---
language: sat
language_name: Santali
language_family: austroasiatic_other
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-austroasiatic_other
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: 4.334
  - name: best_isotropy
    type: isotropy
    value: 0.8573
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Santali - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Santali** 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** | 3.562x | 3.56 | 0.1107% | 614,914 |
| **16k** | 3.887x | 3.89 | 0.1208% | 563,511 |
| **32k** | 4.145x | 4.15 | 0.1289% | 528,448 |
| **64k** | 4.334x 🏆 | 4.34 | 0.1347% | 505,414 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ᱛᱟᱥᱨᱤᱨ ᱛᱚᱵᱜᱮ ᱫᱚ ᱢᱤᱫᱴᱟᱝ ᱵᱷᱩᱴᱟᱱ ᱨᱤᱱᱤᱡ ᱯᱨᱚᱫᱷᱟᱱ ᱢᱚᱱᱛᱨᱤ ᱛᱟᱦᱮ ᱠᱟᱱᱟ᱾ ᱥᱟᱹᱠᱷᱭᱟᱹᱛ ᱵᱟᱦᱨᱮ ᱡᱚ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ᱛᱟᱥ ᱨᱤ ᱨ ▁ᱛ ᱚᱵ ᱜᱮ ▁ᱫᱚ ▁ᱢᱤᱫᱴᱟᱝ ▁ᱵᱷᱩᱴᱟᱱ ▁ᱨᱤᱱᱤᱡ ... (+7 more)` | 17 |
| 16k | `▁ᱛᱟᱥ ᱨᱤ ᱨ ▁ᱛ ᱚᱵ ᱜᱮ ▁ᱫᱚ ▁ᱢᱤᱫᱴᱟᱝ ▁ᱵᱷᱩᱴᱟᱱ ▁ᱨᱤᱱᱤᱡ ... (+7 more)` | 17 |
| 32k | `▁ᱛᱟᱥ ᱨᱤ ᱨ ▁ᱛᱚᱵ ᱜᱮ ▁ᱫᱚ ▁ᱢᱤᱫᱴᱟᱝ ▁ᱵᱷᱩᱴᱟᱱ ▁ᱨᱤᱱᱤᱡ ▁ᱯᱨᱚᱫᱷᱟᱱ ... (+6 more)` | 16 |
| 64k | `▁ᱛᱟᱥ ᱨᱤᱨ ▁ᱛᱚᱵ ᱜᱮ ▁ᱫᱚ ▁ᱢᱤᱫᱴᱟᱝ ▁ᱵᱷᱩᱴᱟᱱ ▁ᱨᱤᱱᱤᱡ ▁ᱯᱨᱚᱫᱷᱟᱱ ▁ᱢᱚᱱᱛᱨᱤ ... (+5 more)` | 15 |

**Sample 2:** `ᱡᱤᱭᱚᱛᱤ ᱫᱚ ᱢᱤᱫ ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ᱠᱟᱵᱟᱰᱤ ᱠᱷᱮᱞᱚᱸᱱᱰᱤᱭᱟᱹ ᱠᱟᱱᱟᱭ ᱾ ᱩᱱᱤ ᱫᱚ ᱮᱥᱤᱭᱟᱱ ᱜᱮᱢᱥ ᱨᱮ ᱥᱚᱱᱟ ᱢ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ᱡ ᱤᱭ ᱚᱛᱤ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ▁ᱠᱟᱵᱟᱰᱤ ▁ᱠᱷᱮᱞᱚᱸᱱᱰ ᱤᱭᱟᱹ ▁ᱠᱟᱱᱟᱭ ... (+16 more)` | 26 |
| 16k | `▁ᱡᱤᱭ ᱚᱛᱤ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ▁ᱠᱟᱵᱟᱰᱤ ▁ᱠᱷᱮᱞᱚᱸᱱᱰᱤᱭᱟᱹ ▁ᱠᱟᱱᱟᱭ ▁᱾ ▁ᱩᱱᱤ ... (+14 more)` | 24 |
| 32k | `▁ᱡᱤᱭ ᱚᱛᱤ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ▁ᱠᱟᱵᱟᱰᱤ ▁ᱠᱷᱮᱞᱚᱸᱱᱰᱤᱭᱟᱹ ▁ᱠᱟᱱᱟᱭ ▁᱾ ▁ᱩᱱᱤ ... (+14 more)` | 24 |
| 64k | `▁ᱡᱤᱭ ᱚᱛᱤ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ▁ᱠᱟᱵᱟᱰᱤ ▁ᱠᱷᱮᱞᱚᱸᱱᱰᱤᱭᱟᱹ ▁ᱠᱟᱱᱟᱭ ▁᱾ ▁ᱩᱱᱤ ... (+14 more)` | 24 |

