---
language: ie
language_name: Interlingue
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: 4.092
  - name: best_isotropy
    type: isotropy
    value: 0.8056
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Interlingue** 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** | 3.608x | 3.61 | 0.0821% | 148,512 |
| **16k** | 3.803x | 3.81 | 0.0866% | 140,899 |
| **32k** | 3.974x | 3.98 | 0.0905% | 134,848 |
| **64k** | 4.092x 🏆 | 4.10 | 0.0932% | 130,939 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Heliconia es un village locat in Antioquia, Columbia. It have un population de h...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁he lic onia ▁es ▁un ▁village ▁locat ▁in ▁antioquia , ... (+9 more)` | 19 |
| 16k | `▁helic onia ▁es ▁un ▁village ▁locat ▁in ▁antioquia , ▁columbia ... (+8 more)` | 18 |
| 32k | `▁helic onia ▁es ▁un ▁village ▁locat ▁in ▁antioquia , ▁columbia ... (+8 more)` | 18 |
| 64k | `▁heliconia ▁es ▁un ▁village ▁locat ▁in ▁antioquia , ▁columbia . ... (+7 more)` | 17 |

**Sample 2:** `Herramélluri es un municipie situat in li comunité autonom de La Rioja, Hispania...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁her ram é ll uri ▁es ▁un ▁municipie ▁situat ▁in ... (+19 more)` | 29 |
| 16k | `▁her ram é ll uri ▁es ▁un ▁municipie ▁situat ▁in ... (+19 more)` | 29 |
| 32k | `▁her ram é ll uri ▁es ▁un ▁municipie ▁situat ▁in ... (+19 more)` | 29 |
| 64k | `▁her ram é ll uri ▁es ▁un ▁municipie ▁situat ▁in ... (+19 more)` | 29 |

**Sample 3:** `Extremaduran es un lingue romanic parlat in li comunité autonom hispan de Extrem...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁extrem ad ur an ▁es ▁un ▁lingue ▁romanic ▁parlat ▁in ... (+10 more)` | 20 |
| 16k | `▁extremad ur an ▁es ▁un ▁lingue ▁romanic ▁parlat ▁in ▁li ... (+8 more)` | 18 |
| 32k | `▁extremad uran ▁es ▁un ▁lingue ▁romanic ▁parlat ▁in ▁li ▁comunité ... (+6 more)` | 16 |
| 64k | `▁extremaduran ▁es ▁un ▁lingue ▁romanic ▁parlat ▁in ▁li ▁comunité ▁autonom ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.092x compression
- **Lowest UNK Rate:** 8k with 0.0821% 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 | 2,631 | 11.36 | 21,646 | 36.0% | 64.2% |
| **2-gram** | Subword | 241 🏆 | 7.91 | 3,184 | 71.3% | 99.2% |
| **3-gram** | Word | 4,146 | 12.02 | 34,445 | 32.6% | 58.5% |
| **3-gram** | Subword | 1,702 | 10.73 | 22,847 | 31.9% | 77.0% |
| **4-gram** | Word | 6,878 | 12.75 | 62,031 | 30.3% | 52.0% |
| **4-gram** | Subword | 7,188 | 12.81 | 108,171 | 20.2% | 51.9% |
| **5-gram** | Word | 5,337 | 12.38 | 50,418 | 33.2% | 55.0% |
| **5-gram** | Subword | 18,128 | 14.15 | 240,674 | 15.2% | 41.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `in li` | 30,772 |
| 2 | `es un` | 12,459 |
| 3 | `provincia de` | 11,763 |
| 4 | `situat in` | 8,192 |
| 5 | `have un` | 7,384 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `situat in li` | 7,870 |
| 2 | `it have un` | 6,504 |
| 3 | `un population de` | 6,452 |
| 4 | `have un population` | 6,414 |
| 5 | `in li comunité` | 6,340 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `have un population de` | 6,414 |
| 2 | `it have un population` | 6,405 |
| 3 | `hispania it have un` | 6,047 |
| 4 | `in li comunité autonom` | 5,959 |
| 5 | `li comunité autonom de` | 5,958 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `it have un population de` | 6,405 |
| 2 | `hispania it have un population` | 6,047 |
| 3 | `in li comunité autonom de` | 5,958 |
| 4 | `situat in li provincia de` | 5,691 |
| 5 | `un municipie situat in li` | 5,426 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 215,243 |
| 2 | `d e` | 150,699 |
| 3 | `_ d` | 138,972 |
| 4 | `n _` | 138,753 |
| 5 | `l i` | 117,810 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 121,852 |
| 2 | `_ l i` | 86,236 |
| 3 | `l i _` | 81,835 |
| 4 | `d e _` | 81,137 |
| 5 | `_ i n` | 65,595 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l i _` | 79,051 |
| 2 | `_ d e _` | 73,928 |
| 3 | `_ i n _` | 48,622 |
| 4 | `n _ l i` | 34,069 |
| 5 | `_ d e l` | 32,612 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _ l i _` | 33,170 |
| 2 | `_ d e l _` | 32,443 |
| 3 | `_ i n _ l` | 31,429 |
| 4 | `i n _ l i` | 31,004 |
| 5 | `a t i o n` | 18,523 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 241
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~41% 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 | 0.7892 | 1.728 | 4.90 | 74,694 | 21.1% |
| **1** | Subword | 1.0068 | 2.009 | 7.54 | 1,050 | 0.0% |
| **2** | Word | 0.2700 | 1.206 | 1.67 | 364,659 | 73.0% |
| **2** | Subword | 0.9485 | 1.930 | 5.61 | 7,906 | 5.2% |
| **3** | Word | 0.1159 | 1.084 | 1.23 | 604,985 | 88.4% |
| **3** | Subword | 0.8121 | 1.756 | 4.04 | 44,321 | 18.8% |
| **4** | Word | 0.0587 🏆 | 1.042 | 1.11 | 737,025 | 94.1% |
| **4** | Subword | 0.6591 | 1.579 | 2.74 | 178,838 | 34.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `li sud ossetia con li comunité autonom de marie agnes sapper comensat interessar les accessibil in`
2. `de wta championships tournament mvp award katharina stark watzinger demissionat li 8 im de bremen 1`
3. `in li max grand cité esset presidente del sale lago inari es nha trang li sobranie`

