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README.md

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+---
+language: gd
+language_name: Scottish Gaelic
+language_family: celtic_goidelic
+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-celtic_goidelic
+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: 4.255
+  - name: best_isotropy
+    type: isotropy
+    value: 0.8836
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-04
+---
+
+# Scottish Gaelic - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Scottish Gaelic** 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** | 3.505x | 3.51 | 0.1554% | 361,085 |
+| **16k** | 3.790x | 3.79 | 0.1680% | 333,933 |
+| **32k** | 4.047x | 4.05 | 0.1794% | 312,732 |
+| **64k** | 4.255x 🏆 | 4.26 | 0.1886% | 297,465 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Cleachdaidhean eile aig Cuach (soilleireachadh) 'S e baile ann an Contae Dhoire ...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁cleachdaidhean ▁eile ▁aig ▁cu ach ▁( s oilleir eachadh ) ... (+20 more)` | 30 |
+| 16k | `▁cleachdaidhean ▁eile ▁aig ▁cuach ▁( soilleireachadh ) ▁' s ▁e ... (+16 more)` | 26 |
+| 32k | `▁cleachdaidhean ▁eile ▁aig ▁cuach ▁( soilleireachadh ) ▁' s ▁e ... (+16 more)` | 26 |
+| 64k | `▁cleachdaidhean ▁eile ▁aig ▁cuach ▁( soilleireachadh ) ▁' s ▁e ... (+16 more)` | 26 |
+
+**Sample 2:** `Fang, feichid, preachan: eun a tha ag ithe beathaichean marbh. Tha sgòrnan fada ...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁f ang , ▁fe ich id , ▁pr eachan : ... (+16 more)` | 26 |
+| 16k | `▁f ang , ▁fe ich id , ▁pr eachan : ... (+15 more)` | 25 |
+| 32k | `▁fang , ▁fe ich id , ▁pr eachan : ▁eun ... (+13 more)` | 23 |
+| 64k | `▁fang , ▁fe ichid , ▁preachan : ▁eun ▁a ▁tha ... (+11 more)` | 21 |
+
+**Sample 3:** `'S e bliadhna-leum a bha ann an (MLXXVI). Tachartasan Breithean Bàsan`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+8 more)` | 18 |
+| 16k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+8 more)` | 18 |
+| 32k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+7 more)` | 17 |
+| 64k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+7 more)` | 17 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.255x compression
+- **Lowest UNK Rate:** 8k with 0.1554% 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 | 7,513 | 12.88 | 45,521 | 23.1% | 48.4% |
+| **2-gram** | Subword | 241 🏆 | 7.91 | 4,942 | 71.6% | 98.7% |
+| **3-gram** | Word | 22,207 | 14.44 | 79,383 | 11.8% | 32.1% |
+| **3-gram** | Subword | 1,855 | 10.86 | 33,559 | 33.3% | 74.9% |
+| **4-gram** | Word | 49,301 | 15.59 | 146,615 | 8.5% | 23.6% |
+| **4-gram** | Subword | 9,340 | 13.19 | 158,296 | 18.3% | 46.8% |
+| **5-gram** | Word | 45,346 | 15.47 | 116,302 | 7.6% | 22.5% |
+| **5-gram** | Subword | 29,576 | 14.85 | 374,322 | 11.3% | 32.2% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `ann an` | 44,901 |
+| 2 | `s e` | 15,127 |
+| 3 | `na h` | 12,468 |
+| 4 | `an t` | 11,551 |
+| 5 | `a tha` | 10,609 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `na h alba` | 6,088 |
+| 2 | `a th ann` | 4,967 |
+| 3 | `a tha ann` | 4,917 |
+| 4 | `ceanglaichean a mach` | 3,964 |
+| 5 | `tha ann an` | 3,533 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a tha ann an` | 3,497 |
+| 2 | `a th ann an` | 2,302 |
+| 3 | `iomraidhean ceanglaichean a mach` | 2,128 |
+| 4 | `a tha ann am` | 1,042 |
+| 5 | `os cionn ìre na` | 1,011 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `os cionn ìre na mara` | 957 |
+| 2 | `a rèir a chunntais shluaigh` | 730 |
+| 3 | `an duais nobel ann an` | 688 |
+| 4 | `a chunntais shluaigh ann an` | 668 |
+| 5 | `rèir a chunntais shluaigh ann` | 667 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ a` | 512,441 |
+| 2 | `a n` | 416,454 |
+| 3 | `n _` | 394,988 |
+| 4 | `a i` | 315,323 |
+| 5 | `c h` | 267,240 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a n _` | 225,121 |
+| 2 | `_ a n` | 207,360 |
+| 3 | `a c h` | 122,355 |
