README.md

---
language: pcm
language_name: Nigerian Pidgin
language_family: germanic_west_anglofrisian
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-germanic_west_anglofrisian
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: 4.488
  - name: best_isotropy
    type: isotropy
    value: 0.6433
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Nigerian Pidgin - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Nigerian Pidgin** 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** | 3.887x | 3.89 | 0.0679% | 407,967 |
| **16k** | 4.155x | 4.16 | 0.0726% | 381,687 |
| **32k** | 4.347x | 4.35 | 0.0759% | 364,797 |
| **64k** | 4.488x 🏆 | 4.49 | 0.0784% | 353,400 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ikot Ibok na dey Nigerian village in the Etinan local government area of Akwa Ib...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ikot ▁ib ok ▁na ▁dey ▁nigerian ▁village ▁in ▁the ▁etinan ... (+8 more)` | 18 |
| 16k | `▁ikot ▁ib ok ▁na ▁dey ▁nigerian ▁village ▁in ▁the ▁etinan ... (+8 more)` | 18 |
| 32k | `▁ikot ▁ib ok ▁na ▁dey ▁nigerian ▁village ▁in ▁the ▁etinan ... (+8 more)` | 18 |
| 64k | `▁ikot ▁ibok ▁na ▁dey ▁nigerian ▁village ▁in ▁the ▁etinan ▁local ... (+7 more)` | 17 |

**Sample 2:** `Jigawa State na one of di 36 state for Naija. Di governor of di state na Badaru ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁j iga wa ▁state ▁na ▁one ▁of ▁di ▁ 3 ... (+20 more)` | 30 |
| 16k | `▁jigawa ▁state ▁na ▁one ▁of ▁di ▁ 3 6 ▁state ... (+17 more)` | 27 |
| 32k | `▁jigawa ▁state ▁na ▁one ▁of ▁di ▁ 3 6 ▁state ... (+16 more)` | 26 |
| 64k | `▁jigawa ▁state ▁na ▁one ▁of ▁di ▁ 3 6 ▁state ... (+16 more)` | 26 |

**Sample 3:** `Greensleeves na kultural song of som pipul in Ingland. Di song "What Child is th...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gre ens le ev es ▁na ▁kult ural ▁song ▁of ... (+32 more)` | 42 |
| 16k | `▁gre ens le eves ▁na ▁kult ural ▁song ▁of ▁som ... (+30 more)` | 40 |
| 32k | `▁greensleeves ▁na ▁kultural ▁song ▁of ▁som ▁pipul ▁in ▁ingland . ... (+22 more)` | 32 |
| 64k | `▁greensleeves ▁na ▁kultural ▁song ▁of ▁som ▁pipul ▁in ▁ingland . ... (+21 more)` | 31 |


### Key Findings

- **Best Compression:** 64k achieves 4.488x compression
- **Lowest UNK Rate:** 8k with 0.0679% unknown tokens
- **Trade-off:** Larger vocabularies improve compression but increase model size
- **Recommendation:** 32k vocabulary provides optimal balance for production use

---
## 2. N-gram Model Evaluation

![N-gram Perplexity](visualizations/ngram_perplexity.png)

![N-gram Unique](visualizations/ngram_unique.png)