**Context Size 2:**

1. `in li nord de germania li subdistrict have 131 662 habitantes e un area de 124 quadrat`
2. `es un actor de dania por li electiones parlamentari ye li 30 im de julí in dallas`
3. `provincia de valladolid in li marte ella fundat li partise del economic e political cariera ivan bra...`

**Context Size 3:**

1. `situat in li sud de germania in li parlament del quinesim republica consiste ex du singul discipline...`
2. `it have un population de habitantes location e geografie historie del provincia de salamanca in li c...`
3. `un population de habitantes del provincia de segovia in li comunité autonom de andalusia hispania it...`

**Context Size 4:**

1. `have un population de habitantes location e geografie historie del provincia de málaga todos zurdos`
2. `it have un population de habitantes location e geografie historie del provincia de teruel liste de m...`
3. `hispania it have un population de inhabitantes de la rioja`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_"gria_a_tre_de_`
2. `enuancipisse_und`
3. `iatkmopopovipxte`

**Context Size 2:**

1. `e_popul,_hectonal`
2. `del_revivego,_il_`
3. `_de_un_popubeia_s`

**Context Size 3:**

1. `_del_e_partise_neč`
2. `_li_ciuda_un_heimn`
3. `li_artipp_li_antes`

**Context Size 4:**

1. `_li_comunité_autono`
2. `_de_saxonia,_nomía_`
3. `_in_li_cupremie_li_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (178,838 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 | 33,220 |
| Total Tokens | 1,149,726 |
| Mean Frequency | 34.61 |
| Median Frequency | 4 |
| Frequency Std Dev | 774.72 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | li | 80,769 |
| 2 | de | 74,091 |
| 3 | in | 49,037 |
| 4 | del | 32,477 |
| 5 | e | 32,108 |
| 6 | un | 31,151 |
| 7 | es | 28,327 |
| 8 | provincia | 12,234 |
| 9 | it | 11,607 |
| 10 | have | 11,493 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ollscoil | 2 |
| 2 | gur | 2 |
| 3 | idirnáisiúnta | 2 |
| 4 | iberoamericana | 2 |
| 5 | caribican | 2 |
| 6 | philipsburg | 2 |
| 7 | marten | 2 |
| 8 | eurohandball | 2 |
| 9 | neckarsulm | 2 |
| 10 | hohm | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0974 |
| R² (Goodness of Fit) | 0.997325 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 54.3% |
| Top 1,000 | 77.4% |
| Top 5,000 | 88.7% |
| Top 10,000 | 93.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9973 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 54.3% of corpus
- **Long Tail:** 23,220 words needed for remaining 6.7% 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 | 0.8056 | 0.3250 | N/A | N/A |
| **mono_64d** | 64 | 0.6386 | 0.2829 | N/A | N/A |
| **mono_128d** | 128 | 0.2078 | 0.2618 | N/A | N/A |
| **aligned_32d** | 32 | 0.8056 🏆 | 0.3257 | 0.0960 | 0.3840 |
| **aligned_64d** | 64 | 0.6386 | 0.2764 | 0.1440 | 0.4740 |
| **aligned_128d** | 128 | 0.2078 | 0.2627 | 0.1760 | 0.5200 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8056 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2891. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 17.6% 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 | **0.341** | 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` | stéphane, selk, summarium |
