---
language: tw
language_name: Twi
language_family: atlantic_kwa
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_kwa
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: 4.425
  - name: best_isotropy
    type: isotropy
    value: 0.8357
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Twi** 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** | 3.861x | 3.86 | 0.5089% | 401,034 |
| **16k** | 4.109x | 4.11 | 0.5416% | 376,877 |
| **32k** | 4.296x | 4.30 | 0.5662% | 360,463 |
| **64k** | 4.425x 🏆 | 4.43 | 0.5832% | 349,974 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `amanyɔsɛm Patriotic Party amanyɔfoɔ mmrahyɛbadwafoɔ mmrahyɛbadwafoɔ`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁amanyɔsɛm ▁patriotic ▁party ▁amanyɔfoɔ ▁mmrahyɛbadwafoɔ ▁mmrahyɛbadwafoɔ` | 6 |
| 16k | `▁amanyɔsɛm ▁patriotic ▁party ▁amanyɔfoɔ ▁mmrahyɛbadwafoɔ ▁mmrahyɛbadwafoɔ` | 6 |
| 32k | `▁amanyɔsɛm ▁patriotic ▁party ▁amanyɔfoɔ ▁mmrahyɛbadwafoɔ ▁mmrahyɛbadwafoɔ` | 6 |
| 64k | `▁amanyɔsɛm ▁patriotic ▁party ▁amanyɔfoɔ ▁mmrahyɛbadwafoɔ ▁mmrahyɛbadwafoɔ` | 6 |

**Sample 2:** `WhatsApp yɛ USA ɔsomafoɔ. Ɔbɔadeɛ yɛ Jan Koum. Nkyekyem:Tɛknɔlɔgyi Nkyekyem:Unit...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁w hat sa pp ▁yɛ ▁usa ▁ɔso mafoɔ . ▁ɔbɔ ... (+16 more)` | 26 |
| 16k | `▁what sa pp ▁yɛ ▁usa ▁ɔso mafoɔ . ▁ɔbɔ adeɛ ... (+15 more)` | 25 |
| 32k | `▁what sapp ▁yɛ ▁usa ▁ɔsomafoɔ . ▁ɔbɔadeɛ ▁yɛ ▁jan ▁koum ... (+8 more)` | 18 |
| 64k | `▁whatsapp ▁yɛ ▁usa ▁ɔsomafoɔ . ▁ɔbɔadeɛ ▁yɛ ▁jan ▁koum . ... (+7 more)` | 17 |

