README.md

---
language: dag
language_name: Dagbani
language_family: atlantic_gur
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_gur
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: 3.794
  - name: best_isotropy
    type: isotropy
    value: 0.8139
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Dagbani** 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** | 3.300x | 3.30 | 0.0720% | 894,994 |
| **16k** | 3.518x | 3.52 | 0.0767% | 839,477 |
| **32k** | 3.682x | 3.68 | 0.0803% | 801,972 |
| **64k** | 3.794x 🏆 | 3.80 | 0.0827% | 778,290 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Nyuwɔɣu / Nawɔɣu (wateryam)Naden, Tony. Dagbani dictionary. Webonary. Kundivihir...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁nyu w ɔɣu ▁/ ▁na w ɔɣu ▁( water yam ... (+11 more)` | 21 |
| 16k | `▁nyu w ɔɣu ▁/ ▁na w ɔɣu ▁( water yam ... (+11 more)` | 21 |
| 32k | `▁nyu w ɔɣu ▁/ ▁naw ɔɣu ▁( water yam ) ... (+10 more)` | 20 |
| 64k | `▁nyu wɔɣu ▁/ ▁naw ɔɣu ▁( water yam ) naden ... (+9 more)` | 19 |

**Sample 2:** `Nakɔhigu nyɛla daankali tuma Dagbaŋ. Ban be di puuni kuri la nima. Di Piligu Be ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁na kɔ higu ▁nyɛla ▁daan kali ▁tuma ▁dagbaŋ . ▁ban ... (+12 more)` | 22 |
| 16k | `▁nakɔ higu ▁nyɛla ▁daan kali ▁tuma ▁dagbaŋ . ▁ban ▁be ... (+11 more)` | 21 |
| 32k | `▁nakɔhigu ▁nyɛla ▁daankali ▁tuma ▁dagbaŋ . ▁ban ▁be ▁di ▁puuni ... (+9 more)` | 19 |
| 64k | `▁nakɔhigu ▁nyɛla ▁daankali ▁tuma ▁dagbaŋ . ▁ban ▁be ▁di ▁puuni ... (+9 more)` | 19 |

**Sample 3:** `LaniNaden, Tony. Dagbani dictionary. Webonary.nyɛla doo dabilim yaɣishɛli. Kundi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lan inaden , ▁tony . ▁dagbani ▁dictionary . ▁webonary . ... (+9 more)` | 19 |
| 16k | `▁lan inaden , ▁tony . ▁dagbani ▁dictionary . ▁webonary . ... (+8 more)` | 18 |
| 32k | `▁lan inaden , ▁tony . ▁dagbani ▁dictionary . ▁webonary . ... (+7 more)` | 17 |
| 64k | `▁lan inaden , ▁tony . ▁dagbani ▁dictionary . ▁webonary . ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 3.794x compression
- **Lowest UNK Rate:** 8k with 0.0720% 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 | 31,979 | 14.96 | 135,270 | 12.8% | 30.3% |
| **2-gram** | Subword | 338 🏆 | 8.40 | 6,640 | 61.2% | 98.8% |
| **3-gram** | Word | 61,233 | 15.90 | 205,091 | 9.7% | 22.3% |
| **3-gram** | Subword | 3,279 | 11.68 | 48,644 | 19.8% | 63.9% |
| **4-gram** | Word | 122,791 | 16.91 | 377,150 | 8.8% | 17.3% |
| **4-gram** | Subword | 20,666 | 14.33 | 280,804 | 9.1% | 31.2% |
| **5-gram** | Word | 83,218 | 16.34 | 277,989 | 11.4% | 19.8% |