**Sample 3:** `ᱯᱩᱡᱟ ᱱᱚᱨᱣᱟᱞ (ᱡᱟᱱᱟᱢ ᱑᱕ ᱢᱟᱨᱪ ᱫᱚ ᱢᱤᱫ ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ᱠᱟᱵᱟᱰᱤ ᱠᱷᱮᱞᱚᱸᱰᱤᱭᱟ. ᱠᱟᱱᱟᱭ ᱾ ᱩᱱᱤ ᱫᱚ ᱮᱥ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ᱯᱩᱡᱟ ▁ᱱᱚᱨ ᱣᱟᱞ ▁( ᱡᱟᱱᱟᱢ ▁᱑᱕ ▁ᱢᱟᱨᱪ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ... (+20 more)` | 30 |
| 16k | `▁ᱯᱩᱡᱟ ▁ᱱᱚᱨ ᱣᱟᱞ ▁( ᱡᱟᱱᱟᱢ ▁᱑᱕ ▁ᱢᱟᱨᱪ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ... (+20 more)` | 30 |
| 32k | `▁ᱯᱩᱡᱟ ▁ᱱᱚᱨᱣᱟᱞ ▁( ᱡᱟᱱᱟᱢ ▁᱑᱕ ▁ᱢᱟᱨᱪ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ▁ᱠᱟᱵᱟᱰᱤ ... (+19 more)` | 29 |
| 64k | `▁ᱯᱩᱡᱟ ▁ᱱᱚᱨᱣᱟᱞ ▁( ᱡᱟᱱᱟᱢ ▁᱑᱕ ▁ᱢᱟᱨᱪ ▁ᱫᱚ ▁ᱢᱤᱫ ▁ᱥᱤᱧᱚᱛᱤᱭᱟᱹ ▁ᱠᱟᱵᱟᱰᱤ ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 64k achieves 4.334x compression
- **Lowest UNK Rate:** 8k with 0.1107% 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 | 20,084 | 14.29 | 97,087 | 14.0% | 34.6% |
| **2-gram** | Subword | 373 🏆 | 8.54 | 7,442 | 61.2% | 97.5% |
| **3-gram** | Word | 54,503 | 15.73 | 165,587 | 7.3% | 21.9% |
| **3-gram** | Subword | 2,810 | 11.46 | 55,355 | 27.5% | 67.4% |
| **4-gram** | Word | 106,952 | 16.71 | 264,198 | 4.3% | 16.9% |
| **4-gram** | Subword | 13,742 | 13.75 | 288,409 | 15.4% | 42.0% |
| **5-gram** | Word | 75,915 | 16.21 | 180,244 | 5.1% | 19.6% |
| **5-gram** | Subword | 43,676 | 15.41 | 734,127 | 10.4% | 30.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ᱩᱱᱤ ᱫᱚ` | 27,097 |
| 2 | `ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ` | 24,265 |
| 3 | `ᱡᱟᱦᱟᱸ ᱫᱚ` | 11,415 |
| 4 | `ᱨᱮ ᱢᱮᱱᱟᱜᱼᱟ` | 9,610 |
| 5 | `ᱫᱚ ᱢᱤᱫ` | 8,714 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ᱠᱚ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ` | 6,636 |
| 2 | `ᱥᱟᱶᱛᱟ ᱩᱛᱷᱱᱟᱹᱣ ᱵᱚᱱᱚᱛ` | 5,033 |
| 3 | `ᱥᱟᱹᱠᱷᱭᱟᱹᱛ ᱵᱟᱦᱨᱮ ᱡᱚᱱᱚᱲ` | 4,990 |
| 4 | `ᱨᱮ ᱩᱱᱤ ᱫᱚ` | 4,504 |
| 5 | `ᱨᱮᱱᱟᱜ ᱦᱚᱲ ᱞᱮᱠᱷᱟ` | 3,803 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ᱨᱮᱱᱟᱜ ᱦᱚᱲ ᱞᱮᱠᱷᱟ ᱡᱚᱠᱷᱟ` | 3,279 |
