---
language: nov
language_name: Novial
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: 4.293
  - name: best_isotropy
    type: isotropy
    value: 0.1555
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Novial** 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** | 3.864x | 3.87 | 0.0651% | 156,765 |
| **16k** | 4.098x | 4.11 | 0.0690% | 147,789 |
| **32k** | 4.293x 🏆 | 4.30 | 0.0723% | 141,092 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Li Isles Malukus (Moluccas) Es un archipelag in li orientale parte de Indonesia....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁li ▁isles ▁mal uk us ▁( mol uc cas ) ... (+15 more)` | 25 |
| 16k | `▁li ▁isles ▁mal uk us ▁( mol uc cas ) ... (+12 more)` | 22 |
| 32k | `▁li ▁isles ▁malukus ▁( moluccas ) ▁es ▁un ▁archipelag ▁in ... (+7 more)` | 17 |

**Sample 2:** `Little Rock es li maxim grandi urbe de Arkansas, Unionati States de Amerika.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁little ▁rock ▁es ▁li ▁maxim ▁grandi ▁urbe ▁de ▁ar k ... (+7 more)` | 17 |
| 16k | `▁little ▁rock ▁es ▁li ▁maxim ▁grandi ▁urbe ▁de ▁arkansas , ... (+5 more)` | 15 |
| 32k | `▁little ▁rock ▁es ▁li ▁maxim ▁grandi ▁urbe ▁de ▁arkansas , ... (+5 more)` | 15 |

**Sample 3:** `Eventes Naskos - George Gamow, rusi-usani fisikisto e skribiste de populari sien...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁eventes ▁naskos ▁- ▁george ▁gamow , ▁rusi - usani ▁fisikisto ... (+7 more)` | 17 |
| 16k | `▁eventes ▁naskos ▁- ▁george ▁gamow , ▁rusi - usani ▁fisikisto ... (+6 more)` | 16 |
| 32k | `▁eventes ▁naskos ▁- ▁george ▁gamow , ▁rusi - usani ▁fisikisto ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 32k achieves 4.293x compression
- **Lowest UNK Rate:** 8k with 0.0651% 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 | 1,178 | 10.20 | 3,283 | 41.9% | 75.7% |
| **2-gram** | Subword | 244 🏆 | 7.93 | 1,418 | 69.7% | 99.7% |
| **3-gram** | Word | 1,168 | 10.19 | 4,001 | 45.5% | 73.4% |
| **3-gram** | Subword | 1,771 | 10.79 | 10,056 | 28.4% | 76.4% |
| **4-gram** | Word | 2,024 | 10.98 | 7,221 | 38.8% | 61.9% |
| **4-gram** | Subword | 7,394 | 12.85 | 40,232 | 15.6% | 48.7% |
| **5-gram** | Word | 1,593 | 10.64 | 5,612 | 40.6% | 64.9% |
| **5-gram** | Subword | 16,261 | 13.99 | 72,530 | 11.2% | 38.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `in li` | 946 |
| 2 | `es li` | 745 |
| 3 | `ek li` | 622 |
| 4 | `de sud` | 594 |
| 5 | `sud afrika` | 563 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de sud afrika` | 551 |
| 2 | `kristiani demokrati partise` | 505 |
| 3 | `un ek li` | 313 |
| 4 | `es un ek` | 300 |
| 5 | `provinse de sud` | 289 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `es un ek li` | 296 |
| 2 | `provinse de sud afrika` | 289 |
| 3 | `es ek li nombro` | 278 |
| 4 | `demarcation board stats sa` | 278 |
| 5 | `li majoritate de lun` | 278 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `statistikes es ek li nombro` | 278 |
| 2 | `stats sa census page independent` | 278 |
| 3 | `independent electoral commission election results` | 278 |
| 4 | `page independent electoral commission election` | 278 |
| 5 | `census page independent electoral commission` | 278 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 34,143 |
| 2 | `i _` | 21,509 |
| 3 | `e s` | 19,756 |
| 4 | `_ d` | 17,368 |
| 5 | `d e` | 16,656 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 12,988 |
| 2 | `_ l i` | 10,620 |
| 3 | `e s _` | 10,569 |
| 4 | `l i _` | 9,707 |
| 5 | `d e _` | 8,712 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l i _` | 8,332 |
| 2 | `_ d e _` | 7,798 |
| 3 | `e _ d e` | 4,960 |
| 4 | `t i o n` | 4,248 |
| 5 | `_ e s _` | 4,034 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _ d e _` | 3,513 |
| 2 | `a t i o n` | 2,270 |
| 3 | `t i o n e` | 1,911 |
| 4 | `_ d e l _` | 1,822 |
| 5 | `_ p a r t` | 1,691 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 244
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~38% 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 | 0.7087 | 1.634 | 3.73 | 23,001 | 29.1% |
| **1** | Subword | 0.9408 | 1.920 | 6.71 | 573 | 5.9% |
| **2** | Word | 0.2002 | 1.149 | 1.39 | 85,181 | 80.0% |
| **2** | Subword | 0.9000 | 1.866 | 5.14 | 3,839 | 10.0% |
| **3** | Word | 0.0646 | 1.046 | 1.10 | 117,051 | 93.5% |
| **3** | Subword | 0.8231 | 1.769 | 3.63 | 19,730 | 17.7% |
| **4** | Word | 0.0276 🏆 | 1.019 | 1.05 | 128,096 | 97.2% |
| **4** | Subword | 0.5739 | 1.488 | 2.29 | 71,462 | 42.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `li ekonomia de vietnam binh vietnam kum y z z li traktate de sinema kino bioskop`
2. `de kwazulu natal provinse de basal supositione provisorim akseptat kel bli jeta plu tardim plu natur...`
3. `es li nombro demografie li rego de bbc news last kingdom de lingues sexu etnikiso politike`

