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---
language: iu
language_name: Inuktitut
language_family: eskimoaleut
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-eskimoaleut
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: 3.905
- name: best_isotropy
type: isotropy
value: 0.2183
- name: vocabulary_size
type: vocab
value: 0
generated: 2026-01-10
---
# Inuktitut - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study
This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Inuktitut** Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.
## ๐Ÿ“‹ 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** | 3.015x | 3.02 | 0.1769% | 75,744 |
| **16k** | 3.468x | 3.47 | 0.2035% | 65,854 |
| **32k** | 3.905x ๐Ÿ† | 3.91 | 0.2292% | 58,476 |
### Tokenization Examples
Below are sample sentences tokenized with each vocabulary size:
**Sample 1:** `แ•™แƒแ”…แณแ’ƒ แ’ฅแŠแ“•แ’แƒแ‘ฆ แ“„แ“‡แ–“แ“แ“‚ แ–ƒแ•†แ‘•แ…แ”ญแ’ƒแ‘ฏแ‘ฆ แ‘แ‘ญแ“ฏแ’‹แŠแ•แ••แ’ƒ แ“ดแ–…แ‘ญแ‘•แ…แ“šแ…แ–…แ“ฏแ’ชแ”ชแ–… แ’ซแ’ƒ แ“ตแ‘ฏแดแ’กแ’งแ‘ฆ. แ•™แƒแ”…แณแ’ƒ แ‘แ“ดแ…แ’ชแ”ญแ…แ“‚แ–…แนแ–‘แ•—แ–… ...`
| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `โ–แ•™แƒแ”…แณแ’ƒ โ–แ’ฅแŠแ“•แ’แƒแ‘ฆ โ–แ“„แ“‡แ–“แ“แ“‚ โ–แ–ƒแ•†แ‘•แ…แ”ญแ’ƒแ‘ฏแ‘ฆ โ–แ‘แ‘ญแ“ฏแ’‹แŠ แ•แ••แ’ƒ โ–แ“ดแ–…แ‘ญแ‘•แ…แ“šแ…แ–…แ“ฏแ’ชแ”ชแ–… โ–แ’ซแ’ƒ โ–แ“ตแ‘ฏ แดแ’ก ... (+16 more)` | 26 |
| 16k | `โ–แ•™แƒแ”…แณแ’ƒ โ–แ’ฅแŠแ“•แ’แƒแ‘ฆ โ–แ“„แ“‡แ–“แ“แ“‚ โ–แ–ƒแ•†แ‘•แ…แ”ญแ’ƒแ‘ฏแ‘ฆ โ–แ‘แ‘ญแ“ฏแ’‹แŠ แ•แ••แ’ƒ โ–แ“ดแ–…แ‘ญแ‘•แ…แ“šแ…แ–…แ“ฏแ’ชแ”ชแ–… โ–แ’ซแ’ƒ โ–แ“ตแ‘ฏแดแ’กแ’งแ‘ฆ . ... (+10 more)` | 20 |
| 32k | `โ–แ•™แƒแ”…แณแ’ƒ โ–แ’ฅแŠแ“•แ’แƒแ‘ฆ โ–แ“„แ“‡แ–“แ“แ“‚ โ–แ–ƒแ•†แ‘•แ…แ”ญแ’ƒแ‘ฏแ‘ฆ โ–แ‘แ‘ญแ“ฏแ’‹แŠแ•แ••แ’ƒ โ–แ“ดแ–…แ‘ญแ‘•แ…แ“šแ…แ–…แ“ฏแ’ชแ”ชแ–… โ–แ’ซแ’ƒ โ–แ“ตแ‘ฏแดแ’กแ’งแ‘ฆ . โ–แ•™แƒแ”…แณแ’ƒ ... (+7 more)` | 17 |
**Sample 2:** `แ…แ“ตแƒแ…โ€”[แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆโ€”Ohio]โ€” ) แƒแ‘ŽแŠแ”ชแ‘ฆ แƒแ“—แŠแ“‚. แ…แ“ตแƒแ… แƒแ“„แ–แ‘Ž แŠแ’ฅแŠแ“•แ‘ฒ. แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ-แ“„แ“‡แ“–แ‘ฆ แ‘ฐแ•‰แ’ปแดแ”… ยซ...`
| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `โ–แ…แ“ตแƒแ… โ€”[ แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆ โ€” ohio ]โ€” โ–) โ–แƒแ‘ŽแŠแ”ชแ‘ฆ โ–แƒแ“—แŠแ“‚ . ... (+27 more)` | 37 |