| 2 | `ᱦᱚᱲ ᱠᱚ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ` | 2,960 |
| 3 | `ᱦᱚᱲ ᱞᱮᱠᱷᱟ ᱡᱚᱠᱷᱟ ᱞᱮᱠᱟᱛᱮ` | 2,711 |
| 4 | `ᱥᱟᱞ ᱨᱮᱱᱟᱜ ᱦᱚᱲ ᱞᱮᱠᱷᱟ` | 2,039 |
| 5 | `ᱥᱟᱶᱛᱟ ᱩᱛᱷᱱᱟᱹᱣ ᱵᱚᱱᱚᱛ ᱨᱮ` | 1,482 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ᱨᱮᱱᱟᱜ ᱦᱚᱲ ᱞᱮᱠᱷᱟ ᱡᱚᱠᱷᱟ ᱞᱮᱠᱟᱛᱮ` | 2,560 |
| 2 | `ᱥᱟᱞ ᱨᱮᱱᱟᱜ ᱦᱚᱲ ᱞᱮᱠᱷᱟ ᱡᱚᱠᱷᱟ` | 2,014 |
| 3 | `ᱠᱚ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱚᱸᱰᱮ ᱠᱷᱚᱱ` | 639 |
| 4 | `ᱦᱚᱲ ᱠᱚ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱚᱸᱰᱮ` | 622 |
| 5 | `ᱨᱮᱱᱟᱜ ᱥᱟᱞ ᱨᱮᱱᱟᱜ ᱦᱚᱲ ᱞᱮᱠᱷᱟ` | 599 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ᱟ _` | 532,897 |
| 2 | `_ ᱠ` | 452,845 |
| 3 | `_ ᱨ` | 441,511 |
| 4 | `ᱨ ᱮ` | 427,576 |
| 5 | `ᱮ _` | 424,447 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ᱨ ᱮ` | 359,020 |
| 2 | `ᱟ ᱜ _` | 216,961 |
| 3 | `ᱨ ᱮ _` | 206,913 |
| 4 | `_ ᱫ ᱚ` | 193,101 |
| 5 | `ᱫ ᱚ _` | 184,355 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ᱨ ᱮ _` | 183,663 |
| 2 | `_ ᱫ ᱚ _` | 173,539 |
| 3 | `ᱮ ᱱ ᱟ ᱜ` | 121,241 |
| 4 | `ᱟ _ ᱾ _` | 118,531 |
| 5 | `_ ᱟ ᱨ _` | 109,370 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ᱮ ᱱ ᱟ ᱜ _` | 88,897 |
| 2 | `_ ᱠ ᱟ ᱱ ᱟ` | 77,004 |
| 3 | `ᱨ ᱮ ᱱ ᱟ ᱜ` | 76,395 |
| 4 | `_ ᱨ ᱮ ᱱ ᱟ` | 76,338 |
| 5 | `ᱠ ᱟ ᱱ ᱟ _` | 56,559 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 373
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.7025 | 1.627 | 5.73 | 274,818 | 29.8% |
| **1** | Subword | 0.8387 | 1.788 | 5.63 | 5,505 | 16.1% |
| **2** | Word | 0.2957 | 1.228 | 1.89 | 1,572,360 | 70.4% |
| **2** | Subword | 0.6641 | 1.585 | 4.27 | 30,957 | 33.6% |
| **3** | Word | 0.1263 | 1.091 | 1.26 | 2,962,389 | 87.4% |
| **3** | Subword | 0.7552 | 1.688 | 3.97 | 132,005 | 24.5% |
| **4** | Word | 0.0549 🏆 | 1.039 | 1.09 | 3,737,893 | 94.5% |
| **4** | Subword | 0.6689 | 1.590 | 2.92 | 523,754 | 33.1% |

