---
language: si
language_name: Sinhala
language_family: indoaryan_insular
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_insular
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: 4.567
  - name: best_isotropy
    type: isotropy
    value: 0.8359
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sinhala** 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** | 3.460x | 3.46 | 0.0794% | 1,490,772 |
| **16k** | 3.888x | 3.89 | 0.0892% | 1,326,900 |
| **32k** | 4.268x | 4.27 | 0.0979% | 1,208,595 |
| **64k** | 4.567x 🏆 | 4.57 | 0.1047% | 1,129,426 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `බක් අව අටවක තිථියට අනුරූපී පෝය දවස බක් අව අටවක පෝය නම් වේ. මූලාශ්‍ර අටවක ඇ.1`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁බක් ▁අව ▁අටවක ▁තිථියට ▁අනුරූප ී ▁පෝය ▁දවස ▁බක් ▁අව ... (+10 more)` | 20 |
| 16k | `▁බක් ▁අව ▁අටවක ▁තිථියට ▁අනුරූපී ▁පෝය ▁දවස ▁බක් ▁අව ▁අටවක ... (+9 more)` | 19 |
| 32k | `▁බක් ▁අව ▁අටවක ▁තිථියට ▁අනුරූපී ▁පෝය ▁දවස ▁බක් ▁අව ▁අටවක ... (+9 more)` | 19 |
| 64k | `▁බක් ▁අව ▁අටවක ▁තිථියට ▁අනුරූපී ▁පෝය ▁දවස ▁බක් ▁අව ▁අටවක ... (+9 more)` | 19 |

**Sample 2:** `උපත් පිලිප් රජතුමා යනු බෙල්ජියමේ රජතුමා වේ. බෙල්ජියමේ රජ පවුල`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁උපත් ▁පිලිප් ▁රජතුමා ▁යනු ▁බෙල්ජිය මේ ▁රජතුමා ▁වේ . ▁බෙල්ජිය ... (+3 more)` | 13 |
| 16k | `▁උපත් ▁පිලිප් ▁රජතුමා ▁යනු ▁බෙල්ජියමේ ▁රජතුමා ▁වේ . ▁බෙල්ජියමේ ▁රජ ... (+1 more)` | 11 |
| 32k | `▁උපත් ▁පිලිප් ▁රජතුමා ▁යනු ▁බෙල්ජියමේ ▁රජතුමා ▁වේ . ▁බෙල්ජියමේ ▁රජ ... (+1 more)` | 11 |
| 64k | `▁උපත් ▁පිලිප් ▁රජතුමා ▁යනු ▁බෙල්ජියමේ ▁රජතුමා ▁වේ . ▁බෙල්ජියමේ ▁රජ ... (+1 more)` | 11 |