| 16k | `โ–แ…แ“ตแƒแ… โ€”[ แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆ โ€” ohio ]โ€” โ–) โ–แƒแ‘ŽแŠแ”ชแ‘ฆ โ–แƒแ“—แŠแ“‚ . ... (+22 more)` | 32 |
| 32k | `โ–แ…แ“ตแƒแ… โ€”[ แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆ โ€” ohio ]โ€” โ–) โ–แƒแ‘ŽแŠแ”ชแ‘ฆ โ–แƒแ“—แŠแ“‚ . ... (+22 more)` | 32 |
**Sample 3:** `แŠแ…แ‘ฆแ“ฏแ“‡แ–…แ‘แ–… แ“ฑแ“•แŠแ–… แŠแ“‚แ–…แธแ“ˆแ–…แ‘‘แ”ญแ–…แ‘แ–… แ…แ“šแฑแ‘‰แน แ“ดแณแ’ปแ’ฅแ•š แ‘Žแ’ฅ. แ…แ‘‰แ”ญแ’ƒแณแ–… แŠแ“แ“„แ•Œแ“‚แ’ƒ`
| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `โ–แŠแ…แ‘ฆแ“ฏแ“‡แ–…แ‘แ–… โ–แ“ฑแ“•แŠแ–… โ–แŠแ“‚แ–…แธแ“ˆแ–…แ‘‘แ”ญแ–…แ‘แ–… โ–แ…แ“šแฑ แ‘‰แน โ–แ“ดแณแ’ปแ’ฅแ•š โ–แ‘Žแ’ฅ . โ–แ…แ‘‰แ”ญแ’ƒแณแ–… โ–แŠแ“แ“„แ•Œแ“‚แ’ƒ` | 10 |
| 16k | `โ–แŠแ…แ‘ฆแ“ฏแ“‡แ–…แ‘แ–… โ–แ“ฑแ“•แŠแ–… โ–แŠแ“‚แ–…แธแ“ˆแ–…แ‘‘แ”ญแ–…แ‘แ–… โ–แ…แ“šแฑแ‘‰แน โ–แ“ดแณแ’ปแ’ฅแ•š โ–แ‘Žแ’ฅ . โ–แ…แ‘‰แ”ญแ’ƒแณแ–… โ–แŠแ“แ“„แ•Œแ“‚แ’ƒ` | 9 |
| 32k | `โ–แŠแ…แ‘ฆแ“ฏแ“‡แ–…แ‘แ–… โ–แ“ฑแ“•แŠแ–… โ–แŠแ“‚แ–…แธแ“ˆแ–…แ‘‘แ”ญแ–…แ‘แ–… โ–แ…แ“šแฑแ‘‰แน โ–แ“ดแณแ’ปแ’ฅแ•š โ–แ‘Žแ’ฅ . โ–แ…แ‘‰แ”ญแ’ƒแณแ–… โ–แŠแ“แ“„แ•Œแ“‚แ’ƒ` | 9 |
### Key Findings
- **Best Compression:** 32k achieves 3.905x compression
- **Lowest UNK Rate:** 8k with 0.1769% 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 | 93 ๐Ÿ† | 6.54 | 126 | 90.8% | 100.0% |
| **2-gram** | Subword | 962 | 9.91 | 3,039 | 37.0% | 87.0% |
| **3-gram** | Word | 130 | 7.03 | 174 | 73.9% | 100.0% |
| **3-gram** | Subword | 5,020 | 12.29 | 12,029 | 15.7% | 49.7% |
| **4-gram** | Word | 694 | 9.44 | 794 | 25.0% | 100.0% |
| **4-gram** | Subword | 14,093 | 13.78 | 28,526 | 8.8% | 30.5% |
| **5-gram** | Word | 607 | 9.25 | 676 | 24.5% | 100.0% |
| **5-gram** | Subword | 19,229 | 14.23 | 32,493 | 7.1% | 24.4% |
### Top 5 N-grams by Size
**2-grams (Word):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `san marino` | 73 |
| 2 | `of the` | 55 |
| 3 | `แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ` | 55 |
| 4 | `แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–…` | 47 |
| 5 | `แ‘•แ•†แ…แ‘‰ แŠแ‘ญแŠแ“‚` | 44 |
**3-grams (Word):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ` | 51 |
| 2 | `แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–… www` | 30 |