**Context Size 2:**

1. `in li sud afrikal general elektione total votes 4 803 31 de total populatione partisevotes inkatha l...`
2. `es li chef urbe es durban li majoritate de lun 193 766 homes parla zulum nombro geografia`
3. `ek li komunies de karu distrikte de nord amerika li nederlandani antilles konsista ek tri asertiones...`

**Context Size 3:**

1. `kristiani demokrati partise unionati demokrati movemente 1 demokrati alianse pac libereso fronte afr...`
2. `un ek li komunies de metsweding distrikte de gauteng provinse de sud afrika li majoritate de lun 92`
3. `de sud afrika fro 14 de june in unionati regia es lande de sud amerika de chile`

**Context Size 4:**

1. `es un ek li distriktes de kwazulu natal provinse de sud afrika li majoritate de lun 32 279 homes`
2. `provinse de sud afrika li chef urbe es li urbe de saitama referos de japan`
3. `sa census page independent electoral commission election results de sud afrika`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_(ri_nkis_1"_]_7`
2. `ese_kan_u_le_enu`
3. `iari_fomesmbete_`

**Context Size 2:**

1. `e_sop_79,09li_nom`
2. `i_go_prolemokre_o`
3. `es_etteoli_pronal`

**Context Size 3:**

1. `_de_esentarabatal_`
2. `_li_yares_de_es_ek`
3. `es_un_spani_isaje_`

**Context Size 4:**

1. `_li_nur:_ove_you._l`
2. `_de_plu_tardim_tenn`
3. `e_de_sami_demokrati`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (71,462 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 | 9,838 |
| Total Tokens | 152,199 |
| Mean Frequency | 15.47 |
| Median Frequency | 3 |
| Frequency Std Dev | 140.97 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | li | 8,569 |
| 2 | de | 7,823 |
| 3 | es | 4,132 |
| 4 | e | 3,243 |
| 5 | in | 2,500 |
| 6 | del | 1,826 |
| 7 | partise | 1,098 |
| 8 | sud | 1,043 |
| 9 | demokrati | 1,042 |
| 10 | en | 921 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | markant | 2 |
| 2 | hosta | 2 |
| 3 | pompidou | 2 |
| 4 | jános | 2 |
| 5 | monet | 2 |
| 6 | impresionisme | 2 |
| 7 | orkestres | 2 |
| 8 | brahms | 2 |
| 9 | operas | 2 |
| 10 | match | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0314 |
| R² (Goodness of Fit) | 0.989703 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 45.2% |
| Top 1,000 | 75.4% |
| Top 5,000 | 92.8% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9897 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 45.2% of corpus
- **Long Tail:** -162 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 | 0.1555 🏆 | 0.4672 | N/A | N/A |
| **mono_64d** | 64 | 0.0258 | 0.4629 | N/A | N/A |
| **mono_128d** | 128 | 0.0036 | 0.4758 | N/A | N/A |
| **aligned_32d** | 32 | 0.1555 | 0.4481 | 0.0160 | 0.1600 |
| **aligned_64d** | 64 | 0.0258 | 0.4683 | 0.0300 | 0.1780 |
| **aligned_128d** | 128 | 0.0036 | 0.4627 | 0.0280 | 0.1860 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.1555 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4642. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.0% 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 | **0.702** | High formulaic/idiomatic 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` | sidney, states, strukture |