| **5-gram** | Subword | 81,311 | 16.31 | 863,645 | 5.8% | 20.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `of the` | 21,162 |
| 2 | `n ti` | 16,066 |
| 3 | `o daa` | 10,740 |
| 4 | `din be` | 10,157 |
| 5 | `ka di` | 10,044 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `of the year` | 4,882 |
| 2 | `n ti pahi` | 4,540 |
| 3 | `zaŋ n ti` | 3,966 |
| 4 | `nyɛla bɛ ni` | 3,631 |
| 5 | `bɛ ni daa` | 3,273 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `biɛlim kalibu baŋsim bɔhimbu` | 2,948 |
| 2 | `ninsali biɛlim kalibu baŋsim` | 2,948 |
| 3 | `zalikpana mini gɔmnanti tali` | 2,947 |
| 4 | `ni nyamma soya economy` | 2,945 |
| 5 | `demographics ninsali biɛlim kalibu` | 2,944 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ninsali biɛlim kalibu baŋsim bɔhimbu` | 2,948 |
| 2 | `demographics ninsali biɛlim kalibu baŋsim` | 2,944 |
| 3 | `tali law and government baŋsim` | 2,943 |
| 4 | `gɔmnanti tali law and government` | 2,943 |
| 5 | `mini gɔmnanti tali law and` | 2,943 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 742,691 |
| 2 | `i _` | 729,151 |
| 3 | `n _` | 496,810 |
| 4 | `a n` | 496,260 |
| 5 | `, _` | 494,751 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n i _` | 223,179 |
| 2 | `_ n i` | 166,766 |
| 3 | `l i _` | 131,067 |
| 4 | `_ m a` | 130,487 |
| 5 | `_ d a` | 130,222 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t h e _` | 96,966 |
| 2 | `_ n i _` | 91,865 |
| 3 | `_ t h e` | 91,838 |
| 4 | `_ o f _` | 86,951 |
| 5 | `_ d a a` | 77,547 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t h e _` | 86,257 |
| 2 | `_ d a a _` | 73,635 |
| 3 | `y ɛ l a _` | 50,822 |
| 4 | `n y ɛ l a` | 50,735 |
| 5 | `_ n y ɛ l` | 49,922 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 338
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~20% 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 | 0.7239 | 1.652 | 6.34 | 344,700 | 27.6% |
| **1** | Subword | 1.1279 | 2.185 | 6.69 | 4,036 | 0.0% |
| **2** | Word | 0.2746 | 1.210 | 1.73 | 2,184,048 | 72.5% |
| **2** | Subword | 0.6246 | 1.542 | 4.19 | 26,994 | 37.5% |
| **3** | Word | 0.1113 | 1.080 | 1.21 | 3,772,159 | 88.9% |
| **3** | Subword | 0.7278 | 1.656 | 4.22 | 112,970 | 27.2% |
| **4** | Word | 0.0540 🏆 | 1.038 | 1.09 | 4,576,663 | 94.6% |
| **4** | Subword | 0.7217 | 1.649 | 3.38 | 476,865 | 27.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ni 146 naɣila ni bɛ 3 mini periodic teebuli maa zaa di yuuni puuni ka buɣujɛmdiba`
2. `the title close to score after the laws ebube ordinary john brascia lucille la kasbah n`
3. `of china art museum swarthmore fullback gene quintano screenplay by burroughsrob bridgett tina mensa...`

