---
language: igl
language_name: Igala
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: 4.453
  - name: best_isotropy
    type: isotropy
    value: 0.5907
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Igala** 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** | 3.669x | 3.67 | 0.3518% | 663,249 |
| **16k** | 4.015x | 4.02 | 0.3850% | 606,041 |
| **32k** | 4.258x | 4.26 | 0.4082% | 571,466 |
| **64k** | 4.453x 🏆 | 4.45 | 0.4269% | 546,459 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Bina (Hausa: Binawa) chi ichi abo Kainji eyi Nigeria. References Kainji language...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁b ina ▁( ha usa : ▁b ina wa ) ... (+12 more)` | 22 |
| 16k | `▁bina ▁( ha usa : ▁bina wa ) ▁chi ▁ichi ... (+10 more)` | 20 |
| 32k | `▁bina ▁( hausa : ▁bina wa ) ▁chi ▁ichi ▁abo ... (+9 more)` | 19 |
| 64k | `▁bina ▁( hausa : ▁binawa ) ▁chi ▁ichi ▁abo ▁kainji ... (+8 more)` | 18 |

**Sample 2:** `I.O.I Ódò Asia (Séoul, Koréa) kù ma gbaluka kù ma ki Mnet.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁i . o . i ▁ódò ▁asia ▁( s é ... (+15 more)` | 25 |
| 16k | `▁i . o . i ▁ódò ▁asia ▁( séoul , ... (+10 more)` | 20 |
| 32k | `▁i . o . i ▁ódò ▁asia ▁( séoul , ... (+10 more)` | 20 |
| 64k | `▁i . o . i ▁ódò ▁asia ▁( séoul , ... (+10 more)` | 20 |

**Sample 3:** `thumb X-Men. Wolverine. Marvel Comics. Stan Lee. Jack Kirby.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁th umb ▁x - men . ▁wol ver ine . ... (+15 more)` | 25 |
| 16k | `▁thumb ▁x - men . ▁wolver ine . ▁marvel ▁com ... (+9 more)` | 19 |
| 32k | `▁thumb ▁x - men . ▁wolver ine . ▁marvel ▁comics ... (+7 more)` | 17 |
| 64k | `▁thumb ▁x - men . ▁wolverine . ▁marvel ▁comics . ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 64k achieves 4.453x compression
- **Lowest UNK Rate:** 8k with 0.3518% 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 | 4,698 | 12.20 | 9,920 | 19.2% | 46.9% |
| **2-gram** | Subword | 343 🏆 | 8.42 | 2,695 | 60.3% | 98.6% |
| **3-gram** | Word | 7,863 | 12.94 | 11,300 | 10.6% | 32.9% |
| **3-gram** | Subword | 3,017 | 11.56 | 19,080 | 21.1% | 64.6% |
| **4-gram** | Word | 15,538 | 13.92 | 18,351 | 4.9% | 18.9% |
| **4-gram** | Subword | 15,606 | 13.93 | 82,376 | 11.5% | 33.4% |
| **5-gram** | Word | 11,217 | 13.45 | 12,263 | 4.4% | 18.5% |
| **5-gram** | Subword | 43,998 | 15.43 | 177,908 | 7.7% | 22.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ku ma` | 2,774 |
| 2 | `of the` | 1,730 |
| 3 | `efu ọdọ` | 1,428 |
| 4 | `in the` | 1,052 |
| 5 | `efu ódò` | 471 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `abo ku ma` | 272 |
| 2 | `local government area` | 232 |
| 3 | `ku ma du` | 212 |
| 4 | `ugbo ku ma` | 205 |
| 5 | `ku ma dọ` | 199 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `birth missing living people` | 59 |
| 2 | `of birth missing living` | 59 |
| 3 | `ku ma bi ọjọ` | 57 |
| 4 | `of the university of` | 42 |
| 5 | `see also list of` | 42 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `of birth missing living people` | 59 |
| 2 | `of the order of the` | 39 |
| 3 | `order of the federal republic` | 28 |
| 4 | `population area and headquarters statoids` | 26 |
| 5 | `male actors nigerian male actors` | 24 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 49,529 |
| 2 | `_ a` | 45,300 |
| 3 | `i _` | 40,232 |
| 4 | `a _` | 40,057 |
| 5 | `u _` | 32,629 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c h` | 16,190 |
| 2 | `h e _` | 15,333 |
| 3 | `_ t h` | 13,392 |
| 4 | `t h e` | 13,335 |
| 5 | `_ m a` | 11,372 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t h e` | 11,598 |
| 2 | `t h e _` | 10,579 |
| 3 | `_ o f _` | 8,160 |
| 4 | `e f u _` | 7,487 |
| 5 | `_ k i _` | 6,358 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t h e _` | 10,382 |
| 2 | `_ e f u _` | 6,139 |
| 3 | `_ a n d _` | 5,510 |
| 4 | `n i g e r` | 4,802 |
| 5 | `_ n i g e` | 4,647 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 343
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.8653 | 1.822 | 5.29 | 47,637 | 13.5% |
| **1** | Subword | 1.4882 | 2.805 | 13.95 | 436 | 0.0% |
| **2** | Word | 0.2269 | 1.170 | 1.47 | 251,576 | 77.3% |
| **2** | Subword | 1.0990 | 2.142 | 6.43 | 6,084 | 0.0% |
| **3** | Word | 0.0721 | 1.051 | 1.11 | 369,976 | 92.8% |
| **3** | Subword | 0.8090 | 1.752 | 3.84 | 39,141 | 19.1% |
| **4** | Word | 0.0245 🏆 | 1.017 | 1.03 | 409,990 | 97.6% |
| **4** | Subword | 0.6089 | 1.525 | 2.57 | 150,279 | 39.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `the burial ceremonies marriage introduction of the windseeker houghton mifflin harcourt ọmọ lẹ gẹ bo...`
2. `of yams are several african language babaown concerned with a high school of industry amwnu ogbògaga`
3. `ma chẹ nẹ tule ojane ileyi nwu acha léfu í chí ijabê senator nigeria èwn íyè`

