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README.md

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+---
+language: udm
+language_name: Udmurt
+language_family: uralic_permian
+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-uralic_permian
+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: 4.565
+  - name: best_isotropy
+    type: isotropy
+    value: 0.6980
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-11
+---
+
+# Udmurt - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Udmurt** 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** | 3.543x | 3.55 | 0.1375% | 258,898 |
+| **16k** | 3.952x | 3.96 | 0.1534% | 232,054 |
+| **32k** | 4.311x | 4.32 | 0.1673% | 212,774 |
+| **64k** | 4.565x 🏆 | 4.57 | 0.1772% | 200,933 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Байраншур () — Удмуртиысь пичи шур. Бызе Яр ёрослэн музъеметӥз но усе Тум шуре. ...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁бай ран шур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ... (+23 more)` | 33 |
+| 16k | `▁бай ран шур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ... (+22 more)` | 32 |
+| 32k | `▁байран шур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ▁яр ... (+20 more)` | 30 |
+| 64k | `▁байраншур ▁() ▁— ▁удмуртиысь ▁пичи ▁шур . ▁бызе ▁яр ▁ёрослэн ... (+19 more)` | 29 |
+
+**Sample 2:** `Олеся Журакивська (; Киев, СССР, — Украин актриса. Фильмъёс Остров Донбас алфави...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁ол ес я ▁ж ур ак ив ська ▁(; ▁киев ... (+13 more)` | 23 |
+| 16k | `▁ол ес я ▁ж ур ак ив ська ▁(; ▁киев ... (+12 more)` | 22 |
+| 32k | `▁ол еся ▁жур акив ська ▁(; ▁киев , ▁ссср , ... (+9 more)` | 19 |
+| 64k | `▁ол еся ▁журакив ська ▁(; ▁киев , ▁ссср , ▁— ... (+8 more)` | 18 |
+
+**Sample 3:** `Кривой Рог метротрам ( укр. Криворізький швидкісний трамвай )`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁кр ив ой ▁ро г ▁метро т рам ▁( ▁ук ... (+17 more)` | 27 |
+| 16k | `▁крив ой ▁рог ▁метро т рам ▁( ▁ук р . ... (+12 more)` | 22 |
+| 32k | `▁крив ой ▁рог ▁метро трам ▁( ▁укр . ▁крив ор ... (+10 more)` | 20 |
+| 64k | `▁кривой ▁рог ▁метротрам ▁( ▁укр . ▁крив ор і зь ... (+5 more)` | 15 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.565x compression
+- **Lowest UNK Rate:** 8k with 0.1375% 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 | 4,224 | 12.04 | 9,045 | 20.2% | 51.2% |
+| **2-gram** | Subword | 646 🏆 | 9.34 | 3,769 | 43.9% | 95.6% |
+| **3-gram** | Word | 4,567 | 12.16 | 10,317 | 20.4% | 49.5% |
+| **3-gram** | Subword | 5,398 | 12.40 | 30,259 | 15.9% | 50.6% |
+| **4-gram** | Word | 9,357 | 13.19 | 19,488 | 14.9% | 37.3% |
+| **4-gram** | Subword | 23,964 | 14.55 | 134,461 | 8.6% | 28.8% |
+| **5-gram** | Word | 7,868 | 12.94 | 14,631 | 14.0% | 37.7% |
+| **5-gram** | Subword | 56,525 | 15.79 | 261,817 | 5.4% | 21.0% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `j j` | 743 |
+| 2 | `1 тӥ` | 662 |
+| 3 | `synonym of` | 638 |
+| 4 | `now synonym` | 606 |
+| 5 | `rchb f` | 601 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `now synonym of` | 604 |
