README.md

---
language: fat
language_name: Fanti
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: 4.360
  - name: best_isotropy
    type: isotropy
    value: 0.8158
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Fanti** 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** | 3.878x | 3.88 | 0.0773% | 470,672 |
| **16k** | 4.117x | 4.12 | 0.0821% | 443,393 |
| **32k** | 4.264x | 4.27 | 0.0850% | 428,052 |
| **64k** | 4.360x 🏆 | 4.36 | 0.0870% | 418,619 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Bishop Herman Nsɔwdo Skuul, a wɔsan frɛ no BIHECO yɛ mbanyin skuul a ɔwɔ Kpando ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁bishop ▁her man ▁nsɔwdo ▁skuul , ▁a ▁wɔsan ▁frɛ ▁no ... (+23 more)` | 33 |
| 16k | `▁bishop ▁herman ▁nsɔwdo ▁skuul , ▁a ▁wɔsan ▁frɛ ▁no ▁bi ... (+22 more)` | 32 |
| 32k | `▁bishop ▁herman ▁nsɔwdo ▁skuul , ▁a ▁wɔsan ▁frɛ ▁no ▁bi ... (+22 more)` | 32 |
| 64k | `▁bishop ▁herman ▁nsɔwdo ▁skuul , ▁a ▁wɔsan ▁frɛ ▁no ▁biheco ... (+20 more)` | 30 |

**Sample 2:** `St. Monica's Senior High School yɛ mbasiafo nsɔwdo skuul a ɔwɔ Mampong wɔ Esuant...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁st . ▁monica ' s ▁senior ▁high ▁school ▁yɛ ▁mbasiafo ... (+12 more)` | 22 |
| 16k | `▁st . ▁monica ' s ▁senior ▁high ▁school ▁yɛ ▁mbasiafo ... (+12 more)` | 22 |
| 32k | `▁st . ▁monica ' s ▁senior ▁high ▁school ▁yɛ ▁mbasiafo ... (+12 more)` | 22 |
| 64k | `▁st . ▁monica ' s ▁senior ▁high ▁school ▁yɛ ▁mbasiafo ... (+12 more)` | 22 |