| 3 | `แƒแ“„แ–แ‘Ž แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ` | 22 |
| 4 | `แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ แ“„แ“‡แ“–แ‘ฆ` | 22 |
| 5 | `แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ` | 22 |
**4-grams (Word):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ` | 48 |
| 2 | `แƒแ“„แ–แ‘Ž แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ` | 22 |
| 3 | `แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ แ“„แ“‡แ“–แ‘ฆ` | 22 |
| 4 | `แ“„แ“‡แ“–แ‘ฆ แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–… www` | 20 |
| 5 | `the grand and general` | 10 |
**5-grams (Word):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ` | 45 |
| 2 | `แƒแ“„แ–แ‘Ž แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ แ“„แ“‡แ“–แ‘ฆ` | 22 |
| 3 | `the grand and general council` | 10 |
| 4 | `แ“„แ“‡ frameless upright 0 3` | 7 |
| 5 | `o canada we stand on` | 5 |
**2-grams (Subword):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `แ‘ฆ _` | 4,757 |
| 2 | `_ แŠ` | 3,099 |
| 3 | `แ–… _` | 2,694 |
| 4 | `_ แƒ` | 2,386 |
| 5 | `, _` | 2,385 |
**3-grams (Subword):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `แŠ แ’ป แ’ช` | 851 |
| 2 | `_ แŠ แ’ป` | 837 |
| 3 | `_ แ“„ แ“‡` | 816 |
| 4 | `แ“‚ แ’ƒ _` | 784 |
| 5 | `แ‘ฆ _ แŠ` | 710 |
**4-grams (Subword):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ แŠ แ’ป แ’ช` | 833 |
| 2 | `แŠ แ’ป แ’ช _` | 420 |
| 3 | `แŠ แ’ป แ’ช แ“—` | 407 |
| 4 | `แ–… แ‘ แ–… _` | 405 |
| 5 | `แ’ป แ’ช แ“— _` | 385 |
**5-grams (Subword):**
| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ แŠ แ’ป แ’ช _` | 418 |
| 2 | `_ แŠ แ’ป แ’ช แ“—` | 400 |
| 3 | `แŠ แ’ป แ’ช แ“— _` | 385 |
| 4 | `_ t h e _` | 346 |
| 5 | `แ‘ฆ _ แŠ แ’ป แ’ช` | 218 |
### Key Findings
- **Best Perplexity:** 2-gram (word) with 93
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.3388 | 1.265 | 1.76 | 15,002 | 66.1% |
| **1** | Subword | 1.4995 | 2.827 | 13.51 | 541 | 0.0% |
| **2** | Word | 0.0479 | 1.034 | 1.07 | 26,047 | 95.2% |
| **2** | Subword | 0.9813 | 1.974 | 4.39 | 7,301 | 1.9% |
| **3** | Word | 0.0129 | 1.009 | 1.02 | 27,517 | 98.7% |
| **3** | Subword | 0.5441 | 1.458 | 2.22 | 31,981 | 45.6% |
