README.md

---
language: sg
language_name: Sango
language_family: atlantic_gur
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-atlantic_gur
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: 3.952
  - name: best_isotropy
    type: isotropy
    value: 0.0186
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sango** 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** | 3.952x 🏆 | 3.96 | 0.9228% | 51,148 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Sêse tî kömändâ-kötä tî Bamïngï-Bangoran yeke sêse tî kömändâ-kötä nî ayeke tî K...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sêse ▁tî ▁kömändâ - kötä ▁tî ▁bamïngï - bangoran ▁yeke ... (+27 more)` | 37 |

**Sample 2:** `Laâ mbênî sêse. Wuhngo tî âzo nî ayeke Tî lo likodoro Kuala Lumpur.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁laâ ▁mbênî ▁sêse . ▁wuhngo ▁tî ▁âzo ▁nî ▁ayeke ▁tî ... (+5 more)` | 15 |

**Sample 3:** `Gbêko tî Ngunuhalëzo tî Brésil yeke sêse nî ayeke tî Amerîka. Tî lo likodoro Bré...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gbêko ▁tî ▁ngunuhalëzo ▁tî ▁brésil ▁yeke ▁sêse ▁nî ▁ayeke ▁tî ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 8k achieves 3.952x compression
- **Lowest UNK Rate:** 8k with 0.9228% 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 | 182 | 7.51 | 544 | 75.4% | 100.0% |
| **2-gram** | Subword | 323 | 8.34 | 1,244 | 61.6% | 99.3% |
| **3-gram** | Word | 134 | 7.07 | 617 | 80.7% | 100.0% |
| **3-gram** | Subword | 1,512 | 10.56 | 5,472 | 29.1% | 79.0% |
| **4-gram** | Word | 148 | 7.21 | 1,001 | 78.5% | 100.0% |
| **4-gram** | Subword | 3,422 | 11.74 | 14,491 | 20.6% | 62.7% |
| **5-gram** | Word | 93 🏆 | 6.54 | 629 | 85.5% | 100.0% |
| **5-gram** | Subword | 4,119 | 12.01 | 17,226 | 18.0% | 59.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nî ayeke` | 342 |
| 2 | `ayeke tî` | 274 |
| 3 | `diki kidiri` | 244 |
| 4 | `sango français` | 241 |
| 5 | `jean marie` | 241 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dictionnaire sango français` | 241 |
| 2 | `vallet jacqueline behaghel` | 240 |
| 3 | `kidiri marcel vallet` | 240 |
| 4 | `diki kidiri marcel` | 240 |
| 5 | `marie diki kidiri` | 240 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kidiri marcel vallet jacqueline` | 240 |
| 2 | `vallet jacqueline behaghel anne` | 240 |
| 3 | `jacqueline behaghel anne dictionnaire` | 240 |
| 4 | `et lexique français sango` | 240 |
| 5 | `lexique français sango paris` | 240 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `lexique français sango paris société` | 240 |
| 2 | `français sango paris société des` | 240 |
| 3 | `sango paris société des etudes` | 240 |
| 4 | `jean marie diki kidiri marcel` | 240 |
| 5 | `paris société des etudes linguistiques` | 240 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 4,452 |
| 2 | `a _` | 3,921 |
| 3 | `_ t` | 3,234 |
| 4 | `a n` | 3,077 |
| 5 | `_ n` | 2,785 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t î` | 1,557 |
| 2 | `t î _` | 1,534 |
| 3 | `n a _` | 1,488 |
| 4 | `_ n a` | 1,435 |
| 5 | `e s _` | 1,233 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t î _` | 1,528 |
| 2 | `_ n a _` | 1,338 |
| 3 | `y e k e` | 1,023 |
| 4 | `e k e _` | 999 |
| 5 | `_ t i _` | 949 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `y e k e _` | 973 |
| 2 | `a y e k e` | 700 |
| 3 | `_ a y e k` | 699 |
| 4 | `s a n g o` | 508 |
| 5 | `_ f r a n` | 499 |


