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README.md

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+---
+language: li
+language_name: Limburgish
+language_family: germanic_west_continental
+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-germanic_west_continental
+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: 4.334
+  - name: best_isotropy
+    type: isotropy
+    value: 0.8428
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-10
+---
+
+# Limburgish - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Limburgish** 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** | 3.459x | 3.46 | 0.1960% | 1,011,080 |
+| **16k** | 3.797x | 3.80 | 0.2151% | 921,278 |
+| **32k** | 4.092x | 4.09 | 0.2319% | 854,737 |
+| **64k** | 4.334x 🏆 | 4.34 | 0.2456% | 807,087 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Andréia Assis Horta (Juiz de Fora, 27 juli is 'n Braziliaanse actrice. luuj geba...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁andré ia ▁ass is ▁h ort a ▁( j u ... (+25 more)` | 35 |
+| 16k | `▁andré ia ▁ass is ▁h ort a ▁( j u ... (+25 more)` | 35 |
+| 32k | `▁andré ia ▁ass is ▁hort a ▁( ju iz ▁de ... (+23 more)` | 33 |
+| 64k | `▁andré ia ▁ass is ▁horta ▁( ju iz ▁de ▁fora ... (+21 more)` | 31 |
+
+**Sample 2:** `'ne Artiest kan zieë: 'ne keunstenaer 'ne vieëarts`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁' ne ▁art ie st ▁kan ▁zieë : ▁' ne ... (+9 more)` | 19 |
+| 16k | `▁' ne ▁art ie st ▁kan ▁zieë : ▁' ne ... (+7 more)` | 17 |
+| 32k | `▁' ne ▁artie st ▁kan ▁zieë : ▁' ne ▁keunstenaer ... (+4 more)` | 14 |
+| 64k | `▁' ne ▁artiest ▁kan ▁zieë : ▁' ne ▁keunstenaer ▁' ... (+3 more)` | 13 |
+
+**Sample 3:** `Sarthe kan verwieze nao: Sarthe, e departement in Frankriek; Sarthe (reveer), 'n...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁s art he ▁kan ▁verwieze ▁nao : ▁s art he ... (+18 more)` | 28 |
+| 16k | `▁sart he ▁kan ▁verwieze ▁nao : ▁sart he , ▁e ... (+15 more)` | 25 |
+| 32k | `▁sart he ▁kan ▁verwieze ▁nao : ▁sart he , ▁e ... (+15 more)` | 25 |
+| 64k | `▁sarthe ▁kan ▁verwieze ▁nao : ▁sarthe , ▁e ▁departement ▁in ... (+12 more)` | 22 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.334x compression
+- **Lowest UNK Rate:** 8k with 0.1960% 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 | 25,519 | 14.64 | 104,821 | 14.0% | 30.4% |
+| **2-gram** | Subword | 290 🏆 | 8.18 | 5,406 | 65.9% | 99.0% |
+| **3-gram** | Word | 57,452 | 15.81 | 140,834 | 5.2% | 20.7% |
+| **3-gram** | Subword | 2,584 | 11.34 | 41,526 | 25.6% | 68.5% |
+| **4-gram** | Word | 92,727 | 16.50 | 222,778 | 5.0% | 19.9% |
+| **4-gram** | Subword | 15,721 | 13.94 | 237,337 | 12.2% | 36.4% |
+| **5-gram** | Word | 56,199 | 15.78 | 150,129 | 7.1% | 25.7% |
+| **5-gram** | Subword | 63,875 | 15.96 | 706,039 | 7.2% | 21.7% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `in de` | 30,200 |
+| 2 | `in t` | 21,536 |
+| 3 | `van de` | 18,942 |
+| 4 | `vaan de` | 18,520 |
+| 5 | `d n` | 16,860 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `in d n` | 3,329 |
+| 2 | `vaan d n` | 1,343 |
+| 3 | `sjtörf op laeftied` | 1,213 |
+| 4 | `d n twintigsten` | 1,212 |
+| 5 | `in nederlands limburg` | 1,211 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `d n twintigsten iew` | 1,191 |
+| 2 | `in d n twintigsten` | 1,188 |
+| 3 | `gebaore in d n` | 922 |
+| 4 | `n gemeinte in de` | 660 |
+| 5 | `gesjtorve in d n` | 648 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `in d n twintigsten iew` | 1,185 |
+| 2 | `gebaore in d n twintigsten` | 849 |
+| 3 | `iew gesjtorve in d n` | 552 |
+| 4 | `is n gemeinte in de` | 512 |
+| 5 | `luuj gebaore in d n` | 473 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `e _` | 1,069,069 |
+| 2 | `n _` | 685,730 |
+| 3 | `e r` | 585,416 |
+| 4 | `d e` | 557,458 |
+| 5 | `_ d` | 524,469 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `d e _` | 338,019 |
+| 2 | `_ d e` | 319,388 |
+| 3 | `e n _` | 204,043 |
+| 4 | `a n _` | 186,738 |
+| 5 | `_ i n` | 184,570 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ d e _` | 262,977 |
+| 2 | `_ i n _` | 141,695 |
+| 3 | `_ ' t _` | 137,201 |
+| 4 | `_ e n _` | 110,552 |
+| 5 | `n _ d e` | 97,695 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `n _ d e _` | 87,044 |
+| 2 | `_ v a n _` | 83,372 |
+| 3 | `_ v a a n` | 69,215 |
+| 4 | `v a a n _` | 67,924 |