| **4** | Word | 0.0049 ๐Ÿ† | 1.003 | 1.01 | 27,602 | 99.5% |
| **4** | Subword | 0.3121 | 1.242 | 1.55 | 70,999 | 68.8% |
### Generated Text Samples (Word-based)
Below are text samples generated from each word-based Markov chain model:
**Context Size 1:**
1. `แŠแ’ปแ’ช แฑแ•ˆแ–…แ“ฏแŠแ–… แ‘ญแ’ƒแ‘ฏแ‘ฆ แ…แŠแ‘Žแ’Œแ“ฏแ•†แ’ฅแ’ปแ’งแ‘ฆ แ“ดแƒแ“‡แ’ƒแ‘ญแ…แ”ชแ–… แŠแ‘Žแ–ƒแ•แ’ฅแ‘•แ…แ“‚แ–แ“แ“‚แ’ƒ แŠแ“‚แ”จแ–ƒแ•†แ”ชแ‘ฆ แ…แ“‚แ–…แ‘•แ–ƒแ•แ‘•แ…แ”ชแ‘ฆ แ…แ‘Žแ“‡แ…แ–ƒแ‘Žแ’Œแ‘ฆ แฑแ’ปแ’ฅแ•แ’ฅแ…แ‘•แ“—แ‘‰ แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–… www...`
2. `แŠแ’ปแ’ชแ“— แŠแ…แ“šแ“ƒแ‘ฆ แฑแ“•แ•†แ–ƒแ‘Žแ’Œแ–ƒแ‘ฆแ‘•แ–…แ‘แ‘ฆ แ‹แ–…แ‘ญแ…แ’ชแ‘Žแ‘ฆแ‘Žแ“‚แŠแ•แ“—แ“‚ แŠแ–แ•แ•‹แ’ฅแ’ƒ แ…แ“—แ•†แŠแ“‡แ™ฑแ‘ฆแ‘แ’ƒแ‘ฏแ‘ฆ แ“ฒแ•แ“— แ••แ‘แ•†แ‘ฏ แƒแ“‡แ“—แ’ƒแ‘ฒ แƒแ’กแ“—แ“แ“‚ แ“„แ“‡แ–ƒแ–…แณแ‘ฆ แธแ‘แ‘Ž แƒแ“•แ“šแ…แ–…แ‘•แ•‹ แŠแ…แ“š...`
3. `the roman republic the sammarinese fascist government declared war on their passports citation neede...`
**Context Size 2:**
1. `san marino appealed to pope boniface viii against the contribution demands by the legate papal gover...`
2. `แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ’ฅแ‘ญแ”ซแ–•แ“‚แ’ƒ แ‘แŠแ‘ŽแŠแ“‚แ’ƒ แŠแ’ปแ’ช แƒแ“›แ“แ“‚แ’ƒแ‘ฏแ‘ฆ แ“ดแ“‡แ”ญแ…แ•™แ’ƒแ–ขแ‘Žแ’ƒ แ’‘แ‘ฒแ’งแ“•แ’งแ‘ฆ แ“ตแ“ชแ“ดแ’งแ‘ฆ แ“‚แ…แ“แ”…แ’งแ‘ฆ แŠแ’ปแ’ช แ“ฏแ“šแ“แ‘แ’งแ‘ฆ แ‘ฏแ•†แ“แ‘ แ’ชแ‘‰แฑ...`
3. `of the european union it is the fifth smallest country in europe after vatican city and state`
**Context Size 3:**
1. `แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ’ƒแ‘ฒแ“แ“‚แ–… แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ`
2. `แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–… www sd gov`
3. `แƒแ“„แ–แ‘Ž แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ แ“„แ“‡แ“–แ‘ฆ แฒแ• แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆ pierre แ“„แ“‡แ“–แ‘ฆ แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–… www ok gov`
**Context Size 4:**
1. `แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ แ–„แ–“แ’แ‘ฆ`
2. `แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ แ“„แ“‡แ“–แ‘ฆ แดแ•แ‘ฆแ“›แ“แ‘ฆ แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆ portland แ“„แ“‡แ“–แ‘ฆ แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–… www nv gov`
