README.md

---
language: awa
language_name: Awadhi
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: 3.892
  - name: best_isotropy
    type: isotropy
    value: 0.7358
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Awadhi** 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** | 3.327x | 3.33 | 0.1230% | 131,731 |
| **16k** | 3.618x | 3.63 | 0.1337% | 121,145 |
| **32k** | 3.892x 🏆 | 3.90 | 0.1439% | 112,611 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `नीलम संजीव रेड्डी (२७ अक्तूबर - ९ नवंबर भारत कय छठवा राष्ट्रपति रहे। वनकय कार्यक...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁नीलम ▁सं जीव ▁रेड्डी ▁( २७ ▁अक्तूबर ▁- ▁९ ▁नवंबर ... (+16 more)` | 26 |
| 16k | `▁नीलम ▁संजीव ▁रेड्डी ▁( २७ ▁अक्तूबर ▁- ▁९ ▁नवंबर ▁भारत ... (+15 more)` | 25 |
| 32k | `▁नीलम ▁संजीव ▁रेड्डी ▁( २७ ▁अक्तूबर ▁- ▁९ ▁नवंबर ▁भारत ... (+15 more)` | 25 |

**Sample 2:** `नकुड, भारत देश के उत्तर प्रदेश प्रान्त के सहारनपुर जिला कय एक्ठु नगर पालिका परिष...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁न कु ड , ▁भारत ▁देश ▁के ▁उत्तर ▁प्रदेश ▁प्रान्त ... (+20 more)` | 30 |
| 16k | `▁न कु ड , ▁भारत ▁देश ▁के ▁उत्तर ▁प्रदेश ▁प्रान्त ... (+20 more)` | 30 |
| 32k | `▁नकुड , ▁भारत ▁देश ▁के ▁उत्तर ▁प्रदेश ▁प्रान्त ▁के ▁सहारनपुर ... (+18 more)` | 28 |