### Generated Text Samples (Word-based)

Below are text samples generated from each word-based Markov chain model:

**Context Size 1:**

1. `ᱨᱮ ᱚᱠᱷᱟ ᱫᱚ ᱯᱚᱱᱚᱛ ᱯᱚᱪᱷᱤᱢ ᱵᱟᱝᱞᱟ ᱨᱮ ᱟᱭᱢᱟ ᱠᱟ ᱥᱱᱤ ᱵᱚᱠᱠᱷᱟᱞᱤ ᱫᱚ ᱥᱮᱨᱢᱟ ᱨᱮᱭᱟᱜ ᱟᱢᱮᱨᱤᱠᱟᱱ ᱮᱠᱥᱯᱨᱮᱥ`
2. `ᱫᱚ ᱢᱤᱴᱚᱨ ᱮᱱᱴᱨᱤ ᱞᱮᱠᱟᱛᱮ ᱱᱚᱸᱰᱮ ᱱᱟᱜ ᱥᱟᱥᱚᱱ ᱨᱮᱱᱟᱜ ᱪᱮᱛᱟᱱ ᱨᱮᱠᱚ ᱨᱚᱲᱼᱟ ᱡᱚᱨᱡᱽ ᱢᱟᱭᱨᱤᱱ ᱟᱜ ᱡᱟᱱᱟᱢ ᱞᱮᱱᱟᱭ`
3. `ᱟᱨ ᱰᱤᱨᱮᱠᱴᱚᱨ ᱞᱟᱹᱜᱤᱫ ᱛᱮ ᱜᱮᱲᱤᱭᱟᱠᱚᱞᱟ ᱟᱹᱛᱩ ᱠᱟᱱᱟ ᱮᱱᱤᱢᱮᱥᱚᱱ ᱨᱮ ᱛᱮᱭᱟᱨ ᱞᱮᱫᱟ ᱟᱭᱢᱟ ᱫᱤᱱ ᱠᱚ ᱵᱟᱰᱟᱭ ᱛᱟᱦᱮᱸᱫ`

**Context Size 2:**

1. `ᱩᱱᱤ ᱫᱚ ᱰᱤᱨᱮᱠᱴᱚᱨ ᱰᱟᱭᱱᱟ ᱞᱳᱨᱮᱱ ᱥᱟᱶ ᱢᱤᱫ ᱥᱟᱹᱜᱟᱹᱭ ᱢᱮᱱᱟᱜ ᱟ ᱫᱚ ᱱᱤᱭᱟᱹ ᱥᱤᱧᱚᱛ ᱨᱮ ᱦᱳᱢᱤᱭᱳᱯᱮᱛᱷᱤ ᱨᱮᱭᱟᱜ ᱮᱛᱦᱚᱵ`
2. `ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱦᱟᱣᱲᱟ ᱱᱤᱭᱩ ᱡᱚᱞᱯᱟᱭᱜᱩᱲᱤ ᱵᱚᱱᱫᱮ ᱵᱷᱟᱨᱚᱛ ᱮᱠᱥᱯᱨᱮᱥ ᱞᱮᱠᱟᱛᱮ ᱪᱟᱞᱟᱣ ᱞᱮᱱᱟ ᱛᱟᱦᱮᱸᱫ ᱥᱟᱹᱠᱷᱭᱟᱹᱛ ᱵᱟᱦᱨᱮ ᱡᱚᱱᱚᱲ...`
3. `ᱡᱟᱦᱟᱸ ᱫᱚ ᱡᱮᱜᱮᱫ ᱵᱤᱨᱫᱟᱹᱜᱟᱲ ᱨᱮᱭᱟᱜ ᱯᱷᱮᱠᱟᱞᱴᱤ ᱚᱯᱷ ᱟᱨᱴᱥ ᱮ ᱯᱩᱨᱟᱹᱣ ᱞᱮᱫ ᱛᱟᱦᱮᱸᱫ ᱨᱮ ᱟᱫᱽᱨᱟ ᱵᱷᱮᱫᱩᱣᱟᱥᱳᱞ ᱥᱮᱠᱴᱚᱨ ᱟᱨ`

**Context Size 3:**

1. `ᱠᱚ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱟᱨ ᱢᱤᱫᱴᱟᱹᱝ ᱥᱮᱠᱮᱱᱰᱟᱨᱤ ᱤᱥᱠᱩᱞ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱦᱚᱲᱢᱚ ᱥᱟᱶᱟᱨ ᱵᱟᱱᱫᱳᱣᱟᱱ ᱨᱮ ᱓᱐ ᱜᱚᱴᱟᱝ ᱵᱮᱰ ᱟᱜ ᱵᱮᱞᱠᱩᱨᱤ`
2. `ᱥᱟᱶᱛᱟ ᱩᱛᱷᱱᱟᱹᱣ ᱵᱚᱱᱚᱛ ᱨᱤᱱ ᱜᱩᱴ ᱦᱚᱲ ᱮᱞ ᱨᱤᱱ ᱑᱗ ᱐᱔ ᱠᱚ ᱦᱩᱭᱩᱜ ᱠᱟᱱᱟ ᱱᱚᱸᱰᱮ ᱠᱚ ᱛᱟᱦᱮᱸᱱ ᱠᱟᱱ ᱵᱟᱡᱟᱨ`
3. `ᱨᱮ ᱩᱱᱤ ᱫᱚ ᱟᱯᱱᱟ ᱥᱟᱯᱱᱟ ᱢᱚᱱᱤ ᱢᱚᱱᱤ ᱯᱷᱤᱞᱢ ᱨᱮ ᱠᱟ ᱠᱚᱱᱱᱚᱰᱟ ᱨᱮ ᱑᱐᱐ ᱜᱚᱴᱟᱝ ᱚᱱᱚᱞ ᱢᱮᱱᱟᱜᱼᱟ ᱱᱟᱜᱟᱢ ᱡᱟᱨᱢᱟᱱ`

