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README.md

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+---
+language: lb
+language_name: Luxembourgish
+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: 4.804
+  - name: best_isotropy
+    type: isotropy
+    value: 0.8333
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-10
+---
+
+# Luxembourgish - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Luxembourgish** 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** | 3.853x | 3.85 | 0.0904% | 659,416 |
+| **16k** | 4.222x | 4.22 | 0.0990% | 601,768 |
+| **32k** | 4.537x | 4.54 | 0.1064% | 560,028 |
+| **64k** | 4.804x 🏆 | 4.81 | 0.1127% | 528,875 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Reclinghem ass eng franséisch Gemeng am Kanton Fruges am Departement Pas-de-Cala...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁re cl ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ... (+20 more)` | 30 |
+| 16k | `▁re cl ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ... (+20 more)` | 30 |
+| 32k | `▁re cl inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ... (+18 more)` | 28 |
+| 64k | `▁re cl inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ... (+18 more)` | 28 |
+
+**Sample 2:** `Bomy ass eng franséisch Gemeng am Kanton Fruges am Departement Pas-de-Calais. am...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁b om y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fru ... (+19 more)` | 29 |
+| 16k | `▁bom y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fru ges ... (+18 more)` | 28 |
+| 32k | `▁bom y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ▁am ... (+17 more)` | 27 |
+| 64k | `▁bom y ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁kanton ▁fruges ▁am ... (+17 more)` | 27 |
+
+**Sample 3:** `Ruminghem ass eng franséisch Gemeng am Departement Pas-de-Calais an der Regioun ...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁rum ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas ... (+21 more)` | 31 |
+| 16k | `▁rum ing hem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas ... (+19 more)` | 29 |
+| 32k | `▁rum inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas - ... (+18 more)` | 28 |
+| 64k | `▁rum inghem ▁ass ▁eng ▁franséisch ▁gemeng ▁am ▁departement ▁pas - ... (+18 more)` | 28 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.804x compression
+- **Lowest UNK Rate:** 8k with 0.0904% 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 | 62,562 | 15.93 | 314,805 | 10.7% | 24.2% |
+| **2-gram** | Subword | 318 🏆 | 8.31 | 7,549 | 63.0% | 98.9% |
+| **3-gram** | Word | 192,148 | 17.55 | 547,285 | 5.0% | 13.5% |
+| **3-gram** | Subword | 2,850 | 11.48 | 64,806 | 23.1% | 66.6% |
+| **4-gram** | Word | 356,085 | 18.44 | 876,356 | 4.3% | 11.3% |
+| **4-gram** | Subword | 16,948 | 14.05 | 383,042 | 12.4% | 36.3% |
+| **5-gram** | Word | 281,035 | 18.10 | 647,259 | 4.7% | 12.1% |
+| **5-gram** | Subword | 67,612 | 16.04 | 1,248,329 | 8.3% | 23.2% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `vun der` | 83,364 |
+| 2 | `an der` | 70,319 |
+| 3 | `um spaweck` | 36,982 |
+| 4 | `vun de` | 26,136 |
+| 5 | `ass eng` | 25,638 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `an der regioun` | 10,968 |
+| 2 | `ass eng franséisch` | 8,527 |
+| 3 | `franséisch administrativ andeelung` | 5,357 |
+| 4 | `administrativ andeelung am` | 5,155 |
+| 5 | `gemeng am departement` | 5,056 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `franséisch administrativ andeelung am` | 5,149 |
+| 2 | `administrativ andeelung am arrondissement` | 4,760 |
+| 3 | `ass eng franséisch gemeng` | 4,208 |
+| 4 | `ëm wat geet et` | 4,198 |
+| 5 | `wat geet et am` | 4,109 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `franséisch administrativ andeelung am arrondissement` | 4,759 |
+| 2 | `ëm wat geet et am` | 4,109 |
+| 3 | `wat geet et am film` | 4,060 |
+| 4 | `ass eng franséisch gemeng am` | 3,394 |
+| 5 | `eng franséisch gemeng am departement` | 3,212 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `e r` | 2,283,425 |
+| 2 | `e n` | 1,750,568 |
+| 3 | `n _` | 1,684,884 |
+| 4 | `_ d` | 1,610,037 |
+| 5 | `e _` | 1,476,507 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `e r _` | 951,492 |
