---
language: ig
language_name: Igbo
language_family: atlantic_yoruba_igbo
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_yoruba_igbo
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: 3.745
  - name: best_isotropy
    type: isotropy
    value: 0.8093
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Igbo** 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** | 3.236x | 3.24 | 0.3842% | 188,457 |
| **16k** | 3.437x | 3.44 | 0.4081% | 177,404 |
| **32k** | 3.614x | 3.62 | 0.4291% | 168,744 |
| **64k** | 3.745x 🏆 | 3.75 | 0.4447% | 162,811 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Duli bu nwere ike izo aka na: Duli, Ardabil, Iran Duli, Hamadan, Iran Duli, Nepa...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁du li ▁bu ▁nwere ▁ike ▁izo ▁aka ▁na : ▁du ... (+31 more)` | 41 |
| 16k | `▁du li ▁bu ▁nwere ▁ike ▁izo ▁aka ▁na : ▁du ... (+31 more)` | 41 |
| 32k | `▁du li ▁bu ▁nwere ▁ike ▁izo ▁aka ▁na : ▁du ... (+31 more)` | 41 |
| 64k | `▁du li ▁bu ▁nwere ▁ike ▁izo ▁aka ▁na : ▁du ... (+31 more)` | 41 |

**Sample 2:** `Purukotó (Purucotó) bụ asụsụ Cariban na-apụ n'anya . Kaufman debere ya na ngalab...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pu ru ko t ó ▁( pu ru co t ... (+30 more)` | 40 |
| 16k | `▁puru kot ó ▁( puru co tó ) ▁bụ ▁asụsụ ... (+24 more)` | 34 |
| 32k | `▁puru kot ó ▁( puru co tó ) ▁bụ ▁asụsụ ... (+22 more)` | 32 |
| 64k | `▁puru kot ó ▁( puru co tó ) ▁bụ ▁asụsụ ... (+22 more)` | 32 |

**Sample 3:** `Manombai (nke a dị ka Wokam) bụ otu n'ime Asụsụ Aru, nke ndị bi na Aru Islands, ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁man om bai ▁( nke ▁a ▁dị ▁ka ▁wo ka ... (+24 more)` | 34 |
| 16k | `▁man om bai ▁( nke ▁a ▁dị ▁ka ▁wo kam ... (+23 more)` | 33 |
| 32k | `▁man om bai ▁( nke ▁a ▁dị ▁ka ▁wo kam ... (+23 more)` | 33 |
| 64k | `▁man om bai ▁( nke ▁a ▁dị ▁ka ▁wo kam ... (+23 more)` | 33 |


### Key Findings

- **Best Compression:** 64k achieves 3.745x compression
- **Lowest UNK Rate:** 8k with 0.3842% 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 | 26,246 | 14.68 | 359,156 | 15.9% | 37.9% |
| **2-gram** | Subword | 280 🏆 | 8.13 | 12,173 | 64.0% | 99.0% |
| **3-gram** | Word | 161,068 | 17.30 | 916,288 | 6.8% | 18.8% |
| **3-gram** | Subword | 2,183 | 11.09 | 87,468 | 30.4% | 71.2% |
| **4-gram** | Word | 532,594 | 19.02 | 1,757,879 | 4.0% | 10.9% |
| **4-gram** | Subword | 11,363 | 13.47 | 475,134 | 17.2% | 44.2% |
| **5-gram** | Word | 559,672 | 19.09 | 1,291,016 | 3.5% | 8.9% |
| **5-gram** | Subword | 42,173 | 15.36 | 1,479,265 | 10.6% | 30.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dị ka` | 140,163 |
| 2 | `a na` | 112,277 |
| 3 | `ọ bụ` | 105,148 |
| 4 | `ya na` | 99,998 |
| 5 | `site na` | 75,118 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ma ọ bụ` | 47,538 |
| 2 | `dị ka onye` | 33,165 |
| 3 | `dị iche iche` | 22,236 |
| 4 | `ndi di ndụ` | 19,640 |
| 5 | `na eme ihe` | 19,264 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mmadụ ndi di ndụ` | 17,108 |
| 2 | `òtù mmadụ ndi di` | 17,101 |
| 3 | `na eme ihe nkiri` | 13,842 |
| 4 | `akụkọ ihe mere eme` | 12,735 |
| 5 | `dị ka onye na` | 9,212 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `òtù mmadụ ndi di ndụ` | 17,099 |
| 2 | `onye na eme ihe nkiri` | 6,973 |
| 3 | `òtù pages with unreviewed translations` | 4,329 |
| 4 | `e dere n ala ala` | 4,004 |
| 5 | `ihe e dere n ala` | 3,927 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n` | 5,638,183 |
| 2 | `a _` | 5,376,024 |
| 3 | `e _` | 4,318,368 |
| 4 | `n a` | 2,708,872 |
| 5 | `_ a` | 2,215,860 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a` | 2,367,266 |
| 2 | `n a _` | 1,687,800 |
| 3 | `a _ n` | 1,387,006 |
| 4 | `e _ n` | 1,187,243 |
| 5 | `_ n k` | 938,041 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a _` | 1,567,660 |
| 2 | `_ n k e` | 743,366 |
| 3 | `n k e _` | 735,578 |
| 4 | `_ n a -` | 656,811 |
| 5 | `a _ n a` | 579,489 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n k e _` | 722,504 |
| 2 | `_ n d ị _` | 399,246 |
| 3 | `_ i h e _` | 373,739 |
| 4 | `_ n a - e` | 351,252 |
| 5 | `a _ n a _` | 349,914 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 280
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.8607 | 1.816 | 9.02 | 510,524 | 13.9% |
| **1** | Subword | 1.0714 | 2.101 | 7.32 | 6,437 | 0.0% |
| **2** | Word | 0.3599 | 1.283 | 2.38 | 4,598,546 | 64.0% |
| **2** | Subword | 0.7215 | 1.649 | 4.70 | 47,137 | 27.9% |
| **3** | Word | 0.1996 | 1.148 | 1.52 | 10,914,867 | 80.0% |
| **3** | Subword | 0.6901 | 1.613 | 3.94 | 221,281 | 31.0% |
| **4** | Word | 0.1054 🏆 | 1.076 | 1.21 | 16,623,256 | 89.5% |
| **4** | Subword | 0.6621 | 1.582 | 3.28 | 871,504 | 33.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `na mmemme ahụ n ọtụtụ ndị dugara na abụọ nke 302 west sepik province nke a`
2. `nke na kaduna kama nke ndị agha ebumnuche na ndị na otu a na ya olulu`
3. `n ime ndị o kwuru na ahụ na eto ya niile na dholuo okpukpe n etiti`