**Sample 3:** `Sherry Ayittey (wɔwoo no yɛ Ghananyi biochemist, amanyɛnyi na mbasiafo ntamgyina...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sh er ry ▁ayi t tey ▁( wɔwoo ▁no ▁yɛ ... (+12 more)` | 22 |
| 16k | `▁sh er ry ▁ayi t tey ▁( wɔwoo ▁no ▁yɛ ... (+10 more)` | 20 |
| 32k | `▁sherry ▁ayittey ▁( wɔwoo ▁no ▁yɛ ▁ghananyi ▁biochemist , ▁amanyɛnyi ... (+4 more)` | 14 |
| 64k | `▁sherry ▁ayittey ▁( wɔwoo ▁no ▁yɛ ▁ghananyi ▁biochemist , ▁amanyɛnyi ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 64k achieves 4.360x compression
- **Lowest UNK Rate:** 8k with 0.0773% 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 | 4,526 | 12.14 | 15,127 | 23.6% | 52.6% |
| **2-gram** | Subword | 248 🏆 | 7.95 | 1,938 | 67.4% | 99.6% |
| **3-gram** | Word | 9,962 | 13.28 | 23,467 | 14.2% | 38.0% |
| **3-gram** | Subword | 1,776 | 10.79 | 15,671 | 30.6% | 75.8% |
| **4-gram** | Word | 18,783 | 14.20 | 36,546 | 9.7% | 28.4% |
| **4-gram** | Subword | 7,938 | 12.95 | 70,574 | 17.1% | 48.4% |
| **5-gram** | Word | 15,862 | 13.95 | 25,853 | 8.7% | 27.5% |
| **5-gram** | Subword | 21,806 | 14.41 | 152,670 | 11.1% | 34.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `no mu` | 5,071 |
| 2 | `mu wɔ` | 3,646 |
| 3 | `a ɔwɔ` | 3,608 |
| 4 | `wɔ afe` | 3,273 |
| 5 | `mu no` | 3,153 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wɔ afe mu` | 1,655 |
| 2 | `a ɔtɔ do` | 1,549 |
| 3 | `mu wɔ ghana` | 1,277 |
| 4 | `mantɔw mu wɔ` | 1,012 |
| 5 | `afe mu no` | 926 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mantɔw mu wɔ ghana` | 820 |
| 2 | `a ɔtɔ do anan` | 604 |
| 3 | `wɔ afe mu no` | 460 |
| 4 | `mbrahyɛbagua a ɔtɔ do` | 370 |
| 5 | `a ogyina hɔ ma` | 356 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wɔ mbrahyɛbagua a ɔtɔ do` | 207 |
| 2 | `a ɔtɔ do anan 4` | 169 |
| 3 | `a ɔtɔ do anan no` | 167 |
| 4 | `a ɔtɔ do anan mu` | 155 |
| 5 | `ghana amansan abatow no mu` | 151 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 136,241 |
| 2 | `_ a` | 102,913 |
| 3 | `_ n` | 97,571 |
| 4 | `a n` | 64,359 |
| 5 | `o _` | 62,300 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ w ɔ` | 39,784 |
| 2 | `_ a _` | 32,667 |
| 3 | `n a _` | 32,487 |
| 4 | `w ɔ _` | 31,620 |
| 5 | `_ n o` | 30,963 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ w ɔ _` | 26,115 |
| 2 | `_ n o _` | 24,203 |
| 3 | `_ n a _` | 18,686 |
| 4 | `_ m u _` | 15,392 |
| 5 | `_ a _ ɔ` | 13,463 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `g h a n a` | 9,543 |
| 2 | `_ g h a n` | 9,134 |
| 3 | `_ w ɔ _ a` | 6,691 |
| 4 | `_ a _ w ɔ` | 6,509 |
| 5 | `h a n a _` | 6,384 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 248
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.8862 | 1.848 | 5.88 | 39,173 | 11.4% |
| **1** | Subword | 0.9055 | 1.873 | 6.35 | 857 | 9.5% |
| **2** | Word | 0.3085 | 1.238 | 1.80 | 229,817 | 69.1% |
| **2** | Subword | 0.9056 | 1.873 | 5.56 | 5,435 | 9.4% |
| **3** | Word | 0.1281 | 1.093 | 1.24 | 411,747 | 87.2% |
| **3** | Subword | 0.8400 | 1.790 | 3.99 | 30,194 | 16.0% |
| **4** | Word | 0.0556 🏆 | 1.039 | 1.09 | 508,226 | 94.4% |
| **4** | Subword | 0.6158 | 1.532 | 2.58 | 120,416 | 38.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a no ono na ɔyɛ hausa kooko ahorow efi etsifi mantɔwmu grace omaboe maame nna ɔko`
2. `no odzii nyia ɔnye dwodze a na ɔka ho esian wɔ hɔ na ebien nsɔwdo skuul`
3. `wɔ ɔberɛfɛw mu maa fomena mpasuar wɔ ablekuma west african bush and entrepreneur citation needed wɔk...`

**Context Size 2:**

1. `no mu a netflix kyerɛwtohɔ no mu no bosoom sanda mu wɔ sunyani polytechnic ɔsanso wɔ mba`
2. `mu wɔ ghana mbrahyɛbagua ambato mu no wɔpaaw no dɛ house prefect wɔ pickard parker house wɔ`
3. `a ɔwɔ mpɔtamu hɔ nye pan african forum pan african mbrahyɛbagua no munyi a ɔgyina hɔ ma`

**Context Size 3:**

1. `wɔ afe mu edwuma namoale yɛ kuadwuma ho ɔbenfo agronomist wɔ n edwuma mu lawyer by profession amanyɛ...`
2. `a ɔtɔ do anan no mbrahyɛbagua a ɔdzi kan a ɔdzii amanyɛsɛm kuw kɛse bi enyim wɔ ghana`
3. `mu wɔ ghana onyaa ne bachelor of education abɔdzin krataa wɔ ghana institute of journalism na ɔbɔɔ n`

**Context Size 4:**

1. `mantɔw mu wɔ ghana wɔ mbrahyɛbagua a ɔtɔ do akrɔn a ɔwɔ fourth republic no mu wɔ ghana dze`
2. `a ɔtɔ do anan 4ɔ no mbrahyɛ bagua a ɔtɔ do enum 5 wɔ ghana amansin a ɔtɔ do`
3. `wɔ afe mu no skuul no hyɛase dze hɔn ho hyɛɛ nkɔmbɔdzi na ɔyɛkyerɛ a mu ahyɛse no nhyiamu`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ahyesak._ɔyinit`
2. `ana_ɔro_ɔ_muer_f`
3. `no_a_poonarafamu`

