README.md

---
language: gom
language_name: Goan Konkani
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: 4.001
  - name: best_isotropy
    type: isotropy
    value: 0.7594
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-09
---

# Goan Konkani - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Goan Konkani** 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** | 3.046x | 3.05 | 0.1017% | 1,326,874 |
| **16k** | 3.432x | 3.43 | 0.1145% | 1,177,828 |
| **32k** | 3.782x | 3.78 | 0.1262% | 1,068,751 |
| **64k** | 4.001x 🏆 | 4.00 | 0.1335% | 1,010,214 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Muhammad Ali – American Boxer and civil rights campaigner Sondorbh Polleiat Muha...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mu ham m ad ▁ali ▁– ▁american ▁b ox er ... (+26 more)` | 36 |
| 16k | `▁mu ham mad ▁ali ▁– ▁american ▁box er ▁and ▁c ... (+22 more)` | 32 |
| 32k | `▁muhammad ▁ali ▁– ▁american ▁box er ▁and ▁civil ▁right s ... (+12 more)` | 22 |
| 64k | `▁muhammad ▁ali ▁– ▁american ▁boxer ▁and ▁civil ▁rights ▁campaigner ▁sondorbh ... (+9 more)` | 19 |

**Sample 2:** `Ddainn vo डाइण zaun asa ek nustem. thumb thumb Vaidneanik nanv: Scomberoides com...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁dd a inn ▁vo ▁ड ा इ ण ▁zaun ▁asa ... (+35 more)` | 45 |
| 16k | `▁dd a inn ▁vo ▁ड ाइ ण ▁zaun ▁asa ▁ek ... (+32 more)` | 42 |
| 32k | `▁dd a inn ▁vo ▁ड ाइ ण ▁zaun ▁asa ▁ek ... (+32 more)` | 42 |
| 64k | `▁dd a inn ▁vo ▁डाइण ▁zaun ▁asa ▁ek ▁nustem . ... (+28 more)` | 38 |

**Sample 3:** `Benazir Bhutto – – Prime Minister of Pakistan Sondorbh Polleiat Benazir_Bhutto P...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ben az ir ▁bh utt o ▁– ▁– ▁pr im ... (+21 more)` | 31 |
| 16k | `▁ben az ir ▁bh utt o ▁– ▁– ▁prim e ... (+19 more)` | 29 |
| 32k | `▁ben az ir ▁bh utto ▁– ▁– ▁prime ▁minister ▁of ... (+14 more)` | 24 |
| 64k | `▁benazir ▁bh utto ▁– ▁– ▁prime ▁minister ▁of ▁pakistan ▁sondorbh ... (+10 more)` | 20 |


