | `_ e` | 871,258 |
| 4 | `_ d` | 779,897 |
| 5 | `l a` | 719,367 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l a _` | 510,264 |
| 2 | `_ d i` | 407,611 |
| 3 | `_ l a` | 400,860 |
| 4 | `i s _` | 310,545 |
| 5 | `_ e s` | 287,503 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l a _` | 353,604 |
| 2 | `_ d i _` | 277,290 |
| 3 | `o _ d i` | 199,478 |
| 4 | `_ e n _` | 177,757 |
| 5 | `e s i s` | 177,202 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e s i s _` | 168,704 |
| 2 | `o _ d i _` | 160,395 |
| 3 | `_ e s i s` | 149,207 |
| 4 | `e s a s _` | 121,319 |
| 5 | `_ e s a s` | 107,177 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 268
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~39% 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 | 0.9058 | 1.874 | 7.11 | 203,018 | 9.4% |
| **1** | Subword | 0.8797 | 1.840 | 6.18 | 2,897 | 12.0% |
| **2** | Word | 0.3104 | 1.240 | 1.87 | 1,423,283 | 69.0% |
| **2** | Subword | 0.8077 | 1.750 | 4.92 | 17,895 | 19.2% |
| **3** | Word | 0.1238 | 1.090 | 1.27 | 2,624,412 | 87.6% |
| **3** | Subword | 0.7203 | 1.648 | 3.90 | 88,062 | 28.0% |
| **4** | Word | 0.0636 🏆 | 1.045 | 1.13 | 3,294,506 | 93.6% |
| **4** | Subword | 0.6809 | 1.603 | 3.13 | 342,746 | 31.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `la urbo amontis a polonia e polona linguo esas turkiana distrikto sieradz komono sideyo końskowola 6`
2. `di iulius caesar vetero pos la demografiala kontado di qui rezidis en provinco białystok e to`
3. `e kinadek e resursi nome illinois usa segun la mezvalora evo esis dum la 28ma di`

**Context Size 2:**

1. `la mezvalora revenuo po familio esis 3 01 personi la procento di habitanti segun evo esis 18`
2. `en la montari serra do mar e zapolyarni referi distrikto yamal nenec e republiko komi denisovka vila...`
3. `de la prezidanto di peru n józef cyrankiewicz chefministro di japonia n chadwick boseman usan aktoro...`

**Context Size 3:**

1. `yari o pluse esis 102 5 viri la mezvalora revenuo po familio esis 38 750 kontre 26 250`
2. `65 yari o pluse qua vivis sole la mezvalora grandeso po hemanaro esis 2 80 personi e la`
3. `min kam 18 yari 7 9 de 18 til 24 yari 27 9 de 25 til 44 yari`

**Context Size 4:**

1. `65 yari o pluse la mezvalora evo esis 29 yari po singla 100 mulieri esis 90 9 viri po`
2. `min kam 18 yari 7 6 de 18 til 24 yari 30 7 de 25 til 44 yari 20`
3. `evante min kam 18 yari en la domo 41 4 esis mariajita e habitis kune en 18 5 muliero`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_e_mbi_e_eri_vik`
2. `adi,_mepha_lamia`
3. `itam_adiestrista`