| `-a` | attaccat, ambiciosi, aguiló |
| `-b` | believe, biddle, baqir |
| `-c` | commercial, chief, cs |
| `-m` | marbode, messages, mataró |
| `-p` | punat, psichic, politiques |
| `-ma` | marbode, mataró, mahesh |
| `-d` | delmonte, dvořák, dunărea |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | klaas, fields, rames |
| `-e` | believe, stéphane, órbite |
| `-n` | eisleben, surprisantmen, precision |
| `-a` | radiologia, nirvana, española |
| `-es` | rames, messages, politiques |
| `-t` | attaccat, punat, influent |
| `-on` | precision, persecution, répartition |
| `-r` | sauber, slender, gostivar |

### 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` | 1.73x | 46 contexts | nation, cation, oratio |
| `tion` | 1.66x | 50 contexts | nation, notion, cation |
| `ntes` | 1.73x | 26 contexts | antes, entes, fontes |
| `lati` | 1.84x | 20 contexts | latif, latin, colati |
| `muni` | 1.69x | 24 contexts | munich, almunia, comunica |
| `onom` | 1.82x | 16 contexts | econom, autonom, astronom |
| `omun` | 1.93x | 12 contexts | comun, comuna, comune |
| `sset` | 1.91x | 12 contexts | esset, musset, essset |
| `inci` | 1.90x | 12 contexts | vinci, finci, coincide |
| `opul` | 1.78x | 14 contexts | popul, populo, popules |
| `itan` | 1.44x | 24 contexts | titan, dritan, britan |
| `rovi` | 1.54x | 19 contexts | šarović, provide, provinz |

### 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` | `-s` | 121 words | capillas, contextus |
| `-c` | `-a` | 87 words | casarabonela, catharina |
| `-p` | `-s` | 82 words | programmas, politicos |
| `-s` | `-s` | 77 words | skvernelis, solanas |
| `-c` | `-e` | 75 words | cive, cove |
| `-c` | `-t` | 74 words | cultivat, consacrat |
| `-s` | `-e` | 73 words | sylvie, seattle |
| `-m` | `-e` | 71 words | matilde, maggie |
| `-m` | `-s` | 67 words | maroons, mills |
| `-s` | `-n` | 65 words | schatten, substitution |

### 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 |
|------|-----------------|------------|------|
| guadalcanal | **`guadalc-an-al`** | 7.5 | `an` |
| villasila | **`villas-i-la`** | 7.5 | `i` |
| deschanel | **`deschan-e-l`** | 7.5 | `e` |
| edmondson | **`edmond-s-on`** | 7.5 | `s` |
| centennie | **`centen-n-ie`** | 7.5 | `n` |
| navarcles | **`navarc-l-es`** | 7.5 | `l` |
| publicmen | **`public-m-en`** | 7.5 | `m` |
| hallesches | **`halles-ch-es`** | 7.5 | `ch` |
| achternbusch | **`achternbu-s-ch`** | 7.5 | `s` |
| kircheisen | **`kirchei-s-en`** | 7.5 | `s` |
| guvernamant | **`guvernam-a-nt`** | 7.5 | `a` |
| chuquisaca | **`chuquis-a-ca`** | 7.5 | `a` |
| tillerson | **`tiller-s-on`** | 7.5 | `s` |
| balineses | **`ba-lines-es`** | 6.0 | `lines` |
| irlandesi | **`irland-es-i`** | 6.0 | `irland` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Interlingue 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 (4.09x) |
| N-gram | **2-gram** | Lowest perplexity (241) |
| Markov | **Context-4** | Highest predictability (94.1%) |
| 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 03:57:27*