+| 2 | `j j sm` | 569 |
+| 3 | `ёросысь улон интыос` | 559 |
+| 4 | `арын 1 тӥ` | 533 |
+| 5 | `1 тӥ толшоре` | 490 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `арын 1 тӥ толшоре` | 484 |
+| 2 | `улӥсьёс арын 1 тӥ` | 482 |
+| 3 | `1 тӥ толшоре гуртын` | 478 |
+| 4 | `ёросысь улон интыос ёросысь` | 414 |
+| 5 | `улон интыос ёросысь гуртъёс` | 414 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `улӥсьёс арын 1 тӥ толшоре` | 482 |
+| 2 | `арын 1 тӥ толшоре гуртын` | 478 |
+| 3 | `ёросысь улон интыос ёросысь гуртъёс` | 414 |
+| 4 | `адями лыдъяськиз ёросысь улон интыос` | 404 |
+| 5 | `лыдъяськиз ёросысь улон интыос ёросысь` | 396 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `н _` | 53,739 |
+| 2 | `. _` | 52,122 |
+| 3 | `с ь` | 44,748 |
+| 4 | `_ к` | 43,958 |
+| 5 | `, _` | 37,972 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `с ь _` | 23,826 |
+| 2 | `_ — _` | 21,444 |
+| 3 | `ы с ь` | 19,313 |
+| 4 | `ъ ё с` | 19,179 |
+| 5 | `ы н _` | 19,081 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `ы с ь _` | 17,835 |
+| 2 | `л э н _` | 16,383 |
+| 3 | `_ н о _` | 10,521 |
+| 4 | `. _ — _` | 9,347 |
+| 5 | `ъ ё с _` | 7,031 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `у д м у р` | 5,330 |
+| 2 | `д м у р т` | 5,329 |
+| 3 | `_ у д м у` | 4,783 |
+| 4 | `_ ё р о с` | 4,592 |
+| 5 | `и ы с ь _` | 4,529 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 646
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~21% 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 | 0.6992 | 1.624 | 3.81 | 87,992 | 30.1% |
+| **1** | Subword | 0.9862 | 1.981 | 7.60 | 1,200 | 1.4% |
+| **2** | Word | 0.1500 | 1.110 | 1.29 | 333,544 | 85.0% |
+| **2** | Subword | 0.9701 | 1.959 | 6.05 | 9,108 | 3.0% |
+| **3** | Word | 0.0464 | 1.033 | 1.08 | 427,340 | 95.4% |
+| **3** | Subword | 0.8614 | 1.817 | 4.08 | 55,078 | 13.9% |
+| **4** | Word | 0.0213 🏆 | 1.015 | 1.04 | 457,825 | 97.9% |
+| **4** | Subword | 0.5986 | 1.514 | 2.45 | 224,742 | 40.1% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `но юскаре атаез агнешка но дунай мм пала адями лыдъяськиз пурга ёрослэн музъеметӥз шунды пуксён палл...`
+2. `арын 1 58 арын распределение бере кузон нефтеразведка участокъёс сад ёросын камбарка карын казахстан...`
+3. `тӥ мае пичи пургаысь сель��есхоз озьы ик сезьы кӧжы ӝук пӧзьто вӧсьсы бере баушев софин ӟуч`
+
+**Context Size 2:**
+
+1. `j j wood in j j sm ex koord schum galeola kuhlii rchb f hook f summerh`
+2. `1 тӥ толшоре гуртын 77 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыоссы ёросысь ул...`
+3. `synonym of didactylus paradoxa luer dalström эквадор stelis nana lindl эквадор stelis pudens luer эк...`
+
+**Context Size 3:**
+
+1. `now synonym of crocodeilanthe cauliflora lindl luer pleurothallis pilostoma коста рика now synonym o...`
+2. `j j sm liparis cyperifolia ridl liparis dalessandroi dodson liparis dalzellii hook f liparis xanthin...`
+3. `арын 1 тӥ толшоре гуртын 378 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыоссы`
+
+**Context Size 4:**
+