### Key Findings

- **Best Compression:** 64k achieves 4.001x compression
- **Lowest UNK Rate:** 8k with 0.1017% 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 | 5,111 | 12.32 | 27,660 | 26.5% | 53.2% |
| **2-gram** | Subword | 1,903 🏆 | 10.89 | 38,505 | 35.0% | 75.7% |
| **3-gram** | Word | 3,053 | 11.58 | 23,678 | 29.6% | 65.3% |
| **3-gram** | Subword | 14,614 | 13.84 | 161,978 | 13.6% | 39.9% |
| **4-gram** | Word | 7,146 | 12.80 | 58,546 | 20.9% | 54.3% |
| **4-gram** | Subword | 60,268 | 15.88 | 513,861 | 9.1% | 23.5% |
| **5-gram** | Word | 7,630 | 12.90 | 51,862 | 16.7% | 51.6% |
| **5-gram** | Subword | 124,655 | 16.93 | 739,149 | 7.5% | 17.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `सगळ्यांत लागीं` | 12,985 |
| 2 | `अंतराचेर आसा` | 11,720 |
| 3 | `आसा गांवांत` | 10,615 |
| 4 | `उपलब्ध ना` | 7,887 |
| 5 | `आसा सगळ्यांत` | 6,281 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `आसा सगळ्यांत लागीं` | 6,260 |
| 2 | `ना सगळ्यांत लागीं` | 6,129 |
| 3 | `उपलब्ध ना सगळ्यांत` | 5,476 |
| 4 | `परस चड अंतराचेर` | 5,262 |
| 5 | `चड अंतराचेर आसा` | 5,261 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `उपलब्ध ना सगळ्यांत लागीं` | 5,455 |
| 2 | `परस चड अंतराचेर आसा` | 5,261 |
| 3 | `किलोमिटर परस चड अंतराचेर` | 5,083 |
| 4 | `१० किलोमिटर परस चड` | 5,079 |
| 5 | `अंतराचेर आसा सगळ्यांत लागीं` | 4,361 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `किलोमिटर परस चड अंतराचेर आसा` | 5,082 |
| 2 | `१० किलोमिटर परस चड अंतराचेर` | 5,079 |
| 3 | `५ ते १० किलोमिटराच्या अंतराचेर` | 3,486 |
| 4 | `ते १० किलोमिटराच्या अंतराचेर आसा` | 3,485 |
| 5 | `परस चड अंतराचेर आसा सगळ्यांत` | 2,545 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 148,478 |
| 2 | `_ आ` | 121,490 |
| 3 | `र _` | 93,882 |
| 4 | `त _` | 93,586 |
| 5 | `a n` | 88,705 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ आ सा` | 37,415 |
| 2 | `_ आ नी` | 34,014 |
| 3 | `आ नी _` | 32,755 |
| 4 | `आ सा .` | 29,612 |
| 5 | `सा . _` | 28,967 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ आ नी _` | 32,519 |
| 2 | `_ आ सा .` | 29,600 |
| 3 | `आ सा . _` | 28,938 |
| 4 | `गां वां त _` | 16,050 |
| 5 | `_ गां वां त` | 15,394 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ आ सा . _` | 28,926 |
| 2 | `_ गां वां त _` | 15,269 |
| 3 | `उ प ल ब्ध _` | 13,831 |
| 4 | `_ उ प ल ब्ध` | 13,829 |
| 5 | `स ग ळ्यां त _` | 13,782 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 1,903
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~18% 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 | 0.6729 | 1.594 | 4.16 | 282,021 | 32.7% |
| **1** | Subword | 1.2577 | 2.391 | 16.60 | 7,296 | 0.0% |
| **2** | Word | 0.1540 | 1.113 | 1.28 | 1,171,944 | 84.6% |
| **2** | Subword | 0.6638 | 1.584 | 4.09 | 121,127 | 33.6% |
| **3** | Word | 0.0305 | 1.021 | 1.04 | 1,503,180 | 97.0% |
| **3** | Subword | 0.5013 | 1.416 | 2.73 | 495,687 | 49.9% |
| **4** | Word | 0.0095 🏆 | 1.007 | 1.01 | 1,566,242 | 99.1% |
| **4** | Subword | 0.3513 | 1.276 | 1.83 | 1,351,866 | 64.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `आनी ग्वाल्हेर इंदूर शारांत १ शासकीय भौशीक वाचपघर उपलब्ध ना सगळ्यांत लागीं चित्रपटगृह व्हिडिओ केंद्र ...`
2. `आसा सगळ्यांत लागीं प्रसूति आनी जर विधिमंडळान केल्ल्या नळाच्या उदकाची नितळसाण गांवांत मंडी कायमचे बाज...`
3. `गांवांत दूरध्वनी केंद्र ५ ०००ते ९ किलोमीटर अंतराचेर आसा बाजार ५ ते १० किलोमिटर परस चड`

