---
language: gpe
language_name: Ghanaian Pidgin English
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: 4.789
  - name: best_isotropy
    type: isotropy
    value: 0.8645
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-09
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ghanaian Pidgin English** 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** | 4.124x | 4.13 | 0.1031% | 720,937 |
| **16k** | 4.434x | 4.44 | 0.1108% | 670,476 |
| **32k** | 4.661x | 4.66 | 0.1165% | 637,864 |
| **64k** | 4.789x 🏆 | 4.79 | 0.1197% | 620,843 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Institutions Abourso CHPs References insyd Ghana insyd Eastern Region (Ghana) pl...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁institutions ▁ab ours o ▁ch ps ▁references ▁insyd ▁ghana ▁insyd ... (+13 more)` | 23 |
| 16k | `▁institutions ▁ab ours o ▁chps ▁references ▁insyd ▁ghana ▁insyd ▁eastern ... (+12 more)` | 22 |
| 32k | `▁institutions ▁ab ours o ▁chps ▁references ▁insyd ▁ghana ▁insyd ▁eastern ... (+12 more)` | 22 |
| 64k | `▁institutions ▁ab ours o ▁chps ▁references ▁insyd ▁ghana ▁insyd ▁eastern ... (+12 more)` | 22 |

**Sample 2:** `References newspapers media insyd Ghana publish insyd Ghana publish insyd Africa`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁references ▁newspapers ▁media ▁insyd ▁ghana ▁publish ▁insyd ▁ghana ▁publish ▁insyd ... (+1 more)` | 11 |
| 16k | `▁references ▁newspapers ▁media ▁insyd ▁ghana ▁publish ▁insyd ▁ghana ▁publish ▁insyd ... (+1 more)` | 11 |
| 32k | `▁references ▁newspapers ▁media ▁insyd ▁ghana ▁publish ▁insyd ▁ghana ▁publish ▁insyd ... (+1 more)` | 11 |
| 64k | `▁references ▁newspapers ▁media ▁insyd ▁ghana ▁publish ▁insyd ▁ghana ▁publish ▁insyd ... (+1 more)` | 11 |

**Sample 3:** `References insyd Ghana insyd Ashanti Region places for Ashanti Region insyd`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁references ▁insyd ▁ghana ▁insyd ▁ashanti ▁region ▁places ▁for ▁ashanti ▁region ... (+1 more)` | 11 |
| 16k | `▁references ▁insyd ▁ghana ▁insyd ▁ashanti ▁region ▁places ▁for ▁ashanti ▁region ... (+1 more)` | 11 |
| 32k | `▁references ▁insyd ▁ghana ▁insyd ▁ashanti ▁region ▁places ▁for ▁ashanti ▁region ... (+1 more)` | 11 |
| 64k | `▁references ▁insyd ▁ghana ▁insyd ▁ashanti ▁region ▁places ▁for ▁ashanti ▁region ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 64k achieves 4.789x compression
- **Lowest UNK Rate:** 8k with 0.1031% 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 | 21,240 | 14.37 | 78,160 | 14.3% | 31.9% |
| **2-gram** | Subword | 267 🏆 | 8.06 | 3,973 | 67.1% | 99.4% |
| **3-gram** | Word | 53,111 | 15.70 | 117,024 | 7.0% | 18.8% |
| **3-gram** | Subword | 2,195 | 11.10 | 30,848 | 25.8% | 72.0% |