3. `แƒแ“„แ–แ‘Ž แŠแ’ฅแŠแ“•แ‘ฒ แŠแ…แ“šแ‘ฆแ‘Žแ”ฉแ‘ฆ แ“ฏแ•—แ“•แ–…แ‘Žแ–“แ‘ฆ แ“„แ“‡แ“–แ‘ฆ แ“‚แ… แ†แ•แ“–แ“แ”… แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆ new orleans แ“„แ“‡แ“–แ‘ฆ แ‘ญแ’ปแ’งแ‘ฆ แ…แ–…แ“ฏแ–… www idaho gov`
### Generated Text Samples (Subword-based)
Below are text samples generated from each subword-based Markov chain model:
**Context Size 1:**
1. `_แ••แ’ƒ_แ’แ”ชแ‘Žแ“ชแ“—แ‘•แ‘ญแ“ฏแŠแ’ปแ’ช_`
2. `แ–…แ‘แ’ƒ_ontunixiteco`
3. `แ‘ฆแ‘•)_แ‘ฒ,_แ–„แ•แ’ฅแ“ฑแŠแ•ˆแ‘ŽแŠแ’ป`
**Context Size 2:**
1. `แ‘ฆ_(แฑแ“šแ•ˆ,_แ‘Žแ‘Žแ“ชแ“—แ“•แ–ƒแ–…แณแ‘ฆ`
2. `_แŠแ…แธแƒแ’ก_แŠแ–•แ“‡แ–…_แ‘ญแ“•แŠแ‘‰_`
3. `แ–…_แ‘•แƒแ‘ฒแ“‚แธ,_แ“„แ“‡แ“–แ‘ฆ_แƒแ’กแ“—`
**Context Size 3:**
1. `แŠแ’ปแ’ชแ“—_แ•ฟแ“šแ’ƒ._แ“ดแ“‚แ‘ญแ“—แŠแ•แ’ฅ.`
2. `_แŠแ’ปแ’ช_แƒแ“—แŠแ“ƒแ‘แ“‚._แƒแ“šแ–ƒแ–…แ‘`
3. `_แ“„แ“‡แ–ƒแƒแ“แ“‡แ•†แŠแ“šแ…แ–…แณแ–…_แŠแ•‹แ••`
**Context Size 4:**
1. `_แŠแ’ปแ’ช_แ‘Žแ“ดแ’ชแ“‚แ’ƒ_แ“„แ“‡แ’ฅแ…แ‘•แ…แ•—แ‘ฆ`
2. `แŠแ’ปแ’ช_แ‘•แ‘ฏแ‘ฆแ‘ŽแŠแ”ชแƒแ“แ“‡แ•แ’ฅแ’ƒ_แฑแ–ƒ`
3. `แŠแ’ปแ’ชแ“—_แ–แ••แŠแ“ฑแ–•แ“‚แ–…")แƒแ™ฑแ…แ“ฏแ–“`
### Key Findings
- **Best Predictability:** Context-4 (word) with 99.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (70,999 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 | 3,802 |
| Total Tokens | 18,925 |
| Mean Frequency | 4.98 |
| Median Frequency | 2 |
| Frequency Std Dev | 13.99 |
### Most Common Words
| Rank | Word | Frequency |
|------|------|-----------|
| 1 | แŠแ’ปแ’ช | 424 |
| 2 | แŠแ’ปแ’ชแ“— | 392 |
| 3 | the | 353 |
| 4 | of | 210 |
| 5 | แƒแ“„แƒแ‘ฆ | 139 |
| 6 | and | 131 |
| 7 | แ…แ•แ•™แ“˜แ“แ“ƒแ‘ฆ | 114 |
| 8 | in | 106 |
| 9 | แ–ƒแ“ชแ“—แ“ˆแ‘Žแ‘แ‘ฆ | 104 |
| 10 | to | 98 |
### Least Common Words (from vocabulary)
| Rank | Word | Frequency |
|------|------|-----------|
| 1 | แ‘•แ‘ฏแ”ญแ’แ–ƒแ•แ••แ…แ”ชแ‘ฆ | 2 |
| 2 | แ’ฅแ…แ“ฏแ… | 2 |
| 3 | แ“ดแ’ƒแ‘ฏแ‘แ–ƒแ•แ“„แ‘ฆ | 2 |
| 4 | แ“ดแ••แ•‹แ”ญแ“„แ‘ฆ | 2 |
| 5 | แŠแ’ฅแŠแ–…แ‘•แ…แ“ฏแ’ชแ”ชแ‘ฆ | 2 |
| 6 | แ‘ญแŠแ•‹แ’ฅ | 2 |
| 7 | แ”จแŠแ“‡แ•† | 2 |
| 8 | แ“ดแ“‡แ“แ–‘แŠแ’แƒแ‘ฆ | 2 |
| 9 | แ“…แ‘‰แธแ“ชแ“•แŠแ”ชแ“„แ‘ฆ | 2 |
| 10 | แ“„แ“‡แ’ฅแ…แ‘•แ“•แ•†แ“‚แ•แ’งแ‘ฆ | 2 |
### Zipf's Law Analysis
| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.6869 |