**Context Size 4:**

1. `ᱨᱮᱱᱟᱜ ᱦᱚᱲ ᱞᱮᱠᱷᱟ ᱡᱚᱠᱷᱟ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱱᱚᱣᱟ ᱥᱟᱞ ᱨᱮ ᱵᱟᱲᱦᱟᱣ ᱠᱟᱛᱮ ᱦᱚᱲ ᱠᱚ ᱦᱩᱭ ᱮᱱᱟ ᱟᱨ ᱟᱨ ᱛᱟᱞᱟ ᱨᱮ`
2. `ᱦᱚᱲ ᱠᱚ ᱛᱟᱦᱮᱸ ᱠᱟᱱᱟ ᱚᱸᱰᱮ ᱠᱷᱚᱱ ᱒᱙ ᱘᱒᱗ ᱗᱙ ᱔᱖ ᱠᱚᱲᱟ ᱟᱨ ᱑᱘ ᱙᱖᱙ ᱔᱙ ᱓᱒ ᱛᱤᱨᱞᱟᱹ ᱠᱚ ᱛᱟᱦᱮᱸ`
3. `ᱦᱚᱲ ᱞᱮᱠᱷᱟ ᱡᱚᱠᱷᱟ ᱞᱮᱠᱟᱛᱮ ᱨᱟᱭᱯᱩᱨ ᱕ ᱔᱗᱐ ᱥᱩᱠᱫᱚᱞ ᱑᱓ ᱐᱙᱓ ᱟᱨ ᱵᱚᱰ ᱵᱚᱰ ᱔ ᱕᱕᱘ ᱜᱚᱞᱥᱤ ᱑ ᱥᱟᱶᱛᱟ ᱩᱛᱷᱱᱟᱹᱣ`


### Generated Text Samples (Subword-based)

Below are text samples generated from each subword-based Markov chain model:

