---
language: ia
language_name: Interlingua
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: 4.964
  - name: best_isotropy
    type: isotropy
    value: 0.8062
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Interlingua** Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

## 📋 Repository Contents

### Models & Assets

- Tokenizers (8k, 16k, 32k, 64k)
- N-gram models (2, 3, 4, 5-gram)
- Markov chains (context of 1, 2, 3, 4 and 5)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions (aligned and unaligned)
- Language Vocabulary
- Language Statistics

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

### Analysis and Evaluation

- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
- [4. Vocabulary Analysis](#4-vocabulary-analysis)
- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
- [7. Summary & Recommendations](#7-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

![Tokenizer Fertility](visualizations/tokenizer_fertility.png)

![Tokenizer OOV](visualizations/tokenizer_oov.png)

![Total Tokens](visualizations/tokenizer_total_tokens.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 4.129x | 4.13 | 0.0662% | 490,604 |
| **16k** | 4.495x | 4.50 | 0.0721% | 450,618 |
| **32k** | 4.779x | 4.78 | 0.0767% | 423,878 |
| **64k** | 4.964x 🏆 | 4.97 | 0.0797% | 408,006 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Oklahoma City es le capital de Oklahoma, Statos Unite de America, in le contato ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁oklahoma ▁city ▁es ▁le ▁capital ▁de ▁oklahoma , ▁statos ▁unite ... (+17 more)` | 27 |
| 16k | `▁oklahoma ▁city ▁es ▁le ▁capital ▁de ▁oklahoma , ▁statos ▁unite ... (+17 more)` | 27 |
| 32k | `▁oklahoma ▁city ▁es ▁le ▁capital ▁de ▁oklahoma , ▁statos ▁unite ... (+17 more)` | 27 |
| 64k | `▁oklahoma ▁city ▁es ▁le ▁capital ▁de ▁oklahoma , ▁statos ▁unite ... (+17 more)` | 27 |

**Sample 2:** `Rusinga es un insula in le parte nordest de Laco Victoria e pertine a Kenya. In ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁rus ing a ▁es ▁un ▁insula ▁in ▁le ▁parte ▁nor ... (+33 more)` | 43 |
| 16k | `▁rus inga ▁es ▁un ▁insula ▁in ▁le ▁parte ▁nordest ▁de ... (+30 more)` | 40 |
| 32k | `▁rus inga ▁es ▁un ▁insula ▁in ▁le ▁parte ▁nordest ▁de ... (+30 more)` | 40 |
| 64k | `▁rus inga ▁es ▁un ▁insula ▁in ▁le ▁parte ▁nordest ▁de ... (+30 more)` | 40 |

**Sample 3:** `Casas de Guijarro es un municipalitate que se trova in le provincia de Cuenca, i...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁casas ▁de ▁gu ij ar ro ▁es ▁un ▁municipalitate ▁que ... (+22 more)` | 32 |
| 16k | `▁casas ▁de ▁gu ij arro ▁es ▁un ▁municipalitate ▁que ▁se ... (+21 more)` | 31 |
| 32k | `▁casas ▁de ▁gu ij arro ▁es ▁un ▁municipalitate ▁que ▁se ... (+21 more)` | 31 |
| 64k | `▁casas ▁de ▁guij arro ▁es ▁un ▁municipalitate ▁que ▁se ▁trova ... (+20 more)` | 30 |


