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README.md

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+---
+language: pms
+language_name: Piedmontese
+language_family: romance_galloitalic
+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-romance_galloitalic
+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: 4.075
+  - name: best_isotropy
+    type: isotropy
+    value: 0.7640
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-10
+---
+
+# Piedmontese - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Piedmontese** 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** | 3.537x | 3.54 | 0.0838% | 171,777 |
+| **16k** | 3.769x | 3.77 | 0.0893% | 161,202 |
+| **32k** | 3.945x | 3.95 | 0.0935% | 153,994 |
+| **64k** | 4.075x 🏆 | 4.08 | 0.0966% | 149,077 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Legnaro a l’é na comun-a ëd la provinsa ëd Pàdoa. Region aministrativa Véneto. S...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁le gn aro ▁a ▁l ’ é ▁na ▁comun - ... (+17 more)` | 27 |
+| 16k | `▁le gn aro ▁a ▁l ’ é ▁na ▁comun - ... (+17 more)` | 27 |
+| 32k | `▁legn aro ▁a ▁l ’ é ▁na ▁comun - a ... (+16 more)` | 26 |
+| 64k | `▁legn aro ▁a ▁l ’ é ▁na ▁comun - a ... (+16 more)` | 26 |
+
+**Sample 2:** `Nozay a l'é 'l nòm: d'un comun fransèis ant ël dipartiment d'Aube d'un comun fra...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁no za y ▁a ▁l ' é ▁' l ▁nòm ... (+23 more)` | 33 |
+| 16k | `▁no zay ▁a ▁l ' é ▁' l ▁nòm : ... (+22 more)` | 32 |
+| 32k | `▁no zay ▁a ▁l ' é ▁' l ▁nòm : ... (+22 more)` | 32 |
+| 64k | `▁nozay ▁a ▁l ' é ▁' l ▁nòm : ▁d ... (+21 more)` | 31 |
+
+**Sample 3:** `Bellefosse a l'é na comun-a fransèisa ant la region aministrativa dl'Alsassia, a...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁belle f osse ▁a ▁l ' é ▁na ▁comun - ... (+22 more)` | 32 |
+| 16k | `▁belle f osse ▁a ▁l ' é ▁na ▁comun - ... (+22 more)` | 32 |
+| 32k | `▁belle fosse ▁a ▁l ' é ▁na ▁comun - a ... (+21 more)` | 31 |
+| 64k | `▁belle fosse ▁a ▁l ' é ▁na ▁comun - a ... (+21 more)` | 31 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.075x compression
+- **Lowest UNK Rate:** 8k with 0.0838% 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 | 3,141 | 11.62 | 77,121 | 41.9% | 64.4% |
+| **2-gram** | Subword | 256 🏆 | 8.00 | 3,836 | 69.3% | 99.4% |
+| **3-gram** | Word | 5,004 | 12.29 | 132,134 | 37.8% | 59.5% |
+| **3-gram** | Subword | 1,638 | 10.68 | 31,027 | 34.2% | 77.5% |
+| **4-gram** | Word | 8,275 | 13.01 | 214,916 | 32.4% | 54.5% |
+| **4-gram** | Subword | 6,362 | 12.64 | 163,804 | 22.7% | 55.2% |
+| **5-gram** | Word | 8,601 | 13.07 | 179,908 | 29.2% | 52.3% |
+| **5-gram** | Subword | 16,383 | 14.00 | 457,622 | 17.6% | 45.3% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a l` | 154,306 |
+| 2 | `l é` | 116,837 |
+| 3 | `ant ël` | 45,088 |
+| 4 | `dipartiment ëd` | 43,742 |
+| 5 | `é na` | 41,435 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a l é` | 116,563 |
+| 2 | `l é na` | 41,283 |
+| 3 | `na comun a` | 36,182 |
+| 4 | `é na comun` | 36,110 |
+| 5 | `ant ël dipartiment` | 33,155 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a l é na` | 41,263 |
+| 2 | `é na comun a` | 36,110 |
+| 3 | `l é na comun` | 36,108 |
+| 4 | `con na densità ëd` | 32,499 |
+| 5 | `na comun a fransèisa` | 30,354 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `l é na comun a` | 36,108 |
+| 2 | `a l é na comun` | 36,104 |
+| 3 | `é na comun a fransèisa` | 30,343 |
+| 4 | `abitant scond ël censiment dël` | 29,591 |
+| 5 | `na comun a fransèisa ant` | 29,152 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a _` | 1,165,352 |
+| 2 | `_ a` | 759,939 |
+| 3 | `a n` | 521,874 |
+| 4 | `_ d` | 517,379 |
+| 5 | `_ l` | 463,625 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ a _` | 302,714 |
+| 2 | `n t _` | 258,541 |
+| 3 | `_ ë d` | 251,242 |
+| 4 | `ë d _` | 246,081 |
+| 5 | `ë l _` | 238,083 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ ë d _` | 245,889 |