+1. `арын 1 тӥ толшоре гуртын 1 адями лыдъяськиз пурга ёросысь улон интыос пурга ёросысь гуртъёс улон инт...`
+2. `улӥсьёс арын 1 тӥ толшоре гуртын 82 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыос...`
+3. `1 тӥ толшоре гуртын 43 адями лыдъяськиз ёросысь улон интыос ёросысь гуртъёс улон интыоссы`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_кеныст_чыни_._д`
+2. `ай,_ктерспёсканы`
+3. `сь._taccyncrs_ва`
+
+**Context Size 2:**
+
+1. `н_1-тӥсь_болос._e`
+2. `._—_вылэсовитич_(`
+3. `сь._—_aglowiedipt`
+
+**Context Size 3:**
+
+1. `сь_выль_венграв_мо`
+2. `_—_кость_садово_пр`
+3. `ысь_еврок_(hoehne_`
+
+**Context Size 4:**
+
+1. `ысь_улос,_кубикет_с`
+2. `лэн_быдӟалаз_дӥсько`
+3. `_но_пичи_луыса._а._`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 97.9% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (224,742 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 | 35,258 |
+| Total Tokens | 485,306 |
+| Mean Frequency | 13.76 |
+| Median Frequency | 3 |
+| Frequency Std Dev | 88.68 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | но | 10,962 |
+| 2 | арын | 3,468 |
+| 3 | тӥ | 2,839 |
+| 4 | удмурт | 2,798 |
+| 5 | luer | 2,289 |
+| 6 | гурт | 2,284 |
+| 7 | ёросысь | 2,189 |
+| 8 | 1 | 2,085 |
+| 9 | со | 1,987 |
+| 10 | j | 1,734 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | телеграм | 2 |
+| 2 | феминизмлы | 2 |
+| 3 | вотчина | 2 |
+| 4 | феминизм | 2 |
+| 5 | глобалистъёслэн | 2 |
+| 6 | пельмень | 2 |
+| 7 | секта | 2 |
+| 8 | версиозы | 2 |
+| 9 | вераськет | 2 |
+| 10 | эрис | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.0076 |
+| R² (Goodness of Fit) | 0.990825 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 22.1% |
+| Top 1,000 | 54.2% |
+| Top 5,000 | 76.3% |
+| Top 10,000 | 85.1% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9908 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 22.1% of corpus
+- **Long Tail:** 25,258 words needed for remaining 14.9% 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 | 0.6980 | 0.3482 | N/A | N/A |
+| **mono_64d** | 64 | 0.4125 | 0.3188 | N/A | N/A |
+| **mono_128d** | 128 | 0.0749 | 0.3189 | N/A | N/A |
+| **aligned_32d** | 32 | 0.6980 🏆 | 0.3505 | 0.0080 | 0.1280 |
+| **aligned_64d** | 64 | 0.4125 | 0.3252 | 0.0260 | 0.1660 |
+| **aligned_128d** | 128 | 0.0749 | 0.3271 | 0.0420 | 0.1880 |
+
+### Key Findings
+
+- **Best Isotropy:** aligned_32d with 0.6980 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.3314. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 4.2% 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 | **0.793** | 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 |
+|--------|----------|
+| `-к` | кит, кубоказ, косметической |
+| `-с` | списокезлэн, серем, сюрреализм |
+| `-п` | петра, прокурорез, пӧйшурало |
+| `-в` | выжонни, выжыысьтызы, валаз |
+| `-б` | берлинэ, бавариысь, борок |
+| `-а` | алжирлэн, австрия, александрович |
+| `-м` | мазунинской, механик, мозмытӥсь |
+| `-т` | театральная, теориен, талибъёслы |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-н` | алжирлэн, гвинеяын, набережнойын |