**Context Size 1:**

1. `_ᱜ_,_ᱨ_ᱡ_ᱩᱴᱤᱫᱚᱣ_`
2. `ᱟᱨᱩᱜ_ᱢ_ᱠᱴᱤᱨᱤᱞ_ᱠᱷ`
3. `ᱚᱦᱚ_᱒_ᱢᱤ_ᱠᱷᱟᱨᱮᱸᱠ`

**Context Size 2:**

1. `ᱟ_ᱞᱟᱹ_ᱨᱮ_ᱱᱤᱭᱟᱱ_ᱠᱚ`
2. `_ᱠᱷᱟᱣ_ᱨᱟᱸᱦᱮ',_ᱵᱟᱡ`
3. `_ᱨᱮ_ᱟᱨ_᱖_ᱠᱚ_ᱪᱟᱞ,_`

**Context Size 3:**

1. `_ᱨᱮᱱᱟᱜᱼᱟ_bum_ᱵᱤᱥᱟᱱ`
2. `ᱟᱜ_ᱯᱟᱹᱨᱤ_ᱢᱟᱞᱟᱜ_ᱢᱟᱨ`
3. `ᱨᱮ_᱑᱒0,᱖᱔᱐_ᱟᱜ_ᱠᱟᱱ_`

**Context Size 4:**

1. `_ᱨᱮ_ᱯᱷᱮᱰ_ᱠᱚ_ᱚᱲᱟᱜ_ᱨᱚ`
2. `_ᱫᱚ_ᱵᱤᱫᱷᱟᱱᱤ_ᱡᱟᱦᱟᱸ_ᱫ`
3. `ᱮᱱᱟᱜ_ᱦᱚᱸ_ᱨᱤᱱ_ᱠᱟᱱ_ᱫᱷ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (523,754 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 | 104,851 |
| Total Tokens | 4,586,629 |
| Mean Frequency | 43.74 |
| Median Frequency | 3 |
| Frequency Std Dev | 1084.86 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ᱨᱮ | 194,411 |
| 2 | ᱫᱚ | 174,300 |
| 3 | ᱟᱨ | 110,495 |
| 4 | ᱨᱮᱱᱟᱜ | 75,922 |
| 5 | ᱠᱚ | 74,024 |
| 6 | ᱠᱟᱱᱟ | 64,170 |
| 7 | ᱠᱷᱚᱱ | 46,273 |
| 8 | ᱩᱱᱤ | 40,257 |
| 9 | ᱢᱤᱫ | 40,250 |
| 10 | ᱨᱮᱭᱟᱜ | 38,160 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ᱜᱟᱲᱤᱢᱟᱭ | 2 |
| 2 | ᱜᱨᱟᱱᱰᱤᱝ | 2 |
| 3 | ᱟᱯᱚᱫᱟ | 2 |
| 4 | ᱵᱮᱵᱚᱥᱛᱟᱯᱚᱱᱟ | 2 |
| 5 | ᱢᱩᱦᱟᱹᱱᱟᱹ | 2 |
| 6 | estuary | 2 |
| 7 | ᱢᱚᱸᱜᱨᱚᱵᱷ | 2 |
| 8 | ᱦᱚᱸᱥᱟ | 2 |
| 9 | ᱞᱮᱛᱤᱯᱩᱨ | 2 |
| 10 | ᱴᱮᱨᱟᱠᱚᱴᱟ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1879 |
| R² (Goodness of Fit) | 0.996295 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 42.8% |
| Top 1,000 | 71.1% |
| Top 5,000 | 84.6% |
| Top 10,000 | 89.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9963 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 42.8% of corpus
- **Long Tail:** 94,851 words needed for remaining 10.9% 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 | 0.8573 | 0.3536 | N/A | N/A |
| **mono_64d** | 64 | 0.8443 | 0.2821 | N/A | N/A |
| **mono_128d** | 128 | 0.7962 | 0.2213 | N/A | N/A |
| **aligned_32d** | 32 | 0.8573 🏆 | 0.3640 | 0.0320 | 0.1660 |
| **aligned_64d** | 64 | 0.8443 | 0.2836 | 0.0440 | 0.2060 |
| **aligned_128d** | 128 | 0.7962 | 0.2203 | 0.0800 | 0.2960 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8573 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2875. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.0% 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 | **-0.348** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-ᱥ` | ᱥᱵᱫᱚ, ᱥᱨᱚᱵᱷᱟᱱ, ᱥᱤᱧᱟᱛ |
| `-ᱠ` | ᱠᱷᱮᱢᱟᱨ, ᱠᱳᱲᱚ, ᱠᱟᱞᱮ |
| `-ᱵ` | ᱵᱤᱨᱫᱟᱹᱜᱟᱲᱤᱭᱩᱱᱤᱵᱷᱟᱨᱥᱤᱴᱮᱴ, ᱵᱷᱳ, ᱵᱟᱫᱽᱞᱟ |
| `-ᱥᱟ` | ᱥᱟᱠᱩᱱᱛᱚᱞᱟ, ᱥᱟᱭᱟᱱᱟ, ᱥᱟᱵᱽᱢᱟᱨᱥᱟᱞ |
| `-ᱟ` | ᱟᱣᱚ, ᱟᱵᱽᱫᱩᱞᱟᱦ, ᱟᱭᱹ |
| `-ᱠᱟ` | ᱠᱟᱞᱮ, ᱠᱟᱨᱟᱭᱠᱟᱞ, ᱠᱟᱨᱠᱟᱛ |
| `-ᱵᱟ` | ᱵᱟᱫᱽᱞᱟ, ᱵᱟᱯᱞᱟᱱᱤᱡ, ᱵᱟᱴᱚᱢ |
| `-ᱯ` | ᱯᱟᱱᱛᱷᱟᱠᱚ, ᱯᱷᱤᱠᱟᱨᱰ, ᱯᱷᱟᱭᱡᱟᱵᱟᱫᱽ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ᱟ` | ᱛᱷᱩᱱᱤᱜᱟ, ᱵᱟᱫᱽᱞᱟ, ᱢᱟᱱᱤᱥᱟ |
| `-ᱤ` | ᱜᱳᱢᱚᱛᱤ, ᱡᱚᱱᱢᱟᱥᱴᱚᱢᱤ, ᱡᱤᱵᱩᱴᱤ |
| `-ᱨ` | ᱠᱷᱮᱢᱟᱨ, ᱪᱮᱱᱫᱩᱨ, ᱠᱣᱟᱰᱨᱮᱝᱜᱩᱞᱟᱨ |
| `-ᱱ` | ᱥᱨᱚᱵᱷᱟᱱ, ᱥᱮᱬᱟᱦᱟᱱ, ᱟᱯᱩᱱ |
| `-ᱚᱱ` | ᱰᱤᱵᱷᱤᱡᱚᱱ, ᱥᱨᱤᱱᱤᱠᱮᱛᱚᱱ, ᱡᱟᱢᱚᱱ |
| `-ᱟᱨ` | ᱠᱷᱮᱢᱟᱨ, ᱠᱣᱟᱰᱨᱮᱝᱜᱩᱞᱟᱨ, ᱥᱴᱮᱞᱟᱨ |
| `-ᱟᱱ` | ᱥᱨᱚᱵᱷᱟᱱ, ᱥᱮᱬᱟᱦᱟᱱ, ᱨᱟᱡᱽᱟᱹᱨᱤᱭᱟᱱ |
| `-ᱞ` | ᱳᱝᱜᱳᱞ, ᱥᱟᱵᱽᱢᱟᱨᱥᱟᱞ, ᱠᱟᱨᱟᱭᱠᱟᱞ |