**Context Size 2:**

1. `सगळ्यांत लागीं पॉलिटेक्निक verna ct १० किलोमिटर परस चड अंतराचेर आसा गावात उपपोस्ट ऑफिस उपलब्ध ना गां...`
2. `अंतराचेर आसा सगळ्यांत लागीं क्षयरोग उपचार केंद्र १० किलोमिटर परस चड अंतराचेर आसा गांवांत कृषी उत्पन्...`
3. `आसा गांवांत शुद्धीकरण केल्लें नळाचें उदक पुरवण ना गांवांत न्हाणीघर सोडून सार्वजनिक स्वच्छता घर उपलब्...`

**Context Size 3:**

1. `आसा सगळ्यांत लागीं अनौपचारिक प्रशिक्षणकेंद्र valpoi ५ किलोमिटरा परस कमी अंतराचेर आसा गांवांत खाजगी क...`
2. `ना सगळ्यांत लागीं कृषी उत्पन्न बाजार समिती उपलब्ध ना सगळ्यांत लागीं सहकारी सावकारी पेडी आसा संदर्भ ग...`
3. `उपलब्ध ना सगळ्यांत लागीं शेतकी कर्ज संस्था १० किलोमिटर परस चड अंतराचेर आसा सगळ्यांत लागीं पॉलिटेक्नि...`

**Context Size 4:**

1. `उपलब्ध ना सगळ्यांत लागीं इंटरनेट सुवीधा १० किलोमिटर परस चड अंतराचेर आसा सगळ्यांत लागीं पॉलिटेक्निक c...`
2. `परस चड अंतराचेर आसा वैजकी सुविधा अशासकीय गांवांत १ बाह्यरुग्ण वैजकी सुविधा आसा पिवपाचे उदक गांवांत श...`
3. `किलोमिटर परस चड अंतराचेर आसा सगळ्यांत लागीं पर्यायी वैजकी रुग्णालय १० किलोमिटर परस चड अंतराचेर आसा ग...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_su_bdeasatsondi`
2. `addannchvokonant`
3. `o_varleden_कुर_ಸೋಡುಂ`

**Context Size 2:**

1. `._स्वतंत्र_समाजवाडाय_मुरली.`
2. `_आसून_गेलो._नामनाथ_वळखुं`
3. `र_ऑफीस_चवथ्या_खरें_लग्नाबद`

**Context Size 3:**

1. `_आसा._गांवांत_अशे_आसा._३६`
2. `_आनीक_आपली_आसा._सगळ्यांत_`
3. `आनी_कार्यात्मक_आनी_पाली_वा_गर`

**Context Size 4:**

1. `_आनी_निळी_रंगाची_उत्तं_गीत._ना`
2. `_आसा._आरोग्य_उपकेंद्र_५_ते_१`
3. `आसा._गांवांतल्या_देशांत_बरोवपाक_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,351,866 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 | 104,377 |
| Total Tokens | 1,826,394 |
| Mean Frequency | 17.50 |
| Median Frequency | 3 |
| Frequency Std Dev | 218.96 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | आनी | 32,869 |
| 2 | आसा | 32,307 |
| 3 | गांवांत | 16,033 |
| 4 | ह्या | 13,866 |
| 5 | उपलब्ध | 13,831 |
| 6 | सगळ्यांत | 13,779 |
| 7 | ani | 13,657 |
| 8 | ना | 13,460 |
| 9 | लागीं | 13,438 |
| 10 | अंतराचेर | 11,895 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | नवादिया | 2 |
| 2 | पर्वतरांगेच्या | 2 |
| 3 | शिमी | 2 |
| 4 | शिमेसावन | 2 |
| 5 | रेंजाच्या | 2 |
| 6 | बफर | 2 |
| 7 | फॅन्टा | 2 |
| 8 | जलविज्ञानीक | 2 |
| 9 | grandis | 2 |
| 10 | बुडलेले | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9897 |
| R² (Goodness of Fit) | 0.993258 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 24.3% |
| Top 1,000 | 49.3% |
| Top 5,000 | 69.2% |
| Top 10,000 | 77.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9933 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 24.3% of corpus
- **Long Tail:** 94,377 words needed for remaining 22.9% 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 | 0.7594 | 0.3761 | N/A | N/A |
| **mono_64d** | 64 | 0.7357 | 0.3105 | N/A | N/A |
| **mono_128d** | 128 | 0.6506 | 0.2584 | N/A | N/A |
| **aligned_32d** | 32 | 0.7594 🏆 | 0.3713 | 0.0100 | 0.1300 |
| **aligned_64d** | 64 | 0.7357 | 0.3144 | 0.0200 | 0.1480 |
| **aligned_128d** | 128 | 0.6506 | 0.2631 | 0.0340 | 0.1920 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7594 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3157. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.4% 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 | **1.887** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-या` | बारश्या, ब्रिटनांतल्या, आशिललया |
| `-्या` | बारश्या, ब्रिटनांतल्या, तपश्र्चर्या |
| `-चो` | ब्रिटिशांचो, लिंबाचो, पीठाचो |
| `-ें` | सायबीणीचें, सुरवातीचें, खोडयें |