**Context Size 2:**

1. `ku ma do casino ugbo ku ma bi ọjó ẹkẹfa ef ochu ẹkẹfa ọdọ ef ewo pategi`
2. `of the year award bayero university gbu nwa nyu gba ènè àròne nwu chì opera ripples alu`
3. `efu ọdọ tagjam cha ẹdufu efu ochu ejodudu odo sanwo olu go gé list of players statistics`

**Context Size 3:**

1. `abo ku ma cha í ko gí ije íbe le efu óchu ekélé nolu ogwu nyo mélu odot`
2. `local government area ígbalé yí ogori manyu amóne magongo ku ma gbí lo egba le che ama ko`
3. `ku ma du nwa chikulu abeki ọtakada ojoji ojoji oka chi am ibo sudan interior mission sim chu`

**Context Size 4:**

1. `of birth missing living people filmmakers producers women fashion designers fashion designers chief ...`
2. `ku ma bi ọjọ ẹkẹla efu ochu ebie efu ọdọ funke akindele ni nigerian rapper jjc skillz yi london`
3. `see also list of nigerian musicians references external links from osun actresses in yoruba cinema f...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_i–_asomuma_pawu`
2. `a_sijalige;_che_`
3. `eme_:_n;_onn_nth`

**Context Size 2:**

1. `e_runyi_ku_ọdọ_li`
2. `_aya_eminigh_nʊan`
3. `i_ibern_ch_unyuse`

**Context Size 3:**

1. `_chí_brand_the_lo_`
2. `he_lẹ,_iko_ké._man`
3. `_thern_chí_oma._īj`

**Context Size 4:**

1. `_these_chi_obotu-ic`
2. `the_second-places_e`
3. `_of_most_soul_(ọdọ_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (150,279 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 | 20,924 |
| Total Tokens | 418,346 |
| Mean Frequency | 19.99 |
| Median Frequency | 4 |
| Frequency Std Dev | 162.13 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | the | 10,534 |
| 2 | of | 8,175 |
| 3 | ma | 6,574 |
| 4 | ki | 6,413 |
| 5 | efu | 6,401 |
| 6 | and | 5,534 |
| 7 | in | 5,104 |
| 8 | chi | 4,478 |
| 9 | a | 3,589 |
| 10 | state | 3,323 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | collider | 2 |
| 2 | giovonnae | 2 |
| 3 | ụlọ | 2 |
| 4 | ükoche | 2 |
| 5 | ńō | 2 |
| 6 | ọ́gwú | 2 |
| 7 | paediatrics | 2 |
| 8 | gynaecology | 2 |
| 9 | itcc | 2 |
| 10 | maxillofacial | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0791 |
| R² (Goodness of Fit) | 0.990670 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 35.7% |
| Top 1,000 | 65.4% |
| Top 5,000 | 86.3% |
| Top 10,000 | 93.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9907 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 35.7% of corpus
- **Long Tail:** 10,924 words needed for remaining 6.5% 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 | 0.5907 🏆 | 0.3728 | N/A | N/A |
| **mono_64d** | 64 | 0.1914 | 0.3611 | N/A | N/A |
| **mono_128d** | 128 | 0.0327 | 0.3640 | N/A | N/A |
| **aligned_32d** | 32 | 0.5907 | 0.3633 | 0.0440 | 0.2520 |
| **aligned_64d** | 64 | 0.1914 | 0.3640 | 0.0860 | 0.3820 |
| **aligned_128d** | 128 | 0.0327 | 0.3638 | 0.1020 | 0.3500 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.5907 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3648. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.2% 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 | **-0.192** | 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` | amokachi, anchor, aran |