| `-a` | arrhenius, alpes, autonoma |
| `-m` | minutes, multes, morocco |
| `-p` | paleontologia, prendit, plural |
| `-k` | kolpa, kampionate, kolpes |
| `-b` | bulbizarre, biofisike, bloemfontein |
| `-d` | damajes, delon, dôme |
| `-t` | tipes, tekte, taiwan |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | bulbizarre, biofisike, kampionate |
| `-s` | racontas, damajes, arrhenius |
| `-es` | damajes, alpes, minutes |
| `-a` | paleontologia, kolpa, resista |
| `-i` | ri, landunionati, religiosi |
| `-ne` | anione, natione, opinione |
| `-o` | cargo, morocco, romejko |
| `-n` | roman, omnen, an |

### 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 |
|------|----------|------------------|----------|
| `tion` | 1.51x | 31 contexts | nation, lation, action |
| `arti` | 1.59x | 22 contexts | partie, martin, partim |
| `lekt` | 1.56x | 20 contexts | lekte, elekte, elekta |
| `atio` | 1.48x | 22 contexts | nation, lation, natione |
| `ekti` | 1.75x | 13 contexts | korekti, direkti, efektivi |
| `ktio` | 1.74x | 12 contexts | aktione, fiktione, funktione |
| `ling` | 1.67x | 12 contexts | lingo, lingua, lingue |
| `ente` | 1.33x | 23 contexts | enter, mente, vente |
| `onte` | 1.58x | 13 contexts | monte, fonte, ponte |
| `nter` | 1.35x | 17 contexts | inter, enter, konter |
| `iona` | 1.49x | 12 contexts | fiona, optional, rational |
| `ntes` | 1.38x | 14 contexts | entes, fontes, dentes |

### 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` | `-e` | 114 words | strukture, suksese |
| `-p` | `-e` | 105 words | politike, pasaje |
| `-k` | `-e` | 97 words | kampionate, kable |
| `-a` | `-e` | 81 words | anione, amerikaante |
| `-m` | `-e` | 79 words | mute, mamifere |
| `-d` | `-e` | 78 words | dôme, desisione |
| `-p` | `-s` | 76 words | paketes, probos |
| `-s` | `-s` | 70 words | states, studies |
| `-p` | `-es` | 59 words | paketes, partisevotes |
| `-p` | `-a` | 57 words | paleontologia, poza |

### 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 |
|------|-----------------|------------|------|
| praktisad | **`prakti-s-ad`** | 7.5 | `s` |
| kompletisat | **`kompleti-s-at`** | 7.5 | `s` |
| transfera | **`transf-e-ra`** | 7.5 | `e` |
| diferensa | **`diferen-s-a`** | 7.5 | `s` |
| medievali | **`mediev-al-i`** | 7.5 | `al` |
| religiosi | **`religio-s-i`** | 7.5 | `s` |
| skriptero | **`skript-e-ro`** | 7.5 | `e` |
| interretal | **`interre-t-al`** | 7.5 | `t` |
| development | **`develop-me-nt`** | 7.5 | `me` |
| skripteti | **`skript-e-ti`** | 7.5 | `e` |
| politikalim | **`politik-al-im`** | 7.5 | `al` |
| fisikalim | **`fisik-al-im`** | 7.5 | `al` |
| afrikansum | **`afrikan-s-um`** | 7.5 | `s` |
| kontenanti | **`konten-an-ti`** | 7.5 | `an` |
| periodale | **`period-al-e`** | 7.5 | `al` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Novial shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **32k BPE** | Best compression (4.29x) |
| N-gram | **2-gram** | Lowest perplexity (244) |
| Markov | **Context-4** | Highest predictability (97.2%) |
| 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 15:52:59*