**Context Size 2:**

1. `dị ka nke abụọ marathon nke etiopia onye otu bọọdụ na achọ ọfịs dabere na ike araromire`
2. `a na enyo enyo ébé ọ bi na ya jide nche anwụ nke all progressives congress apc`
3. `ọ bụ akụkụ nke machar colony akụkụ nke usoro nke na ezere ọkwa nna ya bụ 531`

**Context Size 3:**

1. `ma ọ bụ tin ore ihe ndị fọdụrụ na german army dina na nzuzo na eduga na nkwupụta`
2. `dị ka onye edemede na onye na ezisa ozi ọma na ghana ebe ọ mmụta akwụkwọ na adịbeghị`
3. `dị iche iche nke a ga enyocha n ihu nyocha nke chọpụtara ụzọ agha oke ala nke dara`

**Context Size 4:**

1. `òtù mmadụ ndi di ndụ òtù pages with unreviewed translations __lead_section__ áká_ịkẹngạ thumb ihe ej...`
2. `na eme ihe nkiri kacha mma na ọrụ dị mkpa nke ala ala dị n ibéetiti ahụ áká_èkpè thumb`
3. `akụkọ ihe mere eme na muizenberg cape town mbipụta abụ m na efe efe carapace doo wop girls of`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_i_natọ_nọ_ndona`
2. `a_ngbụ_ondiy_ma_`
3. `e_i_nnropana-e_ụ`