| `-o` | okodu, ogbali, oluwa |
| `-s` | suffixes, sa, swap |
| `-e` | equated, erò, ekó |
| `-m` | mill, mébié, mubi |
| `-d` | danjuma, difficulties, descendant |
| `-k` | kogi, kèkèlè, karen |
| `-i` | idẹpẹ, interpersonal, ichì |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | hughes, suffixes, blackhawks |
| `-e` | chinwe, aiyegunle, phone |
| `-n` | aran, un, foundation |
| `-a` | romania, uzodinma, tarka |
| `-d` | lasted, equated, gathered |
| `-ed` | lasted, equated, gathered |
| `-on` | foundation, compensation, lugbon |
| `-ng` | blacksmithing, leaving, modeling |

### 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 |
|------|----------|------------------|----------|
| `tion` | 1.85x | 32 contexts | action, nation, motion |
| `ther` | 1.78x | 31 contexts | there, other, rather |
| `atio` | 1.90x | 22 contexts | ratio, nation, station |
| `vers` | 1.71x | 25 contexts | verse, rivers, lovers |
| `ment` | 1.73x | 24 contexts | cement, mentor, mental |
| `koch` | 1.68x | 18 contexts | kocha, kochù, koche |
| `sion` | 1.62x | 18 contexts | sioni, fusion, vision |
| `ence` | 1.80x | 11 contexts | hence, fence, science |
| `ctor` | 1.43x | 20 contexts | actor, factor, doctor |
| `iona` | 1.85x | 8 contexts | fiona, optional, regional |
| `nati` | 1.84x | 8 contexts | nation, native, natives |
| `stat` | 1.54x | 11 contexts | statí, state, stats |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-s` | 79 words | sars, statements |
| `-a` | `-e` | 68 words | anymore, alogbe |
| `-d` | `-s` | 54 words | disputes, distances |
| `-o` | `-e` | 46 words | omole, okene |
| `-a` | `-s` | 46 words | abs, assess |
| `-m` | `-s` | 45 words | months, mis |
| `-a` | `-a` | 43 words | azuka, akọla |
| `-a` | `-d` | 42 words | aggrieved, attended |
| `-o` | `-a` | 42 words | ovia, origa |
| `-s` | `-e` | 42 words | statue, shishipe |

### 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 |
|------|-----------------|------------|------|
| mediterranean | **`mediterran-e-an`** | 7.5 | `e` |
| conscience | **`co-n-science`** | 7.5 | `science` |
| contrasts | **`contra-s-ts`** | 7.5 | `s` |
| prehistory | **`pr-e-history`** | 7.5 | `history` |
| financially | **`financi-al-ly`** | 7.5 | `al` |
| economists | **`economi-s-ts`** | 7.5 | `s` |
| nationborno | **`nationbor-n-o`** | 7.5 | `n` |
| partially | **`parti-al-ly`** | 7.5 | `al` |
| roehampton | **`roehamp-t-on`** | 7.5 | `t` |
| proposals | **`propos-al-s`** | 7.5 | `al` |
| redesigned | **`re-design-ed`** | 6.0 | `design` |
| developers | **`develop-er-s`** | 6.0 | `develop` |
| depressed | **`de-press-ed`** | 6.0 | `press` |
| remembered | **`re-member-ed`** | 6.0 | `member` |
| prisoners | **`prison-er-s`** | 6.0 | `prison` |

### 6.6 Linguistic Interpretation

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.45x) |
| N-gram | **2-gram** | Lowest perplexity (343) |
| Markov | **Context-4** | Highest predictability (97.6%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-10 04:02:28*