**Sample 3:** `Auch yε kurow kεseε a ɛwɔ France. Emu nipa dodoɔ yɛ 22 779 Nhwehwɛmu`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁au ch ▁y ε ▁kurow ▁k ε se ε ▁a ... (+15 more)` | 25 |
| 16k | `▁au ch ▁y ε ▁kurow ▁k ε se ε ▁a ... (+15 more)` | 25 |
| 32k | `▁au ch ▁y ε ▁kurow ▁k ε se ε ▁a ... (+15 more)` | 25 |
| 64k | `▁au ch ▁y ε ▁kurow ▁k ε se ε ▁a ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.425x compression
- **Lowest UNK Rate:** 8k with 0.5089% 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 | 10,942 | 13.42 | 45,509 | 17.3% | 41.2% |
| **2-gram** | Subword | 230 🏆 | 7.85 | 2,933 | 69.3% | 99.5% |
| **3-gram** | Word | 32,353 | 14.98 | 83,689 | 9.3% | 24.6% |
| **3-gram** | Subword | 1,755 | 10.78 | 24,366 | 31.4% | 76.6% |
| **4-gram** | Word | 71,214 | 16.12 | 146,613 | 6.4% | 17.1% |
| **4-gram** | Subword | 8,744 | 13.09 | 123,008 | 15.4% | 47.1% |
| **5-gram** | Word | 62,140 | 15.92 | 107,789 | 5.4% | 15.9% |
| **5-gram** | Subword | 28,460 | 14.80 | 301,331 | 8.9% | 30.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `no mu` | 12,900 |
| 2 | `mu no` | 9,987 |
| 3 | `a ɛwɔ` | 8,913 |
| 4 | `wɔ afe` | 8,365 |
| 5 | `a wɔde` | 7,967 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wɔ afe mu` | 3,608 |
| 2 | `a ɛtɔ so` | 3,285 |
| 3 | `mpem mmienu ne` | 2,561 |
| 4 | `afe mu no` | 1,998 |
| 5 | `a menyaa mmoa` | 1,931 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wɔ afe mu no` | 1,682 |
| 2 | `mfeɛ mpem mmienu ne` | 1,544 |
| 3 | `a menyaa mmoa firiiɛ` | 1,493 |
| 4 | `afe apem ahankron ne` | 1,173 |
| 5 | `da a ɛtɔ so` | 1,128 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wɔ mfeɛ mpem mmienu ne` | 956 |
| 2 | `wɔ afe apem ahankron ne` | 765 |
| 3 | `nsɛm a wɔde gyinaa so` | 762 |
| 4 | `mfeɛ mpem mmienu ne du` | 612 |
| 5 | `baabi a menyaa mmoa firiiɛ` | 537 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 436,865 |
| 2 | `_ a` | 388,412 |
| 3 | `_ n` | 346,156 |
| 4 | `e _` | 232,431 |
| 5 | `o _` | 213,784 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ w ɔ` | 138,156 |
| 2 | `_ a _` | 117,981 |
| 3 | `_ n o` | 101,188 |
| 4 | `n o _` | 85,044 |
| 5 | `w ɔ _` | 80,970 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n o _` | 78,636 |
| 2 | `_ w ɔ _` | 65,251 |
| 3 | `_ n e _` | 58,800 |
| 4 | `a _ w ɔ` | 54,457 |
| 5 | `_ m u _` | 44,086 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a _ w ɔ` | 30,622 |
| 2 | `_ w ɔ _ a` | 20,122 |
| 3 | `_ m u _ n` | 18,585 |
| 4 | `_ w ɔ n _` | 17,353 |
| 5 | `d w u m a` | 17,335 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 230
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~31% 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 | 0.9135 | 1.884 | 7.22 | 80,527 | 8.6% |
| **1** | Subword | 0.8772 | 1.837 | 6.99 | 1,034 | 12.3% |
| **2** | Word | 0.3470 | 1.272 | 2.04 | 580,828 | 65.3% |
| **2** | Subword | 0.9954 | 1.994 | 6.26 | 7,228 | 0.5% |
| **3** | Word | 0.1562 | 1.114 | 1.31 | 1,186,259 | 84.4% |
| **3** | Subword | 0.9008 | 1.867 | 4.46 | 45,241 | 9.9% |
| **4** | Word | 0.0666 🏆 | 1.047 | 1.11 | 1,558,096 | 93.3% |
| **4** | Subword | 0.6688 | 1.590 | 2.88 | 201,692 | 33.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a wɔtie no ma awarefoɔ ne nson ne bachelor abodin ahorow mu pii ɛbi nso yɛ`
2. `no mu onyaa abatow mpesua nom the pct in a wɔwɔ great barrier oxford sukuupɔn no`
3. `wɔ mmrahɛbɛdwa a ɔyɛ new patriotic party npp mmarahyɛbadwa a odi kan mpɔtam hɔ wɔ ghana`

**Context Size 2:**

1. `no mu n abrabɔ mu nsɛm parliamentary elections in ghana culture trip retrieved pierre p 55`
2. `mu no gmmb yɛɛ nsiesie bi wɔ ɔpo no ano ɛfiri afe kɔsi afe wɔ afe mu`
3. `a ɛwɔ saa nhwɛsoɔ yi kyerɛ ahoɔyɛa anibrɛ anaa sɛ wɔn mma ho no pii mu ntɛmntɛm`

