---
language: pi
language_name: Pali
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: 2.300
  - name: best_isotropy
    type: isotropy
    value: 0.0330
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Pali** 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** | 2.300x 🏆 | 2.30 | 1.0840% | 94,738 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `वलहि एका सनातन ग्राम अत्थि, ईमा पतिठ्ठापना अंतो सोरठ पदेश।`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁वलहि ▁एका ▁सनातन ▁ग्राम ▁अत्थि , ▁ईमा ▁पतिठ्ठापना ▁अंतो ▁सोरठ ... (+2 more)` | 12 |

**Sample 2:** `+दक्षिण क्यारोलिनाSouth Carolina 125px 125px 300px संदरिभ`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁+ दक्षिण ▁क्यारोलिना south ▁carolina ▁ 1 2 5 px ... (+11 more)` | 21 |

**Sample 3:** `+वासिंगटन डि सिWashington, D.C. 125px 125px 300px वासिंगटन डि सि अभिञ्ञाणा`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁+ वासिंगटन ▁डि ▁सि washington , ▁d . c . ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 8k achieves 2.300x compression
- **Lowest UNK Rate:** 8k with 1.0840% 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 | 266 🏆 | 8.05 | 416 | 54.4% | 100.0% |
| **2-gram** | Subword | 827 | 9.69 | 2,901 | 42.1% | 88.9% |
| **3-gram** | Word | 349 | 8.45 | 534 | 49.9% | 100.0% |
| **3-gram** | Subword | 3,441 | 11.75 | 9,002 | 21.6% | 58.3% |
| **4-gram** | Word | 1,582 | 10.63 | 1,950 | 21.7% | 63.4% |
| **4-gram** | Subword | 8,498 | 13.05 | 20,231 | 15.6% | 40.0% |
| **5-gram** | Word | 1,377 | 10.43 | 1,660 | 22.3% | 68.6% |
| **5-gram** | Subword | 9,937 | 13.28 | 21,227 | 15.3% | 35.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `प्रकाश स्तंभ` | 223 |
| 2 | `yā pana` | 189 |
| 3 | `pana bhikkhunī` | 187 |
| 4 | `टापू समूह` | 98 |
| 5 | `sikkhā karaṇīyā` | 75 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `yā pana bhikkhunī` | 187 |
| 2 | `बालिआरिक टापू समूह` | 64 |
| 3 | `प्रकाश स्तंभ 120px` | 62 |
| 4 | `टापू समूह बालिआरिक` | 32 |
| 5 | `समूह बालिआरिक टापू` | 32 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `बालिआरिक टापू समूह बालिआरिक` | 32 |
| 2 | `टापू समूह बालिआरिक टापू` | 32 |
| 3 | `समूह बालिआरिक टापू समूह` | 32 |
| 4 | `frameless upright 0 2` | 29 |
| 5 | `upright 0 2 link` | 25 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `बालिआरिक टापू समूह बालिआरिक टापू` | 32 |
| 2 | `टापू समूह बालिआरिक टापू समूह` | 32 |
| 3 | `frameless upright 0 2 link` | 25 |
| 4 | `upright 0 2 link frameless` | 25 |
| 5 | `0 2 link frameless upright` | 25 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a ṃ` | 1,530 |
| 2 | `, _` | 1,307 |
| 3 | `p a` | 1,306 |
| 4 | `ṃ _` | 1,294 |
| 5 | `ā _` | 1,256 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a ṃ _` | 1,183 |
| 2 | `k k h` | 938 |
| 3 | `i k k` | 900 |
| 4 | `_ p a` | 621 |
| 5 | `_ b h` | 560 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i k k h` | 881 |
| 2 | `_ b h i` | 455 |
| 3 | `b h i k` | 453 |
| 4 | `h i k k` | 453 |
| 5 | `k k h u` | 452 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `b h i k k` | 453 |
| 2 | `h i k k h` | 453 |
| 3 | `_ b h i k` | 450 |
| 4 | `i k k h u` | 449 |
| 5 | `k k h u n` | 436 |


### Key Findings

- **Best Perplexity:** 2-gram (word) with 266
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~36% 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 | 0.4100 | 1.329 | 2.11 | 10,593 | 59.0% |
| **1** | Subword | 0.9525 | 1.935 | 6.62 | 2,113 | 4.7% |
| **2** | Word | 0.1078 | 1.078 | 1.17 | 22,259 | 89.2% |
| **2** | Subword | 0.4969 | 1.411 | 2.61 | 13,978 | 50.3% |
| **3** | Word | 0.0355 | 1.025 | 1.05 | 25,920 | 96.5% |
| **3** | Subword | 0.3495 | 1.274 | 1.73 | 36,519 | 65.0% |
| **4** | Word | 0.0185 🏆 | 1.013 | 1.03 | 27,208 | 98.1% |
| **4** | Subword | 0.1994 | 1.148 | 1.34 | 63,113 | 80.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `है पूर्ण उदच्यते उत्पन्न होता है गले में किसी मनुष्य अथवा तकनीक है भ्रूण को पार`
2. `के समान ही रह जाता है उसके नीचे क्रमश देवकी और स्वभाव और बहुतों के थे`
3. `में लिखा गया है अंडा एक स्वतन्त्र एक कालाग्नि नामक एक एव बुद्धत्तं ति मञ्ञति सन्दब्भा`