### 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 |
|------|----------|------------------|----------|
| `anch` | 2.38x | 228 contexts | nanch, panch, anchi |
| `antl` | 2.59x | 78 contexts | hantle, tantle, hantli |
| `rant` | 2.59x | 74 contexts | grant, prant, xarant |
| `iche` | 2.46x | 86 contexts | aiche, hiche, liche |
| `nche` | 2.44x | 86 contexts | xanche, tanche, hanche |
| `tach` | 2.30x | 94 contexts | tache, tacho, tachi |
| `rach` | 2.28x | 97 contexts | prachy, sirach, porach |
| `honn` | 2.65x | 47 contexts | mhonn, dhonn, ghonn |
| `orta` | 2.48x | 61 contexts | vorta, sorta, corta |
| `aran` | 2.44x | 56 contexts | daran, faran, xaran |
| `eant` | 2.52x | 44 contexts | leant, goeant, ujeant |
| `eche` | 2.49x | 46 contexts | teche, veche, techem |

### 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`).

| Word | Suggested Split | Confidence | Stem |
|------|-----------------|------------|------|
| दादल्यांचो | **`दादल्यां-चो`** | 4.5 | `दादल्यां` |
| झुजाऱ्यांचो | **`झुजाऱ्यां-चो`** | 4.5 | `झुजाऱ्यां` |
| शांरांतल्या | **`शांरांतल-्या`** | 1.5 | `शांरांतल` |
| देवविद्या | **`देवविद-्या`** | 1.5 | `देवविद` |
| शेतांतलें | **`शेतांतल-ें`** | 1.5 | `शेतांतल` |
| चयापचयांतल्या | **`चयापचयांतल-्या`** | 1.5 | `चयापचयांतल` |
| बेकारीच्या | **`बेकारीच-्या`** | 1.5 | `बेकारीच` |
| रूजायच्या | **`रूजायच-्या`** | 1.5 | `रूजायच` |
| प्रशासनाचें | **`प्रशासनाच-ें`** | 1.5 | `प्रशासनाच` |
| न्युयॉर्कांतल्या | **`न्युयॉर्कांतल-्या`** | 1.5 | `न्युयॉर्कांतल` |
| तोबिताचें | **`तोबिताच-ें`** | 1.5 | `तोबिताच` |
| दक्षिणेकडचो | **`दक्षिणेकड-चो`** | 1.5 | `दक्षिणेकड` |
| राज्यसत्तेच्या | **`राज्यसत्तेच-्या`** | 1.5 | `राज्यसत्तेच` |
| फुडारिल्ल्या | **`फुडारिल्ल-्या`** | 1.5 | `फुडारिल्ल` |
| मोनजातीचें | **`मोनजातीच-ें`** | 1.5 | `मोनजातीच` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Goan Konkani 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 (4.00x) |
| N-gram | **2-gram** | Lowest perplexity (1,903) |
| Markov | **Context-4** | Highest predictability (99.1%) |
| 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: 2026-01-09 23:51:36*