+| 5 | `n _ ' t _` | 47,099 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 290
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.8891 | 1.852 | 6.68 | 294,084 | 11.1% |
+| **1** | Subword | 0.8968 | 1.862 | 7.36 | 2,040 | 10.3% |
+| **2** | Word | 0.2863 | 1.219 | 1.77 | 1,959,482 | 71.4% |
+| **2** | Subword | 0.9152 | 1.886 | 5.69 | 15,015 | 8.5% |
+| **3** | Word | 0.1004 | 1.072 | 1.18 | 3,453,211 | 90.0% |
+| **3** | Subword | 0.8160 | 1.761 | 4.49 | 85,340 | 18.4% |
+| **4** | Word | 0.0334 🏆 | 1.023 | 1.05 | 4,063,251 | 96.7% |
+| **4** | Subword | 0.7481 | 1.680 | 3.35 | 382,984 | 25.2% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `de wereld de vlaot det de groete maot vaan boebij de regio abruzze en zouteveen heraldrywiki`
+2. `in de wetensjap en fugas biamonti 592 680 2 biej casteldelfino frankriek liegk t polletiek erkènning`
+3. `t arrondissemint wat te speule de vikinge geleid de wienterasse en evangelis 94 5 351 gebäörtenisse`
+
+**Context Size 2:**
+
+1. `in de sovjetunie verklaort d n hamer en ne clerus oet ein beukske zitte meistal 20 zjwaegele`
+2. `in t parlemint besteit oet drei verticaol ban vaan hendeg persoeneleke door de arabische minderheid ...`
+3. `van de vrouw op dees vraog brink relizjie en allein t belang van limburg ein van de`
+
+**Context Size 3:**
+
+1. `in d n twintigsten iew gesjtorve in de zeveteenden iew gesjtorve in d n twintigsten iew oet vereinig`
+2. `vaan d n hier boeveur heer sjreef achtiende iewse componiste waore ummers neet vrij meh componeerde ...`
+3. `sjtörf op laeftied leeuwarder courant gerrit ybema overleden 21 jannewarie nederlandj de twiede kame...`
+
+**Context Size 4:**
+
+1. `in d n twintigsten iew oet portugal`
+2. `gebaore in d n twintigsten iew van d n europese raod in de media dèks en eupelek euver sinds`
+3. `d n twintigsten iew gesjtorve in d n twintigsten iew gesjtorve in d n twintigsten iew oet brazilië`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_er_ieg_be_alaao`
+2. `em_5,6_ncachäöbe`
+3. `n_ierbret_dootel`
+
+**Context Size 2:**
+
+1. `e_höbbejetcharaye`
+2. `n_trögkeneulgbeil`
+3. `ert_eënelsjaonao_`
+
+**Context Size 3:**
+
+1. `de_middig._daovan_`
+2. `_de_wat_en_bete_ga`
+3. `en_eintösse_de_weu`
+
+**Context Size 4:**
+
+1. `_de_ajds_strije_was`
+2. `_in_de_hein-load._m`
+3. `_'t_heet,_cern_liek`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 96.7% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (382,984 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 | 133,120 |
+| Total Tokens | 4,585,134 |
+| Mean Frequency | 34.44 |
+| Median Frequency | 4 |
+| Frequency Std Dev | 1100.63 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | de | 268,955 |
+| 2 | in | 146,252 |
+| 3 | t | 144,508 |
+| 4 | en | 112,120 |
+| 5 | van | 84,607 |
+| 6 | n | 69,026 |
+| 7 | vaan | 66,896 |
+| 8 | is | 51,861 |
+| 9 | op | 39,534 |
+| 10 | d | 32,491 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | oeswaal | 2 |
+| 2 | etappenhas | 2 |
+| 3 | elsner | 2 |
+| 4 | denkmaal | 2 |
+| 5 | iezermaat | 2 |
+| 6 | projram | 2 |
+| 7 | klefisch | 2 |
+| 8 | vorbei | 2 |
+| 9 | kozakkevesting | 2 |
+| 10 | jekaterinodar | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.0255 |
+| R² (Goodness of Fit) | 0.998659 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 40.3% |
+| Top 1,000 | 61.8% |
+| Top 5,000 | 77.1% |
+| Top 10,000 | 83.1% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9987 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 40.3% of corpus
+- **Long Tail:** 123,120 words needed for remaining 16.9% 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 | 0.8428 🏆 | 0.3285 | N/A | N/A |
+| **mono_64d** | 64 | 0.8228 | 0.2334 | N/A | N/A |
+| **mono_128d** | 128 | 0.8039 | 0.1762 | N/A | N/A |
+| **aligned_32d** | 32 | 0.8428 | 0.3299 | 0.1080 | 0.3900 |
+| **aligned_64d** | 64 | 0.8228 | 0.2386 | 0.2060 | 0.5560 |
+| **aligned_128d** | 128 | 0.8039 | 0.1760 | 0.3120 | 0.6440 |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.8428 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.2471. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 31.2% 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 | **5.000** | High morphological productivity | Reliable analysis |
+| Idiomaticity Gap | **0.184** | Low formulaic content | - |
+
+### 6.2 Affix Inventory (Productive Units)
+
+These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.