| **4-gram** | Word | 94,293 | 16.52 | 171,368 | 5.3% | 13.6% |
| **4-gram** | Subword | 11,353 | 13.47 | 164,542 | 14.5% | 40.0% |
| **5-gram** | Word | 63,802 | 15.96 | 106,259 | 5.8% | 14.6% |
| **5-gram** | Subword | 38,013 | 15.21 | 434,778 | 9.2% | 27.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `of de` | 20,308 |
| 2 | `for de` | 13,045 |
| 3 | `insyd de` | 12,862 |
| 4 | `wey dey` | 10,251 |
| 5 | `na dem` | 7,893 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `from the original` | 4,522 |
| 2 | `archived from the` | 4,424 |
| 3 | `the original on` | 4,295 |
| 4 | `de university of` | 1,482 |
| 5 | `references external links` | 1,398 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `archived from the original` | 4,424 |
| 2 | `from the original on` | 4,295 |
| 3 | `at the wayback machine` | 842 |
| 4 | `of de national assembly` | 704 |
| 5 | `be one of de` | 605 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `archived from the original on` | 4,199 |
| 2 | `national assembly of south africa` | 578 |
| 3 | `de national assembly of south` | 560 |
| 4 | `of de national assembly of` | 550 |
| 5 | `from the original on retrieved` | 523 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 512,209 |
| 2 | `_ d` | 373,324 |
| 3 | `d e` | 362,084 |
| 4 | `i n` | 287,429 |
| 5 | `n _` | 274,000 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 304,465 |
| 2 | `d e _` | 147,839 |
| 3 | `_ i n` | 103,335 |
| 4 | `_ o f` | 102,797 |
| 5 | `o f _` | 98,533 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 134,879 |
| 2 | `_ o f _` | 96,992 |
| 3 | `_ f o r` | 70,879 |
| 4 | `t i o n` | 67,685 |
| 5 | `_ i n s` | 65,269 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ f o r _` | 62,539 |
| 2 | `i n s y d` | 58,915 |
| 3 | `_ i n s y` | 58,082 |
| 4 | `n s y d _` | 53,327 |
| 5 | `_ d e n _` | 48,301 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 267
- **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 | 1.0024 | 2.003 | 9.14 | 112,922 | 0.0% |
| **1** | Subword | 0.8797 | 1.840 | 6.38 | 1,680 | 12.0% |
| **2** | Word | 0.3635 | 1.287 | 2.00 | 1,031,914 | 63.6% |
| **2** | Subword | 0.9207 | 1.893 | 5.68 | 10,718 | 7.9% |
| **3** | Word | 0.1363 | 1.099 | 1.26 | 2,064,281 | 86.4% |
| **3** | Subword | 0.8539 | 1.807 | 4.49 | 60,872 | 14.6% |
| **4** | Word | 0.0524 🏆 | 1.037 | 1.08 | 2,589,043 | 94.8% |
| **4** | Subword | 0.6904 | 1.614 | 3.06 | 273,196 | 31.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de grand slams for ein birth before he finally establish dis celebration of dakar get one`
2. `of science for di original on retrieved 13 may 7 6 10 of health science report`
3. `for de quarterfinals wer na she participate insyd a quarrel between tropical wey don decide am`

