---
language: dga
language_name: Southern Dagaare
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: 4.080
  - name: best_isotropy
    type: isotropy
    value: 0.8588
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

# Southern Dagaare - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Southern Dagaare** 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** | 3.655x | 3.66 | 0.0592% | 426,016 |
| **16k** | 3.850x | 3.85 | 0.0623% | 404,419 |
| **32k** | 3.987x | 3.99 | 0.0645% | 390,549 |
| **64k** | 4.080x 🏆 | 4.08 | 0.0660% | 381,660 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Lambussie e la tembile ane a Lambussie Karni desekyere teŋkpoŋ, desekyere naŋ be...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lambussie ▁e ▁la ▁tembile ▁ane ▁a ▁lambussie ▁kar ni ▁desekyere ... (+19 more)` | 29 |
| 16k | `▁lambussie ▁e ▁la ▁tembile ▁ane ▁a ▁lambussie ▁kar ni ▁desekyere ... (+19 more)` | 29 |
| 32k | `▁lambussie ▁e ▁la ▁tembile ▁ane ▁a ▁lambussie ▁karni ▁desekyere ▁teŋkpoŋ ... (+18 more)` | 28 |
| 64k | `▁lambussie ▁e ▁la ▁tembile ▁ane ▁a ▁lambussie ▁karni ▁desekyere ▁teŋkpoŋ ... (+18 more)` | 28 |

**Sample 2:** `Lugo e la dabaarãã ba naŋ maŋ ba wagre ŋa ba naŋ wa meɛrɛ dié, lugo maŋ taa la k...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lu go ▁e ▁la ▁da baa r ãã ▁ba ▁naŋ ... (+27 more)` | 37 |
| 16k | `▁lu go ▁e ▁la ▁da baa rãã ▁ba ▁naŋ ▁maŋ ... (+25 more)` | 35 |
| 32k | `▁lugo ▁e ▁la ▁da baa rãã ▁ba ▁naŋ ▁maŋ ▁ba ... (+21 more)` | 31 |
| 64k | `▁lugo ▁e ▁la ▁dabaarãã ▁ba ▁naŋ ▁maŋ ▁ba ▁wagre ▁ŋa ... (+18 more)` | 28 |

**Sample 3:** `Sheikh Osman Nuhu Sharubutu waa la a Ghana zaa Silaamabiiri wideɛrɛ. O dɔgebo be...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁she ikh ▁os man ▁nuhu ▁shar ubu tu ▁waa ▁la ... (+18 more)` | 28 |
| 16k | `▁sheikh ▁osman ▁nuhu ▁shar ubu tu ▁waa ▁la ▁a ▁ghana ... (+14 more)` | 24 |
| 32k | `▁sheikh ▁osman ▁nuhu ▁shar ubutu ▁waa ▁la ▁a ▁ghana ▁zaa ... (+13 more)` | 23 |
| 64k | `▁sheikh ▁osman ▁nuhu ▁sharubutu ▁waa ▁la ▁a ▁ghana ▁zaa ▁silaamabiiri ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.080x compression
- **Lowest UNK Rate:** 8k with 0.0592% unknown tokens
- **Trade-off:** Larger vocabularies improve compression but increase model size
- **Recommendation:** 32k vocabulary provides optimal balance for production use