### Key Findings

- **Best Perplexity:** 5-gram (word) with 93
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~60% 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 | 0.5456 | 1.460 | 2.61 | 5,855 | 45.4% |
| **1** | Subword | 1.8459 | 3.595 | 13.77 | 187 | 0.0% |
| **2** | Word | 0.1805 | 1.133 | 1.32 | 15,119 | 81.9% |
| **2** | Subword | 1.0753 | 2.107 | 4.96 | 2,575 | 0.0% |
| **3** | Word | 0.0672 | 1.048 | 1.10 | 19,680 | 93.3% |
| **3** | Subword | 0.6217 | 1.539 | 2.52 | 12,742 | 37.8% |
| **4** | Word | 0.0283 🏆 | 1.020 | 1.04 | 21,418 | 97.2% |
| **4** | Subword | 0.3412 | 1.267 | 1.61 | 32,005 | 65.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `tî web na text video tî ködörö nî âyeke na institut ed šiprage list karte 1`
2. `na bomoi ya spécialisés pona environnement fabrication asengaka esika ya mvula économie ya boîtier m...`
3. `ti kodoro ti lo yeke tohgbata nî dïngö ïrï tî kömändâ kötä tî attaque trois front`

**Context Size 2:**

1. `nî ayeke 45 421 tî bêafrîka wuhngo tî âzo nî ayeke wuhngo tî âzo nî ayeke tî`
2. `ayeke tî utiliser pou tî écrire document ex word envoyer message ex whatsapp jouer vidéo ex youtube`
3. `diki kidiri marcel vallet jacqueline behaghel anne dictionnaire sango français et lexique français s...`

**Context Size 3:**

1. `dictionnaire sango français et lexique français sango paris société des etudes linguistiques et anth...`
2. `des etudes linguistiques et anthropologiques de france selaf isbn lïndïpa fîtasü ngbônga`
3. `jean marie diki kidiri marcel vallet jacqueline behaghel anne dictionnaire sango français et lexique...`

**Context Size 4:**

1. `français et lexique français sango paris société des etudes linguistiques et anthropologiques de fra...`
2. `paris société des etudes linguistiques et anthropologiques de france selaf isbn lïndïpa fîtasü ngbôn...`
3. `kobozo jean marie diki kidiri marcel vallet jacqueline behaghel anne dictionnaire sango français et ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ya_del;_aprfr_n`
2. `andetidre_zes_ti`
3. `e_goi_rcet,_eoye`