| Rยฒ (Goodness of Fit) | 0.969855 |
| Adherence Quality | **excellent** |
### Coverage Analysis
| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 30.3% |
| Top 1,000 | 65.3% |
| Top 5,000 | 0.0% |
| Top 10,000 | 0.0% |
### Key Findings
- **Zipf Compliance:** Rยฒ=0.9699 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 30.3% of corpus
- **Long Tail:** -6,198 words needed for remaining 100.0% 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 | 0.2183 | 0.4714 | N/A | N/A |
| **mono_64d** | 64 | 0.0445 | 0.4570 | N/A | N/A |
| **mono_128d** | 128 | 0.0046 | 0.4821 | N/A | N/A |
| **aligned_32d** | 32 | 0.2183 ๐Ÿ† | 0.4659 | 0.0189 | 0.1384 |
| **aligned_64d** | 64 | 0.0445 | 0.4550 | 0.0314 | 0.1384 |
| **aligned_128d** | 128 | 0.0046 | 0.4794 | 0.0503 | 0.1509 |
### Key Findings
- **Best Isotropy:** aligned_32d with 0.2183 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4685. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.0% 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 | **3.097** | 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 |
|--------|----------|
| `-แŠ` | แŠแ‘แ–…แ‘•แ…แ“ฏแ’ชแ”ชแ–…, แŠแ”…แ‘ฆแ•Œแ“•แŠ, แŠแ“‚แ’แ–…แ‘Žแ“ชแ“—แ’‹แ‘ฆ |
| `-แƒ` | แƒแ“…แ–ƒแ‘Žแ’Œแ‘ฆ, แƒแ–ƒแ‘ฆแ‘แ–…, แƒแ“ฑ |
| `-แ…` | แ…แ“ชแ“—แ“‚แ’ƒ, แ…แ“›แ“ดแ’ฅ, แ…แ‘ญแ…แ–ƒแ“•แ–…แ‘Žแ“ชแ“—แ’‹แ‘ฆ |
| `-แ…แ–ƒ` | แ…แ–ƒแ“•แ’ซแ’แ“„แ‘ฆ, แ…แ–ƒแ…แ“ฏแ’ƒแ“ดแ“‚แ–แ‘ฆ, แ…แ–ƒแ…แ“ฏแ•แ–“แ…แ‘Žแ–ƒแ•แ’ชแ‘Žแ‘• |
| `-แ“„แ“‡` | แ“„แ“‡แ••แ…แ‘‰, แ“„แ“‡แ–แ‘Žแ–“แ“‚แ’ƒ, แ“„แ“‡แ™ณแŠแ–“ |
| `-แ‘•แƒ` | แ‘•แƒแ’ซแ‘ฆแ“ดแƒแ“แ“‡แ–…, แ‘•แƒแ’ƒแ“ฑแ’ชแ“‚, แ‘•แƒแ’ƒแ‘ฏแ“‡แ“‚ |
| `-แƒแ“„` | แƒแ“„แ’ƒ, แƒแ“„แ’‹แŠแ“›แ–‘แ“ชแ“—แ“‚, แƒแ“„แ–•แ“‚แ’ƒ |
| `-co` | coca, corporate, country |
#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-แ‘ฆ` | แ–ƒแ“šแ’ชแ“แ–แ‘‘แ“—แ‘Žแ“˜แ“แ“ƒแ‘ฆ, แƒแ“…แ–ƒแ‘Žแ’Œแ‘ฆ, แฑแ“•แ•†แ‘ฆแ‘ŽแŠแ•แ“‚แ–แ“แ“„แ‘ฆ |
| `-แ–…` | แƒแ–ƒแ‘ฆแ‘แ–…, แŠแ‘แ–…แ‘•แ…แ“ฏแ’ชแ”ชแ–…, แ“ฏแ…แ•‹แ–… |
| `-แ’ƒ` | แ“ฏแ•—แ“ชแ“•แ–…แนแ’ƒ, แŠแ‘•แ…แ“ฏแ•แ’ฅแ’ƒ, แ…แ“ชแ“—แ“‚แ’ƒ |
| `-แ“‚แ’ƒ` | แ…แ“ชแ“—แ“‚แ’ƒ, แ’ฅแ“•แŠแ“แ“‚แ’ƒ, แ“‚แŠแ–แ•แ“‚แ’ƒ |
| `-แ‘แ–…` | แƒแ–ƒแ‘ฆแ‘แ–…, แ“ฏแ…แ•‹แ…แ”ฎแ–…แ‘แ–…, แƒแ“…แ“•แ–…แ‘แ–… |
| `-แ“„แ‘ฆ` | แฑแ“•แ•†แ‘ฆแ‘ŽแŠแ•แ“‚แ–แ“แ“„แ‘ฆ, แ‘ญแ–‘แ“ชแ“•แ–…แนแ–…แ“ฏแ…แ‘Žแ“„แ‘ฆ, แŠแ‘•แ…แ“ฏแ…แ–ƒแ‘Žแ’Œแ“„แ‘ฆ |
