---
language: sa
language_name: Sanskrit
language_family: indoaryan_central
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-indoaryan_central
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: 4.437
  - name: best_isotropy
    type: isotropy
    value: 0.8264
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sanskrit** 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** | 3.370x | 3.37 | 0.2913% | 717,781 |
| **16k** | 3.776x | 3.78 | 0.3263% | 640,751 |
| **32k** | 4.129x | 4.13 | 0.3569% | 585,907 |
| **64k** | 4.437x 🏆 | 4.44 | 0.3835% | 545,247 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `सः यादवकुलस्य राजा आसीत्। प्राचीनवंशावली स्टब्स् प्राप्तः भाषानुबन्धः अपूर्णलेखा...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)` | 16 |
| 16k | `▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)` | 16 |
| 32k | `▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)` | 16 |
| 64k | `▁सः ▁यादवकुलस्य ▁राजा ▁आसीत् । ▁प्राचीनवंशावली ▁स्टब्स् ▁प्राप्तः ▁भाषानुबन्धः ▁अपूर्णलेखाः ... (+6 more)` | 16 |

**Sample 2:** `सः अयोध्याकुलस्य राजा आसीत्। प्राचीन-वंशावली अयोध्याकुल स्टब्स् अपूर्णलेखाः योजन...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)` | 13 |
| 16k | `▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)` | 13 |
| 32k | `▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)` | 13 |
| 64k | `▁सः ▁अयोध्याकुलस्य ▁राजा ▁आसीत् । ▁प्राचीन - वंशावली ▁अयोध्याकुल ▁स्टब्स् ... (+3 more)` | 13 |

