---
language: mr
language_name: Marathi
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: 4.869
  - name: best_isotropy
    type: isotropy
    value: 0.7987
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Marathi** 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** | 3.596x | 3.60 | 0.0265% | 1,254,728 |
| **16k** | 4.082x | 4.08 | 0.0301% | 1,105,436 |
| **32k** | 4.520x | 4.52 | 0.0334% | 998,240 |
| **64k** | 4.869x 🏆 | 4.87 | 0.0359% | 926,789 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `क्रिकेट विक्रम आंतरराष्ट्रीय एकदिवसीय सामने व्यक्ती`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁क्रिकेट ▁विक्रम ▁आंतरराष्ट्रीय ▁एकदिवसीय ▁सामने ▁व्यक्ती` | 6 |
| 16k | `▁क्रिकेट ▁विक्रम ▁आंतरराष्ट्रीय ▁एकदिवसीय ▁सामने ▁व्यक्ती` | 6 |
| 32k | `▁क्रिकेट ▁विक्रम ▁आंतरराष्ट्रीय ▁एकदिवसीय ▁सामने ▁व्यक्ती` | 6 |
| 64k | `▁क्रिकेट ▁विक्रम ▁आंतरराष्ट्रीय ▁एकदिवसीय ▁सामने ▁व्यक्ती` | 6 |

**Sample 2:** `वांग नदी (थाई: แม่น้ำวัง, रोमन लिप्यंतर: Maenam Wang, आयपीए: [mɛ̂ːnáːm waŋ]) ही ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁व ांग ▁नदी ▁( थ ाई : ▁ แม่น้ําวัง , ... (+49 more)` | 59 |
| 16k | `▁वांग ▁नदी ▁( थ ाई : ▁ แม่น้ําวัง , ▁रोमन ... (+44 more)` | 54 |
| 32k | `▁वांग ▁नदी ▁( थाई : ▁ แม่น้ําวัง , ▁रोमन ▁लिप्यंतर ... (+40 more)` | 50 |
| 64k | `▁वांग ▁नदी ▁( थाई : ▁ แม่น้ําวัง , ▁रोमन ▁लिप्यंतर ... (+39 more)` | 49 |

