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README.md

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+---
+language: inh
+language_name: Ingush
+language_family: caucasian_northeast
+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-caucasian_northeast
+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: 4.589
+  - name: best_isotropy
+    type: isotropy
+    value: 0.7882
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-10
+---
+
+# Ingush - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ingush** 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** | 3.549x | 3.56 | 0.1349% | 201,601 |
+| **16k** | 3.935x | 3.94 | 0.1496% | 181,782 |
+| **32k** | 4.258x | 4.27 | 0.1619% | 168,012 |
+| **64k** | 4.589x 🏆 | 4.60 | 0.1745% | 155,892 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Ме́ксика ( ), официальни — Мексикахой Хетта ШтаташМИД России | | МЕКСИКА () — па...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁ме ́ кс ика ▁( ▁), ▁официальни ▁— ▁мекс ика ... (+19 more)` | 29 |
+| 16k | `▁ме ́ кс ика ▁( ▁), ▁официальни ▁— ▁мексика хой ... (+17 more)` | 27 |
+| 32k | `▁ме ́ кс ика ▁( ▁), ▁официальни ▁— ▁мексика хой ... (+16 more)` | 26 |
+| 64k | `▁ме́ксика ▁( ▁), ▁официальни ▁— ▁мексикахой ▁хетта ▁штаташмид ▁россии ▁| ... (+11 more)` | 21 |
+
+**Sample 2:** `Нотр-Дам-де-Пари е Парижа Даьла Наьна Элгац (, ) — Париже йоалла католикий элгац...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁н от р - дам - де - п ари ... (+27 more)` | 37 |
+| 16k | `▁нот р - дам - де - пари ▁е ▁пари ... (+21 more)` | 31 |
+| 32k | `▁нот р - дам - де - пари ▁е ▁парижа ... (+20 more)` | 30 |
+| 64k | `▁нотр - дам - де - пари ▁е ▁парижа ▁даьла ... (+18 more)` | 28 |
+
+**Sample 3:** `«Нийсхо» (я) () — шера гӀалгӀашкара хьаяьккха́ ГӀалме шахьар юха ГӀалгӀай Респуб...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁« нийс хо » ▁( я ) ▁() ▁— ▁шера ... (+25 more)` | 35 |
+| 16k | `▁« нийс хо » ▁( я ) ▁() ▁— ▁шера ... (+20 more)` | 30 |
+| 32k | `▁« нийсхо » ▁( я ) ▁() ▁— ▁шера ▁гӏалгӏаш ... (+17 more)` | 27 |
+| 64k | `▁« нийсхо » ▁( я ) ▁() ▁— ▁шера ▁гӏалгӏашкара ... (+15 more)` | 25 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.589x compression
+- **Lowest UNK Rate:** 8k with 0.1349% 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 | 2,700 | 11.40 | 4,486 | 18.1% | 59.8% |
+| **2-gram** | Subword | 374 🏆 | 8.55 | 2,693 | 59.4% | 97.6% |
+| **3-gram** | Word | 2,178 | 11.09 | 4,133 | 19.5% | 65.5% |
+| **3-gram** | Subword | 3,053 | 11.58 | 18,826 | 23.3% | 64.6% |
+| **4-gram** | Word | 4,659 | 12.19 | 9,587 | 15.7% | 49.4% |
+| **4-gram** | Subword | 14,259 | 13.80 | 75,178 | 11.2% | 36.9% |
+| **5-gram** | Word | 3,632 | 11.83 | 7,779 | 17.6% | 54.3% |
+| **5-gram** | Subword | 35,588 | 15.12 | 140,686 | 7.5% | 25.1% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `белгалдаккхар тӏатовжамаш` | 415 |
+| 2 | `гӏалгӏай мехка` | 328 |
+| 3 | `з хь` | 315 |
+| 4 | `вай з` | 307 |
+| 5 | `хьажа иштта` | 255 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `вай з хь` | 307 |