**Sample 3:** `स्वर्णगौरीव्रतम् इत्युक्ते गौरीतृतीया एव । तत्र द्रष्टव्यम् । स्टब्स् अपूर्णलेखा...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁स्वर्ण गौ री व्र तम् ▁इत्युक्ते ▁गौरी त ृत ीया ... (+10 more)` | 20 |
| 16k | `▁स्वर्ण गौ री व्रतम् ▁इत्युक्ते ▁गौरी तृत ीया ▁एव ▁। ... (+7 more)` | 17 |
| 32k | `▁स्वर्ण गौरी व्रतम् ▁इत्युक्ते ▁गौरी तृत ीया ▁एव ▁। ▁तत्र ... (+6 more)` | 16 |
| 64k | `▁स्वर्ण गौरी व्रतम् ▁इत्युक्ते ▁गौरी तृतीया ▁एव ▁। ▁तत्र ▁द्रष्टव्यम् ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.437x compression
- **Lowest UNK Rate:** 8k with 0.2913% 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 | 11,133 | 13.44 | 41,507 | 20.4% | 40.2% |
| **2-gram** | Subword | 4,254 🏆 | 12.05 | 77,760 | 29.2% | 59.0% |
| **3-gram** | Word | 6,057 | 12.56 | 36,616 | 30.9% | 49.8% |
| **3-gram** | Subword | 37,749 | 15.20 | 386,589 | 11.4% | 30.0% |
| **4-gram** | Word | 22,497 | 14.46 | 116,572 | 23.9% | 36.9% |
| **4-gram** | Subword | 171,126 | 17.38 | 1,206,214 | 7.0% | 18.9% |
| **5-gram** | Word | 17,943 | 14.13 | 99,332 | 26.0% | 39.2% |
| **5-gram** | Subword | 336,494 | 18.36 | 1,600,156 | 5.2% | 14.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `तमे वर्षे` | 6,311 |
| 2 | `अक्तूबर दिसंबर` | 5,560 |
| 3 | `जनवरी मार्च` | 5,559 |
| 4 | `जुलाई सितंबर` | 5,558 |
| 5 | `मार्च अप्रैल` | 5,558 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `जनवरी मार्च अप्रैल` | 5,556 |
| 2 | `मार्च अप्रैल जून` | 5,555 |
| 3 | `सितंबर अक्तूबर दिसंबर` | 5,554 |
| 4 | `जुलाई सितंबर अक्तूबर` | 5,554 |
| 5 | `अप्रैल जून जुलाई` | 5,553 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `जनवरी मार्च अप्रैल जून` | 5,555 |
| 2 | `जुलाई सितंबर अक्तूबर दिसंबर` | 5,554 |
| 3 | `मार्च अप्रैल जून जुलाई` | 5,552 |
| 4 | `अप्रैल जून जुलाई सितंबर` | 5,552 |
| 5 | `जून जुलाई सितंबर अक्तूबर` | 5,548 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `जनवरी मार्च अप्रैल जून जुलाई` | 5,552 |
| 2 | `मार्च अप्रैल जून जुलाई सितंबर` | 5,551 |
| 3 | `अप्रैल जून जुलाई सितंबर अक्तूबर` | 5,548 |
| 4 | `जून जुलाई सितंबर अक्तूबर दिसंबर` | 5,548 |
| 5 | `सम्बद्धाः लेखाः भारतीयकालमानः ज्योतिषशास्त्रम् संस्कृतम्` | 1,906 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `। _` | 304,328 |
| 2 | `_ अ` | 277,099 |
| 3 | `_ ।` | 243,302 |
| 4 | `स्य _` | 179,722 |
| 5 | `, _` | 145,968 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ । _` | 237,833 |
| 2 | `_ च _` | 50,503 |
| 3 | `। _ अ` | 43,595 |
| 4 | `_ इ ति` | 41,470 |
| 5 | `म् _ अ` | 38,861 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ इ ति _` | 36,444 |
| 2 | `_ । _ अ` | 35,818 |
| 3 | `ति _ । _` | 33,422 |
| 4 | `त् _ । _` | 31,074 |
| 5 | `_ भ व ति` | 24,339 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ भ व ति _` | 17,863 |
| 2 | `_ अ स्ति _ ।` | 17,494 |
| 3 | `अ स्ति _ । _` | 17,320 |
| 4 | `_ आ सी त् _` | 13,617 |
| 5 | `सी त् _ । _` | 13,209 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 4,254
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~15% 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 | 0.4713 | 1.386 | 3.33 | 652,534 | 52.9% |
| **1** | Subword | 0.8678 | 1.825 | 13.92 | 17,979 | 13.2% |
| **2** | Word | 0.1228 | 1.089 | 1.26 | 2,174,445 | 87.7% |
| **2** | Subword | 0.7350 | 1.664 | 4.87 | 250,225 | 26.5% |
| **3** | Word | 0.0305 | 1.021 | 1.05 | 2,734,909 | 96.9% |
| **3** | Subword | 0.5248 | 1.439 | 2.74 | 1,217,332 | 47.5% |
| **4** | Word | 0.0099 🏆 | 1.007 | 1.02 | 2,863,051 | 99.0% |
| **4** | Subword | 0.3365 | 1.263 | 1.79 | 3,333,052 | 66.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `च दूरं १ वचनम् अत्र शीलतायाः आनन्दः एव मनः चित्तम् मनः शरीर शरीरं किं भविष्यति विभिन्नवि`
2. `इति पदसंज्ञाविधायकं सूत्रं त्रिफला एकं मण्डलं मुघल्साम्राज्यस्य अधीनम् अकरोत् विद्यार्थिकालात् एव रा...`
3. `अस्ति या हि साऽवस्था औपनिषदास्तु तां विक्रीतवान् अपि दृश्यते १ २ १ वेदघोष माता प्रसाद नैय्यर`

**Context Size 2:**

1. `तमे वर्षे महामहोपाध्याय प्रशस्तिं दत्त्वा सम्मानितवन्तः चतुर्थं कन्नड साहित्य परिषदः अध्यक्षः आसीत् ...`
2. `अक्तूबर दिसंबर बाह्य सूत्राणि calendopedia ६८२ ६८२ स्टब्स् अपूर्णलेखाः योजनीयम् योजनीया स्टब्स् अपूर...`
3. `जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर निधनानि जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तू...`

**Context Size 3:**

1. `जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर निधनानि जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तू...`
2. `मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर अज्ञात तिथीनां घटनाः जन्मानि जनवरी मार्च अप्रैल जून जुल...`
3. `सितंबर अक्तूबर दिसंबर बाह्य सूत्राणि calendopedia स्टब्स् अपूर्णलेखाः नावश्यके सम्बद्धाः लेखाः भारती...`

