README.md

---
language: ann
language_name: Obolo
language_family: atlantic_other
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_other
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: 4.353
  - name: best_isotropy
    type: isotropy
    value: 0.1716
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Obolo** 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** | 4.116x | 4.12 | 0.1487% | 128,471 |
| **16k** | 4.353x 🏆 | 4.36 | 0.1572% | 121,476 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ida Obolo ìre ikpa etip-usen eyi ebi Ogbo Ikwaan̄ Usem Obolo ekisan̄a isibi me e...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ida ▁obolo ▁ìre ▁ikpa ▁etip - usen ▁eyi ▁ebi ▁ogbo ... (+22 more)` | 32 |
| 16k | `▁ida ▁obolo ▁ìre ▁ikpa ▁etip - usen ▁eyi ▁ebi ▁ogbo ... (+21 more)` | 31 |

**Sample 2:** `Jameni (òrere Deutschland me usem Jameni, mè ire Germany me usem Ebeke) ìre ido ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁jameni ▁( òrere ▁de uts ch land ▁me ▁usem ▁jameni ... (+15 more)` | 25 |
| 16k | `▁jameni ▁( òrere ▁deutschland ▁me ▁usem ▁jameni , ▁mè ▁ire ... (+12 more)` | 22 |

**Sample 3:** `ìre ikọ ekisa ìjeen̄ uyok uyok ekiket kubọk nriki ònan̄a me inu ikeke ene chieen...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ìre ▁ikọ ▁ekisa ▁ìjeen̄ ▁uyok ▁uyok ▁ekiket ▁kubọk ▁nriki ▁ònan̄a ... (+17 more)` | 27 |
| 16k | `▁ìre ▁ikọ ▁ekisa ▁ìjeen̄ ▁uyok ▁uyok ▁ekiket ▁kubọk ▁nriki ▁ònan̄a ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 16k achieves 4.353x compression
- **Lowest UNK Rate:** 8k with 0.1487% 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 | 1,077 | 10.07 | 2,406 | 36.6% | 78.7% |
| **2-gram** | Subword | 236 🏆 | 7.88 | 1,214 | 68.6% | 99.7% |
| **3-gram** | Word | 1,871 | 10.87 | 3,155 | 25.1% | 66.0% |
| **3-gram** | Subword | 1,382 | 10.43 | 7,013 | 32.7% | 80.9% |
| **4-gram** | Word | 3,277 | 11.68 | 4,661 | 17.3% | 49.0% |
| **4-gram** | Subword | 4,770 | 12.22 | 23,560 | 20.3% | 56.1% |
| **5-gram** | Word | 2,207 | 11.11 | 2,786 | 18.0% | 56.1% |
| **5-gram** | Subword | 9,921 | 13.28 | 38,424 | 14.8% | 42.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `me lek` | 1,069 |
| 2 | `me agan̄` | 831 |
| 3 | `me emen` | 791 |
| 4 | `ido ya` | 458 |
| 5 | `ichit me` | 380 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `agan̄ ichep ura` | 215 |
| 2 | `me ido ya` | 190 |
| 3 | `me agan̄ osiki` | 182 |
| 4 | `agan̄ mbum ura` | 174 |
| 5 | `me agan̄ inyọn̄` | 171 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `me agan̄ mbum ura` | 103 |
| 2 | `me agan̄ ichep ura` | 96 |
| 3 | `me ido ya ìre` | 62 |
| 4 | `agan̄ inyọn̄ mbum ura` | 55 |
| 5 | `me usem uket chieen̄` | 50 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ene ewabe ichit me emen` | 48 |
| 2 | `me agan̄ inyọn̄ mbum ura` | 38 |
| 3 | `me agan̄ osiki mbum ura` | 37 |
| 4 | `me agan̄ osiki ichep ura` | 36 |
| 5 | `otu ifuk ebi ìluk me` | 33 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 19,047 |
| 2 | `_ i` | 16,640 |
| 3 | `_ m` | 14,795 |
| 4 | `_ e` | 11,553 |
| 5 | `a _` | 9,463 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m e` | 7,633 |
| 2 | `m e _` | 7,573 |
| 3 | `r e _` | 4,030 |
| 4 | `a n̄ _` | 3,973 |
| 5 | `e _ i` | 3,231 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m e _` | 7,454 |
| 2 | `_ m è _` | 2,866 |
| 3 | `l e k _` | 2,314 |
| 4 | `_ a g a` | 1,867 |
| 5 | `_ e b i` | 1,856 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a g a n̄` | 1,844 |
| 2 | `_ e b i _` | 1,713 |
| 3 | `_ m e _ a` | 1,652 |
| 4 | `_ ì r e _` | 1,547 |
| 5 | `a g a n̄ _` | 1,513 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 236
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~43% 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 | 0.7698 | 1.705 | 4.61 | 9,664 | 23.0% |
| **1** | Subword | 1.1244 | 2.180 | 8.63 | 290 | 0.0% |
| **2** | Word | 0.2727 | 1.208 | 1.60 | 44,320 | 72.7% |
| **2** | Subword | 1.0645 | 2.091 | 5.47 | 2,502 | 0.0% |
| **3** | Word | 0.1063 | 1.076 | 1.18 | 70,635 | 89.4% |
| **3** | Subword | 0.7756 | 1.712 | 3.20 | 13,671 | 22.4% |
| **4** | Word | 0.0452 🏆 | 1.032 | 1.07 | 82,762 | 95.5% |
| **4** | Subword | 0.4895 | 1.404 | 2.03 | 43,657 | 51.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `me atasuk eyi akọp ìkigwat lek ogugo ijọn̄ afirika etete udun̄nde òrere dmitri mendeleev me esese`
2. `mè anam ge me ere ònire agan̄ inyọn̄ me lek ijọn̄ sudan îgbuku igwook mè ikisa`
3. `agan̄ erumfaka kiristien itap mè mbit pọtugalu ekisabe ibọp ekwu òkukup me usem obolo usini ekilọk`