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

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

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

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

### Results

| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|---------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | Word | 5,247 | 12.36 | 23,604 | 25.2% | 52.5% |
| **2-gram** | Subword | 261 🏆 | 8.03 | 3,102 | 67.0% | 99.0% |
| **3-gram** | Word | 15,091 | 13.88 | 40,759 | 12.7% | 34.8% |
| **3-gram** | Subword | 2,130 | 11.06 | 23,753 | 29.7% | 72.3% |
| **4-gram** | Word | 37,462 | 15.19 | 77,183 | 7.6% | 22.9% |
| **4-gram** | Subword | 10,952 | 13.42 | 113,607 | 15.0% | 44.1% |
| **5-gram** | Word | 33,178 | 15.02 | 59,664 | 7.6% | 22.1% |
| **5-gram** | Subword | 34,072 | 15.06 | 261,669 | 9.2% | 29.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `la a` | 8,318 |
| 2 | `e la` | 8,255 |
| 3 | `ka o` | 5,097 |
| 4 | `naŋ be` | 4,526 |
| 5 | `o da` | 4,441 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `naŋ be a` | 2,381 |
| 2 | `e la a` | 1,581 |
| 3 | `o e la` | 1,352 |
| 4 | `da e la` | 1,226 |
| 5 | `sommo yizie zaa` | 1,176 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sommo yizie zaa africa` | 1,004 |
| 2 | `o da e la` | 534 |
| 3 | `of the 4th republic` | 440 |
| 4 | `4th republic of ghana` | 439 |
| 5 | `parliament of the 4th` | 439 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `parliament of the 4th republic` | 438 |
| 2 | `the 4th republic of ghana` | 434 |
| 3 | `of the 4th republic of` | 434 |
| 4 | `4th republic of ghana zaa` | 348 |
| 5 | `republic of ghana zaa africa` | 341 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 295,811 |
| 2 | `e _` | 179,385 |
| 3 | `_ a` | 141,327 |
| 4 | `_ n` | 88,607 |
| 5 | `a n` | 84,293 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a _` | 75,684 |
| 2 | `_ l a` | 47,173 |
| 3 | `l a _` | 44,354 |
| 4 | `_ n a` | 42,956 |
| 5 | `a ŋ _` | 41,497 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l a _` | 40,459 |
| 2 | `n a ŋ _` | 25,681 |
| 3 | `_ n a ŋ` | 24,499 |
| 4 | `_ d a _` | 21,223 |
| 5 | `_ k a _` | 20,083 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a ŋ _` | 24,351 |
| 2 | `e _ l a _` | 16,215 |
| 3 | `_ a n e _` | 12,136 |
| 4 | `g h a n a` | 10,185 |
| 5 | `_ g h a n` | 9,611 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 261
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.7877 | 1.726 | 5.30 | 76,185 | 21.2% |
| **1** | Subword | 0.9123 | 1.882 | 7.16 | 1,143 | 8.8% |
| **2** | Word | 0.2777 | 1.212 | 1.73 | 402,963 | 72.2% |
| **2** | Subword | 0.9272 | 1.902 | 5.67 | 8,182 | 7.3% |
| **3** | Word | 0.1241 | 1.090 | 1.24 | 697,461 | 87.6% |
| **3** | Subword | 0.8532 | 1.807 | 4.16 | 46,384 | 14.7% |
| **4** | Word | 0.0565 🏆 | 1.040 | 1.09 | 865,473 | 94.4% |
| **4** | Subword | 0.6504 | 1.570 | 2.74 | 193,130 | 35.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a dudu taa la taa la martha hyer spainunited states be la rev r b enfuomo`
2. `la 27 june how lucky philip dube akon kanye kanye west african universities african cinema hosts`
3. `o teŋkpoŋ geogarapi a 21 december ane o ba meŋ da eɛ bonwuoraa dagaaba naŋ be`

**Context Size 2:**

1. `la a ghana ports ane coastal eŋgyinia poɔ o da nyeε gyerema aŋa pɔge ko a paalikaara`
2. `e la desekyere ayi eŋɛ twifo atti morkwa desekyere a o south sɛŋ ne fumesua a o`
3. `ka o fãã a kyɛ a na toɔ di a kogi ne 14 391 vootuu ka lɛ`

**Context Size 3:**

1. `naŋ be a gaana paaloo mr hackman owusu agyeman la a diplomats mine naŋ baare knust aliu mahama`
2. `e la a is bolgatanga munisipal naŋ taa tensɔgɔ yɛlloŋ naŋ na baŋ pare pie ne anuu te`
3. `o e la neŋkpoŋ naŋ kaara a naasaala mine nimikpɛ kyaare ne a silla ane goryeo saŋa naŋ`

**Context Size 4:**

1. `o da e la business development officer of fonak technologies ltd and chief executive officer of the ...`
2. `of the 4th republic of ghana zaa africa parliament of the 4th republic of ghana zaa africa parliamen...`
3. `parliament of the 4th republic of ghana zaa africa parliament of the 4th republic of ghana zaa afric...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_erwiamarles_a_l`
2. `anest,_nelica_a_`
3. `e_pra,_ssi_aaɡba`