**Context Size 4:**

1. `जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर बाह्य सूत्राणि calendopedia स्टब्स् अपूर्णलेखाः न...`
2. `जुलाई सितंबर अक्तूबर दिसंबर अज्ञात तिथीनां घटनाः जन्मानि जनवरी मार्च अप्रैल जून जुलाई सितंबर अक्तूबर...`
3. `अप्रैल जून जुलाई सितंबर अक्तूबर दिसंबर अज्ञात तिथीनां घटनाः जन्मानि जनवरी मार्च अप्रैल जून जुलाई सित...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_स्म_वादः_स्था_विताः_‘विषम्_`
2. `।_वितुं_पि_इति_व्यव_शिरोम`
3. `व_एवत्_ले_()_जैनयत्_`

**Context Size 2:**

1. `।_ततश्च_।_अस्ति_इत्याख्यस्य_के`
2. `_अभवति।_मता_एलायाः_१,२`
3. `_।_एव_सुमेर_।_वा"_नास्ति`

**Context Size 3:**

1. `_।_अनेकों_उपस्थितिर्भवति_।_स`
2. `_च_दृढकार्यनीतिः_आवश्यकम्_उत्त`
3. `।_अस्मिन्_नगरे_अरुणाचलप्रदेश`

**Context Size 4:**

1. `_इति_।_पारिजातवृक्षं,_भागवतस्य`
2. `_।_अजमेर-रतन-फर्निचर_इष्णु`
3. `ति_।_प्रमाभेदात्_त्रिविधाः_प्रधानमन्त्रि`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (3,333,052 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 | 183,249 |
| Total Tokens | 2,768,645 |
| Mean Frequency | 15.11 |
| Median Frequency | 3 |
| Frequency Std Dev | 241.86 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | च | 52,641 |
| 2 | इति | 38,813 |
| 3 | अस्ति | 30,239 |
| 4 | भवति | 24,354 |
| 5 | न | 20,240 |
| 6 | आसीत् | 18,819 |
| 7 | अपि | 18,333 |
| 8 | एव | 17,673 |
| 9 | सन्ति | 13,702 |
| 10 | तस्य | 13,542 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | एन्क्रिप्शनस्य | 2 |
| 2 | अनधिकृतप्रवेशात् | 2 |
| 3 | क्रिप्टोग्राफी | 2 |
| 4 | अङ्कीयहस्ताक्षरस्य | 2 |
| 5 | गुप्तीकरणं | 2 |
| 6 | बीमयोः | 2 |
| 7 | व्यवहारौ | 2 |
| 8 | जोखिममूल्याङ्कनम् | 2 |
| 9 | संकटेभ्यः | 2 |
| 10 | pmfby | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9504 |
| R² (Goodness of Fit) | 0.998392 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 24.7% |
| Top 1,000 | 46.2% |
| Top 5,000 | 63.2% |
| Top 10,000 | 70.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9984 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 24.7% of corpus
- **Long Tail:** 173,249 words needed for remaining 29.4% 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 | 0.8179 | 0.3126 | N/A | N/A |
| **mono_64d** | 64 | 0.8264 | 0.2265 | N/A | N/A |
| **mono_128d** | 128 | 0.8039 | 0.1686 | N/A | N/A |
| **aligned_32d** | 32 | 0.8179 | 0.3205 | 0.0060 | 0.0740 |
| **aligned_64d** | 64 | 0.8264 🏆 | 0.2281 | 0.0060 | 0.0840 |
| **aligned_128d** | 128 | 0.8039 | 0.1677 | 0.0120 | 0.1360 |

### Key Findings

- **Best Isotropy:** aligned_64d with 0.8264 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2374. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.2% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **1.652** | 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 |
|--------|----------|
| `-स` | सम्पन्नमासीदिति, सर्वोत्तमं, स्वप्रशासनम् |
| `-क` | क्रीतवान्, कृण्वती, कृशः |
| `-म` | मूलभूतं, मांसाशी, महिषासुरमर्दिनी |
| `-अ` | अस्वास्थ्यं, अहम्, अथासौ |
| `-प` | प्रतिपादन, पर्यटनस्य, पीलीभीतनगरम् |
| `-व` | वाचमुपासते, व्यक्तित्वैक्यं, व्यञ्जनयोः |
| `-न` | निर्भरति, निष्पाद्यते, निरोद्धव्याः |
| `-ब` | बाङ्ला, बॉटनिकल, बलूची |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-य` | पर्यटनस्य, गणकयन्त्रस्य, मुख्यभवनस्य |
| `-न` | प्रतिपादन, भारतसम्राट्त्वेन, एकाग्रीकरणेन |
| `-ण` | महाभाष्येण, आनन्दवर्धनाचार्येण, कृतिरूपेण |
| `-व` | मिलित्व, एतेषामेव, सुविदितमेव |
| `-र` | चचार, हरिदुष्ट्र, कालचक्र |
| `-च` | वाक्यपदीयकारश्च, मरिच, आश्रमाणाञ्च |
| `-s` | overlays, metals, properties |
| `-त` | चालित, स्वीक्रियन्त, अवर्तन्त |