| `-แ“‚` | แ“ฏแ“šแ‘–แ“‚, แƒแ“šแ…แ™ฑแ–ฆแ–ขแ“‚, แ–ƒแ“‚แ’‹แ”ญแ–“แ“‚ |
| `-t` | aallatqiit, pitquhiinit, anngutikhaqanngittagaangat |
### 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 |
|------|----------|------------------|----------|
| `แ•—แ“ชแ“•แ–…` | 1.82x | 6 contexts | แ“ฏแ•—แ“ชแ“•แ–…, แ“ฏแ•—แ“ชแ“•แ–…แนแ’ƒ, แ“ฏแ•—แ“ชแ“•แ–…แนแ–… |
| `แ“ฏแ•—แ“ชแ“•` | 1.82x | 5 contexts | แ“ฏแ•—แ“ชแ“•แ–…, แ“ฏแ•—แ“ชแ“•แ•แ’ฅ, แ“ฏแ•—แ“ชแ“•แ–…แนแ’ƒ |
| `แ–…แ“ฏแ’ชแ”ช` | 1.50x | 6 contexts | แ“‡แƒแ“ˆแ–…แ“ฏแ’ชแ”ชแ–…, แ‘Žแ‘Žแ•‹แ–…แ“ฏแ’ชแ”ชแ–…, แ‘Žแ‘Žแ•‹แ–…แ“ฏแ’ชแ”ชแ’ฅ |
| `แ“ฏแ’ชแ”ชแ–…` | 1.72x | 4 contexts | แƒแ“šแ“ฏแ’ชแ”ชแ–…, แ“ดแ“‡แ“ฏแ’ชแ”ชแ–…, แ“ดแ–…แ‘ญแ“ฏแ’ชแ”ชแ–… |
| `แ–‘แ“ชแ“—แ“‚` | 1.89x | 3 contexts | แ’ฅแ‘ญแ“›แ–‘แ“ชแ“—แ“‚, แŠแ–แ“›แ–‘แ“ชแ“—แ“‚, แŠแ–แ“›แ–‘แ“ชแ“—แ“‚แ“— |
### 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 |
|--------|--------|-----------|----------|
| `-แŠ` | `-แ‘ฆ` | 61 words | แŠแ“‚แ’แ–…แ‘Žแ“ชแ“—แ’‹แ‘ฆ, แŠแ…แ“šแ‘ฆแ‘ŽแŠแ•ˆแ“แ“ƒแ–…แ‘แ‘ฆ |
| `-แƒ` | `-แ–…` | 47 words | แƒแ–ƒแ‘ฆแ‘แ–…, แƒแ“…แ“•แ–…แ‘แ–… |
| `-แƒ` | `-แ‘ฆ` | 46 words | แƒแ“…แ–ƒแ‘Žแ’Œแ‘ฆ, แƒแ“ฏแ’แƒแ‘ฆ |
| `-แ…` | `-แ‘ฆ` | 41 words | แ…แ‘ญแ…แ–ƒแ“•แ–…แ‘Žแ“ชแ“—แ’‹แ‘ฆ, แ…แ–ƒแ“•แ’ซแ’แ“„แ‘ฆ |
| `-แŠ` | `-แ–…` | 37 words | แŠแ‘แ–…แ‘•แ…แ“ฏแ’ชแ”ชแ–…, แŠแ–แ“›แ–‘แ”ชแ–… |
| `-แƒ` | `-แ’ƒ` | 33 words | แƒแ“„แ’ƒ, แƒแ“•แ“แ“‚แŠแ•ˆแ‘Žแ’ฅแ’ƒ |
| `-แŠ` | `-แ’ƒ` | 24 words | แŠแ‘•แ…แ“ฏแ•แ’ฅแ’ƒ, แŠแ‘ฏแ“•แ••แ’ƒ |
| `-แƒ` | `-แ“‚แ’ƒ` | 19 words | แƒแ“„แ–•แ“‚แ’ƒ, แƒแ•แ•‹แ••แ–แ“แ“‚แ’ƒ |
| `-แ…` | `-แ–…` | 19 words | แ…แฑแ•แ–“แ–…, แ…แ–ƒแ…แ“ฏแ–… |
| `-แŠ` | `-แ“‚` | 17 words | แŠแ‘แ–…แ‘•แ…แ“ชแ“—แ“‚, แŠแ–แ”ชแ’ปแ’ชแ•†แŠแ“˜แ“ชแ“—แ“‚ |
### 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 |
|------|-----------------|------------|------|
| แ‹แ–…แ‘ญแ’ƒแ“ฏแ’ชแ“‚แ–“แ“„แ‘ฆ | **`แ‹แ–…แ‘ญแ’ƒแ“ฏแ’ชแ“‚แ–“-แ“„แ‘ฆ`** | 4.5 | `แ‹แ–…แ‘ญแ’ƒแ“ฏแ’ชแ“‚แ–“` |
| presented | **`present-ed`** | 4.5 | `present` |
| uniformed | **`uniform-ed`** | 4.5 | `uniform` |
| แ“„แ“‡แ“•แธแ…แ”ญแ–“แ“„แ‘ฆ | **`แ“„แ“‡แ“•แธแ…แ”ญแ–“-แ“„แ‘ฆ`** | 4.5 | `แ“„แ“‡แ“•แธแ…แ”ญแ–“` |
| แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Žแ‘ฆ | **`แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Ž-แ‘ฆ`** | 4.5 | `แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Ž` |
| แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Žแ“„แ‘ฆ | **`แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Ž-แ“„แ‘ฆ`** | 4.5 | `แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Ž` |
| แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Žแ“‚แ’ƒ | **`แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Ž-แ“‚แ’ƒ`** | 4.5 | `แ‘–แ’ƒแ“ฐแ”ญแƒแ”ญแ•ˆแ‘Ž` |
| แ’ซแ“แ‘Žแ••แ…แ“ชแ‘แ’งแ‘ฆ | **`แ’ซแ“แ‘Žแ••แ…แ“ชแ‘-แ’งแ‘ฆ`** | 4.5 | `แ’ซแ“แ‘Žแ••แ…แ“ชแ‘` |
| แŠแ••แ‘ฆแ‘แ–…แ“ฏแ’ชแ”ชแ“‚แ‘ฆ | **`แŠแ••แ‘ฆแ‘แ–…แ“ฏแ’ชแ”ชแ“‚-แ‘ฆ`** | 4.5 | `แŠแ••แ‘ฆแ‘แ–…แ“ฏแ’ชแ”ชแ“‚` |
| แƒแ“•แ“แ“‚แŠแ•ˆแ‘Žแ’ฅแ’ƒ | **`แƒแ“•แ“แ“‚แŠแ•ˆแ‘Ž-แ’ฅแ’ƒ`** | 4.5 | `แƒแ“•แ“แ“‚แŠแ•ˆแ‘Ž` |
| แƒแ“•แ“แ“‚แŠแ–…แ‘Žแ“‚แ’ƒ | **`แƒแ“•แ“แ“‚แŠแ–…แ‘Ž-แ“‚แ’ƒ`** | 4.5 | `แƒแ“•แ“แ“‚แŠแ–…แ‘Ž` |
| แ‹แ–…แ‘ญแ’ƒแ“ฏแ’ชแ“‚แ–“แ“‚แ’ƒ | **`แ‹แ–…แ‘ญแ’ƒแ“ฏแ’ชแ“‚แ–“-แ“‚แ’ƒ`** | 4.5 | `แ‹แ–…แ‘ญแ’ƒแ“ฏแ’ชแ“‚แ–“` |
| แƒแ“šแ’‹แ”ญแ…แ“•แ–…แ‘แ–… | **`แƒแ“šแ’‹แ”ญแ…แ“•-แ–…-แ‘แ–…`** | 3.0 | `แƒแ“šแ’‹แ”ญแ…แ“•` |
| แŠแ’ฅแŠแ–…แ‘•แ…แ“ฏแ’ชแ”ชแ‘ฆ | **`แŠ-แ’ฅแŠแ–…แ‘•แ…แ“ฏแ’ชแ”ช-แ‘ฆ`** | 3.0 | `แ’ฅแŠแ–…แ‘•แ…แ“ฏแ’ชแ”ช` |
| แƒแ“„แ‘แƒแ“แ“‡แ•แ“‚แ’ƒ | **`แƒแ“„-แ‘แƒแ“แ“‡แ•-แ“‚แ’ƒ`** | 3.0 | `แ‘แƒแ“แ“‡แ•` |
### 6.6 Linguistic Interpretation
> **Automated Insight:**
The language Inuktitut 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 | **32k BPE** | Best compression (3.91x) |
| N-gram | **2-gram** | Lowest perplexity (93) |
| Markov | **Context-4** | Highest predictability (99.5%) |
| 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) ร— 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.
**Rยฒ (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* Rยฒ near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* Rยฒ > 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
- ๐ŸŒ Website: [wikilangs.org](https://wikilangs.org)
- ๐Ÿค— Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- ๐Ÿ“Š Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- ๐Ÿ‘ค Author: [Omar Kamali](https://huggingface.co/omarkamali)
- ๐Ÿค Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*
*Report Date: 2026-01-10 04:55:45*