**Sample 3:** `වසාවාසි () යනු කුළු බඩු විශේෂයකි. මූලාශ්‍ර ආශ්‍රිත සගන්ධ තෙල් සාදික්කා බඩු`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁වස ාවා සි ▁() ▁යනු ▁කු ළු ▁බ ඩු ▁විශේෂයකි ... (+12 more)` | 22 |
| 16k | `▁වස ාවා සි ▁() ▁යනු ▁කුළු ▁බඩු ▁විශේෂයකි . ▁මූලාශ්‍ර ... (+8 more)` | 18 |
| 32k | `▁වසාවාසි ▁() ▁යනු ▁කුළු ▁බඩු ▁විශේෂයකි . ▁මූලාශ්‍ර ▁ආශ්‍රිත ▁සග ... (+4 more)` | 14 |
| 64k | `▁වසාවාසි ▁() ▁යනු ▁කුළු ▁බඩු ▁විශේෂයකි . ▁මූලාශ්‍ර ▁ආශ්‍රිත ▁සගන්ධ ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 4.567x compression
- **Lowest UNK Rate:** 8k with 0.0794% 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 | 91,979 | 16.49 | 262,122 | 6.4% | 17.0% |
| **2-gram** | Subword | 2,119 🏆 | 11.05 | 50,624 | 32.0% | 72.3% |
| **3-gram** | Word | 150,233 | 17.20 | 288,151 | 3.5% | 11.6% |
| **3-gram** | Subword | 20,524 | 14.33 | 333,353 | 10.5% | 33.2% |
| **4-gram** | Word | 393,476 | 18.59 | 561,828 | 2.2% | 6.9% |
| **4-gram** | Subword | 119,419 | 16.87 | 1,506,827 | 5.6% | 18.0% |
| **5-gram** | Word | 312,338 | 18.25 | 419,011 | 2.5% | 7.2% |
| **5-gram** | Subword | 385,462 | 18.56 | 3,075,495 | 3.4% | 11.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `වන අතර` | 18,056 |
| 2 | `කරන ලදී` | 14,152 |
| 3 | `කරන ලද` | 12,560 |
| 4 | `වූ අතර` | 10,420 |
| 5 | `අතර එය` | 8,750 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `වන අතර එය` | 2,889 |
| 2 | `කරන ලද අතර` | 2,759 |
| 3 | `කර ඇති අතර` | 1,579 |
| 4 | `බවට පත් විය` | 1,565 |
| 5 | `ප්‍රාදේශීය ලේකම් කොට්ඨාසය` | 1,405 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `සඳහා ප්‍රතිඵල අපේක්ෂකයාපක්ෂයසංකේතයඡන්ද සංඛ්‍යාව` | 919 |
| 2 | `පාර්ලිමේන්තු මැතිවරණයෙහි මෙම මැතිවරණ` | 914 |
| 3 | `ඡන්ද ඡන්ද ඡන්දදායක භාවිත` | 819 |
| 4 | `ඡන්ද ඡන්ද ඡන්ද ඡන්දදායක` | 819 |
| 5 | `ලංකාවේ ප්‍රාදේශීය ලේකම් කොට්ඨාස` | 649 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ඡන්ද ඡන්ද ඡන්ද ඡන්දදායක භාවිත` | 819 |
| 2 | `ඡන්ද ඡන්ද ඡන්දදායක භාවිත කිරීමේ` | 555 |
| 3 | `on wikidata using gadget wikiminiatlas` | 428 |
| 4 | `ta m 1 5 3` | 418 |
| 5 | `බැඳිය විසින් මුළු දින දසුන` | 415 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ය _` | 775,809 |
| 2 | `න් _` | 649,429 |
| 3 | `. _` | 564,248 |
| 4 | `_ අ` | 537,926 |
| 5 | `න _` | 506,185 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ස හ` | 149,125 |
| 2 | `_ ප්‍ ර` | 144,256 |
| 3 | `_ ක ර` | 142,975 |
| 4 | `ස හ _` | 136,850 |
| 5 | `ව න _` | 132,647 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ස හ _` | 136,177 |
| 2 | `_ අ ත ර` | 100,547 |
| 3 | `_ ව න _` | 79,031 |
| 4 | `අ ත ර _` | 68,009 |
| 5 | `_ ලෙ ස _` | 64,807 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ අ ත ර _` | 67,941 |
| 2 | `_ ක ර න _` | 50,645 |
| 3 | `_ t h e _` | 50,119 |
| 4 | `_ ස ඳ හා _` | 46,525 |
| 5 | `_ වි සි න් _` | 43,861 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 2,119
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~12% 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 | 0.8654 | 1.822 | 8.35 | 622,772 | 13.5% |
| **1** | Subword | 0.9820 | 1.975 | 12.62 | 11,028 | 1.8% |
| **2** | Word | 0.2799 | 1.214 | 1.70 | 5,190,673 | 72.0% |
| **2** | Subword | 0.7847 | 1.723 | 5.98 | 139,154 | 21.5% |
| **3** | Word | 0.0782 | 1.056 | 1.14 | 8,825,385 | 92.2% |
| **3** | Subword | 0.5783 | 1.493 | 3.73 | 832,002 | 42.2% |
| **4** | Word | 0.0239 🏆 | 1.017 | 1.03 | 9,999,542 | 97.6% |
| **4** | Subword | 0.4793 | 1.394 | 2.50 | 3,101,075 | 52.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `සහ සැමුවෙල් බේකර් ඇල්ල හා මිනිස් ඇසුරින් මෙහිදී ඩිජිටල් අධ්‍යාපන අමාත්‍යාංශයේ නියෝජිතායතනයක් ද ඇගේ ක...`
2. `අතර සංකීර්ණ ක්‍රම නිර්වචනය වන්නේ ඒවායේ කොටස් වලින් මෙම ද්විමණ්ඩල පාර්ලිමේන්තුව මත තීන්ත ඒවා සමහරක් ඇ...`
3. `වන ඔහු අභියාචනාධිකරණයට අභියාචනා අධිකරණය විසින් නොවැම්බර් 21 උප්පත්තියෙන්ම ලබන පගසම් pagasam එකකි ඓති...`