+| 2 | `шераш вай з` | 232 |
+| 3 | `нах баха моттигаш` | 153 |
+| 4 | `хь шераш вай` | 130 |
+| 5 | `з хь шераш` | 130 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `шераш вай з хь` | 232 |
+| 2 | `вай з хь шераш` | 130 |
+| 3 | `з хь шераш вай` | 130 |
+| 4 | `хь шераш вай з` | 130 |
+| 5 | `шахьара нах баха моттигаш` | 130 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `вай з хь шераш вай` | 130 |
+| 2 | `з хь шераш вай з` | 130 |
+| 3 | `хь шераш вай з хь` | 130 |
+| 4 | `шераш вай з хь шераш` | 117 |
+| 5 | `гӏа шераш вай з хь` | 100 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `а _` | 75,922 |
+| 2 | `а р` | 27,088 |
+| 3 | `ӏ а` | 26,314 |
+| 4 | `а л` | 24,378 |
+| 5 | `р а` | 24,271 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `х ь а` | 13,086 |
+| 2 | `г ӏ а` | 13,029 |
+| 3 | `а ш _` | 11,108 |
+| 4 | `р а _` | 10,332 |
+| 5 | `ч а _` | 9,547 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `а р а _` | 4,962 |
+| 2 | `а ч а _` | 4,074 |
+| 3 | `_ х ь а` | 3,915 |
+| 4 | `г ӏ а л` | 3,870 |
+| 5 | `а г ӏ а` | 3,736 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `х и н н а` | 3,488 |
+| 2 | `_ х и н н` | 3,331 |
+| 3 | `г ӏ а л г` | 3,121 |
+| 4 | `ӏ а л г ӏ` | 3,119 |
+| 5 | `а л г ӏ а` | 3,111 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 374
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~25% 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 | 0.6550 | 1.575 | 3.54 | 50,260 | 34.5% |
+| **1** | Subword | 1.2189 | 2.328 | 9.47 | 622 | 0.0% |
+| **2** | Word | 0.1442 | 1.105 | 1.26 | 177,219 | 85.6% |
+| **2** | Subword | 1.1111 | 2.160 | 6.21 | 5,892 | 0.0% |
+| **3** | Word | 0.0357 | 1.025 | 1.05 | 221,229 | 96.4% |
+| **3** | Subword | 0.8323 | 1.781 | 3.70 | 36,562 | 16.8% |
+| **4** | Word | 0.0120 🏆 | 1.008 | 1.02 | 230,572 | 98.8% |
+| **4** | Subword | 0.5706 | 1.485 | 2.34 | 135,317 | 42.9% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `а долаш ший йоазонашта юкъе лелаш хул цхьайолча хана денз цун бизнес дегӏакхувлара дукха мехкарий ам...`
+2. `я лоам жӏайраха шахьаре я аьдагӏий мотт хьехаш аьлте юрта хьисапе моттиг хиннай шера мальсагов дошлу...`
+3. `гӏалгӏай мохк баьккха́ ва́гӏача моастагӏчунга паргӏата ма дарра аьлча гӏалгӏаша къаьстта кубчий пх��а...`
+
+**Context Size 2:**
+
+1. `белгалдаккхар тӏатовжамаш чеботарев а и робакидзеи даьча тохкамех фаьппий кхаькхалоех е ӏадатех а е ...`
+2. `гӏалгӏай мехка паччахьалкъен филармони хамхой ахьмада цӏерагӏа я юрт ларс жӏайрахой баьха моттиг улл...`
+3. `з хь 590 гӏа шераш 390 гӏа шераш vii бӏаьшу 600 гӏа шераш вай з хь xcix`
+
+**Context Size 3:**
+
+1. `вай з хь шераш вай з хь xxx xxix xxviii xxvii xxvi xxv xxiv xxiii xxii xxi 2`
+2. `шераш вай з хь 830 гӏа шераш вай з хь шераш вай з хь 7 шу i бӏаьшера`
+3. `з хь шераш вай з хь шераш вай з хь шераш вай з хь шераш вай з хь`
+
+**Context Size 4:**
+
+1. `шераш вай з хь 720 гӏа шераш вай з хь 50 гӏа шераш вай з хь шераш вай з`
+2. `хь шераш вай з хь шераш вай з хь 400 гӏа шераш вай з хь шераш вай з хь`
