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README.md

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+---
+language: myv
+language_name: Erzya
+language_family: uralic_volgaic
+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_volgaic
+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: 4.104
+  - name: best_isotropy
+    type: isotropy
+    value: 0.8628
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-10
+---
+
+# Erzya - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Erzya** 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** | 3.359x | 3.36 | 0.1174% | 282,726 |
+| **16k** | 3.657x | 3.66 | 0.1279% | 259,662 |
+| **32k** | 3.923x | 3.93 | 0.1371% | 242,074 |
+| **64k** | 4.104x 🏆 | 4.11 | 0.1435% | 231,386 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Киислова () — те велесь Эстэнь Масторсо Вырумаа ёнкссо. Сёрм. Мастор Масторонть ...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |
+| 16k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |
+| 32k | `▁ки ис лова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ... (+7 more)` | 17 |
+| 64k | `▁киислова ▁() ▁— ▁те ▁велесь ▁эстэнь ▁масторсо ▁вырумаа ▁ёнкссо . ... (+5 more)` | 15 |
+
+**Sample 2:** `Лепамиця лымбамот — лымбиця лыкамось, кона альмезэ аламолгады шканьберть.`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁ле па м иця ▁лы мба мот ▁— ▁лы мб ... (+16 more)` | 26 |
+| 16k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+15 more)` | 25 |
+| 32k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+12 more)` | 22 |
+| 64k | `▁ле пам иця ▁лы мба мот ▁— ▁лы мб иця ... (+9 more)` | 19 |
+
+**Sample 3:** `Мария Гулегина (); чач. Умарьковонь 9 чистэ, Одесса ош, СССР) — морыця (сопрано)...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁мария ▁гу ле г ина ▁(); ▁чач . ▁умарьковонь ▁ ... (+14 more)` | 24 |
+| 16k | `▁мария ▁гу ле гина ▁(); ▁чач . ▁умарьковонь ▁ 9 ... (+12 more)` | 22 |
+| 32k | `▁мария ▁гу ле гина ▁(); ▁чач . ▁умарьковонь ▁ 9 ... (+12 more)` | 22 |
+| 64k | `▁мария ▁гулегина ▁(); ▁чач . ▁умарьковонь ▁ 9 ▁чистэ , ... (+10 more)` | 20 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.104x compression
+- **Lowest UNK Rate:** 8k with 0.1174% 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 | 5,234 | 12.35 | 13,565 | 19.1% | 50.0% |
+| **2-gram** | Subword | 451 🏆 | 8.82 | 4,411 | 55.9% | 96.7% |
+| **3-gram** | Word | 5,809 | 12.50 | 17,643 | 20.4% | 49.4% |
+| **3-gram** | Subword | 3,849 | 11.91 | 34,647 | 20.1% | 61.1% |
+| **4-gram** | Word | 9,800 | 13.26 | 32,090 | 18.1% | 43.0% |
+| **4-gram** | Subword | 19,085 | 14.22 | 156,710 | 10.3% | 34.9% |
+| **5-gram** | Word | 7,606 | 12.89 | 25,413 | 19.9% | 46.5% |
+| **5-gram** | Subword | 51,060 | 15.64 | 321,204 | 6.8% | 24.6% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `вн истяжо` | 1,572 |
+| 2 | `содавикс ломанть` | 1,490 |
+| 3 | `ломанть те` | 1,467 |
+| 4 | `те велестэнть` | 1,405 |
+| 5 | `веленть лемденть` | 1,393 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `содавикс ломанть те` | 1,461 |
+| 2 | `ломанть те велестэнть` | 1,405 |
+| 3 | `эрицятне раськень состав` | 1,059 |
+| 4 | `раськень состав весероссиянь` | 1,054 |
+| 5 | `состав весероссиянь перепись` | 1,039 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `содавикс ломанть те велестэнть` | 1,405 |
+| 2 | `эрицятне раськень состав весероссиянь` | 1,044 |
+| 3 | `раськень состав весероссиянь перепись` | 1,039 |
+| 4 | `весероссиянь перепись населения ие` | 1,039 |
+| 5 | `состав весероссиянь перепись населения` | 1,039 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `состав весероссиянь перепись населения ие` | 1,039 |
+| 2 | `раськень состав весероссиянь перепись населения` | 1,039 |
+| 3 | `эрицятне раськень состав весероссиянь перепись` | 1,032 |
+| 4 | `содавикс ломанть те велестэнть эрицятне` | 946 |
+| 5 | `эрямозо содавикс ломанть те велестэнть` | 917 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `ь _` | 153,248 |
+| 2 | `. _` | 92,452 |
+| 3 | `н ь` | 90,818 |
+| 4 | `с т` | 68,788 |
+| 5 | `, _` | 66,880 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `н ь _` | 80,150 |
+| 2 | `т ь _` | 36,047 |
+| 3 | `_ — _` | 29,408 |
+| 4 | `о н ь` | 26,266 |
+| 5 | `е н ь` | 26,109 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `о н ь _` | 24,242 |
+| 2 | `е н ь _` | 22,554 |