**Context Size 2:**

1. `වන අතර මුස්ලිම් සංස්කෘතිය මාලදිවයිනේ පැලපදියම් වීමට නම් එය ලිංගික ප්‍රදේශ ස්පර්ශ කිරීමක් වීම ද සිදු ...`
2. `කරන ලදී එහෙත් ඔඩිසි සහ ඉලියඩ් සඳහා පෙළඹීමද වූ බව පැවසේ එවක පැවති ඉංග්‍රීසි පාලකයන්ට විරුද්ධව අරගලයක`
3. `කරන ලද වඩාත් අභිලාෂකාමී මූර්ති උත්සාහ කර ඇත එම සංකේතනය මඟින් අන්තර්ගතය පිටපත් කිරීම පිලිබඳ ජාතික කමි...`

**Context Size 3:**

1. `වන අතර එය මුලින් අයිරෝ වීල් ගුවන් වීල් සහ රොන් දණ්ඩ ලෙසද හැඳින්වේ රෝද නිර්මාණය විශාල රෝදය සමාන්තරව`
2. `කරන ලද අතර එය මගින් ප්‍රාරම්භක අවස්ථාවේ අවහිර කරන ලද ගීතයන් ජර්මනියේ යූ ටියුබ් ප්‍රේක්ෂකයින්ට අලෙවි ...`
3. `කර ඇති අතර සමාගම්වල ප්‍රතිලාභී හිමිකාරිත්ව තොරතුරු සත්‍යාපනය කර ඇති අතර එසේ වුවද ආණ්ඩුක්‍රම ව්‍යවස්ථ...`

**Context Size 4:**

1. `සඳහා ප්‍රතිඵල අපේක්ෂකයාපක්ෂයසංකේතයඡන්ද සංඛ්‍යාව ඒ එම් මොහමඩ් ජලාල්දීන්එක්සත් ජාතික කනගරත්නම්දෙමළ එක්...`
2. `පාර්ලිමේන්තු මැතිවරණයෙහි මෙම මැතිවරණ කොට්ඨාසය සඳහා ප්‍රතිඵල අපේක්ෂකයාපක්ෂයසංකේතයඡන්ද සංඛ්‍යාව එම් සී...`
3. `ඡන්ද ඡන්ද ඡන්ද ඡන්දදායක භාවිත කිරීමේ පාර්ලිමේන්තු මහා මැතිවරණය 5 අප්‍රේල් සහ 10 අප්‍රේල් කාලය අතරතුර...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_bsto_එහිමිදුසුවභාවර_`
2. `යම,_සමාද්‍ය_පාසහඳු_ca`
3. `වය"_nin_ත_සයි._රක්`

**Context Size 2:**

1. `ය_සමාන_ලබා_ඇත්තේ_සල්වැසි`
2. `න්_සම_ක්‍රමය:_hows_m`
3. `._වෙනත්_(හෙක්ටර්_ලාක්_සාග`