+3. `з хь шераш вай з хь xiv бӏаьшу вай з хь тӏатовжамаш`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `аш_дндолега_афал`
+2. `_коа,_—_«цхьерми`
+3. `оаллг_пргӏе._мап`
+
+**Context Size 2:**
+
+1. `а_сийчеи_бе._хьа_`
+2. `архойиха_худжамаӏ`
+3. `ӏайча_хаязыкнофи_`
+
+**Context Size 3:**
+
+1. `хьалкхар_тӏа_—_«бӏ`
+2. `гӏалаходкуменна_ба`
+3. `аш_лелал_ха́ннай._б`
+
+**Context Size 4:**
+
+1. `ара_арахой_2_обозна`
+2. `ача_между_из,_нохчи`
+3. `_хьаяхача_багарга_х`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 98.8% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (135,317 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 | 19,260 |
+| Total Tokens | 235,079 |
+| Mean Frequency | 12.21 |
+| Median Frequency | 3 |
+| Frequency Std Dev | 72.65 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | а | 6,393 |
+| 2 | я | 2,455 |
+| 3 | гӏалгӏай | 2,253 |
+| 4 | из | 2,010 |
+| 5 | шера | 1,966 |
+| 6 | да | 1,931 |
+| 7 | и | 1,329 |
+| 8 | белгалдаккхар | 1,258 |
+| 9 | в | 1,233 |
+| 10 | тӏа | 1,139 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | ориентальни | 2 |
+| 2 | балтий | 2 |
+| 3 | лорала́ | 2 |
+| 4 | кхерамзеи | 2 |
+| 5 | wie | 2 |
+| 6 | дарбанчаш | 2 |
+| 7 | легализаци | 2 |
+| 8 | целители | 2 |
+| 9 | практикаш | 2 |
+| 10 | лоралгахь | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.0116 |
+| R² (Goodness of Fit) | 0.991479 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 28.1% |
+| Top 1,000 | 59.7% |
+| Top 5,000 | 82.4% |
+| Top 10,000 | 91.3% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9915 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 28.1% of corpus
+- **Long Tail:** 9,260 words needed for remaining 8.7% 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 | 0.7882 🏆 | 0.3485 | N/A | N/A |
+| **mono_64d** | 64 | 0.3727 | 0.3608 | N/A | N/A |
+| **mono_128d** | 128 | 0.0496 | 0.3296 | N/A | N/A |
+| **aligned_32d** | 32 | 0.7882 | 0.3541 | 0.0140 | 0.1220 |
+| **aligned_64d** | 64 | 0.3727 | 0.3473 | 0.0180 | 0.1180 |
+| **aligned_128d** | 128 | 0.0496 | 0.3275 | 0.0380 | 0.1560 |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.7882 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.3446. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 3.8% 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 | **1.160** | High formulaic/idiomatic 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 |
+|--------|----------|
+| `-д` | дийхка, довта, даьржаи |
+| `-к` | классификациям, кӏориганаькъан, кодекса |
+| `-с` | сулак, сомали, статьяш |
+| `-б` | бунак, берашта, белгалъеш |
+| `-м` | мусульманами, мухтарова, мальта |
+| `-а` | астрале, аьтта, амхарой |
+| `-т` | тӏахьелхаш, тайпового, тийна |
+| `-хьа` | хьалхадоахаш, хьалхашкарча, хьаста |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-а` | община, мухтарова, юххьанцарча |
+| `-и` | мусульманами, жигули, экзотермически |
+| `-й` | лезгинский, регулярный, амхарой |
+| `-аш` | тӏахьелхаш, воагӏаш, яхараш |
+| `-ш` | тӏахьелхаш, воагӏаш, яхараш |
+| `-е` | астрале, йолае, ӏомаде |
