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README.md

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+---
+language: sc
+language_name: Sardinian
+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: 4.260
+  - name: best_isotropy
+    type: isotropy
+    value: 0.8587
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-10
+---
+
+# Sardinian - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sardinian** 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** | 3.473x | 3.47 | 0.0446% | 549,623 |
+| **16k** | 3.769x | 3.77 | 0.0484% | 506,460 |
+| **32k** | 4.039x | 4.04 | 0.0518% | 472,647 |
+| **64k** | 4.260x 🏆 | 4.26 | 0.0547% | 448,103 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Thomas Duane "Tom" Lister, Jr. (Compton, California, 24 làmpadas, – Marina del R...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁thomas ▁du ane ▁" t om " ▁l ister , ... (+36 more)` | 46 |
+| 16k | `▁thomas ▁du ane ▁" t om " ▁l ister , ... (+34 more)` | 44 |
+| 32k | `▁thomas ▁du ane ▁" tom " ▁l ister , ▁jr ... (+32 more)` | 42 |
+| 64k | `▁thomas ▁du ane ▁" tom " ▁l ister , ▁jr ... (+31 more)` | 41 |
+
+**Sample 2:** `Harly est unu comunu frantzesu de 1.803 abitantes posti in su dipartimentu de s'...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁h arl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 ... (+30 more)` | 40 |
+| 16k | `▁h arl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 ... (+27 more)` | 37 |
+| 32k | `▁h arl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 ... (+25 more)` | 35 |
+| 64k | `▁harl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 . ... (+24 more)` | 34 |
+
+**Sample 3:** `Wikipedia in danesu est sa versione in limba danesa de Wikipedia. Ligàmenes este...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁dan esa ... (+7 more)` | 17 |
+| 16k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁danesa ▁de ... (+5 more)` | 15 |
+| 32k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁danesa ▁de ... (+5 more)` | 15 |
+| 64k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁danesa ▁de ... (+5 more)` | 15 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.260x compression
+- **Lowest UNK Rate:** 8k with 0.0446% 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 | 10,116 | 13.30 | 48,306 | 21.8% | 41.6% |
+| **2-gram** | Subword | 212 🏆 | 7.73 | 4,052 | 75.4% | 99.3% |
+| **3-gram** | Word | 34,903 | 15.09 | 73,271 | 6.8% | 22.4% |
+| **3-gram** | Subword | 1,622 | 10.66 | 28,188 | 33.1% | 78.3% |
+| **4-gram** | Word | 67,185 | 16.04 | 105,292 | 4.7% | 13.9% |
+| **4-gram** | Subword | 8,775 | 13.10 | 131,212 | 17.0% | 45.8% |
+| **5-gram** | Word | 45,338 | 15.47 | 61,362 | 4.7% | 14.0% |
+| **5-gram** | Subword | 32,250 | 14.98 | 327,721 | 10.4% | 28.7% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `de su` | 26,241 |
+| 2 | `de sa` | 19,958 |
+| 3 | `in su` | 16,843 |
+| 4 | `de s` | 13,070 |
+| 5 | `a su` | 7,083 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a pustis de` | 2,120 |
+| 2 | `sa provìntzia de` | 1,125 |
+| 3 | `de sa provìntzia` | 923 |
+| 4 | `e in su` | 665 |
+| 5 | `de su de` | 661 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `de sa provìntzia de` | 812 |
+| 2 | `a pustis de sa` | 566 |
+| 3 | `est una bidda de` | 362 |
+| 4 | `àteros progetos de s` | 351 |
+| 5 | `in su mese de` | 325 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `nùmeros romanos est un annu` | 223 |
+| 2 | `in nùmeros romanos est un` | 223 |
+| 3 | `romanos est un annu incomintzadu` | 213 |
+| 4 | `àteros progetos de s ispagna` | 191 |
+| 5 | `progetos de s ispagna de` | 187 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `e _` | 405,145 |
+| 2 | `_ s` | 350,527 |
+| 3 | `a _` | 339,728 |
+| 4 | `u _` | 299,991 |
+| 5 | `s _` | 254,458 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `d e _` | 190,941 |
+| 2 | `_ d e` | 187,576 |
+| 3 | `e _ s` | 119,077 |
+| 4 | `_ s u` | 115,536 |
+| 5 | `s u _` | 104,724 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ d e _` | 170,944 |
+| 2 | `_ s u _` | 92,319 |
+| 3 | `d e _ s` | 79,656 |
+| 4 | `_ i n _` | 69,238 |
+| 5 | `_ s a _` | 67,044 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ d e _ s` | 77,101 |