**Context Size 3:**

1. `_සහ_කවි_ඔට්ජොසොන්_අස්_වූ_`
2. `_ප්‍රදේශයේ_ජයග්‍රහලෝකයක්_ලැ`
3. `_කරනු_ලැබේ._එසේ_පිහිටුවීමේ_`

**Context Size 4:**

1. `_සහ_සංවර්ධනය_දෙසැම්බර්_15`
2. `_අතර,_ඊජිප්තුවේ_දෙවන_චීන_`
3. `_වන_අතර,_කාලාන්තරය._ආර්`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (3,101,075 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 | 264,267 |
| Total Tokens | 10,742,411 |
| Mean Frequency | 40.65 |
| Median Frequency | 4 |
| Frequency Std Dev | 643.07 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | සහ | 137,360 |
| 2 | අතර | 95,187 |
| 3 | වන | 79,704 |
| 4 | ලෙස | 67,370 |
| 5 | හා | 59,489 |
| 6 | වූ | 53,884 |
| 7 | the | 52,310 |
| 8 | විය | 51,836 |
| 9 | කරන | 50,957 |
| 10 | මෙම | 50,905 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | වොජික් | 2 |
| 2 | ස්ලැට්කොයිච් | 2 |
| 3 | ග්‍රැඩිස්කා | 2 |
| 4 | ග්‍රැඩිෂ්කා | 2 |
| 5 | ටෙසාන්ජ් | 2 |
| 6 | bsp | 2 |
| 7 | gdnp | 2 |
| 8 | මිකොයාන් | 2 |
| 9 | දැවිතෙල් | 2 |
| 10 | ditwah | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9861 |
| R² (Goodness of Fit) | 0.991091 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.3% |
| Top 1,000 | 47.8% |
| Top 5,000 | 69.0% |
| Top 10,000 | 77.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9911 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.3% of corpus
- **Long Tail:** 254,267 words needed for remaining 22.8% 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 | 0.8352 | 0.3629 | N/A | N/A |
| **mono_64d** | 64 | 0.8359 | 0.2849 | N/A | N/A |
| **mono_128d** | 128 | 0.7985 | 0.2254 | N/A | N/A |
| **aligned_32d** | 32 | 0.8352 | 0.3678 | 0.0600 | 0.2940 |
| **aligned_64d** | 64 | 0.8359 🏆 | 0.2739 | 0.1220 | 0.4500 |
| **aligned_128d** | 128 | 0.7985 | 0.2241 | 0.2100 | 0.5660 |

### Key Findings

- **Best Isotropy:** aligned_64d with 0.8359 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2898. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 21.0% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.378** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

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

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-ස` | සිරගතකර, සැදුවේ, සාමාජිකයෙකුගෙන් |
| `-ක` | කුසලතාපූර්ණ, කෙටවීම, කරණලදී |
| `-ප` | පරිනත, පමුණවා, ප්‍රමාණන |
| `-ම` | මෙතර්ඩ්, මොංගල්වරු, මැතිනියට |
| `-ව` | වුඞ්බරි, විලගෙදර, විචාරයෙන් |
| `-අ` | අනුප්‍රාණේ, අපහසුම, අපසාරී |
| `-බ` | බ්‍රහස්පති, බෝයගනේ, බාජන |
| `-න` | නයිස්, නොපිළිගනී, නංවා |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ය` | ලෝකාන්තය, නොයෙදවිය, කෙරුනේය |
| `-ට` | දෙවියාට, නිවෙසට, කොලොනියකරණයට |
| `-s` | australias, chandras, wetas |
| `-ව` | රජතුමන්ව, එක්ව, නාගමුව |
| `-ම` | අපහසුම, කෙටවීම, කාව්‍යම |
| `-e` | fertile, licence, clandestine |
| `-ක` | ක‍්‍රමික, කුළුණක, කොයික |
| `-a` | yulia, taifa, nacaduba |