**Sample 3:** `बागेश्वर भारताच्या उत्तराखंड राज्यातील एक शहर आहे. हे शहर बागेश्वर जिल्ह्याचे प्...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁बाग ेश्वर ▁भारताच्या ▁उत्तराखंड ▁राज्यातील ▁एक ▁शहर ▁आहे . ▁हे ... (+10 more)` | 20 |
| 16k | `▁बाग ेश्वर ▁भारताच्या ▁उत्तराखंड ▁राज्यातील ▁एक ▁शहर ▁आहे . ▁हे ... (+10 more)` | 20 |
| 32k | `▁बाग ेश्वर ▁भारताच्या ▁उत्तराखंड ▁राज्यातील ▁एक ▁शहर ▁आहे . ▁हे ... (+10 more)` | 20 |
| 64k | `▁बागेश्वर ▁भारताच्या ▁उत्तराखंड ▁राज्यातील ▁एक ▁शहर ▁आहे . ▁हे ▁शहर ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.869x compression
- **Lowest UNK Rate:** 8k with 0.0265% 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 | 44,480 | 15.44 | 303,193 | 12.1% | 30.0% |
| **2-gram** | Subword | 3,013 🏆 | 11.56 | 99,256 | 32.0% | 65.8% |
| **3-gram** | Word | 37,251 | 15.18 | 373,992 | 14.2% | 35.3% |
| **3-gram** | Subword | 27,826 | 14.76 | 567,090 | 11.0% | 32.6% |
| **4-gram** | Word | 50,586 | 15.63 | 647,616 | 13.3% | 34.8% |
| **4-gram** | Subword | 139,762 | 17.09 | 2,373,076 | 6.7% | 21.1% |
| **5-gram** | Word | 35,691 | 15.12 | 496,499 | 13.2% | 37.4% |
| **5-gram** | Subword | 345,464 | 18.40 | 4,168,486 | 5.0% | 16.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `इ स` | 28,260 |
| 2 | `गाव आहे` | 24,605 |
| 3 | `तालुक्यातील गावे` | 23,569 |
| 4 | `महाराष्ट्र राज्यातील` | 23,529 |
| 5 | `एक गाव` | 23,223 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `एक गाव आहे` | 23,076 |
| 2 | `तालुक्यातील एक गाव` | 22,339 |
| 3 | `आहे भौगोलिक स्थान` | 21,986 |
| 4 | `गाव आहे भौगोलिक` | 21,751 |
| 5 | `गावे जिल्ह्यातील गावे` | 21,436 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `तालुक्यातील एक गाव आहे` | 22,320 |
| 2 | `गाव आहे भौगोलिक स्थान` | 21,736 |
| 3 | `एक गाव आहे भौगोलिक` | 21,639 |
| 4 | `तालुक्यातील गावे जिल्ह्यातील गावे` | 21,421 |
| 5 | `नागरी सुविधा जवळपासची गावे` | 20,857 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `एक गाव आहे भौगोलिक स्थान` | 21,628 |
| 2 | `तालुक्यातील एक गाव आहे भौगोलिक` | 21,414 |
| 3 | `गाव आहे भौगोलिक स्थान हवामान` | 20,737 |
| 4 | `प्रेक्षणीय स्थळे नागरी सुविधा जवळपासची` | 20,395 |
| 5 | `स्थळे नागरी सुविधा जवळपासची गावे` | 20,366 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 1,075,142 |
| 2 | `_ आ` | 877,178 |
| 3 | `न _` | 850,236 |
| 4 | `र _` | 756,039 |
| 5 | `त _` | 730,857 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ आ हे` | 325,056 |
| 2 | `ती ल _` | 268,297 |
| 3 | `आ णि _` | 247,875 |
| 4 | `_ आ णि` | 246,412 |
| 5 | `आ हे .` | 223,076 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ आ णि _` | 246,124 |
| 2 | `_ आ हे .` | 221,341 |
| 3 | `आ हे . _` | 211,377 |
| 4 | `_ ए क _` | 94,479 |
| 5 | `_ आ हे त` | 65,226 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ आ हे . _` | 209,660 |
| 2 | `_ ह वा मा न` | 56,036 |
| 3 | `ह वा मा न _` | 55,820 |
| 4 | `_ जि ल्ह्या ती ल` | 54,055 |
| 5 | `जि ल्ह्या ती ल _` | 54,006 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 3,013
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~16% 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 | 0.8169 | 1.762 | 7.56 | 823,720 | 18.3% |
| **1** | Subword | 0.9531 | 1.936 | 14.76 | 18,974 | 4.7% |
| **2** | Word | 0.2535 | 1.192 | 1.66 | 6,217,934 | 74.7% |
| **2** | Subword | 0.6651 | 1.586 | 5.29 | 280,021 | 33.5% |
| **3** | Word | 0.0778 | 1.055 | 1.14 | 10,278,116 | 92.2% |
| **3** | Subword | 0.5226 | 1.436 | 3.55 | 1,481,275 | 47.7% |
| **4** | Word | 0.0291 🏆 | 1.020 | 1.05 | 11,679,006 | 97.1% |
| **4** | Subword | 0.4218 | 1.340 | 2.28 | 5,255,477 | 57.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `आहे आणि घडामोडी पहिले बोर्ड सदस्यांना पकडण्यासाठी पुरावा सापडतो भारताच्या महाराष्ट्र राज्यातील जिल्ह...`
2. `आणि नोव्हेंबर ते सजावटीचे शिल्पकला चित्रकला यज्ञाच्या वेळी उपलब्ध आहे पॉलिटेक्निक गडचिरोली हे टोपण न...`
3. `हे भारतातील महाराष्ट्र राज्यातील मध्य प्रदेशातील विभाग धर्मादाय बिगर सरकारी असलेल्या सुविधा पुरवते स...`

**Context Size 2:**

1. `इ स धाई अक्षर प्रेम के योगीच्या आईच्या भूमिकेत निर्मिती एक अशी भाषा आहे बाह्य दुवे प्रिफेक्चर`
2. `गाव आहे भौगोलिक स्थान हवामान पावसाळ्यात येथे भातशेती केली जाते लोकजीवन प्रेक्षणीय स्थळे नागरी सुविधा...`
3. `महाराष्ट्र राज्यातील मध्य कोकणातील रायगड जिल्ह्यातील सुधागड तालुक्यातील एक गाव आहे भौगोलिक स्थान कसे...`