+| 2 | `_ d e` | 876,571 |
+| 3 | `e n _` | 679,558 |
+| 4 | `s c h` | 638,025 |
+| 5 | `n _ d` | 455,328 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `n _ d e` | 312,530 |
+| 2 | `d e r _` | 303,229 |
+| 3 | `_ a n _` | 280,443 |
+| 4 | `_ d e _` | 275,944 |
+| 5 | `_ d e r` | 254,059 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ d e r _` | 250,063 |
+| 2 | `_ v u n _` | 204,878 |
+| 3 | `n _ d e r` | 163,335 |
+| 4 | `_ v u m _` | 162,050 |
+| 5 | `_ a n _ d` | 155,413 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 318
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.9491 | 1.931 | 7.90 | 521,387 | 5.1% |
+| **1** | Subword | 0.9460 | 1.927 | 6.76 | 3,270 | 5.4% |
+| **2** | Word | 0.3309 | 1.258 | 1.98 | 4,108,190 | 66.9% |
+| **2** | Subword | 0.8550 | 1.809 | 5.87 | 22,062 | 14.5% |
+| **3** | Word | 0.1377 | 1.100 | 1.27 | 8,097,151 | 86.2% |
+| **3** | Subword | 0.8305 | 1.778 | 4.76 | 129,396 | 17.0% |
+| **4** | Word | 0.0569 🏆 | 1.040 | 1.09 | 10,254,064 | 94.3% |
+| **4** | Subword | 0.7479 | 1.679 | 3.58 | 615,656 | 25.2% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `de la résistance boîte vun der haiteger perspektiv am juni huet zur trounfollgerin akzeptabel d shir...`
+2. `an technik gebuer den oflaf vum walter hill haaptacteuren nathalie reuter lëtzebuergesch grammaire d...`
+3. `der iau offiziell nom brittesche science 2 etapp 50 m den traité vu montpellier am arrondissement`
+
+**Context Size 2:**
+
+1. `vun der gemeng miersch e läit um zesammenfluss vun der zäit wou en zanterhier all kéier fréizäiteg`
+2. `an der atmosphär ionosphär magnetosphär plasmasphär no physiko cheemesche prozesser ozonosphär respe...`
+3. `um spaweck chris s 33 35 artikel aus der circonscriptioun vun de ponts et chaussées zu lëtzebuerg`
+
+**Context Size 3:**
+
+1. `an der regioun bretagne bei der kantonalreform vun gouf de kanton gegrënnt gemengen am kanton bellev...`
+2. `ass eng franséisch harfspillerin mat néng joer hat an eng ofsécherungze vill e groussen deel vun de ...`
+3. `franséisch administrativ andeelung am arrondissement thonon les bains ouest war bis mäerz eng fransé...`
+
+**Context Size 4:**
+
+1. `franséisch administrativ andeelung am arrondissement bayonne am arrondissement bayonne op der via po...`
+2. `administrativ andeelung am arrondissement toulon am departement var an der regioun provence alpes cô...`
+3. `ass eng franséisch gemeng an de vogesen an der regioun grand est d gemeng val de meuse ass duerch`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_den_(kitesinge_`
+2. `enit_wäerengi_lë`
+3. `nodun_1_che_hen:`
+
+**Context Size 2:**
+
+1. `errevo,_opgebsäit`
+2. `en_ster_den._joen`
+3. `n_ofeng_mist_um_(`
+
+**Context Size 3:**
+
+1. `er_war_bruce_filme`
+2. `_de_mobizent_gi_ma`
+3. `en_1_ster_-_repren`
+
+**Context Size 4:**
+
+1. `n_den_eng_belschaft`
+2. `der_revolumbahnen_d`
+3. `_an_der_a_pilger_im`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 94.3% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (615,656 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 | 248,214 |
+| Total Tokens | 13,192,531 |
+| Mean Frequency | 53.15 |
+| Median Frequency | 4 |
+| Frequency Std Dev | 1571.96 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | de | 305,799 |
+| 2 | an | 283,342 |
+| 3 | der | 250,632 |
+| 4 | d | 249,992 |
+| 5 | vun | 205,518 |
+| 6 | a | 182,029 |
+| 7 | vum | 162,657 |
+| 8 | den | 146,511 |
+| 9 | am | 141,289 |
+| 10 | ass | 127,097 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | enquêteprozedur | 2 |
+| 2 | notifikatioun | 2 |
+| 3 | jauferbësch | 2 |
+| 4 | jauf | 2 |
+| 5 | sabigotho | 2 |
+| 6 | proprietärintern | 2 |
+| 7 | lëtzebuergfir | 2 |
+| 8 | multicentrisch | 2 |
+| 9 | urbanem | 2 |
+| 10 | neytiri | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.0100 |
+| R² (Goodness of Fit) | 0.999149 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 37.9% |
+| Top 1,000 | 60.1% |
+| Top 5,000 | 75.1% |
+| Top 10,000 | 81.5% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9991 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 37.9% of corpus