**Context Size 3:**

1. `wɔ afe mu no afrika nneduafoɔ a wɔn dodoɔ no ara taa kyerɛkyerɛ adamfofa mu denam nneɛma te`
2. `a ɛtɔ so nsia a ɛwɔ republic a ɛtɔ so nnan mu firi 7 ɔbɛnem kɔsi 6 ɔbɛnem`
3. `mpem mmienu ne nwɔtwe abatoɔ mu no ɔde 170 000 mfiri a wɔde nsu a ɛyɛ nwini yiye`

**Context Size 4:**

1. `wɔ afe mu no bagua a ɛhwɛ hokwan a nnipa wɔ human rights hokwan a ɔwɔ sɛ onya nsu`
2. `mfeɛ mpem mmienu ne du mmienu ghana mmarahyɛbedwafoɔ abatoɔfm peace ghana election results sene east...`
3. `afe apem ahankron ne aduosia mu ɔsan toaa ne nnwomasua so wɔ kwame nkrumah suapɔn a ɛhwɛ nyansahu ne`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ma_aho,_ɛ_ɔ_ara`
2. `ahoupan_am_n_ba_`
3. `nkɔhu._ar,_mpifi`

**Context Size 2:**

1. `a_ako)_ni._wɔdeɛ_`
2. `_afoɔ_kɔɔmpii_wɔ_`
3. `_naa_new_adwumin_`

**Context Size 3:**

1. `_wɔn_so_a_ɛka_ghan`
2. `_a_no_din_dii_manf`
3. `_no_dii_wɔ_ghango.`

**Context Size 4:**

1. `_no_"barré_syndroid`
2. `_wɔ_ka_yɛ_adwin_kaa`
3. `_ne_efi_apueɛ_ghana`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (201,692 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 | 38,515 |
| Total Tokens | 1,980,760 |
| Mean Frequency | 51.43 |
| Median Frequency | 4 |
| Frequency Std Dev | 1064.86 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 122,548 |
| 2 | no | 98,025 |
| 3 | wɔ | 65,834 |
| 4 | mu | 60,900 |
| 5 | ne | 59,434 |
| 6 | na | 38,529 |
| 7 | sɛ | 32,430 |
| 8 | so | 28,669 |
| 9 | ho | 24,708 |
| 10 | yɛ | 18,806 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | abubakars | 2 |
| 2 | donation | 2 |
| 3 | failures | 2 |
| 4 | virgo | 2 |
| 5 | lynxxx | 2 |
| 6 | rover | 2 |
| 7 | jobberman | 2 |
| 8 | jcdf | 2 |
| 9 | celebritydi | 2 |
| 10 | aotearoa | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2329 |
| R² (Goodness of Fit) | 0.991137 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 48.4% |
| Top 1,000 | 76.1% |
| Top 5,000 | 90.5% |
| Top 10,000 | 94.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9911 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 48.4% of corpus
- **Long Tail:** 28,515 words needed for remaining 5.4% 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 | 0.8357 🏆 | 0.3535 | N/A | N/A |
| **mono_64d** | 64 | 0.8309 | 0.2722 | N/A | N/A |
| **mono_128d** | 128 | 0.7186 | 0.2172 | N/A | N/A |
| **aligned_32d** | 32 | 0.8357 | 0.3605 | 0.0600 | 0.2920 |
| **aligned_64d** | 64 | 0.8309 | 0.2691 | 0.1340 | 0.4460 |
| **aligned_128d** | 128 | 0.7186 | 0.2167 | 0.2060 | 0.5400 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8357 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2815. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 20.6% 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 | **-0.480** | 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` | aboaboa, akontaa, adanseɛ |
| `-s` | soa, sumiiɛ, stunning |
| `-m` | mmeamudua, mechatronics, miranda |
| `-n` | nandi, nitiwulnew, nhwewhɛmu |
| `-b` | bishop, botwe, batch |
| `-k` | kaipro, kɔkɔɔkɔ, kinship |
| `-w` | www, wikimedia, wɔsie |
| `-d` | dillard, dream, defassa |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | pirapirae, perspective, infobase |
| `-a` | aboaboa, akontaa, garcia |
| `-s` | thats, guns, cosmos |
| `-n` | ramon, wɔanyin, eyison |
| `-o` | hugo, kaipro, rosario |
| `-i` | nandi, yiyi, krakyi |
| `-oɔ` | ahoɔdoɔ, guanfoɔ, emufoɔ |
| `-ɔ` | kɔkɔɔkɔ, kabɔɔ, ahoɔdoɔ |