**Context Size 2:**

1. `of the treasure of pancho villa as mimi alexis puig as militar adriana russo kundiviha the film`
2. `n ti best supporting actress go go girl m net mytv formerly astv newzroom afrika nongoma tv`
3. `o daa pilli shɛli yuuni puuni n nyɛ toon tibo suhudoo dabsili yuuni ŋɔ churi critics lists`

**Context Size 3:**

1. `of the year amy grant southern gospel album of the year invade my soul by the tree chuck`
2. `n ti pahi 503 votes ntoso daa dolila ghanas independence din daa n niŋ ka bindirigu bi niŋ`
3. `zaŋ n ti master of medicine mmed in internal medicine since master of medicine n ti pahi princess`

**Context Size 4:**

1. `ninsali biɛlim kalibu baŋsim bɔhimbu bomma ni nyamma soya economy zalikpana mini gɔmnanti tali law a...`
2. `biɛlim kalibu baŋsim bɔhimbu bomma ni nyamma soya economy zalikpana mini gɔmnanti tali law and gover...`
3. `zalikpana mini gɔmnanti tali law and government baŋsim bɔbu education kaya ni taada lahabali churi m...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ryɛld_baninasou`
2. `a_y_benteso_plag`
3. `iound_n_na_ni_er`

**Context Size 2:**

1. `a_bes_tuma_prishe`
2. `i_st_a_le_rickinm`
3. `n_naner_fation,_d`

**Context Size 3:**

1. `ni_daa_niŋ_maŋsim_`
2. `_ni_sam_kyung_high`
3. `li_ary_la_of_the_d`

**Context Size 4:**

1. `the_illum,_alexande`
2. `_ni_di_rhondon_hee-`
3. `_the_museum._frases`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (476,865 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 | 131,415 |
| Total Tokens | 5,756,455 |
| Mean Frequency | 43.80 |
| Median Frequency | 4 |
| Frequency Std Dev | 759.26 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ni | 104,912 |
| 2 | the | 89,996 |
| 3 | of | 87,067 |
| 4 | daa | 75,848 |
| 5 | o | 71,090 |
| 6 | ka | 70,258 |
| 7 | n | 52,198 |
| 8 | nyɛla | 49,965 |
| 9 | din | 48,314 |
| 10 | di | 45,125 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | yikonim | 2 |
| 2 | asj | 2 |
| 3 | fiqhi | 2 |
| 4 | sapuhi | 2 |
| 5 | hoti | 2 |
| 6 | breams | 2 |
| 7 | xai | 2 |
| 8 | coloboma | 2 |
| 9 | ziɛ | 2 |
| 10 | bɔɔlɔ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0507 |
| R² (Goodness of Fit) | 0.994879 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 31.6% |
| Top 1,000 | 58.6% |
| Top 5,000 | 77.5% |
| Top 10,000 | 84.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9949 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 31.6% of corpus
- **Long Tail:** 121,415 words needed for remaining 15.5% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.7990 | 0.3615 | N/A | N/A |
| **mono_64d** | 64 | 0.8035 | 0.2926 | N/A | N/A |
| **mono_128d** | 128 | 0.8139 | 0.2158 | N/A | N/A |
| **aligned_32d** | 32 | 0.7990 | 0.3542 | 0.1220 | 0.4920 |
| **aligned_64d** | 64 | 0.8035 | 0.2751 | 0.2420 | 0.6800 |
| **aligned_128d** | 128 | 0.8139 🏆 | 0.2184 | 0.3840 | 0.7540 |

### Key Findings

- **Best Isotropy:** aligned_128d with 0.8139 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2863. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 38.4% 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 | **-0.010** | 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 |
|--------|----------|
| `-ma` | mazzotta, malvína, manilyn |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-er` | sanger, schmucker, reefroger |
| `-ed` | aliunited, hayekunited, affected |
| `-an` | statestarzan, parisian, cappleman |
| `-on` | gudnason, bronston, verdon |

### 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 |
|------|----------|------------------|----------|
| `uuni` | 2.43x | 37 contexts | guuni, yuuni, duuni |
| `ihir` | 2.32x | 42 contexts | vihir, pihiri, lihira |
| `ison` | 2.11x | 60 contexts | isong, mison, isono |
| `nter` | 1.90x | 69 contexts | enter, inter, unter |
| `ctor` | 1.95x | 43 contexts | actor, sector, factor |
| `atio` | 1.88x | 46 contexts | ratio, patio, ation |
| `ture` | 1.79x | 54 contexts | mature, cuture, future |
| `reen` | 1.97x | 37 contexts | reena, breen, green |
| `tern` | 1.84x | 48 contexts | stern, terns, terna |
| `riso` | 2.21x | 23 contexts | arison, prison, bɔriso |
| `rect` | 2.19x | 22 contexts | recta, rector, direct |
| `ogra` | 1.95x | 32 contexts | dogra, yograj, biograd |

### 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 |
|--------|--------|-----------|----------|
| `-ma` | `-an` | 8 words | mariaan, mailman |
| `-ma` | `-ed` | 8 words | matched, marloweunited |
| `-ma` | `-on` | 5 words | malnutrition, marsbyron |
| `-ma` | `-er` | 1 words | marmer, mayweather |

### 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 |
|------|-----------------|------------|------|
| nyankpalan | **`nyankpal-an`** | 4.5 | `nyankpal` |
| schweiger | **`schweig-er`** | 4.5 | `schweig` |
| cricketer | **`cricket-er`** | 4.5 | `cricket` |
| michelson | **`michels-on`** | 4.5 | `michels` |
| shipwrecked | **`shipwreck-ed`** | 4.5 | `shipwreck` |
| macgruber | **`ma-cgrub-er`** | 3.0 | `cgrub` |
| madhunandan | **`ma-dhunand-an`** | 3.0 | `dhunand` |
| chalcedon | **`chalc-ed-on`** | 3.0 | `chalc` |
| skycameron | **`skycam-er-on`** | 3.0 | `skycam` |
| malnutrition | **`ma-lnutriti-on`** | 3.0 | `lnutriti` |
| metropolitansan | **`metropolitans-an`** | 1.5 | `metropolitans` |
| trevorunited | **`trevorunit-ed`** | 1.5 | `trevorunit` |
| meaneyunited | **`meaneyunit-ed`** | 1.5 | `meaneyunit` |
| cattrallunited | **`cattrallunit-ed`** | 1.5 | `cattrallunit` |
| margherita | **`ma-rgherita`** | 1.5 | `rgherita` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Dagbani 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 (3.79x) |
| N-gram | **2-gram** | Lowest perplexity (338) |
| Markov | **Context-4** | Highest predictability (94.6%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-04 01:58:15*