+| 2 | `_ a _ l` | 160,115 |
+| 3 | `a _ l '` | 147,963 |
+| 4 | `e n t _` | 137,969 |
+| 5 | `m e n t` | 134,438 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ a _ l '` | 139,497 |
+| 2 | `m e n t _` | 128,287 |
+| 3 | `_ d ë l _` | 126,779 |
+| 4 | `i m e n t` | 119,300 |
+| 5 | `a _ l ' é` | 108,685 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 256
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~45% 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 | 0.8327 | 1.781 | 5.52 | 169,530 | 16.7% |
+| **1** | Subword | 0.8751 | 1.834 | 6.71 | 1,490 | 12.5% |
+| **2** | Word | 0.3305 | 1.257 | 1.89 | 927,581 | 67.0% |
+| **2** | Subword | 0.8947 | 1.859 | 6.10 | 9,975 | 10.5% |
+| **3** | Word | 0.1336 | 1.097 | 1.29 | 1,740,248 | 86.6% |
+| **3** | Subword | 0.7906 | 1.730 | 4.36 | 60,753 | 20.9% |
+| **4** | Word | 0.0669 🏆 | 1.047 | 1.14 | 2,223,801 | 93.3% |
+| **4** | Subword | 0.6809 | 1.603 | 3.09 | 264,501 | 31.9% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `a së stend për na comun a l é parlà minca casela a l anglèis national`
+2. `ëd le ròche o gbiri niragu o kaqchikel akatenango sud con na densità a fransèisa ant`
+3. `l é vincenzo civitali vincenzo andrea guglielminetti lese ij cas assolù la region sardëgna d américa`
+
+**Context Size 2:**
+
+1. `a l é na comun a fransèisa ant la literatura a l é un comun dla lombardìa`
+2. `l é gemelà con anliure esterne sit istitussional dla provincia ëd turin a l é parlà la`
+3. `ant ël dipartiment ëd vaucluse as dëstend an sna surfassa ëd 85 ab km dël dipartiment dla`
+
+**Context Size 3:**
+
+1. `a l é na comun a fransèisa ant la region aministrativa dl àuta normandìa ant ël dipartiment ëd`
+2. `l é na comun a fransèisa ant la region aministrativa dla picardìa ant ël dipartiment ëd creuse a`
+3. `na comun a fransèisa ant la region aministrativa dla bassa normandìa ant ël dipartiment ëd la nièvre...`
+
+**Context Size 4:**
+
+1. `a l é na comun a fransèisa ant la region aministrativa dla picardìa ant ël dipartiment ëd cantal a`
+2. `é na comun a fransèisa ant la region aministrativa ëd champagne ardënne ant ël dipartiment d allier ...`
+3. `l é na comun a fransèisa ant la region aministrativa ëd champagne ardënne ant ël dipartiment d hérau...`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_pondan-ntré_d_t`
+2. `a_sst_latrsio_so`
+3. `n_chentet_pel'al`
+
+**Context Size 2:**
+
+1. `a_ëd_a_la_cottera`
+2. `_agna_la_rep_decì`
+3. `an_gruzeyrus_a_tu`
+
+**Context Size 3:**
+
+1. `_a_concorphan._com`
+2. `nt_ëd_va_a_l'é_d'u`
+3. `_ëd_km²,_cons_(tal`
+
+**Context Size 4:**
+
+1. `_ëd_tarda_ant_ij_27`
+2. `_a_l'arnota_l'é_par`
+3. `a_l'é_na_dense_regi`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 93.3% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (264,501 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 | 80,217 |
+| Total Tokens | 5,297,235 |
+| Mean Frequency | 66.04 |
+| Median Frequency | 5 |
+| Frequency Std Dev | 2213.41 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | a | 388,771 |
+| 2 | ëd | 246,106 |
+| 3 | l | 200,451 |
+| 4 | dël | 126,964 |
+| 5 | é | 118,244 |
+| 6 | na | 116,817 |
+| 7 | ël | 109,927 |
+| 8 | la | 108,231 |
+| 9 | ant | 97,115 |
+| 10 | e | 91,172 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | andividuassion | 2 |
+| 2 | sètim | 2 |
+| 3 | guacamole | 2 |
+| 4 | anviromentaj | 2 |
+| 5 | tonelé | 2 |
+| 6 | spurgh | 2 |
+| 7 | solidëssa | 2 |
+| 8 | ruscha | 2 |
+| 9 | houten | 2 |
+| 10 | maudagna | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.1911 |
+| R² (Goodness of Fit) | 0.999309 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 61.6% |
+| Top 1,000 | 80.4% |
+| Top 5,000 | 89.7% |
+| Top 10,000 | 92.9% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9993 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 61.6% of corpus