**Context Size 2:**

1. `a_nyimadzii_yɛ_fo`
2. `_abagen_yɔsoseens`
3. `_nna_oso_antakyɛb`

**Context Size 3:**

1. `_wɔyɛ_gholicturany`
2. `_a_ɔkyekunyi_nyim_`
3. `na_ma_yi_no_no_mum`

**Context Size 4:**

1. `_wɔ_sempɔnhen_ho_ɔs`
2. `_no_so_boayikuw_no_`
3. `_na_ɔyɛ_ato_no_ekyi`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (120,416 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 | 18,588 |
| Total Tokens | 611,715 |
| Mean Frequency | 32.91 |
| Median Frequency | 4 |
| Frequency Std Dev | 474.47 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 33,761 |
| 2 | no | 29,750 |
| 3 | wɔ | 26,234 |
| 4 | mu | 22,593 |
| 5 | na | 18,784 |
| 6 | ghana | 8,469 |
| 7 | do | 7,315 |
| 8 | dɛ | 7,230 |
| 9 | ho | 5,744 |
| 10 | afe | 5,715 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | tampuli | 2 |
| 2 | gcpp | 2 |
| 3 | akomeah | 2 |
| 4 | miif | 2 |
| 5 | agyapa | 2 |
| 6 | sdo | 2 |
| 7 | dzɛmdzi | 2 |
| 8 | wta | 2 |
| 9 | slam | 2 |
| 10 | excision | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1854 |
| R² (Goodness of Fit) | 0.994799 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 50.5% |
| Top 1,000 | 77.9% |
| Top 5,000 | 92.1% |
| Top 10,000 | 96.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9948 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 50.5% of corpus
- **Long Tail:** 8,588 words needed for remaining 3.3% 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 | 0.8158 | 0.3399 | N/A | N/A |
| **mono_64d** | 64 | 0.6643 | 0.2886 | N/A | N/A |
| **mono_128d** | 128 | 0.2510 | 0.2768 | N/A | N/A |
| **aligned_32d** | 32 | 0.8158 🏆 | 0.3415 | 0.0320 | 0.1880 |
| **aligned_64d** | 64 | 0.6643 | 0.2904 | 0.0540 | 0.2820 |
| **aligned_128d** | 128 | 0.2510 | 0.2769 | 0.0980 | 0.3500 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8158 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3023. 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 | **-0.206** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-fo` | mamfo, skuulfo, nkontaabufo |

### 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 |
|------|----------|------------------|----------|
| `yerɛ` | 1.92x | 49 contexts | kyerɛ, ɔkyerɛ, ɛkyerɛ |
| `yina` | 1.87x | 52 contexts | oyina, gyina, nyina |
| `gyin` | 1.86x | 44 contexts | egyin, gyina, agyin |
| `wuma` | 1.82x | 38 contexts | dwuma, adwuma, edwuma |
| `atio` | 1.94x | 17 contexts | ratio, nation, ratios |
| `dwum` | 1.76x | 22 contexts | dwuma, adwuma, edwuma |
| `kuul` | 2.22x | 11 contexts | skuul, skuuls, skuula |
| `tion` | 1.78x | 17 contexts | nation, action, option |
| `abat` | 1.97x | 11 contexts | abata, abato, abatoɔ |
| `bato` | 1.93x | 11 contexts | abato, ambato, abatoɔ |
| `brah` | 2.28x | 5 contexts | debrah, ibrahim, mbrahyɛ |
| `pany` | 1.96x | 7 contexts | panyin, mpanyin, opanyin |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| semeiskiefo | **`semeiskie-fo`** | 4.5 | `semeiskie` |
| abedziekyirfo | **`abedziekyir-fo`** | 4.5 | `abedziekyir` |
| britainfo | **`britain-fo`** | 4.5 | `britain` |
| finlandfo | **`finland-fo`** | 4.5 | `finland` |
| ekyingyefo | **`ekyingye-fo`** | 4.5 | `ekyingye` |
| mpanyinfo | **`mpanyin-fo`** | 4.5 | `mpanyin` |
| edwindzefo | **`edwindze-fo`** | 4.5 | `edwindze` |
| albaniafo | **`albania-fo`** | 4.5 | `albania` |
| turkmenfo | **`turkmen-fo`** | 4.5 | `turkmen` |
| armeniafo | **`armenia-fo`** | 4.5 | `armenia` |
| dagombafo | **`dagomba-fo`** | 4.5 | `dagomba` |
| nyimdzefo | **`nyimdze-fo`** | 4.5 | `nyimdze` |
| konyimdzifo | **`konyimdzi-fo`** | 4.5 | `konyimdzi` |
| amandzebɔfo | **`amandzebɔ-fo`** | 4.5 | `amandzebɔ` |
| akandzifo | **`akandzi-fo`** | 4.5 | `akandzi` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Fanti 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 (4.36x) |
| N-gram | **2-gram** | Lowest perplexity (248) |
| Markov | **Context-4** | Highest predictability (94.4%) |
| 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: 2026-01-04 14:49:17*