![N-gram Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|---------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | Word | 5,069 | 12.31 | 13,342 | 20.2% | 49.4% |
| **2-gram** | Subword | 249 🏆 | 7.96 | 1,956 | 69.0% | 99.6% |
| **3-gram** | Word | 9,350 | 13.19 | 16,820 | 12.8% | 34.7% |
| **3-gram** | Subword | 2,025 | 10.98 | 14,262 | 26.7% | 73.0% |
| **4-gram** | Word | 14,669 | 13.84 | 22,527 | 10.2% | 25.9% |
| **4-gram** | Subword | 10,389 | 13.34 | 66,396 | 14.2% | 40.4% |
| **5-gram** | Word | 8,268 | 13.01 | 11,704 | 12.1% | 31.0% |
| **5-gram** | Subword | 32,215 | 14.98 | 156,798 | 8.7% | 27.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wey dey` | 2,591 |
| 2 | `for di` | 2,440 |
| 3 | `of di` | 2,155 |
| 4 | `wey dem` | 1,785 |
| 5 | `dem bon` | 1,401 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dem bon am` | 620 |
| 2 | `how e tek` | 619 |
| 3 | `wey dem dey` | 420 |
| 4 | `wey dem bon` | 382 |
| 5 | `bon am for` | 369 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dem bon am for` | 356 |
| 2 | `dem gada di tori` | 337 |
| 3 | `wey dem bon for` | 337 |
| 4 | `e tek stat life` | 241 |
| 5 | `how e tek stat` | 219 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wie dem gada di tori` | 193 |
| 2 | `how e tek stat life` | 179 |
| 3 | `wia dem gada di tori` | 139 |
| 4 | `e tek stat life an` | 108 |
| 5 | `di tori abaut pipul life` | 80 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d` | 59,136 |
| 2 | `n _` | 51,333 |
| 3 | `e _` | 50,359 |
| 4 | `_ a` | 49,736 |
| 5 | `i _` | 45,649 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e y _` | 29,288 |
| 2 | `_ d e` | 23,834 |
| 3 | `_ d i` | 23,563 |
| 4 | `_ f o` | 23,098 |
| 5 | `o r _` | 23,038 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `f o r _` | 19,631 |
| 2 | `_ f o r` | 19,386 |
| 3 | `_ d i _` | 18,549 |
| 4 | `w e y _` | 13,808 |
| 5 | `_ w e y` | 13,590 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ f o r _` | 18,549 |
| 2 | `_ w e y _` | 13,534 |
| 3 | `_ d e y _` | 12,165 |
| 4 | `_ d e m _` | 7,432 |
| 5 | `w e y _ d` | 5,568 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 249
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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 | 0.9199 | 1.892 | 6.12 | 38,924 | 8.0% |
| **1** | Subword | 1.3238 | 2.503 | 11.10 | 395 | 0.0% |
| **2** | Word | 0.3059 | 1.236 | 1.74 | 237,554 | 69.4% |
| **2** | Subword | 1.0876 | 2.125 | 6.38 | 4,381 | 0.0% |
| **3** | Word | 0.1110 | 1.080 | 1.18 | 411,842 | 88.9% |
| **3** | Subword | 0.8589 | 1.814 | 4.11 | 27,929 | 14.1% |
| **4** | Word | 0.0379 🏆 | 1.027 | 1.05 | 486,600 | 96.2% |
| **4** | Subword | 0.6482 | 1.567 | 2.73 | 114,736 | 35.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `di buk i rich an som of oxford gardens na one wuman too how e for`
2. `for na november na im hav bin liv air lahore an octave one wey bi boy`
3. `wey lead and university of empires for folkmuzik of lanzarote on 8 goals in naijá for`

**Context Size 2:**

1. `wey dey stodi difren difren instrument wey dem dey uze to tek mek buk wey shi dey`
2. `for di american folklore center`
3. `of di futbol klub wey di nem na tørris toresen dey bon am for e honor dem`

**Context Size 3:**

1. `dem bon am on 19 august na pesin wey no get promoshon sins david mark tel dem sey`
2. `how e tek do fashon pared ukah fest stat fashon pared in wen e be 18 years for`
3. `wey dem dey also call argungu dance festival na one festival inside kebbi state plus including oda n...`

**Context Size 4:**

1. `dem bon am for e bi naijá singa olamide david e bi naijá man pikin akto olamide faison dem`
2. `wey dem bon for for naija`
3. `dem gada di tori pipul wuman wey dem bon for wey kpai for pipul politishan abaut pipul life`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_bey_l_s,_m_wene`
2. `e_deman_pelisoma`
3. `anetatbofar_pllf`