**Context Size 2:**

1. `of de prayer hall give students de degree of specialization wey range from 56 for de total`
2. `for de standard entry times oqt oct paris swimming info world aquatics championshipsfukuoka july mol...`
3. `insyd de centuries na dem enact by ordering all of ein permanent campus na de average millennial`

**Context Size 3:**

1. `from the original on 27 june on top convention peoples party c p p plus some other arab`
2. `archived from the original on 13 march retrieved 7 march insyd de ghana premier league club al hilal`
3. `the original on 29 september de electoral authority come talk say de cave be de original owners as`

**Context Size 4:**

1. `archived from the original on 3 january retrieved 17 may references of education winneba institution...`
2. `from the original on 11 july retrieved 31 july early life den education dem born pravin gordhan on 1...`
3. `at the wayback machine cricketarchive retrieved 2 january elizabeth tracing the journey the vice cha...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_om_oon_o-orof_d`
2. `es_a_fangaplmala`
3. `al,_3_wirintmptt`

**Context Size 2:**

1. `e_nes_ber's_beent`
2. `_distrycle_fish_a`
3. `dento_di_clu_bas_`

**Context Size 3:**

1. `_dey_dey_for_65._e`
2. `de_politadiye,_buf`
3. `_infor_de_greem),_`

**Context Size 4:**

1. `_de_wale,_municipal`
2. `_of_convictories_di`
3. `_for_south_dis_gran`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (273,196 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 | 53,888 |
| Total Tokens | 3,007,969 |
| Mean Frequency | 55.82 |
| Median Frequency | 4 |
| Frequency Std Dev | 1006.84 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 136,329 |
| 2 | of | 97,116 |
| 3 | for | 62,865 |
| 4 | insyd | 58,595 |
| 5 | den | 48,591 |
| 6 | dem | 45,328 |
| 7 | wey | 45,073 |
| 8 | dey | 39,231 |
| 9 | be | 34,093 |
| 10 | ein | 30,298 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | tɔra | 2 |
| 2 | ntebe | 2 |
| 3 | principia | 2 |
| 4 | malingering | 2 |
| 5 | fdis | 2 |
| 6 | catlett | 2 |
| 7 | modif | 2 |
| 8 | outbursts | 2 |
| 9 | impulse | 2 |
| 10 | excoriation | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1693 |
| R² (Goodness of Fit) | 0.988970 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.6% |
| Top 1,000 | 69.9% |
| Top 5,000 | 87.3% |
| Top 10,000 | 92.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9890 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.6% of corpus
- **Long Tail:** 43,888 words needed for remaining 7.4% 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 | 0.8634 | 0.3326 | N/A | N/A |
| **mono_64d** | 64 | 0.8645 | 0.2673 | N/A | N/A |
| **mono_128d** | 128 | 0.8465 | 0.1986 | N/A | N/A |
| **aligned_32d** | 32 | 0.8634 | 0.3488 | 0.2620 | 0.6480 |
| **aligned_64d** | 64 | 0.8645 🏆 | 0.2624 | 0.4380 | 0.8040 |
| **aligned_128d** | 128 | 0.8465 | 0.1961 | 0.5700 | 0.8700 |

### Key Findings

- **Best Isotropy:** aligned_64d with 0.8645 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2677. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 57.0% 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 | **-0.460** | 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 |
|--------|----------|
| `-co` | commendations, consumption, corona |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | étoiles, ibs, seriesjenifas |
| `-es` | étoiles, cinématographiques, bapes |
| `-ng` | offsetting, subverting, visiting |
| `-on` | koomson, rodinson, consumption |
| `-ed` | administered, categorized, overcrowded |
| `-ing` | offsetting, subverting, visiting |
| `-er` | mulder, turnover, longer |

### 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 |
|------|----------|------------------|----------|
| `nter` | 1.66x | 48 contexts | unter, inter, enter |
| `atio` | 1.56x | 49 contexts | natio, ratio, ratios |
| `tion` | 1.44x | 64 contexts | option, lation, notion |
| `ment` | 1.51x | 46 contexts | mente, lament, moment |
| `ican` | 1.96x | 17 contexts | rican, vatican, pelican |
| `ence` | 1.70x | 27 contexts | pence, fence, hence |
| `iver` | 1.52x | 35 contexts | hiver, giver, river |
| `mber` | 1.74x | 21 contexts | mberi, amber, member |
| `ersi` | 1.78x | 19 contexts | persia, versity, version |
| `embe` | 1.80x | 18 contexts | embed, lembe, kpembe |
| `ieve` | 1.83x | 14 contexts | nieve, thieves, achieve |
| `nive` | 2.19x | 8 contexts | niven, nivera, univen |

### 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 |
|--------|--------|-----------|----------|
| `-co` | `-s` | 39 words | contributes, conservations |
| `-co` | `-on` | 16 words | contraception, constitution |
| `-co` | `-ed` | 13 words | committed, commanded |
| `-co` | `-ng` | 10 words | counselling, connecting |
| `-co` | `-ing` | 9 words | counselling, connecting |
| `-co` | `-es` | 8 words | contributes, comprises |
| `-co` | `-er` | 5 words | contender, colder |

### 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 |
|------|-----------------|------------|------|
| descended | **`descend-ed`** | 4.5 | `descend` |
| assaulted | **`assault-ed`** | 4.5 | `assault` |
| requested | **`request-ed`** | 4.5 | `request` |
| approaching | **`approach-ing`** | 4.5 | `approach` |
| universes | **`univers-es`** | 4.5 | `univers` |
| distracted | **`distract-ed`** | 4.5 | `distract` |
| encompasses | **`encompass-es`** | 4.5 | `encompass` |
| choreographed | **`choreograph-ed`** | 4.5 | `choreograph` |
| fermented | **`ferment-ed`** | 4.5 | `ferment` |
| reprinted | **`reprint-ed`** | 4.5 | `reprint` |
| abstained | **`abstain-ed`** | 4.5 | `abstain` |
| transformed | **`transform-ed`** | 4.5 | `transform` |
| mistresses | **`mistress-es`** | 4.5 | `mistress` |
| reporting | **`report-ing`** | 4.5 | `report` |
| entertainer | **`entertain-er`** | 4.5 | `entertain` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ghanaian Pidgin English 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 (4.79x) |
| N-gram | **2-gram** | Lowest perplexity (267) |
| Markov | **Context-4** | Highest predictability (94.8%) |
| 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: 2026-01-09 23:55:27*