+| `-ий` | лезгинский, къарший, советский |
+| `-ча` | юххьанцарча, йолалуча, хьогденнача |
+
+### 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 |
+|------|----------|------------------|----------|
+| `ккха` | 1.67x | 69 contexts | яккха, йоккха, аьккха |
+| `ькъа` | 1.96x | 30 contexts | шаькъа, ӏаькъа, даькъа |
+| `хьар` | 1.58x | 67 contexts | пхьар, хьарп, хьарме |
+| `амаш` | 1.70x | 45 contexts | тамаш, замаш, ӏамаш |
+| `хача` | 1.85x | 28 contexts | яхача, ухача, кхача |
+| `инна` | 1.92x | 24 contexts | хинна, шинна, хиннар |
+| `аькъ` | 1.78x | 30 contexts | наькъ, даькъ, шаькъа |
+| `аккх` | 1.89x | 24 contexts | боаккх, воаккх, чаккхе |
+| `кхар` | 1.70x | 33 contexts | кхарт, декхар, акхаре |
+| `ахьа` | 1.38x | 55 contexts | кхахьа, арахьа, дахьаш |
+| `лгал` | 1.78x | 21 contexts | кулгал, белгал, белгала |
+| `хинн` | 1.93x | 16 contexts | хинна, хиннар, хиннад |
+
+### 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 |
+|--------|--------|-----------|----------|
+| `-д` | `-а` | 176 words | длина, дешагара |
+| `-к` | `-а` | 148 words | кӏезигагӏа, кепагӏа |
+| `-б` | `-а` | 110 words | баьлча, бийтта |
+| `-м` | `-а` | 104 words | малхбоалега, мукха |
+| `-г` | `-а` | 91 words | гӏалгӏайченна, галашкархоша |
+| `-т` | `-а` | 80 words | тайпарча, тӏаргамара |
+| `-а` | `-а` | 79 words | арадийна, арахецарца |
+| `-п` | `-а` | 67 words | принципаца, произведенеша |
+| `-с` | `-а` | 61 words | секретара, сша |
+| `-к` | `-и` | 59 words | клавиши, критически |
+
+### 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 |
+|------|-----------------|------------|------|
+| шоллагӏчох | **`шоллагӏч-о-х`** | 7.5 | `о` |
+| кепатехача | **`кепатех-а-ча`** | 7.5 | `а` |
+| кулгалдара | **`кулгалд-а-ра`** | 7.5 | `а` |
+| баьцакомар | **`баьцако-м-ар`** | 7.5 | `м` |
+| дӏатиллай | **`дӏатилл-а-й`** | 7.5 | `а` |
+| наькъахои | **`наькъах-о-и`** | 7.5 | `о` |
+| исбахьлен | **`исбахь-л-ен`** | 7.5 | `л` |
+| кириллицай | **`кириллиц-а-й`** | 7.5 | `а` |
+| латтандаь | **`латтанд-а-ь`** | 7.5 | `а` |
+| гӏалгӏашкара | **`гӏалгӏаш-ка-ра`** | 7.5 | `ка` |
+| гӏоазотаца | **`гӏоазот-а-ца`** | 7.5 | `а` |
+| моттигашкара | **`моттигаш-ка-ра`** | 7.5 | `ка` |
+| хьаракаца | **`хьара-ка-ца`** | 7.5 | `ка` |
+| малхбоалехьаи | **`малхбоалехь-а-и`** | 7.5 | `а` |
+| республикаца | **`республик-а-ца`** | 7.5 | `а` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Ingush shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.
+
+> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.
+
+---
+## 7. Summary & Recommendations
+
+![Performance Dashboard](visualizations/performance_dashboard.png)
+
+### Production Recommendations
+
+| Component | Recommended | Rationale |
+|-----------|-------------|-----------|
+| Tokenizer | **64k BPE** | Best compression (4.59x) |
+| N-gram | **2-gram** | Lowest perplexity (374) |
+| Markov | **Context-4** | Highest predictability (98.8%) |
+| 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 04:22:21*

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