### 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` | 2.42x | 29 contexts | option, nation, motion |
| `atio` | 2.42x | 29 contexts | nation, ratios, station |
| `gyin` | 1.94x | 59 contexts | gyina, ɛgyina, egyina |
| `yina` | 1.79x | 83 contexts | gyina, nyina, nayina |
| `kyer` | 1.64x | 120 contexts | kyerɛ, kyerε, kyerɜ |
| `wuma` | 1.95x | 49 contexts | nwuma, dwuma, nnwuma |
| `afoɔ` | 1.96x | 41 contexts | wafoɔ, gafoɔ, kafoɔ |
| `dwum` | 2.03x | 32 contexts | adwum, dwuma, edwuma |
| `mant` | 2.07x | 27 contexts | mante, mantɛm, mantey |
| `bato` | 2.65x | 12 contexts | batoɔ, abato, abatoo |
| `mien` | 2.21x | 17 contexts | mienu, damien, miensa |
| `mmie` | 2.26x | 14 contexts | mmiesa, mmiemu, mmienu |

### 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` | 140 words | atese, adjaye |
| `-a` | `-a` | 121 words | abiεsa, akwaaba |
| `-a` | `-o` | 93 words | americafo, anwono |
| `-a` | `-ɔ` | 82 words | akontaabufoɔ, akunafoɔ |
| `-a` | `-oɔ` | 68 words | akontaabufoɔ, akunafoɔ |
| `-a` | `-n` | 67 words | ahenkron, akwan |
| `-w` | `-a` | 59 words | wɔakeka, wͻanya |
| `-n` | `-a` | 57 words | nungua, nevada |
| `-a` | `-m` | 56 words | atififam, asrafodɔm |
| `-s` | `-s` | 55 words | shares, soldiers |

### 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 |
|------|-----------------|------------|------|
| kpobiapem | **`kpobiap-e-m`** | 7.5 | `e` |
| endometriosis | **`endometrio-s-is`** | 7.5 | `s` |
| dentekrom | **`dentekr-o-m`** | 7.5 | `o` |
| laurajane | **`lauraj-an-e`** | 7.5 | `an` |
| mmarahyɛbedwaani | **`mmarahyɛbedwa-a-ni`** | 7.5 | `a` |
| internally | **`internal-l-y`** | 7.5 | `l` |
| ɔkyerɛwee | **`ɔkyerɛw-e-e`** | 7.5 | `e` |
| panafrican | **`p-an-african`** | 7.5 | `african` |
| institution | **`institut-i-on`** | 7.5 | `i` |
| wɔrekyerɛkyerɛ | **`wɔ-re-kyerɛkyerɛ`** | 7.5 | `kyerɛkyerɛ` |
| wɔrebɛhwehwɛ | **`wɔ-re-bɛhwehwɛ`** | 7.5 | `bɛhwehwɛ` |
| adwumayeni | **`adwumay-e-ni`** | 7.5 | `e` |
| paralympians | **`paralympi-an-s`** | 7.5 | `an` |
| wɔrentumi | **`wɔ-re-ntumi`** | 7.5 | `ntumi` |
| wɔrebisabisa | **`wɔ-re-bisabisa`** | 7.5 | `bisabisa` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Twi 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 (4.42x) |
| N-gram | **2-gram** | Lowest perplexity (230) |
| Markov | **Context-4** | Highest predictability (93.3%) |
| 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: 2026-01-11 02:01:25*