+
+#### Productive Prefixes
+| Prefix | Examples |
+|--------|----------|
+| `-s` | steile, sjtadssentrum, stuhlmanni |
+| `-ge` | gelaegeheje, gelangentied, gedeputeerdje |
+| `-a` | aonbeit, aftonbladet, alaajd |
+| `-b` | blikveld, burink, begreujde |
+| `-be` | begreujde, belles, beaucamps |
+| `-k` | kolonos, korehalme, kaajman |
+| `-m` | mermaid, monogram, meinberg |
+| `-g` | grensgebede, gulliva, gelaegeheje |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-e` | einziejige, contraroterendje, korehalme |
+| `-s` | kolonos, wirkers, pretenties |
+| `-n` | kaajman, hallen, gassmann |
+| `-r` | taer, raor, harder |
+| `-er` | taer, harder, soeker |
+| `-g` | verdraag, óntwiekkeling, meinberg |
+| `-d` | blikveld, mermaid, gelangentied |
+| `-en` | hallen, wijnbergen, vastelaovessezoen |
+
+### 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 |
+|------|----------|------------------|----------|
+| `onde` | 2.10x | 119 contexts | zonde, sonde, konde |
+| `esjt` | 2.13x | 107 contexts | gesjt, haesjt, eesjte |
+| `oond` | 2.16x | 80 contexts | hoond, poond, roond |
+| `nger` | 1.80x | 164 contexts | enger, ônger, anger |
+| `gesj` | 1.98x | 77 contexts | gesjt, ungesj, gesjat |
+| `erla` | 1.79x | 98 contexts | verlag, erlang, ierland |
+| `ersj` | 1.65x | 137 contexts | bersj, iersj, versj |
+| `atie` | 1.91x | 69 contexts | satie, natie, katie |
+| `chte` | 1.52x | 207 contexts | achte, echte, échte |
+| `fran` | 2.33x | 31 contexts | frang, frans, franc |
+| `euve` | 1.95x | 57 contexts | euver, leuve, beuve |
+| `rlan` | 2.03x | 42 contexts | ørland, erlang, furlan |
+
+### 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 |
+|--------|--------|-----------|----------|
+| `-b` | `-e` | 169 words | bènnevalle, beriechte |
+| `-s` | `-e` | 163 words | stórve, snellere |
+| `-a` | `-e` | 113 words | angelsakse, abchaze |
+| `-ge` | `-e` | 100 words | gehalte, gelaegeheje |
+| `-m` | `-e` | 100 words | macfarlane, move |
+| `-k` | `-e` | 96 words | kaapse, kasse |
+| `-t` | `-e` | 84 words | tesrizzeltate, tandjheilkónde |
+| `-s` | `-s` | 76 words | souvenirs, serres |
+| `-s` | `-n` | 59 words | stean, sjtein |
+| `-ge` | `-d` | 58 words | gevoed, gewijzigd |
+
+### 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 |
+|------|-----------------|------------|------|
+| namdalseid | **`namdals-e-id`** | 7.5 | `e` |
+| hóngerddoezjend | **`hóngerddoezj-e-nd`** | 7.5 | `e` |
+| besjtuurslid | **`besjtuurs-l-id`** | 7.5 | `l` |
+| seriemaordeneer | **`seriemaorden-e-er`** | 7.5 | `e` |
+| valkenvalei | **`valkenval-e-i`** | 7.5 | `e` |
+| zieësjpegel | **`zieësjpe-ge-l`** | 7.5 | `ge` |
+| monumaent | **`monuma-e-nt`** | 7.5 | `e` |
+| roxenisse | **`roxenis-s-e`** | 7.5 | `s` |
+| weltergewiech | **`weltergewi-e-ch`** | 7.5 | `e` |
+| vriendinne | **`vriendin-n-e`** | 7.5 | `n` |
+| brónnegebeed | **`brónnegebe-e-d`** | 7.5 | `e` |
+| poolgebeed | **`poolgebe-e-d`** | 7.5 | `e` |
+| kinderleke | **`kinderl-e-ke`** | 7.5 | `e` |
+| viemerret | **`viemerr-e-t`** | 7.5 | `e` |
+| blokbreke | **`blokbr-e-ke`** | 7.5 | `e` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Limburgish shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.
+
+---
+## 7. Summary & Recommendations
+
+![Performance Dashboard](visualizations/performance_dashboard.png)
+
+### Production Recommendations
+
+| Component | Recommended | Rationale |
+|-----------|-------------|-----------|
+| Tokenizer | **64k BPE** | Best compression (4.33x) |
+| N-gram | **2-gram** | Lowest perplexity (290) |
+| Markov | **Context-4** | Highest predictability (96.7%) |
+| 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 11:01:05*

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