+| 2 | `u _ d e _` | 40,816 |
+| 3 | `a _ d e _` | 38,441 |
+| 4 | `e _ s u _` | 37,005 |
+| 5 | `s _ d e _` | 34,532 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 212
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.8701 | 1.828 | 5.46 | 151,383 | 13.0% |
+| **1** | Subword | 1.0011 | 2.002 | 7.08 | 1,758 | 0.0% |
+| **2** | Word | 0.3078 | 1.238 | 1.81 | 823,593 | 69.2% |
+| **2** | Subword | 0.8639 | 1.820 | 4.95 | 12,441 | 13.6% |
+| **3** | Word | 0.1271 | 1.092 | 1.24 | 1,483,665 | 87.3% |
+| **3** | Subword | 0.7559 | 1.689 | 3.77 | 61,608 | 24.4% |
+| **4** | Word | 0.0475 🏆 | 1.033 | 1.07 | 1,828,163 | 95.3% |
+| **4** | Subword | 0.6290 | 1.547 | 2.78 | 232,073 | 37.1% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `de su nùmeru de custu casu est cunsiderau su laboratòriu suu fiat però cherian prenare sos`
+2. `su mesi de monk dizzy miss italia nelle collezioni civiche del film pro sa contea de`
+3. `in diversas sa metade de deghe annos chimbanta detzidende cale aiad appidu puru si repitit comenti`
+
+**Context Size 2:**
+
+1. `de su deretu chi su protzessore esistent vàrios algoritmos de pianificatzione chi òrdinat in su nche...`
+2. `de sa scrivania e is musulmanos in sa rivolutzione de làmpadas tatjana rojc limba islovenu joan isaa...`
+3. `in su sud de sa fae su casteddu de crabas s agatat in bèrziu in uccle a`
+
+**Context Size 3:**
+
+1. `a pustis de sa gherra at progetadu su computadore ace e at fatu sos primos istùdios in nùgoro`
+2. `sa provìntzia de nùgoro su sartu a segunda si podet narrer de gastone chi est istada a fatu`
+3. `de sa provìntzia de cùllieri e in su suzuki umpare a ei ichi negishi e akira suzuki aian`
+
+**Context Size 4:**
+
+1. `de sa provìntzia de aristanis de 945 abitantes de sa provìntzia de aristanis de sa provìntzia de su ...`
+2. `a pustis de sa ruta de su regìmene comunista ghiadu dae su conducator faeddu rumenu chi currespondet...`
+3. `est una bidda de sa provìntzia de aristanis s agatat a 165 metros in pitzu de su mare e`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_ba,_ta_pe_cu_in`
+2. `addet._fiabamesu`
+3. `e_dun_pomulmamic`
+
+**Context Size 2:**
+
+1. `e_casariettis_ber`
+2. `_sa_coreges._“abb`
+3. `a_is_s'it_e_un_un`
+
+**Context Size 3:**
+
+1. `de_sud_altarrùbica`
+2. `_de_sa_madde_sa_de`
+3. `e_s'impostoresu,_c`
+
+**Context Size 4:**
+
+1. `_de_orrosa,_candiga`
+2. `_su_lìgure)._in_s'a`
+3. `de_sos_aiat_pinness`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 95.3% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (232,073 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 | 69,823 |
+| Total Tokens | 2,025,890 |
+| Mean Frequency | 29.01 |
+| Median Frequency | 4 |
+| Frequency Std Dev | 942.93 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | de | 171,535 |
+| 2 | su | 94,182 |
+| 3 | in | 71,523 |
+| 4 | sa | 68,420 |
+| 5 | a | 60,170 |
+| 6 | e | 54,061 |
+| 7 | s | 51,018 |
+| 8 | est | 30,045 |
+| 9 | chi | 26,027 |
+| 10 | sos | 20,994 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | activitystreams | 2 |
+| 2 | hubzilla | 2 |
+| 3 | pleroma | 2 |
+| 4 | əm | 2 |
+| 5 | bonòmine | 2 |
+| 6 | henley | 2 |
+| 7 | cuntribuidore | 2 |
+| 8 | fowey | 2 |
+| 9 | acres | 2 |
+| 10 | holywell | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 0.9676 |
+| R² (Goodness of Fit) | 0.998085 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 48.9% |
+| Top 1,000 | 66.1% |
+| Top 5,000 | 80.2% |
+| Top 10,000 | 86.3% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9981 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 48.9% of corpus
+- **Long Tail:** 59,823 words needed for remaining 13.7% coverage
+
+---
+## 5. Word Embeddings Evaluation
+
+![Embedding Isotropy](visualizations/embedding_isotropy.png)
+
+![Similarity Matrix](visualizations/embedding_similarity.png)
+
+![t-SNE Words](visualizations/tsne_words.png)
+
+![t-SNE Sentences](visualizations/tsne_sentences.png)
+
+
+### 5.1 Cross-Lingual Alignment
+
+![Alignment Quality](visualizations/embedding_alignment_quality.png)
+
+![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)
+
+
+### 5.2 Model Comparison
+
+| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
+|-------|-----------|----------|------------------|---------------|----------------|
+| **mono_32d** | 32 | 0.8587 🏆 | 0.3155 | N/A | N/A |
+| **mono_64d** | 64 | 0.8247 | 0.2399 | N/A | N/A |
+| **mono_128d** | 128 | 0.5602 | 0.1987 | N/A | N/A |
+| **aligned_32d** | 32 | 0.8587 | 0.3275 | 0.0680 | 0.2960 |
+| **aligned_64d** | 64 | 0.8247 | 0.2427 | 0.1140 | 0.4040 |
+| **aligned_128d** | 128 | 0.5602 | 0.1921 | 0.1720 | 0.4840 |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.8587 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.2527. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 17.2% 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 | **-0.511** | 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` | aparcadores, aràbbia, alter |
+| `-s` | stromboli, struth, spargi |
+| `-c` | clannad, contant, cosmològicu |
+| `-p` | prumonite, printzipiada, pelle |
+| `-b` | bagazos, berb, bahn |
+| `-m` | male, metrologia, meridiana |
+| `-t` | temperadura, tinto, tzicatritzes |
+| `-ma` | male, mascia, maidan |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-s` | bagazos, aparcadores, ingendradas |
+| `-a` | jonia, metrologia, temperadura |
+| `-e` | male, àbside, ɔampanile |
+| `-u` | individuu, cosmològicu, circùitu |
+| `-os` | bagazos, interventos, rènnios |
+| `-as` | ingendradas, liliàceas, calicunas |
+| `-i` | stromboli, spargi, cardinali |
+| `-es` | aparcadores, tzicatritzes, immazines |
+
+### 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 |
+|------|----------|------------------|----------|
+| `atzi` | 2.19x | 81 contexts | fatzi, latziu, capatzi |
+| `adas` | 2.35x | 59 contexts | ladas, adasl, badas |
+| `ados` | 2.31x | 53 contexts | dados, lados, nados |
+| `zion` | 2.07x | 65 contexts | azioni, azione, rezione |
+| `tzio` | 1.88x | 92 contexts | tzios, sòtzio, sotzio |
+| `ores` | 2.00x | 69 contexts | cores, mores, oreste |
+| `ntzi` | 1.88x | 63 contexts | àntzis, antzis, dòntzi |
+| `tadu` | 1.89x | 58 contexts | itadu, stadu, istadu |
+| `idad` | 1.80x | 55 contexts | fidada, midade, fidadu |
+| `cont` | 1.66x | 76 contexts | contu, contr, conta |
+| `sard` | 2.26x | 23 contexts | sarde, sardi, sardu |
+| `ntza` | 1.88x | 43 contexts | untza, mantza, lantza |
+
+### 6.4 Affix Compatibility (Co-occurrence)
+
+This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.
+
+| Prefix | Suffix | Frequency | Examples |
+|--------|--------|-----------|----------|
+| `-c` | `-s` | 218 words | cuns, cuntatos |
+| `-a` | `-s` | 169 words | amministrados, antzianos |
+| `-c` | `-a` | 164 words | càndia, cunfinada |
+| `-a` | `-u` | 155 words | altipianu, au |
+| `-p` | `-s` | 146 words | principalis, predis |
+| `-c` | `-e` | 136 words | cambiende, controllare |
+| `-c` | `-u` | 135 words | contu, chidàriu |
+| `-a` | `-a` | 132 words | afetada, anastàtica |
+| `-p` | `-u` | 121 words | provau, potàssiu |
+| `-p` | `-a` | 121 words | parodia, professionista |
+
+### 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 |
+|------|-----------------|------------|------|
+| bielorùssia | **`bielorùs-s-ia`** | 7.5 | `s` |
+| apostrofadu | **`apostrof-a-du`** | 7.5 | `a` |
+| controidu | **`contro-i-du`** | 7.5 | `i` |
+| cuntzedit | **`cuntze-di-t`** | 7.5 | `di` |
+| anteriores | **`anterio-re-s`** | 7.5 | `re` |
+| henderson | **`hender-s-on`** | 7.5 | `s` |
+| apartment | **`apartm-e-nt`** | 7.5 | `e` |
+| atzellerada | **`atzeller-a-da`** | 7.5 | `a` |
+| venetzuela | **`venetzu-e-la`** | 7.5 | `e` |
+| parlophone | **`parloph-o-ne`** | 7.5 | `o` |
+| lentiscus | **`lentis-cu-s`** | 7.5 | `cu` |
+| averguadu | **`avergu-a-du`** | 7.5 | `a` |
+| française | **`françai-s-e`** | 7.5 | `s` |
+| intervìsta | **`intervì-s-ta`** | 7.5 | `s` |
+| percursos | **`percur-s-os`** | 7.5 | `s` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Sardinian 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 (4.26x) |
+| N-gram | **2-gram** | Lowest perplexity (212) |
+| Markov | **Context-4** | Highest predictability (95.3%) |
+| 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 19:44:03*

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