**Context Size 2:**

1. `a_nund_te_8_me._o`
2. `e_a_e_a_tho/_ⓘ_in`
3. `_a_garebɔloolijew`

**Context Size 3:**

1. `_a_baŋ_bebiri_daga`
2. `_la_bare_poɔ._a_yu`
3. `la_kology._oble_ma`

**Context Size 4:**

1. `_la_doŋ_kaa_naŋ_naŋ`
2. `naŋ_be_a_kaŋa_naŋ_b`
3. `_naŋ_be_tigiri_a_de`


### 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 (193,130 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 | 33,219 |
| Total Tokens | 1,069,636 |
| Mean Frequency | 32.20 |
| Median Frequency | 4 |
| Frequency Std Dev | 610.71 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 77,430 |
| 2 | la | 41,562 |
| 3 | o | 29,242 |
| 4 | naŋ | 24,554 |
| 5 | da | 21,295 |
| 6 | ka | 20,388 |
| 7 | ba | 17,329 |
| 8 | e | 16,396 |
| 9 | poɔ | 14,743 |
| 10 | ane | 12,198 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | buorεε | 2 |
| 2 | libirɩ | 2 |
| 3 | kpɩ | 2 |
| 4 | yεltarihɩ | 2 |
| 5 | jaʋ | 2 |
| 6 | daahe | 2 |
| 7 | tigrihi | 2 |
| 8 | pileehi | 2 |
| 9 | revive | 2 |
| 10 | ekewaolu | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1395 |
| R² (Goodness of Fit) | 0.997636 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 51.3% |
| Top 1,000 | 75.0% |
| Top 5,000 | 88.7% |
| Top 10,000 | 93.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9976 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 51.3% of corpus
- **Long Tail:** 23,219 words needed for remaining 6.6% coverage

---
## 5. Word Embeddings Evaluation

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

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

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

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


### 5.1 Cross-Lingual Alignment

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

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


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.8588 🏆 | 0.3392 | N/A | N/A |
| **mono_64d** | 64 | 0.7947 | 0.2830 | N/A | N/A |
| **mono_128d** | 128 | 0.5119 | 0.2439 | N/A | N/A |
| **aligned_32d** | 32 | 0.8588 | 0.3417 | 0.0440 | 0.3200 |
| **aligned_64d** | 64 | 0.7947 | 0.2829 | 0.1180 | 0.4400 |
| **aligned_128d** | 128 | 0.5119 | 0.2497 | 0.2020 | 0.5080 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8588 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2901. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 20.2% 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 | **-0.253** | 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 |
|--------|----------|
| `-e` | service, kpeɛmine, dɔre |
| `-re` | dɔre, core, sefaare |
| `-ng` | providing, serving, keeling |

### 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 |
|------|----------|------------------|----------|
| `aare` | 1.84x | 72 contexts | zaare, daare, gaare |
| `igyi` | 2.52x | 15 contexts | rigyiŋ, firigyi, irigyiŋ |
| `aalo` | 1.78x | 43 contexts | gaalo, maalo, saalo |
| `atio` | 2.19x | 20 contexts | matio, nation, station |
| `eɛre` | 1.75x | 39 contexts | jeɛre, weɛre, neɛre |
| `paal` | 1.62x | 50 contexts | paali, paale, paalo |
| `tion` | 1.99x | 22 contexts | motion, nation, action |
| `aale` | 1.53x | 47 contexts | laale, waale, paale |
| `aloŋ` | 2.09x | 16 contexts | baloŋ, zaloŋ, yaloŋ |
| `yaar` | 1.73x | 28 contexts | yaari, yaaro, yaara |
| `rigy` | 2.15x | 14 contexts | rigyiŋ, firigyi, irigyiŋ |
| `irig` | 2.40x | 9 contexts | irigiŋ, irigin, firigyi |

### 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 |
|------|-----------------|------------|------|
| pɔgesarre | **`pɔgesar-re`** | 4.5 | `pɔgesar` |
| lomboring | **`lombori-ng`** | 4.5 | `lombori` |
| counselling | **`counselli-ng`** | 1.5 | `counselli` |
| processing | **`processi-ng`** | 1.5 | `processi` |
| containing | **`containi-ng`** | 1.5 | `containi` |
| sasefaare | **`sasefaa-re`** | 1.5 | `sasefaa` |
| schoolboarding | **`schoolboardi-ng`** | 1.5 | `schoolboardi` |
| parodying | **`parodyi-ng`** | 1.5 | `parodyi` |
| transforming | **`transformi-ng`** | 1.5 | `transformi` |
| derbyshire | **`derbyshi-re`** | 1.5 | `derbyshi` |
| dankwasere | **`dankwase-re`** | 1.5 | `dankwase` |
| bonyɔgere | **`bonyɔge-re`** | 1.5 | `bonyɔge` |
| sɛgebikparre | **`sɛgebikpar-re`** | 1.5 | `sɛgebikpar` |
| nimbitɔɔre | **`nimbitɔɔ-re`** | 1.5 | `nimbitɔɔ` |
| chongqing | **`chongqi-ng`** | 1.5 | `chongqi` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Southern Dagaare 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 (4.08x) |
| N-gram | **2-gram** | Lowest perplexity (261) |
| 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 02:08:16*