**Context Size 2:**

1. `a_sen_8_yaro_estr`
2. `o_pozukto_(n._cia`
3. `_esis_milietri._c`

**Context Size 3:**

1. `la_di_ventora_graf`
2. `_dil_24_yarmin_kam`
3. `_la_un_l'ado_e_la_`

**Context Size 4:**

1. `_la_denseso_portuo_`
2. `_di_esis_hemanaro_o`
3. `o_di_interko_di_rus`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (342,746 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 | 101,186 |
| Total Tokens | 7,375,821 |
| Mean Frequency | 72.89 |
| Median Frequency | 4 |
| Frequency Std Dev | 2039.44 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | la | 358,980 |
| 2 | di | 277,525 |
| 3 | e | 204,731 |
| 4 | en | 181,179 |
| 5 | de | 158,269 |
| 6 | esis | 149,214 |
| 7 | esas | 107,376 |
| 8 | yari | 80,594 |
| 9 | 0 | 61,043 |
| 10 | dil | 50,131 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | fekala | 2 |
| 2 | 24h | 2 |
| 3 | pisuisse | 2 |
| 4 | gilliams | 2 |
| 5 | stokely | 2 |
| 6 | arĝentisto | 2 |
| 7 | servisoj | 2 |
| 8 | kandelingi | 2 |
| 9 | aplicata | 2 |
| 10 | tarcisius | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2179 |
| R² (Goodness of Fit) | 0.996161 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 50.8% |
| Top 1,000 | 78.9% |
| Top 5,000 | 88.8% |
| Top 10,000 | 92.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9962 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 50.8% of corpus
- **Long Tail:** 91,186 words needed for remaining 7.6% 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 | 0.7983 | 0.3307 | N/A | N/A |
| **mono_64d** | 64 | 0.7791 | 0.2594 | N/A | N/A |
| **mono_128d** | 128 | 0.7299 | 0.2100 | N/A | N/A |
| **aligned_32d** | 32 | 0.7983 🏆 | 0.3377 | 0.1260 | 0.5080 |
| **aligned_64d** | 64 | 0.7791 | 0.2656 | 0.2460 | 0.6360 |
| **aligned_128d** | 128 | 0.7299 | 0.2168 | 0.2800 | 0.6480 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7983 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2700. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 28.0% 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 | **0.105** | 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` | stolbova, skripta, sɔsˈnufka |
| `-a` | arnhim, avioni, adlard |
| `-k` | klozado, kano, kalm |
| `-ma` | makedonian, maher, macbride |
| `-b` | bret, beggars, bombard |
| `-m` | mineirão, mobilizita, millán |
| `-p` | pontono, probez, pirat |
| `-t` | turkian, templego, très |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | mobilizita, neseparebla, stolbova |
| `-o` | editero, pontono, mineirão |
| `-i` | cieli, enskriburi, slobodskoi |
| `-s` | ramis, beggars, efstratios |
| `-e` | opolskie, macbride, impe |
| `-n` | millán, turkian, makedonian |
| `-ta` | mobilizita, skripta, dicinta |
| `-ra` | letra, teklinowopropra, mieczkipropra |

### 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 |
|------|----------|------------------|----------|
| `vant` | 1.93x | 47 contexts | vanto, avant, levant |
| `olon` | 1.90x | 45 contexts | solon, polon, rolon |
| `trik` | 1.97x | 36 contexts | triki, striki, striko |
| `abit` | 2.17x | 23 contexts | habiti, habito, abitov |
| `istr` | 1.76x | 49 contexts | istra, istro, istros |
| `kont` | 1.74x | 48 contexts | kontr, konto, konti |
| `metr` | 1.85x | 32 contexts | metro, metri, metra |
| `itan` | 1.46x | 82 contexts | eitan, titan, titano |
| `rovi` | 1.77x | 34 contexts | rovin, trovis, provis |
| `habi` | 2.02x | 18 contexts | habis, habib, dhabi |
| `ovin` | 1.84x | 23 contexts | rovin, lovin, bovino |
| `omet` | 1.76x | 26 contexts | comet, domett, dometo |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-s` | `-a` | 143 words | senoia, senforma |
| `-k` | `-a` | 138 words | kalorizita, kruˈlɛfska |
| `-k` | `-o` | 127 words | kaloro, kreinto |
| `-p` | `-o` | 121 words | pleanto, poniardago |
| `-p` | `-a` | 119 words | prishtina, progresema |
| `-a` | `-o` | 113 words | anulo, arbusto |
| `-a` | `-a` | 101 words | andréa, australa |
| `-s` | `-o` | 88 words | sanatorio, sproso |
| `-d` | `-a` | 82 words | dekesisesma, dalayna |
| `-p` | `-s` | 76 words | pezas, pleasures |

### 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 |
|------|-----------------|------------|------|
| davisboro | **`davisb-o-ro`** | 7.5 | `o` |
| personaro | **`person-a-ro`** | 7.5 | `a` |
| kompozado | **`kompoz-a-do`** | 7.5 | `a` |
| dinastiala | **`dinasti-a-la`** | 7.5 | `a` |
| militaral | **`milit-ar-al`** | 7.5 | `ar` |
| billboard | **`billbo-ar-d`** | 7.5 | `ar` |
| singulara | **`singu-la-ra`** | 7.5 | `la` |
| senmariajita | **`se-n-mariajita`** | 7.5 | `mariajita` |
| exercesis | **`exerce-s-is`** | 7.5 | `s` |
| grafikala | **`grafi-ka-la`** | 7.5 | `ka` |
| provincial | **`provinc-i-al`** | 7.5 | `i` |
| companheiro | **`companhe-i-ro`** | 7.5 | `i` |
| landskrona | **`landskr-o-na`** | 7.5 | `o` |
| konskriptis | **`ko-n-skriptis`** | 7.5 | `skriptis` |
| chanjesis | **`chanje-s-is`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ido 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 (4.20x) |
| N-gram | **2-gram** | Lowest perplexity (268) |
| Markov | **Context-4** | Highest predictability (93.6%) |
| 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: 2026-01-10 04:52:07*