**Context Size 2:**

1. `_didon,_an_an_bik`
2. `n_em_ti_pai_dem_h`
3. `e_bon,_p.shan_shi`

**Context Size 3:**

1. `ey_sout._na_engin_`
2. `_dey_oyo_e_kar_for`
3. `_dis_for_unival_an`

**Context Size 4:**

1. `for_babatunder-17_c`
2. `_for_dey_rili_la_li`
3. `_di_aablanker_di_pe`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (114,736 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 | 18,108 |
| Total Tokens | 520,860 |
| Mean Frequency | 28.76 |
| Median Frequency | 4 |
| Frequency Std Dev | 327.08 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | di | 18,819 |
| 2 | for | 18,818 |
| 3 | wey | 13,794 |
| 4 | dey | 12,381 |
| 5 | of | 12,090 |
| 6 | e | 11,367 |
| 7 | an | 9,408 |
| 8 | na | 9,331 |
| 9 | dem | 8,867 |
| 10 | to | 5,138 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | fir | 2 |
| 2 | feirense | 2 |
| 3 | invention | 2 |
| 4 | ahl | 2 |
| 5 | sunnah | 2 |
| 6 | broader | 2 |
| 7 | asg | 2 |
| 8 | sogato | 2 |
| 9 | strategies | 2 |
| 10 | kompinies | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1589 |
| R² (Goodness of Fit) | 0.993730 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.4% |
| Top 1,000 | 75.8% |
| Top 5,000 | 91.4% |
| Top 10,000 | 96.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9937 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.4% of corpus
- **Long Tail:** 8,108 words needed for remaining 3.6% 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 | 0.6433 🏆 | 0.4025 | N/A | N/A |
| **mono_64d** | 64 | 0.3018 | 0.3833 | N/A | N/A |
| **mono_128d** | 128 | 0.0480 | 0.3642 | N/A | N/A |
| **aligned_32d** | 32 | 0.6433 | 0.3875 | 0.0600 | 0.3120 |
| **aligned_64d** | 64 | 0.3018 | 0.3929 | 0.0980 | 0.3220 |
| **aligned_128d** | 128 | 0.0480 | 0.3729 | 0.0980 | 0.3400 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6433 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3839. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 9.8% 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 | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.149** | 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` | anorda, achievement, adura |
| `-s` | spanner, seen, system |
| `-o` | ospital, oloore, odg |
| `-b` | biginin, bitwin, belfast |
| `-m` | mcgill, meenin, memba |
| `-e` | exploits, emeritus, eku |
| `-k` | kanye, kontris, komunitis |
| `-t` | tsm, tottenham, tool |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | rhymes, kontris, komunitis |
| `-n` | patan, meenin, investigation |
| `-e` | raise, kanye, oloore |
| `-a` | memba, grandma, anorda |
| `-on` | investigation, madison, lexikon |
| `-t` | profit, pct, belfast |
| `-i` | gidi, jaji, olusi |
| `-y` | galaxy, newly, fidelity |

### 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 |
|------|----------|------------------|----------|
| `ight` | 1.65x | 34 contexts | eight, light, night |
| `ther` | 1.71x | 28 contexts | there, other, rather |
| `tion` | 1.63x | 26 contexts | motion, option, action |
| `ment` | 1.47x | 31 contexts | mento, menta, mental |
| `atio` | 1.71x | 17 contexts | ratio, nation, nations |
| `esho` | 1.57x | 21 contexts | mesho, naesho, neshon |
| `kont` | 1.55x | 19 contexts | kontat, kontan, kontro |
| `isho` | 1.37x | 26 contexts | pisho, bishop, pishon |
| `liti` | 1.64x | 14 contexts | realiti, politis, abiliti |
| `nter` | 1.52x | 17 contexts | enter, inter, hunter |
| `ress` | 1.52x | 16 contexts | press, aress, tress |
| `asho` | 1.51x | 16 contexts | ashok, vashon, ashoka |

### 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` | 72 words | ajiwere, alive |
| `-s` | `-s` | 65 words | scelles, somtimes |
| `-p` | `-s` | 61 words | patterns, plaets |
| `-a` | `-s` | 52 words | aktivis, aleros |
| `-a` | `-a` | 52 words | anorda, ahoada |
| `-k` | `-n` | 45 words | kitchen, kabon |
| `-s` | `-e` | 45 words | spotlite, shake |
| `-a` | `-n` | 44 words | akan, alabukun |
| `-o` | `-e` | 42 words | ogbe, okezie |
| `-a` | `-i` | 41 words | abdullahi, alli |

### 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 |
|------|-----------------|------------|------|
| panafrican | **`pa-n-african`** | 7.5 | `african` |
| peaceland | **`peace-la-nd`** | 7.5 | `la` |
| aristotle | **`aristo-t-le`** | 7.5 | `t` |
| orijinali | **`orijin-al-i`** | 7.5 | `al` |
| friesland | **`fries-la-nd`** | 7.5 | `la` |
| seventeen | **`sevente-e-n`** | 7.5 | `e` |
| producing | **`produc-i-ng`** | 7.5 | `i` |
| williamson | **`william-s-on`** | 7.5 | `s` |
| bestseller | **`be-st-seller`** | 7.5 | `seller` |
| musicians | **`music-ia-ns`** | 6.0 | `music` |
| yunivasiti | **`yunivasit-i`** | 4.5 | `yunivasit` |
| activists | **`activist-s`** | 4.5 | `activist` |
| chartered | **`charter-ed`** | 4.5 | `charter` |
| celebrities | **`celebriti-es`** | 4.5 | `celebriti` |
| festivals | **`festival-s`** | 4.5 | `festival` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Nigerian Pidgin 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 (4.49x) |
| N-gram | **2-gram** | Lowest perplexity (249) |
| Markov | **Context-4** | Highest predictability (96.2%) |
| 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 17:35:04*