### 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 |
|------|----------|------------------|----------|
| `ᱟᱦᱮᱸ` | 2.13x | 43 contexts | ᱪᱟᱦᱮᱸ, ᱠᱟᱦᱮᱸ, ᱴᱟᱦᱮᱸ |
| `ᱟᱹᱨᱥ` | 2.33x | 28 contexts | ᱯᱟᱹᱨᱥ, ᱟᱹᱨᱥᱤ, ᱠᱟᱹᱨᱥᱤ |
| `ᱟᱹᱜᱤ` | 2.06x | 41 contexts | ᱛᱟᱹᱜᱤ, ᱜᱟᱹᱜᱤ, ᱞᱟᱹᱜᱤ |
| `ᱮᱥᱚᱱ` | 1.90x | 47 contexts | ᱠᱮᱥᱚᱱ, ᱴᱮᱥᱚᱱ, ᱡᱮᱥᱚᱱ |
| `ᱞᱟᱹᱜ` | 2.30x | 23 contexts | ᱞᱟᱹᱜᱽ, ᱞᱟᱹᱜᱤ, ᱞᱟᱹᱜᱫ |
| `ᱹᱨᱥᱤ` | 2.40x | 19 contexts | ᱟᱹᱨᱥᱤ, ᱯᱹᱨᱥᱤ, ᱠᱟᱹᱨᱥᱤ |
| `ᱮᱱᱟᱣ` | 2.03x | 33 contexts | ᱢᱮᱱᱟᱣ, ᱵᱮᱱᱟᱣ, ᱞᱮᱱᱟᱣ |
| `ᱷᱤᱞᱢ` | 2.47x | 15 contexts | 0ᱷᱤᱞᱢ, ᱳᱷᱤᱞᱢ, ᱯᱷᱤᱞᱢ |
| `ᱱᱟᱜᱼ` | 2.18x | 20 contexts | ᱟᱱᱟᱜᱼ, ᱮᱱᱟᱜᱼᱟ, ᱟᱱᱟᱜᱼᱟ |
| `ᱹᱜᱤᱫ` | 2.38x | 15 contexts | ᱟᱹᱜᱤᱫ, ᱞᱟᱹᱜᱤᱫ, ᱯᱟᱹᱜᱤᱫ |
| `ᱮᱠᱟᱛ` | 2.15x | 20 contexts | ᱞᱮᱠᱟᱛ, ᱪᱮᱠᱟᱛᱮ, ᱞᱮᱠᱟᱛᱮ |
| `ᱟᱦᱟᱸ` | 1.70x | 45 contexts | ᱦᱟᱦᱟᱸ, ᱛᱟᱦᱟᱸ, ᱨᱟᱦᱟᱸ |