**Context Size 2:**

1. `_ng_porosii_nke_a`
2. `a_ọdụ_na_ka_hasụ_`
3. `e_12.2,_ndihe_ọzọ`

**Context Size 3:**

1. `_na-ụdị_nwunyere_o`
2. `na_nke_na_gọzi_na_`
3. `a_nke_umuagest_6_k`

**Context Size 4:**

1. `_na_baltham_taa_aː_`
2. `_nke_12,_ndị_burugb`
3. `nke_ọrụ_egypt_mara_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 89.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (871,504 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 | 220,608 |
| Total Tokens | 24,129,478 |
| Mean Frequency | 109.38 |
| Median Frequency | 4 |
| Frequency Std Dev | 5866.90 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | na | 2,239,768 |
| 2 | nke | 735,052 |
| 3 | n | 615,909 |
| 4 | ihe | 410,419 |
| 5 | ndị | 405,283 |
| 6 | ọ | 395,253 |
| 7 | ya | 384,400 |
| 8 | a | 339,042 |
| 9 | dị | 325,019 |
| 10 | onye | 319,693 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | agbalagbo | 2 |
| 2 | akpalagu | 2 |
| 3 | okwule | 2 |
| 4 | otuogene | 2 |
| 5 | ovili | 2 |
| 6 | anyansi | 2 |
| 7 | ifediorah | 2 |
| 8 | chidalu | 2 |
| 9 | okebo | 2 |
| 10 | pdna | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2680 |
| R² (Goodness of Fit) | 0.992771 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 50.1% |
| Top 1,000 | 75.8% |
| Top 5,000 | 88.4% |
| Top 10,000 | 91.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9928 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 50.1% of corpus
- **Long Tail:** 210,608 words needed for remaining 8.2% 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 | 0.8093 | 0.4233 | N/A | N/A |
| **mono_64d** | 64 | 0.7925 | 0.3195 | N/A | N/A |
| **mono_128d** | 128 | 0.7531 | 0.2578 | N/A | N/A |
| **aligned_32d** | 32 | 0.8093 🏆 | 0.4482 | 0.2740 | 0.7140 |
| **aligned_64d** | 64 | 0.7925 | 0.3263 | 0.4540 | 0.8100 |
| **aligned_128d** | 128 | 0.7531 | 0.2597 | 0.6140 | 0.8900 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8093 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3391. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 61.4% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.708** | 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 |
|--------|----------|
| `-a` | agathon, aboudia, ankusha |
| `-m` | mertsalov, millionaire, müttererholungsverein |
| `-n` | naimdb, nasril, nwpl |
| `-ma` | malitereihe, matsumoto, mackerdhuj |
| `-s` | schnee, shabaka, shuaibiu |
| `-b` | beloved, bourguiba, brunhild |
| `-k` | kechie, kareem, kilolo |
| `-e` | edekọrọ, eribake, edremoda |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | kechie, millionaire, ghọtahie |
| `-a` | yulia, hekka, bourguiba |
| `-s` | hypochlorous, pleiades, morcus |
| `-n` | müttererholungsverein, fleischman, agathon |
| `-i` | wabehi, hajjaji, adefarati |
| `-r` | mountaineer, leaver, br |
| `-o` | turbo, wamco, kilolo |
| `-t` | chiat, rajput, zuidoost |

### 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 |
|------|----------|------------------|----------|
| `atio` | 2.41x | 79 contexts | ation, ratio, patio |
| `fric` | 2.53x | 46 contexts | afric, frick, friche |
| `nati` | 2.46x | 46 contexts | natij, inati, natie |
| `epụt` | 2.22x | 64 contexts | kepụta, ndepụt, mepụta |
| `alit` | 1.92x | 109 contexts | alita, alito, palit |
| `kwad` | 2.39x | 40 contexts | kwadi, kwado, kwada |
| `wany` | 1.95x | 71 contexts | wanyä, nwany, wanye |
| `gbas` | 2.08x | 54 contexts | gbasa, egbas, ịgbasa |
| `nwan` | 1.93x | 73 contexts | nwany, enwan, nwana |
| `ụtar` | 2.04x | 56 contexts | ụtara, ụtarị, tụtara |
| `ọpụt` | 1.94x | 68 contexts | ọpụta, kọpụta, họpụta |
| `nwet` | 2.21x | 39 contexts | nweta, nwetụ, nwete |

### 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` | `-a` | 92 words | amazônia, arema |
| `-m` | `-e` | 74 words | montefiore, mmachineke |
| `-m` | `-s` | 70 words | marthinus, missionaries |
| `-m` | `-a` | 69 words | mgbasasa, mëhneja |
| `-a` | `-e` | 69 words | adae, adamorobe |
| `-s` | `-s` | 66 words | schreiners, strives |
| `-a` | `-s` | 62 words | antiperspirants, autonomous |
| `-s` | `-e` | 55 words | stalemate, sute |
| `-k` | `-a` | 53 words | kadina, katọkwara |
| `-s` | `-a` | 51 words | spelaea, shadia |

### 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 |
|------|-----------------|------------|------|
| avanzadoras | **`avanzador-a-s`** | 7.5 | `a` |
| commutata | **`commu-ta-ta`** | 7.5 | `ta` |
| starfruit | **`starfru-i-t`** | 7.5 | `i` |
| johnsonmain | **`johnsonm-a-in`** | 7.5 | `a` |
| maniapoto | **`maniapo-t-o`** | 7.5 | `t` |
| hollywoodland | **`hollywoodl-an-d`** | 7.5 | `an` |
| camptoceras | **`camptoce-ra-s`** | 7.5 | `ra` |
| expressway | **`express-wa-y`** | 7.5 | `wa` |
| minnijean | **`minnij-e-an`** | 7.5 | `e` |
| multiflora | **`multifl-o-ra`** | 7.5 | `o` |
| christened | **`christe-n-ed`** | 7.5 | `n` |
| westfälisch | **`westfälis-c-h`** | 7.5 | `c` |
| caballero | **`ca-baller-o`** | 6.0 | `baller` |
| personnel | **`person-ne-l`** | 6.0 | `person` |
| ameringer | **`ameri-ng-er`** | 6.0 | `ameri` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Igbo 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 (3.75x) |
| N-gram | **2-gram** | Lowest perplexity (280) |
| Markov | **Context-4** | Highest predictability (89.5%) |
| 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: 2026-01-10 05:45:06*