### Key Findings

- **Best Compression:** 64k achieves 4.964x compression
- **Lowest UNK Rate:** 8k with 0.0662% 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 | 9,565 | 13.22 | 65,254 | 26.4% | 43.5% |
| **2-gram** | Subword | 200 🏆 | 7.65 | 4,997 | 75.8% | 99.4% |
| **3-gram** | Word | 10,048 | 13.29 | 84,416 | 29.4% | 44.3% |
| **3-gram** | Subword | 1,440 | 10.49 | 32,260 | 34.7% | 80.6% |
| **4-gram** | Word | 7,829 | 12.93 | 111,593 | 34.5% | 51.8% |
| **4-gram** | Subword | 7,014 | 12.78 | 150,126 | 19.6% | 50.1% |
| **5-gram** | Word | 3,186 | 11.64 | 63,744 | 39.7% | 64.3% |
| **5-gram** | Subword | 22,941 | 14.49 | 370,309 | 12.7% | 35.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `in le` | 55,568 |
| 2 | `es un` | 26,092 |
| 3 | `provincia de` | 20,168 |
| 4 | `que se` | 17,233 |
| 5 | `se trova` | 16,715 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `se trova in` | 16,409 |
| 2 | `que se trova` | 16,272 |
| 3 | `trova in le` | 15,902 |
| 4 | `in le provincia` | 14,747 |
| 5 | `le provincia de` | 13,549 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `que se trova in` | 16,238 |
| 2 | `se trova in le` | 15,889 |
| 3 | `trova in le provincia` | 14,472 |
| 4 | `in le provincia de` | 13,361 |
| 5 | `municipalitate que se trova` | 12,978 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `que se trova in le` | 15,792 |
| 2 | `se trova in le provincia` | 14,472 |
| 3 | `trova in le provincia de` | 13,137 |
| 4 | `un municipalitate que se trova` | 12,978 |
| 5 | `municipalitate que se trova in` | 12,977 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 891,207 |
| 2 | `n _` | 348,091 |
| 3 | `a _` | 345,002 |
| 4 | `d e` | 337,147 |
| 5 | `_ d` | 332,162 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 276,143 |
| 2 | `l e _` | 237,543 |
| 3 | `_ l e` | 219,619 |
| 4 | `t e _` | 182,433 |
| 5 | `d e _` | 178,815 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e _` | 208,922 |
| 2 | `_ d e _` | 159,871 |
| 3 | `_ i n _` | 122,513 |
| 4 | `_ d e l` | 83,921 |
| 5 | `d e l _` | 83,369 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e l _` | 82,961 |
| 2 | `n _ l e _` | 62,694 |
| 3 | `_ i n _ l` | 58,365 |
| 4 | `i n _ l e` | 56,016 |
| 5 | `_ q u e _` | 46,954 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 200
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.9014 | 1.868 | 6.61 | 153,361 | 9.9% |
| **1** | Subword | 0.8741 | 1.833 | 6.28 | 2,440 | 12.6% |
| **2** | Word | 0.3335 | 1.260 | 1.91 | 1,009,131 | 66.6% |
| **2** | Subword | 0.8487 | 1.801 | 4.86 | 15,325 | 15.1% |
| **3** | Word | 0.1169 | 1.084 | 1.21 | 1,914,967 | 88.3% |
| **3** | Subword | 0.7305 | 1.659 | 3.71 | 74,443 | 27.0% |
| **4** | Word | 0.0351 🏆 | 1.025 | 1.05 | 2,305,892 | 96.5% |
| **4** | Subword | 0.6102 | 1.526 | 2.76 | 276,390 | 39.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `le schola technic esseva membros cuje collaboration inter feminas le patrenostre patro nue kvu esten...`
2. `de civitas libera identificate plus parve insulas henery and technology applied in tote qui le inexa...`
3. `in nederlandthe dutch e isto da un cyclon refere a george f strauss publicava dece duo`

**Context Size 2:**

1. `in le ied marcate con le fabricas es usate in theoria e practica in le imperio byzantine`
2. `es un municipalitate que se trova in le historia de tabasco con predominio del agricultura mycenas e...`
3. `provincia de varese in le provincia de soria in le region de apulia in italia del nord`

**Context Size 3:**

1. `se trova in le provincia de castellon in le communitate autonome de castilia la mancha espania in gu...`
2. `que se trova in le provincia de lleida in catalonia espania illo ha un population de habitantes del`
3. `trova in le provincia de milano in le region del lombardia in italia illo ha un population de`

**Context Size 4:**

1. `que se trova in biscaya in le pais basc espania illo ha un population de habitantes del provincia de`
2. `se trova in le provincia de varese in le region del abruzzo in italia del abruzzo`
3. `trova in le provincia de guadalajara in le communitate autonome de castilia e leon espania in avila`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_cinisabalppreve`
2. `e_at_fiorell_ve_`
3. `afo_itene_justa_`

**Context Size 2:**

1. `e_paismonteratrap`
2. `n_a_e_de_molution`
3. `a_illopt._—,_sion`

**Context Size 3:**

1. `_de_humania,_e_gue`
2. `le_arra_in_espania`
3. `_le_usqui_hez_e_le`

**Context Size 4:**

1. `_le_quala_premie_es`
2. `_de_communa_como_si`
3. `_in_campo_que_recio`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (276,390 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 | 68,849 |
| Total Tokens | 2,897,665 |
| Mean Frequency | 42.09 |
| Median Frequency | 4 |
| Frequency Std Dev | 1319.86 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | le | 214,803 |
| 2 | de | 160,489 |
| 3 | in | 124,844 |
| 4 | un | 84,395 |
| 5 | del | 83,230 |
| 6 | e | 74,199 |
| 7 | es | 55,031 |
| 8 | que | 47,611 |
| 9 | se | 28,507 |
| 10 | a | 25,139 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | scotes | 2 |
| 2 | winchelsea | 2 |
| 3 | turbamento | 2 |
| 4 | löss | 2 |
| 5 | ductores | 2 |
| 6 | terpes | 2 |
| 7 | menapios | 2 |
| 8 | cananefates | 2 |
| 9 | sucedeva | 2 |
| 10 | sbn | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0457 |
| R² (Goodness of Fit) | 0.994554 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.6% |
| Top 1,000 | 69.0% |
| Top 5,000 | 84.1% |
| Top 10,000 | 89.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9946 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.6% of corpus
- **Long Tail:** 58,849 words needed for remaining 10.3% 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 | 0.8002 | 0.3587 | N/A | N/A |
| **mono_64d** | 64 | 0.8062 | 0.2657 | N/A | N/A |
| **mono_128d** | 128 | 0.7401 | 0.1964 | N/A | N/A |
| **aligned_32d** | 32 | 0.8002 | 0.3463 | 0.1700 | 0.5640 |
| **aligned_64d** | 64 | 0.8062 🏆 | 0.2608 | 0.3280 | 0.6860 |
| **aligned_128d** | 128 | 0.7401 | 0.1983 | 0.3720 | 0.7120 |