**Context Size 3:**

1. `एक गाव आहे भौगोलिक स्थान हवामान येथील वातावरण साधारणपणे उष्ण व कोरडे असते पावसाळ्यात भरपूर प्रमाणात ...`
2. `तालुक्यातील एक गाव आहे भौगोलिक स्थान हवामान येथील सर्वसाधारण हवामान उष्ण व विषम असते वार्षिक पर्जन्य...`
3. `आहे भौगोलिक स्थान हवामान पावसाळ्यात येथे भरपूर प्रमाणात पाऊस पडतो आणि हवामान समशीतोष्ण राहते हिवाळ्य...`

**Context Size 4:**

1. `तालुक्यातील एक गाव आहे भौगोलिक स्थान हवामान पावसाळ्यात येथे भरपूर प्रमाणात पाऊस पडतो व हवामान समशीतो...`
2. `गाव आहे भौगोलिक स्थान हवामान येथील हवामान उष्ण व कोरडे आहे हवामानातील बदलानुसार प्रत्येक वर्षात मुख्...`
3. `एक गाव आहे भौगोलिक स्थान हवामान लोकजीवन प्रेक्षणीय स्थळे नागरी सुविधा जवळपासची गावे संदर्भ १ २ ३ ४ ५`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_आली._ले_सामान_त्यांच्या_विज्ञा`
2. `र_आफ्रिकार्यभागणे._mul_न्हा`
3. `त_पाळया_झाल्या_किमीचा_त्यांनी_`

**Context Size 2:**

1. `._तिची_परत_ठाणे_२._पारो`
2. `_आहे._ब्रिटिश_केले._cf_६`
3. `न_कॅलकर्णी_-_५_मिली_जातं.`

**Context Size 3:**

1. `_आहेत.झापडे।_आजि_येईतो_म`
2. `तील_समुदाय_भटक्या_(अध्याय_-`
3. `आणि_कवितेचा_आरोग्यसेवा,_-_ह`

**Context Size 4:**

1. `_आणि_नोंदी_*_काउंटी_आहे._इति`
2. `_आहे._त्यामुळे_त्यांच्या_वडिलांचे_कमां`
3. `आहे._कोपनहेगन,_गो.स.,_आ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (5,255,477 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 | 339,552 |
| Total Tokens | 15,792,161 |
| Mean Frequency | 46.51 |
| Median Frequency | 4 |
| Frequency Std Dev | 988.74 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | आहे | 261,035 |
| 2 | आणि | 247,940 |
| 3 | हे | 125,128 |
| 4 | या | 122,731 |
| 5 | व | 121,359 |
| 6 | एक | 96,016 |
| 7 | ते | 86,215 |
| 8 | हा | 78,992 |
| 9 | गावे | 71,549 |
| 10 | आहेत | 65,186 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | doo | 2 |
| 2 | actresskim | 2 |
| 3 | gook | 2 |
| 4 | actresslee | 2 |
| 5 | जीएसआरटीसी | 2 |
| 6 | gsrtc | 2 |
| 7 | वायएम | 2 |
| 8 | एडिलसी | 2 |
| 9 | डिफाइन | 2 |
| 10 | लेक्सचे | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0672 |
| R² (Goodness of Fit) | 0.991445 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 24.7% |
| Top 1,000 | 53.4% |
| Top 5,000 | 72.6% |
| Top 10,000 | 79.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9914 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 24.7% of corpus
- **Long Tail:** 329,552 words needed for remaining 20.6% 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 | 0.7987 | 0.3628 | N/A | N/A |
| **mono_64d** | 64 | 0.7960 | 0.2807 | N/A | N/A |
| **mono_128d** | 128 | 0.7639 | 0.2177 | N/A | N/A |
| **aligned_32d** | 32 | 0.7987 🏆 | 0.3565 | 0.0260 | 0.1620 |
| **aligned_64d** | 64 | 0.7960 | 0.2765 | 0.0540 | 0.2620 |
| **aligned_128d** | 128 | 0.7639 | 0.2171 | 0.0940 | 0.3600 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7987 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2852. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 9.4% 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 | **1.310** | 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 |
|--------|----------|
| `-क` | कूनर, किनारपट्टीवरील, कथास्पर्धेत |
| `-स` | संघगुणसाविहाअणिसमनेरर, सातत्याची, समीकरणांद्वारे |
| `-म` | मॅंग्रोव्ह, मुलींसाठी, मेर्सिन |
| `-प` | पृथ्वीसदृश, पनवेलपासून, पुर्वेकडे |
| `-ब` | बॉटलिंग, बोधकथांचा, बुचर |
| `-अ` | अनफेथफुलने, अनाक्रमण, अँटार्क्टिका |
| `-व` | वित्‍त, वीररत्न, वरंगळ |
| `-र` | रिडझुआन, रॉयल्सकए, राधिकाची |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-र` | संघगुणसाविहाअणिसमनेरर, कूनर, पांढराशुभ्र |
| `-न` | पनवेलपासून, रिडझुआन, लघुकोन |
| `-त` | घाबरत, नाचत, कथास्पर्धेत |
| `-ल` | छल, किनारपट्टीवरील, पदरचनेतील |
| `-स` | हेंड्रिक्स, चुरस, वाल्स |
| `-वर` | मेंब्रेनवर, उपनिषदावर, आयझेनहावर |
| `-क` | रजतपदक, विषाणूप्रतिबंधक, सौसेक |
| `-य` | सेंद्रीय, बाह्य, अनन्वय |