+- **Long Tail:** 238,214 words needed for remaining 18.5% 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 | 0.8333 🏆 | 0.3443 | N/A | N/A |
+| **mono_64d** | 64 | 0.8177 | 0.2743 | N/A | N/A |
+| **mono_128d** | 128 | 0.7923 | 0.2124 | N/A | N/A |
+| **aligned_32d** | 32 | 0.8333 | 0.3472 | 0.1420 | 0.4680 |
+| **aligned_64d** | 64 | 0.8177 | 0.2730 | 0.2800 | 0.6120 |
+| **aligned_128d** | 128 | 0.7923 | 0.2086 | 0.3360 | 0.7540 |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.8333 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.2766. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 33.6% 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 | **-0.481** | 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` | saviez, storeria, semoy |
+| `-a` | autrichienne, antiker, augh |
+| `-b` | baleareschen, bongaert, braunsberger |
+| `-ma` | markéieren, maserati, marsas |
+| `-m` | markéieren, methodologescher, montlauzun |
+| `-p` | puren, premièren, prange |
+| `-d` | diestro, dumcke, dinas |
+| `-c` | chrétienne, cazilhac, carvifolia |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-n` | markéieren, zommen, guzman |
+| `-en` | markéieren, zommen, baleareschen |
+| `-e` | chrétienne, hennie, dumcke |
+| `-er` | methodologescher, antiker, gruppementer |
+| `-r` | methodologescher, antiker, gruppementer |
+| `-t` | bongaert, renfort, individualitéit |
+| `-s` | fraissines, oenomaus, fourons |
+| `-g` | verëffentlechung, udeng, combining |
+
+### 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 |
+|------|----------|------------------|----------|
+| `chte` | 1.91x | 259 contexts | achte, echte, fechte |
+| `tiou` | 2.50x | 52 contexts | actioun, natioun, optioun |
+| `nner` | 1.82x | 209 contexts | inner, önner, anner |
+| `ller` | 1.73x | 232 contexts | eller, aller, iller |
+| `atio` | 2.10x | 88 contexts | natio, ratio, patio |
+| `teur` | 2.17x | 71 contexts | teuro, moteur, steurs |
+| `emen` | 2.10x | 82 contexts | jemen, gemen, semen |
+| `erge` | 1.82x | 145 contexts | perge, uerge, verge |
+| `cteu` | 2.83x | 22 contexts | acteur, vecteur, facteur |
+| `nger` | 1.74x | 150 contexts | inger, anger, unger |
+| `ioun` | 2.23x | 44 contexts | aioun, spioun, unioun |
+| `regi` | 2.12x | 38 contexts | regis, regia, regie |
+
+### 6.4 Affix Compatibility (Co-occurrence)
+
+This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.
+
+| Prefix | Suffix | Frequency | Examples |
+|--------|--------|-----------|----------|
+| `-s` | `-n` | 115 words | schouluniformen, siphonen |
+| `-s` | `-e` | 106 words | semide, schreckliche |
+| `-s` | `-r` | 103 words | saulzoir, schmidhauser |
+| `-a` | `-e` | 88 words | arbeitspapiere, aushale |
+| `-s` | `-er` | 88 words | schmidhauser, stralungsdetekter |
+| `-s` | `-en` | 82 words | schouluniformen, siphonen |
+| `-b` | `-e` | 76 words | bewäertbare, breve |
+| `-g` | `-n` | 73 words | guidesektioun, germaniséieren |
+| `-p` | `-n` | 71 words | plädéieren, phalempin |
+| `-c` | `-s` | 71 words | companions, crus |
+
+### 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 |
+|------|-----------------|------------|------|
+| moschtgewiicht | **`moschtgewii-ch-t`** | 7.5 | `ch` |
+| approcher | **`appro-ch-er`** | 7.5 | `ch` |
+| sommernacht | **`sommerna-ch-t`** | 7.5 | `ch` |
+| opgebauscht | **`opgebaus-ch-t`** | 7.5 | `ch` |
+| haaptobjet | **`haaptobj-e-t`** | 7.5 | `e` |
+| disquisitiones | **`disquisitio-n-es`** | 7.5 | `n` |
+| iwwerierdesche | **`iwwerierdes-ch-e`** | 7.5 | `ch` |
+| interprétations | **`interprétatio-n-s`** | 7.5 | `n` |
+| bekanntlich | **`bekanntl-i-ch`** | 7.5 | `i` |
+| schläicht | **`schläi-ch-t`** | 7.5 | `ch` |
+| averstanen | **`aversta-n-en`** | 7.5 | `n` |
+| gestatten | **`gestat-t-en`** | 7.5 | `t` |
+| dokumentaresche | **`dokumentares-ch-e`** | 7.5 | `ch` |
+| criticism | **`critici-s-m`** | 7.5 | `s` |
+| concoules | **`concou-le-s`** | 7.5 | `le` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Luxembourgish 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 (4.80x) |
+| N-gram | **2-gram** | Lowest perplexity (318) |
+| Markov | **Context-4** | Highest predictability (94.3%) |
+| 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 11:34:33*

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