+- **Long Tail:** 70,217 words needed for remaining 7.1% 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 | 0.7640 🏆 | 0.3601 | N/A | N/A |
+| **mono_64d** | 64 | 0.7270 | 0.2907 | N/A | N/A |
+| **mono_128d** | 128 | 0.6128 | 0.2654 | N/A | N/A |
+| **aligned_32d** | 32 | 0.7640 | 0.3674 | 0.0740 | 0.3760 |
+| **aligned_64d** | 64 | 0.7270 | 0.2772 | 0.1400 | 0.5080 |
+| **aligned_128d** | 128 | 0.6128 | 0.2519 | 0.1600 | 0.5340 |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.7640 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.3021. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 16.0% 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 | **0.156** | 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 |
+|--------|----------|
+| `-a` | anvità, anetù, awun |
+| `-s` | sie, sorcière, surrender |
+| `-c` | conession, cyrano, celtica |
+| `-b` | bassin, be, braunfels |
+| `-ma` | magnolia, martinsicuro, marchisio |
+| `-m` | mecatrònich, magnolia, miria |
+| `-p` | pratica, prèivi, passo |
+| `-t` | teatino, thomasset, tip |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-a` | ghilarza, hepatica, magnolia |
+| `-e` | sie, urbe, sorcière |
+| `-n` | bassin, conession, ecitassion |
+| `-s` | facilitates, braunfels, heidekreis |
+| `-o` | teatino, cyrano, martinsicuro |
+| `-i` | flavi, canzoni, gritti |
+| `-on` | conession, ecitassion, incursion |
+| `-t` | nuriment, riconossiment, thomasset |
+
+### 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 |
+|------|----------|------------------|----------|
+| `assa` | 1.63x | 143 contexts | lassa, nassa, fassa |
+| `ssio` | 1.80x | 86 contexts | possio, fassio, lassio |
+| `ensi` | 1.52x | 80 contexts | sensi, kensiu, mensis |
+| `imen` | 1.81x | 39 contexts | imeni, ciment, crimen |
+| `cond` | 1.63x | 59 contexts | condé, conde, scond |
+| `sten` | 1.54x | 51 contexts | stend, osten, stent |
+| `leng` | 1.83x | 26 contexts | eleng, lengo, lenga |
+| `nist` | 1.72x | 31 contexts | sniste, snistr, snista |
+| `inis` | 1.55x | 43 contexts | finiss, cinism, inisse |
+| `istr` | 1.43x | 53 contexts | istro, bistr, istria |
+| `itan` | 1.36x | 59 contexts | titan, ritan, gitan |
+| `engh` | 1.77x | 20 contexts | fengh, vengh, lenghe |
+
+### 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` | `-a` | 149 words | cussìtica, castagnòla |
+| `-p` | `-a` | 136 words | predecessora, praetoria |
+| `-a` | `-a` | 126 words | agta, arcostruìa |
+| `-s` | `-a` | 105 words | sewa, sarvaja |
+| `-c` | `-o` | 94 words | capitignano, caivano |
+| `-c` | `-e` | 84 words | cane, castroreale |
+| `-c` | `-s` | 72 words | candicans, cruzières |
+| `-a` | `-e` | 68 words | avvenire, abele |
+| `-b` | `-a` | 63 words | bauma, brunetta |
+| `-s` | `-e` | 62 words | suceduje, strutture |
+
+### 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 |
+|------|-----------------|------------|------|
+| williamson | **`william-s-on`** | 7.5 | `s` |
+| lombardore | **`lombard-o-re`** | 7.5 | `o` |
+| spantiasse | **`spantia-s-se`** | 7.5 | `s` |
+| yutanduchi | **`yutandu-ch-i`** | 7.5 | `ch` |
+| castiadas | **`castiad-a-s`** | 7.5 | `a` |
+| costituent | **`costitu-e-nt`** | 7.5 | `e` |
+| rochester | **`ro-ch-ester`** | 7.5 | `ester` |
+| condorcet | **`condorc-e-t`** | 7.5 | `e` |
+| camposano | **`campo-sa-no`** | 7.5 | `sa` |
+| lalacelle | **`la-la-celle`** | 7.5 | `celle` |
+| franchetii | **`franchet-i-i`** | 7.5 | `i` |
+| napolioni | **`napoli-on-i`** | 6.0 | `napoli` |
+| alcantara | **`al-cantar-a`** | 6.0 | `cantar` |
+| paternità | **`pa-terni-tà`** | 6.0 | `terni` |
+| franchista | **`franch-is-ta`** | 6.0 | `franch` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Piedmontese 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 (4.08x) |
+| N-gram | **2-gram** | Lowest perplexity (256) |
+| Markov | **Context-4** | Highest predictability (93.3%) |
+| 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 18:09:59*

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