**Sample 3:** `नसीराबाद, भारत देश के उत्तर प्रदेश प्रान्त के रायबरेली जिला कय एक्ठु नगर पंचायत ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁न सी राबाद , ▁भारत ▁देश ▁के ▁उत्तर ▁प्रदेश ▁प्रान्त ... (+18 more)` | 28 |
| 16k | `▁न सी राबाद , ▁भारत ▁देश ▁के ▁उत्तर ▁प्रदेश ▁प्रान्त ... (+18 more)` | 28 |
| 32k | `▁नसीराबाद , ▁भारत ▁देश ▁के ▁उत्तर ▁प्रदेश ▁प्रान्त ▁के ▁रायबरेली ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 32k achieves 3.892x compression
- **Lowest UNK Rate:** 8k with 0.1230% 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 | 2,396 | 11.23 | 5,750 | 28.4% | 58.2% |
| **2-gram** | Subword | 1,608 🏆 | 10.65 | 12,278 | 39.9% | 73.3% |
| **3-gram** | Word | 1,666 | 10.70 | 5,103 | 35.8% | 65.6% |
| **3-gram** | Subword | 10,335 | 13.34 | 44,364 | 17.1% | 41.3% |
| **4-gram** | Word | 4,269 | 12.06 | 12,850 | 27.4% | 49.6% |
| **4-gram** | Subword | 30,718 | 14.91 | 110,971 | 11.6% | 28.3% |
| **5-gram** | Word | 3,586 | 11.81 | 10,699 | 28.4% | 52.8% |
| **5-gram** | Subword | 44,082 | 15.43 | 123,963 | 10.3% | 23.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `प्रदेश कय` | 1,242 |
| 2 | `कय एक्ठु` | 1,217 |
| 3 | `नगर पंचायत` | 932 |
| 4 | `शहरी निकाय` | 837 |
| 5 | `उत्तर प्रदेश` | 774 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `कय एक्ठु नगर` | 700 |
| 2 | `भारत देश के` | 696 |
| 3 | `जिला कय एक्ठु` | 680 |
| 4 | `कय शहरी निकाय` | 667 |
| 5 | `के उत्तर प्रदेश` | 586 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `जिला कय एक्ठु नगर` | 661 |
| 2 | `के उत्तर प्रदेश प्रान्त` | 582 |
| 3 | `प्रदेश कय शहरी निकाय` | 581 |
| 4 | `कय शहरी निकाय प्रदेश` | 581 |
| 5 | `शहरी निकाय प्रदेश कय` | 581 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `शहरी निकाय प्रदेश कय नगर` | 581 |
| 2 | `कय शहरी निकाय प्रदेश कय` | 581 |
| 3 | `प्रदेश कय शहरी निकाय प्रदेश` | 581 |
| 4 | `देश के उत्तर प्रदेश प्रान्त` | 580 |
| 5 | `भारत देश के उत्तर प्रदेश` | 580 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `र _` | 19,312 |
| 2 | `य _` | 17,947 |
| 3 | `_ क` | 16,677 |
| 4 | `न _` | 14,033 |
| 5 | `। _` | 12,197 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `क य _` | 10,878 |
| 2 | `_ क य` | 10,634 |
| 3 | `_ के _` | 7,599 |
| 4 | `_ से _` | 4,267 |
| 5 | `_ में _` | 4,065 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ क य _` | 10,589 |
| 2 | `_ प्र दे श` | 2,239 |
| 3 | `प्र दे श _` | 2,188 |
| 4 | `_ है । _` | 2,147 |
| 5 | `भा र त _` | 2,022 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ प्र दे श _` | 2,171 |
| 2 | `_ भा र त _` | 1,826 |
| 3 | `_ न ग र _` | 1,779 |
| 4 | `_ क य _ ए` | 1,494 |
| 5 | `_ अ उ र _` | 1,449 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 1,608
- **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 | 0.7360 | 1.666 | 4.24 | 38,944 | 26.4% |
| **1** | Subword | 1.0397 | 2.056 | 10.73 | 3,744 | 0.0% |
| **2** | Word | 0.1950 | 1.145 | 1.36 | 164,372 | 80.5% |
| **2** | Subword | 0.5443 | 1.458 | 3.48 | 40,149 | 45.6% |
| **3** | Word | 0.0479 | 1.034 | 1.07 | 222,536 | 95.2% |
| **3** | Subword | 0.4540 | 1.370 | 2.32 | 139,753 | 54.6% |
| **4** | Word | 0.0142 🏆 | 1.010 | 1.02 | 236,208 | 98.6% |
| **4** | Subword | 0.2417 | 1.182 | 1.52 | 323,693 | 75.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `कय सुविधाजनक बनावेक अन्तर्राष्ट्रीय हवाईगिरान फाप्लु भोजपुर फर्रुखाबाद 195 कासगंज जिला आवत हैं मेघाल...`
2. `के उत्तर भारतीय रुपया लेख आसानी से खेले रहें घरेलू क्रिकेट रहें आदित्यनाथ कय राजनीति में`
3. `से दक्षिण दिल्ली मेट्रो फ़िल्मफ़ेयर सर्वश्रेष्ठ तमिल तेलुगू వికారాబాదు జిల్లా अंग्रेज़ी में गंगा नदी...`

**Context Size 2:**

1. `प्रदेश कय शहरी निकाय प्रदेश कय नगर पंचायत होय संदर्भ प्रदेश कय शहरी निकाय प्रदेश कय नगर`
2. `कय एक्ठु भाषा होय ई ईलेक्ट्रोन प्रोटोन अव न्युट्रोन से बना है हिमालय क्षेत्र में मनुष्यों का`
3. `उत्तर प्रदेश प्रान्त के शामली जिला कय एक्ठु नगर पालिका परिषद कय शहरी निकाय प्रदेश कय नगर`