+| `-эн` | алжирлэн, цехезлэн, ельцинлэн |
+| `-a` | parvula, michelia, glaucophylla |
+| `-з` | валаз, кубоказ, прокурорез |
+| `-сь` | бавариысь, мозмытӥсь, дэремлэсь |
+| `-ь` | бавариысь, мозмытӥсь, дэремлэсь |
+| `-ын` | гвинеяын, набережнойын, европаын |
+| `-ы` | выжыысьтызы, ӝутӥськизы, шудӥсьлы |
+
+### 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 |
+|------|----------|------------------|----------|
+| `иськ` | 1.61x | 95 contexts | иськем, миськон, иськеме |
+| `anth` | 2.47x | 18 contexts | euanthe, panther, anthrax |
+| `тъёс` | 1.67x | 59 contexts | юртъёс, кутъёс, катъёс |
+| `тэмы` | 2.15x | 22 contexts | итэмын, актэмыр, ватэмын |
+| `ръёс` | 1.52x | 81 contexts | ӧръёс, аръёс, шуръёс |
+| `тӥсь` | 1.61x | 61 contexts | кутӥсь, чутӥсь, потӥсь |
+| `эмын` | 2.07x | 23 contexts | улэмын, алэмын, луэмын |
+| `ъёсы` | 1.46x | 83 contexts | ожъёсы, аръёсы, ужъёсыз |
+| `ской` | 2.07x | 20 contexts | чудской, рижской, вотской |
+| `нъёс` | 1.70x | 39 contexts | дунъёс, вынъёс, синъёс |
+| `яськ` | 1.57x | 28 contexts | сяська, сяськае, сяськая |
+| `емын` | 1.71x | 18 contexts | ваемын, ошемын, утемын |
+
+### 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 |
+|--------|--------|-----------|----------|
+| `-к` | `-н` | 157 words | кубертен, кудымкарын |
+| `-т` | `-н` | 71 words | тропинин, трактэн |
+| `-п` | `-н` | 70 words | петровичлэн, план |
+| `-к` | `-з` | 70 words | катэныз, коллегиез |
+| `-к` | `-ы` | 64 words | кивалтӥсезлы, кузьымлы |
+| `-п` | `-з` | 64 words | пыронэз, палозяз |
+| `-к` | `-эн` | 64 words | кивалтэтэзлэн, калыкъёслэн |
+| `-с` | `-н` | 63 words | суданлэн, спринтын |
+| `-в` | `-н` | 61 words | валамон, валтӥсьёсызлэн |
+| `-г` | `-н` | 53 words | героезлэн, гербезлэн |
+
+### 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 |
+|------|-----------------|------------|------|
+| комитетсы | **`комитет-с-ы`** | 7.5 | `с` |
+| факультетсэ | **`факультет-с-э`** | 7.5 | `с` |
+| процентысь | **`процент-ы-сь`** | 6.0 | `процент` |
+| ссылкаысь | **`ссылка-ы-сь`** | 6.0 | `ссылка` |
+| шормуӵысь | **`шормуӵ-ы-сь`** | 6.0 | `шормуӵ` |
+| школаослы | **`школа-ос-лы`** | 6.0 | `школа` |
+| группаослы | **`группа-ос-лы`** | 6.0 | `группа` |
+| историысь | **`истори-ы-сь`** | 6.0 | `истори` |
+| округъёсы | **`округъёс-ы`** | 4.5 | `округъёс` |
+| планетаос | **`планета-ос`** | 4.5 | `планета` |
+| журналистикая | **`журналистика-я`** | 4.5 | `журналистика` |
+| системаын | **`система-ын`** | 4.5 | `система` |
+| куартолэзен | **`куартолэзе-н`** | 4.5 | `куартолэзе` |
+| возьматон | **`возьмато-н`** | 4.5 | `возьмато` |
+| разделъёсыз | **`разделъёс-ыз`** | 4.5 | `разделъёс` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Udmurt 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 (4.56x) |
+| N-gram | **2-gram** | Lowest perplexity (646) |
+| Markov | **Context-4** | Highest predictability (97.9%) |
+| 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: 2026-01-11 02:18:53*

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