### 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 |
|--------|--------|-----------|----------|
| `-ᱵ` | `-ᱤ` | 74 words | ᱵᱤᱥᱥᱚᱼᱵᱷᱟᱨᱚᱛᱤ, ᱵᱚᱨᱠᱤ |
| `-ᱵ` | `-ᱟ` | 73 words | ᱵᱷᱟᱫᱩᱨᱟ, ᱵᱤᱛᱟ |
| `-ᱥ` | `-ᱟ` | 70 words | ᱥᱚᱨᱚᱱᱠᱷᱚᱞᱟ, ᱥᱞᱮᱥᱢᱟ |
| `-ᱠ` | `-ᱟ` | 66 words | ᱠᱷᱩᱫᱟ, ᱠᱷᱟᱞᱮᱫᱟ |
| `-ᱥ` | `-ᱤ` | 60 words | ᱥᱳᱱᱤ, ᱥᱤᱝᱡᱤ |
| `-ᱠ` | `-ᱤ` | 58 words | ᱠᱟᱣᱮᱨᱤ, ᱠᱩᱱᱴᱤ |
| `-ᱯ` | `-ᱟ` | 57 words | ᱯᱚᱞᱥᱩᱸᱰᱟ, ᱯᱩᱸᱪᱟ |
| `-ᱵ` | `-ᱨ` | 54 words | ᱵᱷᱚᱣᱟᱱᱤᱯᱩᱨ, ᱵᱷᱤᱴᱤᱨ |
| `-ᱵ` | `-ᱱ` | 52 words | ᱵᱨᱤᱱᱫᱟᱣᱟᱱ, ᱵᱚᱸᱜᱟᱛᱷᱟᱱ |
| `-ᱯ` | `-ᱤ` | 50 words | ᱯᱟᱹᱫᱽᱨᱤ, ᱯᱨᱚᱡᱟᱛᱚᱱᱛᱨᱤ |

### 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 |
|------|-----------------|------------|------|
| ᱫᱟᱫᱮᱝᱜᱤᱨᱤ | **`ᱫᱟᱫᱮᱝᱜ-ᱤ-ᱨᱤ`** | 7.5 | `ᱤ` |
| ᱵᱚᱨᱟᱵᱟᱡᱟᱨ | **`ᱵᱚ-ᱨᱟ-ᱵᱟᱡᱟᱨ`** | 7.5 | `ᱵᱟᱡᱟᱨ` |
| ᱥᱟᱬᱮᱸᱥᱤᱭᱟ | **`ᱥᱟᱬᱮᱸᱥ-ᱤ-ᱭᱟ`** | 7.5 | `ᱤ` |
| ᱜᱚᱢᱠᱮᱭᱟᱱᱤ | **`ᱜᱚᱢᱠᱮ-ᱭᱟ-ᱱᱤ`** | 6.0 | `ᱜᱚᱢᱠᱮ` |
| ᱢᱮᱠᱟᱱᱤᱠᱮᱞ | **`ᱢᱮ-ᱠᱟ-ᱱᱤᱠᱮᱞ`** | 6.0 | `ᱱᱤᱠᱮᱞ` |
| ᱥᱟᱵᱰᱤᱵᱤᱡᱚᱱ | **`ᱥᱟ-ᱵ-ᱰᱤᱵᱤᱡᱚᱱ`** | 6.0 | `ᱰᱤᱵᱤᱡᱚᱱ` |
| ᱨᱟᱡᱟᱵᱟᱡᱟᱨ | **`ᱨᱟ-ᱡᱟ-ᱵᱟᱡᱟᱨ`** | 6.0 | `ᱵᱟᱡᱟᱨ` |
| strangers | **`stranger-s`** | 4.5 | `stranger` |
| proposals | **`proposal-s`** | 4.5 | `proposal` |
| ᱨᱤᱯᱷᱟᱭᱤᱱᱰ | **`ᱨᱤᱯᱷᱟᱭᱤᱱ-ᱰ`** | 4.5 | `ᱨᱤᱯᱷᱟᱭᱤᱱ` |
| ᱟᱹᱠᱷᱨᱤᱧᱟᱱ | **`ᱟᱹᱠᱷᱨᱤᱧ-ᱟᱱ`** | 4.5 | `ᱟᱹᱠᱷᱨᱤᱧ` |
| ᱯᱨᱚᱠᱨᱤᱛᱤᱥ | **`ᱯᱨᱚᱠᱨᱤᱛᱤ-ᱥ`** | 4.5 | `ᱯᱨᱚᱠᱨᱤᱛᱤ` |
| instituted | **`institute-d`** | 4.5 | `institute` |
| ᱯᱨᱳᱰᱟᱠᱥᱟᱱᱥ | **`ᱯᱨᱳᱰᱟᱠᱥᱟᱱ-ᱥ`** | 4.5 | `ᱯᱨᱳᱰᱟᱠᱥᱟᱱ` |
| quarterfinals | **`quarterfinal-s`** | 4.5 | `quarterfinal` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Santali shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.33x) |
| N-gram | **2-gram** | Lowest perplexity (373) |
| Markov | **Context-4** | Highest predictability (94.5%) |
| 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) × 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 19:38:19*