### 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` | 3.55x | 49 contexts | action, motion, notion |
| `atio` | 3.59x | 41 contexts | ratio, ratios, ration |
| `ment` | 3.62x | 25 contexts | moment, mental, cement |
| `indi` | 3.51x | 27 contexts | hindi, indie, indic |

### 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 |
|--------|--------|-----------|----------|
| `-स` | `-न` | 47 words | संकेतस्थळांवरून, संमेलनातुन |
| `-प` | `-न` | 41 words | पेपिन, पंढरपुरातून |
| `-स` | `-र` | 40 words | संमातर, सुदंर |
| `-म` | `-र` | 36 words | माणसांवर, मुहाजिर |
| `-क` | `-र` | 36 words | काल्लूर, कमलकिशोर |
| `-स` | `-त` | 35 words | स्वातंत्र्यापर्यंत, संमेलनानिमित्त |
| `-प` | `-र` | 34 words | पंचकोशचक्र, प्रदीपकुमार |
| `-स` | `-ल` | 33 words | स्तरांतील, सनीव्हेल |
| `-क` | `-न` | 31 words | किशान, कोलकातापासून |
| `-व` | `-न` | 31 words | वीर्यस्खलन, वोलॅस्टन |

### 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 |
|------|-----------------|------------|------|
| आज्ञाधारक | **`आज्ञाधा-र-क`** | 7.5 | `र` |
| रोगनिवारक | **`रोगनिवा-र-क`** | 7.5 | `र` |
| सर्वांवरच | **`सर्वां-वर-च`** | 6.0 | `सर्वां` |
| अप्रसिद्ध | **`अ-प्रसिद्ध`** | 4.5 | `प्रसिद्ध` |
| अन्यायाचा | **`अ-न्यायाचा`** | 4.5 | `न्यायाचा` |
| पद्धतीतल्या | **`प-द-्धतीतल्या`** | 4.5 | `्धतीतल्या` |
| द्याव्यात | **`द्याव्या-त`** | 4.5 | `द्याव्या` |
| युगोस्लाव्हियावर | **`युगोस्लाव्हिया-वर`** | 4.5 | `युगोस्लाव्हिया` |
| मल्ल्याच्या | **`म-ल-्ल्याच्या`** | 4.5 | `्ल्याच्या` |
| अक्षमालिका | **`अ-क-्षमालिका`** | 4.5 | `्षमालिका` |
| sequences | **`sequence-s`** | 4.5 | `sequence` |
| आख्तरहाएसवर | **`आख्तरहाएस-वर`** | 4.5 | `आख्तरहाएस` |
| भक्तिगीतांचे | **`भ-क-्तिगीतांचे`** | 4.5 | `्तिगीतांचे` |
| उपक्रमशीलता | **`उ-प-क्रमशीलता`** | 4.5 | `क्रमशीलता` |
| सरकारवरील | **`सर-क-ारवरील`** | 4.5 | `ारवरील` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Marathi 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 (4.87x) |
| N-gram | **2-gram** | Lowest perplexity (3,013) |
| Markov | **Context-4** | Highest predictability (97.1%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 14:51:28*