### Key Findings

- **Best Isotropy:** aligned_64d with 0.8062 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2710. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 37.2% 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 | **4.753** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.824** | 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` | seele, schermo, subsp |
| `-a` | avio, adolescentes, arana |
| `-c` | consulter, caesarion, correia |
| `-p` | posteriori, paise, propositional |
| `-b` | bacin, burguete, běhų |
| `-m` | millardo, matina, mercantilistic |
| `-ma` | matina, massarica, malteses |
| `-d` | denominationes, disfaceva, detallatemente |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | seele, ocurre, finistère |
| `-s` | lletres, denominationes, richessas |
| `-a` | nobunaga, disfaceva, arana |
| `-te` | humiliante, detallatemente, recepite |
| `-o` | avio, schermo, kontakto |
| `-es` | lletres, denominationes, adolescentes |
| `-n` | yinchuan, govorukhin, bacin |
| `-os` | arrestos, nativos, refractarios |

### 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 |
|------|----------|------------------|----------|
| `atio` | 2.17x | 95 contexts | latio, natio, ratio |
| `ento` | 2.31x | 68 contexts | tento, lento, bento |
| `itat` | 2.04x | 99 contexts | itate, mitate, citate |
| `alit` | 2.31x | 36 contexts | galit, aliter, halite |
| `lita` | 2.34x | 34 contexts | elita, lolita, hoplita |
| `enti` | 1.65x | 135 contexts | entia, senti, entis |
| `nter` | 1.90x | 54 contexts | inter, unter, enter |
| `lati` | 1.83x | 53 contexts | latio, latin, latino |
| `muni` | 2.20x | 22 contexts | munin, munich, muninca |
| `rova` | 2.02x | 25 contexts | trova, prova, provar |
| `ntia` | 2.21x | 18 contexts | entia, agentia, frantia |
| `ntes` | 1.92x | 26 contexts | antes, entes, contes |

### 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 |
|--------|--------|-----------|----------|
| `-c` | `-e` | 171 words | causative, caritative |
| `-c` | `-s` | 158 words | chessgames, cartuchas |
| `-p` | `-e` | 151 words | protestante, promittite |
| `-s` | `-e` | 139 words | subalterne, siete |
| `-c` | `-a` | 136 words | catta, cabella |
| `-p` | `-s` | 134 words | photos, pastas |
| `-a` | `-a` | 128 words | alfedena, acceptava |
| `-a` | `-s` | 121 words | accidentos, albans |
| `-a` | `-e` | 119 words | alteritate, adoptive |
| `-p` | `-a` | 106 words | pascha, pederasta |

### 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 |
|------|-----------------|------------|------|
| cortesano | **`cortes-a-no`** | 7.5 | `a` |
| revolveva | **`revolv-e-va`** | 7.5 | `e` |
| electromagnete | **`electromagn-e-te`** | 7.5 | `e` |
| extenderea | **`extender-e-a`** | 7.5 | `e` |
| neunkirchen | **`neunkirch-e-n`** | 7.5 | `e` |
| cubomedusas | **`cubomedu-s-as`** | 7.5 | `s` |
| taraporewala | **`taraporew-al-a`** | 7.5 | `al` |
| premisare | **`premis-ar-e`** | 7.5 | `ar` |
| produceva | **`produc-e-va`** | 7.5 | `e` |
| exercente | **`exerce-n-te`** | 7.5 | `n` |
| samuelson | **`samuel-s-on`** | 7.5 | `s` |
| premoderne | **`p-re-moderne`** | 7.5 | `moderne` |
| openwilare | **`openwil-ar-e`** | 7.5 | `ar` |
| indoeuropeo | **`indoeurop-e-o`** | 7.5 | `e` |
| statuaria | **`statu-ar-ia`** | 7.5 | `ar` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Interlingua 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 | **64k BPE** | Best compression (4.96x) |
| N-gram | **2-gram** | Lowest perplexity (200) |
| Markov | **Context-4** | Highest predictability (96.5%) |
| 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 03:48:16*