+| 3 | `н т ь _` | 20,388 |
+| 4 | `_ в е л` | 13,694 |
+| 5 | `в е л е` | 12,902 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ в е л е` | 12,574 |
+| 2 | `е н т ь _` | 8,208 |
+| 3 | `в о н ь _` | 7,157 |
+| 4 | `о в о н ь` | 6,844 |
+| 5 | `и я н ь _` | 6,197 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 451
+- **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 | 0.6530 | 1.572 | 3.67 | 122,977 | 34.7% |
+| **1** | Subword | 1.2973 | 2.458 | 11.50 | 833 | 0.0% |
+| **2** | Word | 0.1469 | 1.107 | 1.28 | 449,631 | 85.3% |
+| **2** | Subword | 1.1429 | 2.208 | 6.92 | 9,577 | 0.0% |
+| **3** | Word | 0.0456 | 1.032 | 1.08 | 573,707 | 95.4% |
+| **3** | Subword | 0.8768 | 1.836 | 4.15 | 66,234 | 12.3% |
+| **4** | Word | 0.0224 🏆 | 1.016 | 1.04 | 613,293 | 97.8% |
+| **4** | Subword | 0.6169 | 1.534 | 2.56 | 274,547 | 38.3% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `ды касы седе ламо м и б в финно угорский прорыв текст биографический фильм без источников`
+2. `в суздаль на южния полюс с рус эрзян isbn url consultato il 21 8 чистэ калиновка`
+3. `и д в рузанкин н новгород англо хинди русский словарь ок назв а кенерезь лёмзёркссо почодозь`
+
+**Context Size 2:**
+
+1. `вн истяжо таштамковонь 12 чистэ саран ошсо калмазо апак ёвта секскак велень продештяст истямо сынст ...`
+2. `содавикс ломанть те велестэнть веленть эрямозо содавикс ломанть те велестэнть веленть эрямозо содави...`
+3. `ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 56 велеть ошо...`
+
+**Context Size 3:**
+
+1. `содавикс ломанть те велестэнть веленть эрямозо эрицятне раськень состав весероссиянь перепись населе...`
+2. `ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 93 велеть вел...`
+3. `эрицятне раськень состав весероссиянь эрицятнень сёрмадстоманть ие коряс рузт 100 содавикс ломанть т...`
+
+**Context Size 4:**
+
+1. `содавикс ломанть те велестэнть эрицятне раськень состав весероссиянь перепись населения ие рузт 95 с...`
+2. `эрицятне раськень состав весероссиянь перепись населения ие рузт 100 велеть буень велеть`
+3. `весероссиянь перепись населения ие печкаст 100 велеть велеть`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_вень_кулмиистес`
+2. `олияморх_с_мениз`
+3. `ав_покрявась_а_к`
+
+**Context Size 2:**
+
+1. `ь_ких_новияс_эле_`
+2. `._валриц_мень_(юу`
+3. `нь_эритортаранили`
+
+**Context Size 3:**
+
+1. `нь_аштемантоликани`
+2. `ть_экось_оплангсо_`
+3. `_—_ведческие_с_евр`
+
+**Context Size 4:**
+
+1. `онь_сал,_запись_нас`
+2. `ень_ды_уманический_`
+3. `нть_эрямонзо_токаль`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 97.8% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (274,547 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 | 47,484 |
+| Total Tokens | 705,946 |
+| Mean Frequency | 14.87 |
+| Median Frequency | 3 |
+| Frequency Std Dev | 119.73 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | ды | 10,760 |
+| 2 | в | 8,187 |
+| 3 | и | 6,467 |
+| 4 | с | 6,350 |
+| 5 | а | 5,547 |
+| 6 | те | 5,228 |
+| 7 | м | 4,398 |
+| 8 | иестэ | 3,988 |
+| 9 | ульнесь | 3,596 |
+| 10 | ие | 3,563 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | якшаматянть | 2 |
+| 2 | аналогозо | 2 |
+| 3 | доминияк | 2 |
+| 4 | indeks | 2 |
+| 5 | grup | 2 |
+| 6 | zawodowych | 2 |
+| 7 | muzea | 2 |
+| 8 | britishpedia | 2 |
+| 9 | osobistości | 2 |
+| 10 | bph | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.0126 |
+| R² (Goodness of Fit) | 0.996053 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 27.1% |
+| Top 1,000 | 55.8% |
+| Top 5,000 | 75.1% |
+| Top 10,000 | 83.0% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9961 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 27.1% of corpus
+- **Long Tail:** 37,484 words needed for remaining 17.0% 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 | 0.8628 🏆 | 0.3405 | N/A | N/A |
+| **mono_64d** | 64 | 0.7101 | 0.2786 | N/A | N/A |
+| **mono_128d** | 128 | 0.2558 | 0.2702 | N/A | N/A |
+| **aligned_32d** | 32 | 0.8628 | 0.3424 | 0.0280 | 0.1300 |
+| **aligned_64d** | 64 | 0.7101 | 0.2772 | 0.0360 | 0.1540 |
+| **aligned_128d** | 128 | 0.2558 | 0.2675 | 0.0700 | 0.2380 |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.8628 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.2961. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 7.0% R@1 in cross-lingual retrieval.