### 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 |
|------|----------|------------------|----------|
| `ther` | 3.40x | 70 contexts | ether, thera, other |
| `nter` | 3.32x | 49 contexts | unter, inter, enter |
| `atio` | 3.27x | 50 contexts | ratio, ratios, ration |
| `inte` | 3.27x | 38 contexts | intel, inter, cintec |
| `stor` | 3.25x | 36 contexts | stork, store, story |
| `ctio` | 3.34x | 30 contexts | action, sectio, auction |
| `pres` | 3.23x | 32 contexts | presl, press, preset |
| `ical` | 3.42x | 25 contexts | comical, topical, musical |
| `sion` | 3.38x | 26 contexts | fusion, vision, passion |
| `indi` | 3.29x | 27 contexts | indii, indie, india |
| `mber` | 3.33x | 24 contexts | amber, bomber, member |
| `ence` | 3.27x | 23 contexts | pence, fence, sence |

### 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 |
|--------|--------|-----------|----------|
| `-ප` | `-ය` | 60 words | පුමානය, පීතෘවංශීය |
| `-ප` | `-ට` | 47 words | පතිකුලයට, පීඩාවලට |
| `-ස` | `-ය` | 47 words | ස්තූපය, සුභය |
| `-ස` | `-ට` | 43 words | සුර්යාට, සංස්ලේෂණයට |
| `-ව` | `-ට` | 41 words | විබෙදීමට, වාදයට |
| `-ව` | `-ය` | 41 words | වුල්ෆ්ය, විශිෂ්ටය |
| `-අ` | `-ය` | 36 words | අසබඩය, අභ්‍යන්තරාවරණය |
| `-ක` | `-ය` | 34 words | කිරිමටය, කේතලය |
| `-අ` | `-ට` | 31 words | අශ්වයන්ට, අභිචාරයන්ට |
| `-ක` | `-ට` | 29 words | කලිමන්තන්ට, කවුන්සිලයට |

### 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 |
|------|-----------------|------------|------|
| ප්‍රදානවල | **`ප්‍රදා-න-වල`** | 7.5 | `න` |
| අනුපිළිවෙලටම | **`අනුපිළිවෙල-ට-ම`** | 7.5 | `ට` |
| ති‍්‍රපිටක | **`ති‍්‍රපි-ට-ක`** | 7.5 | `ට` |
| ජර්මනියටය | **`ජර්මනි-යට-ය`** | 6.0 | `ජර්මනි` |
| සොයාගත්තේය | **`සොයාගත්තේ-ය`** | 4.5 | `සොයාගත්තේ` |
| ව්‍යාපෘතිය | **`ව්‍යාපෘති-ය`** | 4.5 | `ව්‍යාපෘති` |
| භූමිප්‍රදේශයන්ද | **`භූමිප්‍රදේශයන්-ද`** | 4.5 | `භූමිප්‍රදේශයන්` |
| සංවේදකයකට | **`සංවේදකයක-ට`** | 4.5 | `සංවේදකයක` |
| doctorate | **`doctorat-e`** | 4.5 | `doctorat` |
| එරිත්‍රියාවට | **`එරිත්‍රියාව-ට`** | 4.5 | `එරිත්‍රියාව` |
| ක්‍රමලේඛය | **`ක්‍රමලේඛ-ය`** | 4.5 | `ක්‍රමලේඛ` |
| යුරේසියාවට | **`යුරේසියාව-ට`** | 4.5 | `යුරේසියාව` |
| හදුනාගනීම | **`හදුනාගනී-ම`** | 4.5 | `හදුනාගනී` |
| colombians | **`colombian-s`** | 4.5 | `colombian` |
| parliamentarians | **`parliamentarian-s`** | 4.5 | `parliamentarian` |

### 6.6 Linguistic Interpretation

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.57x) |
| N-gram | **2-gram** | Lowest perplexity (2,119) |
| Markov | **Context-4** | Highest predictability (97.6%) |
| 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: 2026-01-10 21:32:02*