**Context Size 2:**

1. `प्रकाश स्तंभ 120px आन्दलूसिया मालागा मारबिआ प्रकाश स्तंभ देल बाखो दे पोरतमान मूर्किया का कारतागेना ओ...`
2. `yā pana bhikkhunī nānappakārakaṃ kayavikkayaṃ samāpajjeyya nissaggiyaṃ pācittiyaṃ aññacetāpana sikkh...`
3. `pana bhikkhunī paripuṇṇavīsativassaṃ kumāribhūtaṃ dve vassāni chasu dhammesu sikkhitasikkhaṃ saṅghen...`

**Context Size 3:**

1. `yā pana bhikkhunī āsandiṃ vā pallaṅkaṃ vā paribhuñjeyya pācittiyaṃ suttakantanasikkhāpadaṃ 43 yā pan...`
2. `बालिआरिक टापू समूह इबिसा और फोरमैनतेरा तागोमागो प्रकाश स्तंभ बालिआरिक टापू समूह मेनोरका सिउतादेया प्...`
3. `प्रकाश स्तंभ 120px गालिसिया केप ओमे प्रकाश स्तंभ 120px बालिआरिक टापू समूह माखोरका केप गरोस प्रकाश स्...`

**Context Size 4:**

1. `समूह बालिआरिक टापू समूह इबिसा और फोरमैनतेरा पोएनसा प्रकाश स्तंभ बालिआरिक टापू समूह बालिआरिक टापू समू...`
2. `टापू समूह बालिआरिक टापू समूह माखोरका पोरतो कोलोम प्रकाश स्तंभ बालिआरिक टापू समूह बालिआरिक टापू समूह ...`
3. `बालिआरिक टापू समूह बालिआरिक टापू समूह माखोरका केप बलांक प्रकाश स्तंभ 120px बालिआरिक टापू समूह बालिआर...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_paṃ,_सिक्खामकूपनेत्तिभ_र`
2. `aexy_स्तंभकी_o_sikki`
3. `i._कृष्णवासमूहम्_suṇat`

**Context Size 2:**

1. `aṃ_–_"आभीर_एका_शुभदर्शी`
2. `,_na_(कम्प्युटर_शून्य:_मिसि`
3. `padaṃ_pāṇijabaṇīy`

**Context Size 3:**

1. `aṃ_bhikkhuniyo_bhi`
2. `kkhuni_cells_theva`
3. `ikkhā_evamerittikk`

**Context Size 4:**

1. `ikkhāpadaṃ_43._yā_p`
2. `_bhikkhāpadaṃ_1._yā`
3. `hikkhā_kareyya_‘‘ap`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (63,113 contexts)
- **Recommendation:** Context-3 or Context-4 for text generation

---
## 4. Vocabulary Analysis

![Zipf's Law](visualizations/zipf_law.png)

![Top Words](visualizations/top20_words.png)

![Coverage Curve](visualizations/vocab_coverage.png)