+| 4 | `n _ a` | 119,942 |
+| 5 | `a n n` | 106,926 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ a n _` | 121,672 |
+| 2 | `_ a n n` | 77,613 |
+| 3 | `a n n _` | 71,439 |
+| 4 | `n n _ a` | 66,595 |
+| 5 | `n _ a n` | 59,630 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a n n _ a` | 59,213 |
+| 2 | `_ a n n _` | 58,945 |
+| 3 | `n _ a n _` | 50,924 |
+| 4 | `n n _ a n` | 48,309 |
+| 5 | `_ a g u s` | 39,355 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 241
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~32% 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 | 0.8527 | 1.806 | 5.97 | 117,662 | 14.7% |
+| **1** | Subword | 0.8777 | 1.837 | 6.88 | 2,032 | 12.2% |
+| **2** | Word | 0.2808 | 1.215 | 1.75 | 699,420 | 71.9% |
+| **2** | Subword | 0.8889 | 1.852 | 5.20 | 13,963 | 11.1% |
+| **3** | Word | 0.1273 | 1.092 | 1.27 | 1,221,448 | 87.3% |
+| **3** | Subword | 0.7487 | 1.680 | 3.81 | 72,603 | 25.1% |
+| **4** | Word | 0.0625 🏆 | 1.044 | 1.11 | 1,546,357 | 93.7% |
+| **4** | Subword | 0.6229 | 1.540 | 2.73 | 276,636 | 37.7% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `an aghaidh poileasaidh airson na h uile dùinte a th ann an old man wins nobel`
+2. `a tha denver na gàidhealtachd agus thogadh e dìreach ri bràthair agus tha co chruthachd còmhla`
+3. `ann an t ainm oifigeil na h alba pàrlamaid à alba chlach ghràin a mhoncaidh lùchairt`
+
+**Context Size 2:**
+
+1. `ann an sealtainn eadar unst agus fetlar a tha ealantach cruthachail air cuan dubh drilseach bho n`
+2. `s e 0 5 km 0 3 km 1 7 ha 4 7 acair s e am`
+3. `na h alba a stiuireadh rugbaidh ann an altaibh air teicneòlasaibh mar eisimpleir theirear gun robh c...`
+
+**Context Size 3:**
+
+1. `na h alba a tha ann an càrn deas tha e ainmeil gus ar làithean lunds universitetchaochail an`
+2. `a th ann an ainmean àite cuideachd mar eispimpleir sgùrr alasdair a bheinn as àirde ann an agri`
+3. `a tha ann an sgoil air a bheil shambellie house trust iomraidhean na h eilbheise suidhichte ri taobh`
+
+**Context Size 4:**
+
+1. `a tha ann an diospròsium le samhla dy agus àireamh atamach 66 s e meatailt bog agus lantanach a`
+2. `a th ann an chernihivska oblast ucràinis черні́гівська о́бласть ainm neo fhoirmeil khmelnychchyna s ...`
+3. `iomraidhean ceanglaichean a mach dealbhan aig geograph org na h alba ann an arcaibh`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_botile_lbr.omin`
+2. `achnnnnomzogheat`
+3. `nnbhchùtiaseir_m`
+
+**Context Size 2:**
+
+1. `_an_logha_ghearai`
+2. `an_na_daidhe_fhom`
+3. `n_bh_a_'s_jonzoli`
+
+**Context Size 3:**
+
+1. `an_nan_breithrìomh`
+2. `_an-riagh_sìos_(ga`
+3. `ach_(pàrt_aireadh_`
+
+**Context Size 4:**
+
+1. `_an_àitean_cervus_e`
+2. `_ann_an_ierus_cionn`
+3. `ann_an_na_phàrtaidh`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 93.7% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (276,636 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 | 52,313 |
+| Total Tokens | 2,168,944 |
+| Mean Frequency | 41.46 |
+| Median Frequency | 4 |
+| Frequency Std Dev | 965.84 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | an | 124,281 |
+| 2 | a | 122,798 |
+| 3 | ann | 64,022 |
+| 4 | na | 56,811 |
+| 5 | e | 46,001 |
+| 6 | tha | 39,597 |
+| 7 | agus | 39,434 |
+| 8 | air | 34,639 |
+| 9 | s | 20,787 |
+| 10 | am | 19,741 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | według | 2 |
+| 2 | kodu | 2 |
+| 3 | grup | 2 |
+| 4 | zawodowych | 2 |
+| 5 | sztuka | 2 |
+| 6 | muzea | 2 |
+| 7 | britishpedia | 2 |
+| 8 | osobistości | 2 |
+| 9 | bph | 2 |
+| 10 | frightened | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.1387 |
+| R² (Goodness of Fit) | 0.997741 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 47.5% |
+| Top 1,000 | 72.9% |
+| Top 5,000 | 86.6% |
+| Top 10,000 | 91.4% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9977 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 47.5% of corpus