### 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 |
|------|----------|------------------|----------|
| `tion` | 3.78x | 25 contexts | notion, nation, motion |
| `atio` | 3.63x | 19 contexts | nation, station, nations |
| `ture` | 3.78x | 16 contexts | nature, future, futures |
| `nter` | 3.65x | 16 contexts | inter, enter, unter |
| `ment` | 3.56x | 14 contexts | mental, cement, moment |
| `ical` | 3.83x | 6 contexts | radical, logical, ethical |
| `inte` | 3.67x | 6 contexts | inter, winter, interna |
| `comm` | 3.65x | 4 contexts | common, comment, commons |
| `enta` | 3.56x | 3 contexts | mental, dental, oriental |

### 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 |
|--------|--------|-----------|----------|
| `-प` | `-य` | 78 words | परिश्रम्य, प्रियदासस्य |
| `-स` | `-य` | 75 words | सारानाथस्य, सम्बोद्ध्य |
| `-व` | `-य` | 67 words | वर्णधर्मस्य, वेङ्कटमाधवस्य |
| `-अ` | `-य` | 66 words | अधर्माय, अपसारणाय |
| `-क` | `-य` | 53 words | कन्नडसाहित्यसम्मेलनस्य, कूपिय |
| `-म` | `-य` | 39 words | महाराजस्य, मान्यखेटस्य |
| `-न` | `-य` | 39 words | निश्चिकाय, निर्गमनाय |
| `-प` | `-न` | 29 words | पूरणेन, प्रतिमानेन |
| `-ज` | `-य` | 26 words | जापानीय, जीवेश्वरभेदस्य |
| `-स` | `-न` | 26 words | स्वप्रयत्नेन, सोमेन |

### 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 |
|------|-----------------|------------|------|
| उत्पादनेन | **`उत्पादने-न`** | 4.5 | `उत्पादने` |
| upanishads | **`upanishad-s`** | 4.5 | `upanishad` |
| अवस्थितिः | **`अव-स्थितिः`** | 4.5 | `स्थितिः` |
| अशस्त्रम् | **`अ-श-स्त्रम्`** | 4.5 | `स्त्रम्` |
| उपनायकत्वेन | **`उप-नायकत्वेन`** | 4.5 | `नायकत्वेन` |
| आक्षिपन्ति | **`आ-क्षिपन्ति`** | 4.5 | `क्षिपन्ति` |
| भक्तियोगेन | **`भक्तियोगे-न`** | 4.5 | `भक्तियोगे` |
| योगानन्देन | **`योगानन्दे-न`** | 4.5 | `योगानन्दे` |
| उपलभ्यमाने | **`उप-लभ्यमाने`** | 4.5 | `लभ्यमाने` |
| गुजरातराज्येण | **`गुजरातराज्ये-ण`** | 4.5 | `गुजरातराज्ये` |
| उत्तेजकानि | **`उ-त-्तेजकानि`** | 4.5 | `्तेजकानि` |
| अल्पतमाङ्कस्य | **`अ-ल-्पतमाङ्कस्य`** | 4.5 | `्पतमाङ्कस्य` |
| आरम्भकर्तृषु | **`आर-म-्भकर्तृषु`** | 4.5 | `्भकर्तृषु` |
| रक्तपित्ते | **`र-क-्तपित्ते`** | 4.5 | `्तपित्ते` |
| कार्यकरणेन | **`कार्यकरणे-न`** | 4.5 | `कार्यकरणे` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Sanskrit 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 (4.44x) |
| N-gram | **2-gram** | Lowest perplexity (4,254) |
| Markov | **Context-4** | Highest predictability (99.0%) |
| 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 19:34:50*