**Context Size 2:**

1. `me lek èwê sayara me emen ido yi usem komoros furenchi mè usem afarì mè igwen okwaan̄`
2. `me agan̄ inyọn̄ sabum mgbọ keyi ebi ene ewa ichit ebi un enyibe me acha ifofo belin`
3. `me emen kan̄ mgbọ îkanabe ogwu biriten îsan̄a nchọi iba me emen utikpa ya okisibi igwook me`

**Context Size 3:**

1. `agan̄ ichep ura otutuuk ekup me lek ogbọn̄ ikput lek ema ekitim akọn̄ me lek ido india me`
2. `me ido ya efele oka agan̄ mkpulu gongola isa ichili taraba me 27 ọgọs me ukot mkpulu kè`
3. `me agan̄ osiki ichep ura egwen agan̄ mkpulu rivas mè delita ijọ ijaw ore usem eikimalek itumu me`

**Context Size 4:**

1. `me agan̄ mbum ura me agan̄ ichep ura îre ido ini ingilan skọtilan weelis mè ailan agan̄ inyọn̄ me`
2. `me agan̄ ichep ura isi ire lek emen awaji pàsifik me agan̄ mbum ura sudan me agan̄ osiki mbum`
3. `me ido ya ìre mamoudizou me grande terree acho eyi ilile usem mkpulu ìre furenchi eyi owuwa ene ekit...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_me_e_mọọn̄),_eki`
2. `eranlatenctiko._`
3. `ik_e_e_gbe_okire`