**Context Size 3:**

1. `कय एक्ठु नगर पंचायत होय संदर्भ प्रदेश कय शहरी निकाय प्रदेश कय नगर पंचायत पंचायत कय शहरी निकाय`
2. `भारत देश के उत्तर प्रदेश प्रान्त कय एक्ठु जिला होय इहौ देखैं कामारेड्डी तेलंगाना तेलंगाना कय जिला सन...`
3. `जिला कय एक्ठु नगर पालिका परिषद होय संदर्भ 1 उत्तराखंड के सगरौ शहरी निकाय कय सूची 2 उत्तराखंड`

**Context Size 4:**

1. `जिला कय एक्ठु नगर पंचायत होय संदर्भ प्रदेश कय शहरी निकाय प्रदेश कय नगर पंचायत noinclude`
2. `के उत्तर प्रदेश प्रान्त के सीतापुर जिला कय एक्ठु नगर पालिका परिषद होय संदर्भ प्रदेश कय शहरी निकाय प्...`
3. `निकाय प्रदेश कय नगर पंचायत देहात`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_के_हंयन_ह_सहइ_पालव`
2. `रतह_रें।_केर_प_10_प्रा`
3. `कय_की।_के_इति_-atem`

**Context Size 2:**

1. `र_हरा_गांव_परिषद_पार्टी_(`
2. `य_संगीत-होल्सटीन,_आंध्रप्रदेश`
3. `_कय_जन्म_३_मद्रास)_शिक्षा_`

**Context Size 3:**

1. `कय_निकोसिया_का_यश_चोपड़ा_आ`
2. `_कय_शहर_सिरसा_16_44_`
3. `_के_भेस_अनुवादित_तब_ओका_`

**Context Size 4:**

1. `_कय_१५वाँ_राष्ट्रपति_रहे।_यह`
2. `_प्रदेश_कय_भी_अविवाहित_भाई_`
3. `प्रदेश_प्रान्त_के_गाजियाबाद_जिला_क`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (323,693 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 | 16,641 |
| Total Tokens | 263,395 |
| Mean Frequency | 15.83 |
| Median Frequency | 3 |
| Frequency Std Dev | 138.02 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | कय | 10,633 |
| 2 | के | 7,622 |
| 3 | से | 4,333 |
| 4 | में | 4,224 |
| 5 | है | 3,954 |
| 6 | मा | 3,849 |
| 7 | होय | 2,668 |
| 8 | का | 2,628 |
| 9 | प्रदेश | 2,217 |
| 10 | भारत | 1,996 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | मोड़ा | 2 |
| 2 | कीमा | 2 |
| 3 | चौकोरन | 2 |
| 4 | दर्रे | 2 |
| 5 | गिजर | 2 |
| 6 | तड़हुंग | 2 |
| 7 | कलाकृति | 2 |
| 8 | स्टेपी | 2 |
| 9 | ओलेक्सान्ड्रोविच | 2 |
| 10 | टीएसएन | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0518 |
| R² (Goodness of Fit) | 0.990696 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 38.1% |
| Top 1,000 | 66.2% |
| Top 5,000 | 87.3% |
| Top 10,000 | 94.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9907 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 38.1% of corpus
- **Long Tail:** 6,641 words needed for remaining 5.2% 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 | 0.7358 | 0.3755 | N/A | N/A |
| **mono_64d** | 64 | 0.3489 | 0.3581 | N/A | N/A |
| **mono_128d** | 128 | 0.0808 | 0.3463 | N/A | N/A |
| **aligned_32d** | 32 | 0.7358 🏆 | 0.3759 | 0.0299 | 0.1549 |
| **aligned_64d** | 64 | 0.3489 | 0.3500 | 0.0245 | 0.1848 |
| **aligned_128d** | 128 | 0.0808 | 0.3480 | 0.0571 | 0.2636 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7358 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3590. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.7% 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 | **1.225** | 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.

*No productive affixes detected.*


### 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.

*No significant bound stems detected.*


### 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.

*No significant affix co-occurrences detected.*


### 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`).

*Insufficient data for recursive segmentation.*


### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Awadhi 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 (3.89x) |
| N-gram | **2-gram** | Lowest perplexity (1,608) |
| Markov | **Context-4** | Highest predictability (98.6%) |
| 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: 2026-01-03 17:51:14*