+- **Long Tail:** 42,313 words needed for remaining 8.6% 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 | 0.8836 | 0.3460 | N/A | N/A |
+| **mono_64d** | 64 | 0.8732 | 0.2710 | N/A | N/A |
+| **mono_128d** | 128 | 0.8209 | 0.2012 | N/A | N/A |
+| **aligned_32d** | 32 | 0.8836 🏆 | 0.3541 | 0.0940 | 0.4500 |
+| **aligned_64d** | 64 | 0.8732 | 0.2677 | 0.1360 | 0.4920 |
+| **aligned_128d** | 128 | 0.8209 | 0.2012 | 0.2460 | 0.6360 |
+
+### Key Findings
+
+- **Best Isotropy:** aligned_32d with 0.8836 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.2735. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 24.6% 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 | **-0.299** | 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 |
+|--------|----------|
+| `-ch` | chlabhier, chraobh, chleachdaidhean |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-n` | elfyn, newton, pàisdean |
+| `-h` | dhiadhaidh, dhùnleibh, uralach |
+| `-an` | pàisdean, seaghan, bliadhaichean |
+| `-ch` | uralach, catailiseach, shealbhach |
+| `-dh` | dhiadhaidh, tràghaidh, bhrathadh |
+| `-ach` | uralach, catailiseach, shealbhach |
+| `-ean` | pàisdean, bliadhaichean, bawean |
+| `-adh` | bhrathadh, fòrladh, caochladh |
+
+### 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 |
+|------|----------|------------------|----------|
+| `ilea` | 1.69x | 137 contexts | eilean, àilean, bileag |
+| `irea` | 1.60x | 117 contexts | coirea, èireas, uiread |
+| `aidh` | 1.48x | 165 contexts | taidh, uaidh, faidh |
+| `raid` | 1.74x | 75 contexts | òraid, àraid, braid |
+| `inne` | 1.47x | 158 contexts | rinne, tinne, inner |
+| `reac` | 1.87x | 51 contexts | reach, breac, creach |
+| `isea` | 1.53x | 112 contexts | isean, lùisea, misean |
+| `ainn` | 1.61x | 81 contexts | uainn, rainn, lainn |
+| `hean` | 1.74x | 56 contexts | bhean, shean, mhean |
+| `bhai` | 1.45x | 112 contexts | bhain, bhail, ubhail |
+| `hadh` | 2.17x | 20 contexts | achadh, chadha, iadhadh |
+| `chai` | 1.45x | 89 contexts | chain, chaid, chair |
+
+### 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 |
+|--------|--------|-----------|----------|
+| `-ch` | `-h` | 75 words | choltach, chraoibh |
+| `-ch` | `-n` | 62 words | chomharran, christiaan |
+| `-ch` | `-ch` | 35 words | choltach, chòigeach |
+| `-ch` | `-an` | 29 words | chomharran, christiaan |
+| `-ch` | `-dh` | 29 words | chòmhradh, cheasnachadh |
+| `-ch` | `-ach` | 23 words | choltach, chòigeach |
+| `-ch` | `-ean` | 17 words | chomharraidhean, chlachairean |
+| `-ch` | `-adh` | 17 words | chòmhradh, cheasnachadh |
+| `-ch` | `-in` | 12 words | chruinnein, chaocháin |
+| `-ch` | `-idh` | 12 words | chàraidh, chnagaidh |
+
+### 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 |
+|------|-----------------|------------|------|
+| cruthachadh | **`cruth-ach-adh`** | 6.0 | `cruth` |
+| teasachadh | **`teas-ach-adh`** | 6.0 | `teas` |
+| blàthachadh | **`blàth-ach-adh`** | 6.0 | `blàth` |
+| adhartachadh | **`adhart-ach-adh`** | 6.0 | `adhart` |
+| srònachadh | **`sròn-ach-adh`** | 6.0 | `sròn` |
+| ceàrnaidhean | **`ceàrna-idh-ean`** | 6.0 | `ceàrna` |
+| ràitheachan | **`ràithe-ach-an`** | 6.0 | `ràithe` |
+| itealachadh | **`iteal-ach-adh`** | 6.0 | `iteal` |
+| ealainean | **`eala-in-ean`** | 6.0 | `eala` |
+| chliathach | **`ch-liath-ach`** | 6.0 | `liath` |
+| sinnsirean | **`sinnsir-ean`** | 4.5 | `sinnsir` |
+| prionnsabalan | **`prionnsabal-an`** | 4.5 | `prionnsabal` |
+| feumalachdan | **`feumalachd-an`** | 4.5 | `feumalachd` |
+| sheinneadairean | **`sheinneadair-ean`** | 4.5 | `sheinneadair` |
+| breitheamhan | **`breitheamh-an`** | 4.5 | `breitheamh` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Scottish Gaelic 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 (4.25x) |
+| N-gram | **2-gram** | Lowest perplexity (241) |
+| Markov | **Context-4** | Highest predictability (93.7%) |
+| 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: 2026-01-04 15:23:34*

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