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README.md

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+---
+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*

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