**Context Size 2:**

1. `e_nathe_in_iritim`
2. `_igọọn̄_mîturusiny`
3. `_me_ban̄_ge_ema_mf`

**Context Size 3:**

1. `_me_òbeluk_sọn_bro`
2. `me_ere_<gdp>_òkike`
3. `re_ere_òta_irọ_yi_`

**Context Size 4:**

1. `_me_emen_oka_akat._`
2. `_mè_onan̄a_me_efit_e`
3. `lek_ichit_me_agan̄_i`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (43,657 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 | 4,154 |
| Total Tokens | 89,919 |
| Mean Frequency | 21.65 |
| Median Frequency | 4 |
| Frequency Std Dev | 152.24 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | me | 7,502 |
| 2 | mè | 2,898 |
| 3 | agan̄ | 1,854 |
| 4 | ebi | 1,728 |
| 5 | ìre | 1,597 |
| 6 | lek | 1,576 |
| 7 | ido | 1,514 |
| 8 | eyi | 1,242 |
| 9 | ya | 1,165 |
| 10 | emen | 1,065 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | lanzarote | 2 |
| 2 | iyaak | 2 |
| 3 | medvedev | 2 |
| 4 | race | 2 |
| 5 | lenin | 2 |
| 6 | ọkọlọba | 2 |
| 7 | ǹkọọn̄ | 2 |
| 8 | edeh | 2 |
| 9 | ogwuile | 2 |
| 10 | bruxelles | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1652 |
| R² (Goodness of Fit) | 0.990704 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 59.9% |
| Top 1,000 | 87.9% |
| Top 5,000 | 0.0% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9907 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 59.9% of corpus
- **Long Tail:** -5,846 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 | 0.1716 🏆 | 0.5548 | N/A | N/A |
| **mono_64d** | 64 | 0.0315 | 0.5662 | N/A | N/A |
| **mono_128d** | 128 | 0.0057 | 0.5736 | N/A | N/A |
| **aligned_32d** | 32 | 0.1716 | 0.5361 | 0.0083 | 0.1330 |
| **aligned_64d** | 64 | 0.0315 | 0.5580 | 0.0166 | 0.1745 |
| **aligned_128d** | 128 | 0.0057 | 0.5602 | 0.0139 | 0.1717 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.1716 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.5582. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.7% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.314** | 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 |
|--------|----------|
| `-ek` | ekijeje, ekpukpo, ekwukwu |
| `-ik` | ikira, ikikween̄, ikpọkpọ |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n̄` | kpekaan̄, utọn̄, ikikween̄ |
| `-be` | ojotbe, erọkọbe, egobobe |

### 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 |
|------|----------|------------------|----------|
| `tumu` | 1.48x | 21 contexts | etumu, îtumu, itumu |
| `gọọk` | 1.52x | 19 contexts | agọọk, egọọk, îgọọk |
| `kpul` | 1.59x | 16 contexts | ìkpulu, îkpulu, òkpulu |
| `sibi` | 1.51x | 18 contexts | ìsibi, îsibi, osibi |
| `kikp` | 1.46x | 19 contexts | ìkikpa, òkikpọ, òkikpa |
| `kana` | 1.42x | 20 contexts | nkana, îkana, ekana |
| `kisa` | 1.45x | 17 contexts | îkisa, ikisa, ìkisa |
| `chie` | 1.54x | 14 contexts | chief, nchieek, chieen̄ |
| `riọọ` | 1.62x | 12 contexts | riọọn̄, nriọọk, iriọọn̄ |
| `gbaa` | 1.47x | 15 contexts | igbaan̄, egbaan̄, ogbaan̄ |
| `ikaa` | 1.61x | 11 contexts | ikaan̄, ìkikaan̄, ebikaan̄ |
| `kpọk` | 1.39x | 16 contexts | okpọk, ukpọk, ikpọk |

### 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 |
|--------|--------|-----------|----------|
| `-ik` | `-n̄` | 15 words | ikikween̄, ikpan̄ |
| `-ek` | `-be` | 13 words | ekpan̄be, ekpukbe |
| `-ek` | `-n̄` | 10 words | ekigbaan̄, ekimun̄ |

### 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 |
|------|-----------------|------------|------|
| ekitumube | **`ek-itumu-be`** | 6.0 | `itumu` |
| ekinyambe | **`ek-inyam-be`** | 6.0 | `inyam` |
| ekigwenbe | **`ek-igwen-be`** | 6.0 | `igwen` |
| ikichieek | **`ik-ichieek`** | 4.5 | `ichieek` |
| echichinibe | **`echichini-be`** | 4.5 | `echichini` |
| ekekikpulu | **`ek-ek-ik-pulu`** | 4.5 | `pulu` |
| ekiweweek | **`ek-iweweek`** | 4.5 | `iweweek` |
| echieekbe | **`echieek-be`** | 4.5 | `echieek` |
| ekikpulube | **`ek-ik-pulu-be`** | 4.5 | `pulu` |
| ekichichini | **`ek-ichichini`** | 4.5 | `ichichini` |
| ikikween̄ | **`ik-ik-ween̄`** | 3.0 | `ween̄` |
| ekigbaan̄ | **`ek-igbaa-n̄`** | 3.0 | `igbaa` |
| îriọọn̄be | **`îriọọ-n̄-be`** | 3.0 | `îriọọ` |
| eriọọn̄be | **`eriọọ-n̄-be`** | 3.0 | `eriọọ` |
| egbaan̄be | **`egbaa-n̄-be`** | 3.0 | `egbaa` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Obolo 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 | **16k BPE** | Best compression (4.35x) |
| N-gram | **2-gram** | Lowest perplexity (236) |
| Markov | **Context-4** | Highest predictability (95.5%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-03 16:25:38*