### Statistics

| Metric | Value |
|--------|-------|
| Vocabulary Size | 3,395 |
| Total Tokens | 23,559 |
| Mean Frequency | 6.94 |
| Median Frequency | 3 |
| Frequency Std Dev | 20.62 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | है | 395 |
| 2 | के | 395 |
| 3 | में | 356 |
| 4 | vā | 314 |
| 5 | से | 276 |
| 6 | और | 265 |
| 7 | हैं | 261 |
| 8 | bhikkhunī | 254 |
| 9 | प्रकाश | 229 |
| 10 | स्तंभ | 224 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | नामान्तरण | 2 |
| 2 | मिलाबट | 2 |
| 3 | घटनाओं | 2 |
| 4 | वेदिक | 2 |
| 5 | शबदस्स | 2 |
| 6 | दरुश | 2 |
| 7 | गरिंथात | 2 |
| 8 | अनूसार | 2 |
| 9 | करविन | 2 |
| 10 | हिंदू | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.8293 |
| R² (Goodness of Fit) | 0.980447 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 37.8% |
| Top 1,000 | 75.0% |
| Top 5,000 | 0.0% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9804 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 37.8% of corpus
- **Long Tail:** -6,605 words needed for remaining 100.0% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.0330 🏆 | 0.5234 | N/A | N/A |
| **mono_64d** | 64 | 0.0047 | 0.5510 | N/A | N/A |
| **mono_128d** | 128 | 0.0008 | 0.5621 | N/A | N/A |
| **aligned_32d** | 32 | 0.0330 | 0.5288 | 0.0240 | 0.1377 |
| **aligned_64d** | 64 | 0.0047 | 0.5520 | 0.0240 | 0.1257 |
| **aligned_128d** | 128 | 0.0008 | 0.5541 | 0.0180 | 0.1437 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.0330 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.5452. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 2.4% 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 | **0.910** | 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` | सच्चानीति, स्टेम, संवाद |
| `-प` | प्रवृति, पाताल, प्रभुने |
| `-sa` | saṅghikaṃ, samayā, sambhuñjeyya |
| `-pa` | paṭiggahetabbaṃ, paṭisevato, pakkameyya |
| `-पर` | परिपूर्णतम, परायण, परवर्ती |
| `-an` | announcement, anniversary, and |
| `-vi` | via, vikappaṃ, vinassā |
| `-मह` | महावग्गो, महाविराट्के, महेश्वर |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-aṃ` | saṅghikaṃ, dhammaṃ, nālaṃ |
| `-ṃ` | saṅghikaṃ, dhammaṃ, nālaṃ |
| `-a` | wikimania, acchindāpeyya, uddhareyya |
| `-ya` | acchindāpeyya, uddhareyya, pakkameyya |
| `-ā` | vuccamānā, āpannā, cetāpetvā |
| `-na` | saññācikena, saṅghikena, dhammena |
| `-yo` | bhikkhuniyo, māyyāyo, ayyāyo |
| `-yā` | samayā, dubbalyā, karaṇīyā |

### 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 |
|------|----------|------------------|----------|
| `eyya` | 1.78x | 8 contexts | seyyaṃ, cāveyya, kareyya |
| `ikkh` | 1.65x | 6 contexts | sikkhā, sikkhaṃ, bhikkhu |
| `kkhu` | 1.78x | 5 contexts | bhikkhu, bhikkhuṃ, bhikkhunī |
| `añña` | 1.76x | 3 contexts | aññaṃ, aññatra, anaññaṃ |

### 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 |
|--------|--------|-----------|----------|
| `-pa` | `-a` | 20 words | pakkameyya, paggaṇheyya |
| `-sa` | `-a` | 19 words | sambhuñjeyya, saññācikena |
| `-sa` | `-ṃ` | 15 words | saṅghikaṃ, saṅghādisesaṃ |
| `-pa` | `-ṃ` | 15 words | paṭiggahetabbaṃ, paraṃ |
| `-pa` | `-ya` | 14 words | pakkameyya, paggaṇheyya |
| `-sa` | `-aṃ` | 13 words | saṅghikaṃ, saṅghādisesaṃ |
| `-pa` | `-aṃ` | 12 words | paṭiggahetabbaṃ, paraṃ |
| `-sa` | `-ā` | 10 words | samayā, saṅghādisesā |
| `-vi` | `-a` | 8 words | via, vivekaññeva |
| `-sa` | `-ya` | 7 words | sambhuñjeyya, saṃvaṇṇeyya |

### 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 |
|------|-----------------|------------|------|
| communities | **`communi-ti-es`** | 3.0 | `communi` |
| ukkhittakāya | **`ukkhittak-ā-ya`** | 3.0 | `ukkhittak` |
| bhaginīnaṃ | **`bhaginīn-aṃ`** | 1.5 | `bhaginīn` |
| vūpasamāya | **`vūpasamā-ya`** | 1.5 | `vūpasamā` |
| ubbhatasmiṃ | **`ubbhatasmi-ṃ`** | 1.5 | `ubbhatasmi` |
| sahadhammena | **`sa-hadhammena`** | 1.5 | `hadhammena` |
| sattarasa | **`sattaras-a`** | 1.5 | `sattaras` |
| pañcakkhattuṃ | **`pañcakkhattu-ṃ`** | 1.5 | `pañcakkhattu` |
| dvattikkhattuṃ | **`dvattikkhattu-ṃ`** | 1.5 | `dvattikkhattu` |
| susaṃvutā | **`susaṃvut-ā`** | 1.5 | `susaṃvut` |
| सीहनादवग्गो | **`स-ीहनादवग्गो`** | 1.5 | `ीहनादवग्गो` |
| sannidhikārakaṃ | **`sannidhikārak-aṃ`** | 1.5 | `sannidhikārak` |
| pattavaggo | **`pa-ttavaggo`** | 1.5 | `ttavaggo` |
| desessāmīti | **`desessāmī-ti`** | 1.5 | `desessāmī` |
| सुत्तपिटक | **`स-ुत्तपिटक`** | 1.5 | `ुत्तपिटक` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Pali 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 | **8k BPE** | Best compression (2.30x) |
| N-gram | **2-gram** | Lowest perplexity (266) |
| Markov | **Context-4** | Highest predictability (98.1%) |
| 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 17:45:44*