**Context Size 2:**

1. `e_tî_fonnazo,_let`
2. `a_victi_irie;_köd`
3. `_tî_bênî_bur_tî_a`

**Context Size 3:**

1. `_tî_piècle_tî_lexi`
2. `tî_bê_na_mbit_envi`
3. `na_portablet,_jean`

**Context Size 4:**

1. `_tî_19_june_♆_sêse_`
2. `_na_ngoi_ni_matéris`
3. `eke_na_nde,_safety_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (32,005 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 | 2,202 |
| Total Tokens | 28,828 |
| Mean Frequency | 13.09 |
| Median Frequency | 3 |
| Frequency Std Dev | 63.07 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | tî | 1,555 |
| 2 | na | 1,394 |
| 3 | ti | 954 |
| 4 | ayeke | 700 |
| 5 | sango | 501 |
| 6 | français | 491 |
| 7 | et | 490 |
| 8 | nî | 429 |
| 9 | ya | 353 |
| 10 | de | 348 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | cryptocurrency | 2 |
| 2 | revenue | 2 |
| 3 | annually | 2 |
| 4 | networking | 2 |
| 5 | kômbûtêrê | 2 |
| 6 | ebimisaki | 2 |
| 7 | makambo | 2 |
| 8 | versions | 2 |
| 9 | linyama | 2 |
| 10 | pasëpë | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0050 |
| R² (Goodness of Fit) | 0.981661 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 64.3% |
| Top 1,000 | 90.5% |
| Top 5,000 | 0.0% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9817 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 64.3% of corpus
- **Long Tail:** -7,798 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 | 0.0186 | 0.6671 | N/A | N/A |
| **mono_64d** | 64 | 0.0028 | 0.7207 | N/A | N/A |
| **mono_128d** | 128 | 0.0006 | 0.7186 | N/A | N/A |
| **aligned_32d** | 32 | 0.0186 🏆 | 0.6706 | 0.0181 | 0.1088 |
| **aligned_64d** | 64 | 0.0028 | 0.7005 | 0.0181 | 0.0967 |
| **aligned_128d** | 128 | 0.0006 | 0.7069 | 0.0181 | 0.0967 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.0186 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.6974. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.8% 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 | **2.386** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.669** | 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 |
|--------|----------|
| `-a` | ahébreu, aider, arm |
| `-m` | mitindá, mîlyon, microsoft |
| `-co` | contenus, consecutivos, company |
| `-ma` | market, marie, matthieu |
| `-ba` | bakarî, bakurê, basalelaka |
| `-mo` | modèle, mobile, moke |
| `-mb` | mbala, mbâgë, mbilimbili |
| `-pr` | produit, projets, produits |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | chronique, renaissance, wande |
| `-s` | temps, cross, platforms |
| `-a` | kopeta, kamâra, mbala |
| `-on` | mîlyon, billion, distraction |
| `-er` | aider, créer, afficher |
| `-es` | patrocinadores, externes, tendances |
| `-re` | décembre, transmettre, vêre |
| `-le` | modèle, gbele, symbole |

### 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 |
|------|----------|------------------|----------|
| `ango` | 1.40x | 15 contexts | angoi, sango, fango |
| `anga` | 1.35x | 10 contexts | yanga, kanga, banga |
| `ique` | 1.32x | 6 contexts | logique, lexique, cliquer |

### 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 |
|--------|--------|-----------|----------|
| `-a` | `-e` | 20 words | attaque, akomanse |
| `-m` | `-e` | 17 words | modèle, marie |
| `-co` | `-s` | 12 words | contenus, consecutivos |
| `-in` | `-e` | 11 words | industrielle, informatique |
| `-a` | `-a` | 10 words | akpa, asara |
| `-a` | `-s` | 9 words | anglais, accès |
| `-pr` | `-s` | 8 words | projets, produits |
| `-in` | `-on` | 5 words | integration, information |
| `-m` | `-s` | 5 words | mariages, melhores |
| `-a` | `-re` | 5 words | agriculture, arrière |

### 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 |
|------|-----------------|------------|------|
| platforms | **`platform-s`** | 4.5 | `platform` |
| développeurs | **`développeur-s`** | 4.5 | `développeur` |
| environnemental | **`environnement-al`** | 4.5 | `environnement` |
| applications | **`application-s`** | 4.5 | `application` |
| standards | **`standard-s`** | 4.5 | `standard` |
| institute | **`institut-e`** | 4.5 | `institut` |
| utilisateurs | **`utilisateur-s`** | 4.5 | `utilisateur` |
| informations | **`information-s`** | 4.5 | `information` |
| importante | **`important-e`** | 4.5 | `important` |
| processeurs | **`processeur-s`** | 4.5 | `processeur` |
| fonctions | **`fonction-s`** | 4.5 | `fonction` |
| pratiques | **`pr-a-tiques`** | 4.5 | `tiques` |
| documenter | **`document-er`** | 4.5 | `document` |
| computers | **`computer-s`** | 4.5 | `computer` |
| logiciels | **`logiciel-s`** | 4.5 | `logiciel` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Sango 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 (3.95x) |
| N-gram | **5-gram** | Lowest perplexity (93) |
| Markov | **Context-4** | Highest predictability (97.2%) |
| 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 19:55:01*