+- **Recommendation:** 128d aligned for best cross-lingual performance
+
+---
+## 6.  Morphological Analysis (Experimental)
+
+This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.
+
+### 6.1 Productivity & Complexity
+
+| Metric | Value | Interpretation | Recommendation |
+|--------|-------|----------------|----------------|
+| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
+| Idiomaticity Gap | **0.892** | 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` | кемкавтово, кантнить, клавдий |
+| `-с` | сайнелень, сабан, скульптуры |
+| `-п` | пильгеоскань, политиканьветий, паросто |
+| `-ка` | кантнить, казаньсэ, кайсеви |
+| `-а` | абус, андонь, англиясо |
+| `-т` | тамары, таштоюрьево, туинек |
+| `-в` | венстизе, вагриус, венок |
+| `-м` | матвеево, монастырень, массрэнь |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-ь` | пильгеоскань, сайнелень, кантнить |
+| `-нь` | пильгеоскань, сайнелень, раввинэнь |
+| `-о` | кемкавтово, матвеево, ярмаконзо |
+| `-ть` | кантнить, художникенть, эрсить |
+| `-а` | задонска, божена, улянка |
+| `-е` | венстизе, характеристикатне, европе |
+| `-й` | клавдий, политиканьветий, учебной |
+| `-сь` | ловомась, куломачись, кельесь |
+
+### 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 |
+|------|----------|------------------|----------|
+| `ково` | 2.01x | 50 contexts | ковол, беково, ковозо |
+| `енть` | 1.92x | 55 contexts | генть, денть, менть |
+| `овон` | 2.23x | 30 contexts | човонь, ловонь, ковонь |
+| `арка` | 2.00x | 42 contexts | парка, тарка, аркат |
+| `риця` | 2.25x | 20 contexts | эриця, триця, мариця |
+| `ской` | 1.90x | 34 contexts | арской, южской, ямской |
+| `анть` | 1.83x | 38 contexts | канть, панть, манть |
+| `вонь` | 2.26x | 18 contexts | орвонь, сёвонь, лувонь |
+| `асто` | 1.74x | 44 contexts | тасто, састо, часто |
+| `стор` | 1.63x | 48 contexts | сторож, мастор, стороны |
+| `ятне` | 1.76x | 33 contexts | цятне, ятнень, атятне |
+| `тарк` | 2.14x | 16 contexts | тарка, таркат, тарксо |
+
+### 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` | `-ь` | 242 words | компаниянть, кшить |
+| `-п` | `-ь` | 182 words | палсь, политикень |
+| `-с` | `-ь` | 168 words | семиянь, сельмтнень |
+| `-в` | `-ь` | 134 words | вирьавань, вейсветямонь |
+| `-т` | `-ь` | 123 words | токалить, термодинамикань |
+| `-м` | `-ь` | 118 words | марясть, максоманть |
+| `-к` | `-нь` | 117 words | каминь, клеткантень |
+| `-а` | `-ь` | 103 words | ашомештень, азребайджанонь |
+| `-л` | `-ь` | 94 words | лемдезь, людикинь |
+| `-п` | `-нь` | 85 words | политикень, псакань |
+
+### 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 |
+|------|-----------------|------------|------|
+| инязорава | **`инязор-а-ва`** | 7.5 | `а` |
+| материалам | **`материал-а-м`** | 7.5 | `а` |
+| пандомась | **`пандо-ма-сь`** | 7.5 | `ма` |
+| группанень | **`группа-не-нь`** | 7.5 | `не` |
+| экономистов | **`экономи-ст-ов`** | 7.5 | `ст` |
+| васеньценть | **`васеньце-н-ть`** | 7.5 | `н` |
+| маритьнень | **`марить-не-нь`** | 7.5 | `не` |
+| участкась | **`участ-ка-сь`** | 7.5 | `ка` |
+| ломаньстэ | **`ломань-ст-э`** | 7.5 | `ст` |
+| кемекстись | **`кемекст-и-сь`** | 7.5 | `и` |
+| невтемакс | **`невте-ма-кс`** | 7.5 | `ма` |
+| чугункасто | **`чугунка-ст-о`** | 7.5 | `ст` |
+| велетнесэ | **`велет-не-сэ`** | 7.5 | `не` |
+| премиятне | **`премия-т-не`** | 7.5 | `т` |
+| медицинань | **`медици-на-нь`** | 7.5 | `на` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Erzya 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 (4.10x) |
+| N-gram | **2-gram** | Lowest perplexity (451) |
+| Markov | **Context-4** | Highest predictability (97.8%) |
+| 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 14:15:51*

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