---
language: lg
language_name: Ganda
language_family: bantu_eastern
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-bantu_eastern
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: 4.749
  - name: best_isotropy
    type: isotropy
    value: 0.8731
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ganda** 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** | 3.693x | 3.70 | 0.2870% | 259,571 |
| **16k** | 4.077x | 4.08 | 0.3168% | 235,148 |
| **32k** | 4.439x | 4.44 | 0.3449% | 215,974 |
| **64k** | 4.749x 🏆 | 4.75 | 0.3690% | 201,887 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Kigulu, ekibuga mu Kira Town mu Wakiso mu Yuganda.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ki gulu , ▁ekibuga ▁mu ▁kira ▁town ▁mu ▁wakiso ▁mu ... (+2 more)` | 12 |
| 16k | `▁ki gulu , ▁ekibuga ▁mu ▁kira ▁town ▁mu ▁wakiso ▁mu ... (+2 more)` | 12 |
| 32k | `▁kigulu , ▁ekibuga ▁mu ▁kira ▁town ▁mu ▁wakiso ▁mu ▁yuganda ... (+1 more)` | 11 |
| 64k | `▁kigulu , ▁ekibuga ▁mu ▁kira ▁town ▁mu ▁wakiso ▁mu ▁yuganda ... (+1 more)` | 11 |

**Sample 2:** `Kibuku nsi e disitulikit wa Yuganda. Obugazi: 490.2 km². Abantu: 181 700 mu Yuga...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kibu ku ▁nsi ▁e ▁disitulikit ▁wa ▁yuganda . ▁obugazi : ... (+21 more)` | 31 |
| 16k | `▁kibuku ▁nsi ▁e ▁disitulikit ▁wa ▁yuganda . ▁obugazi : ▁ ... (+20 more)` | 30 |
| 32k | `▁kibuku ▁nsi ▁e ▁disitulikit ▁wa ▁yuganda . ▁obugazi : ▁ ... (+20 more)` | 30 |
| 64k | `▁kibuku ▁nsi ▁e ▁disitulikit ▁wa ▁yuganda . ▁obugazi : ▁ ... (+20 more)` | 30 |

**Sample 3:** `thumbnail Flippy lwe e okuba mu naye nga Happy Tree Friends.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁thumb na il ▁f li pp y ▁lwe ▁e ▁okuba ... (+12 more)` | 22 |
| 16k | `▁thumb na il ▁f lipp y ▁lwe ▁e ▁okuba ▁mu ... (+8 more)` | 18 |
| 32k | `▁thumb na il ▁f lipp y ▁lwe ▁e ▁okuba ▁mu ... (+7 more)` | 17 |
| 64k | `▁thumbnail ▁flippy ▁lwe ▁e ▁okuba ▁mu ▁naye ▁nga ▁ha ppy ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 4.749x compression
- **Lowest UNK Rate:** 8k with 0.2870% 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 | 14,199 | 13.79 | 38,632 | 12.7% | 34.6% |
| **2-gram** | Subword | 219 🏆 | 7.77 | 2,147 | 71.2% | 99.8% |
| **3-gram** | Word | 26,700 | 14.70 | 56,796 | 9.4% | 25.1% |
| **3-gram** | Subword | 1,669 | 10.70 | 19,121 | 29.6% | 78.5% |
| **4-gram** | Word | 70,764 | 16.11 | 118,544 | 6.5% | 15.1% |
| **4-gram** | Subword | 8,452 | 13.05 | 97,188 | 14.1% | 45.2% |
| **5-gram** | Word | 61,726 | 15.91 | 94,350 | 7.0% | 14.7% |
| **5-gram** | Subword | 28,463 | 14.80 | 255,792 | 7.8% | 27.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `okuva mu` | 5,167 |
| 2 | `mu uganda` | 4,435 |
| 3 | `y e` | 3,265 |
| 4 | `ya uganda` | 2,854 |
| 5 | `mu mwaka` | 2,411 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `disitulikiti y e` | 1,864 |
| 2 | `mu mwaka gwa` | 1,837 |
| 3 | `mu disitulikiti y` | 1,235 |
| 4 | `okuva mu okutuuka` | 888 |
| 5 | `mu okutuuka mu` | 872 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mu disitulikiti y e` | 1,155 |
| 2 | `okuva mu okutuuka mu` | 831 |
| 3 | `mu ssaza ly e` | 811 |
| 4 | `united states of america` | 742 |
| 5 | `erisangibwa mu ssaza ly` | 735 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `erisangibwa mu ssaza ly e` | 735 |
| 2 | `mu nsi ya united states` | 734 |
| 3 | `states of america g e` | 733 |
| 4 | `united states of america g` | 733 |
| 5 | `ya united states of america` | 733 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 510,380 |
| 2 | `m u` | 198,216 |
| 3 | `u _` | 192,024 |
| 4 | `_ e` | 166,670 |
| 5 | `_ m` | 159,088 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `m u _` | 121,316 |
| 2 | `_ m u` | 114,905 |
| 3 | `o k u` | 71,249 |
| 4 | `w a _` | 70,500 |
| 5 | `a _ e` | 66,280 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m u _` | 89,059 |
| 2 | `a _ m u` | 52,454 |
| 3 | `_ o k u` | 49,017 |
| 4 | `n g a _` | 45,054 |
| 5 | `b w a _` | 32,976 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ m u _` | 43,937 |
| 2 | `_ n g a _` | 29,244 |
| 3 | `a _ o k u` | 23,484 |
| 4 | `g a n d a` | 23,102 |
| 5 | `u g a n d` | 22,563 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 219
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.7920 | 1.731 | 5.69 | 115,787 | 20.8% |
| **1** | Subword | 1.1968 | 2.292 | 11.50 | 360 | 0.0% |
| **2** | Word | 0.2704 | 1.206 | 1.67 | 657,016 | 73.0% |
| **2** | Subword | 1.2119 | 2.316 | 7.94 | 4,135 | 0.0% |
| **3** | Word | 0.1023 | 1.073 | 1.18 | 1,092,887 | 89.8% |
| **3** | Subword | 0.9620 | 1.948 | 4.72 | 32,782 | 3.8% |
| **4** | Word | 0.0425 🏆 | 1.030 | 1.06 | 1,288,031 | 95.7% |
| **4** | Subword | 0.6947 | 1.619 | 3.00 | 154,616 | 30.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `mu mutwe gwayo kwe yali mukiise mu mawanga g e kenya visa pour la masaka n`
2. `ku modern uganda olw amanyi mu kitundu ekisooka difiiri bw ebyoto ebisatu by ebijanjaalo biwerako er...`
3. `nga 7 223 530 mu mukundani eyatometa n asuulibwa eddalu lya uganda premier soccer league uganda`

**Context Size 2:**

1. `okuva mu bumannyirivu bwe ne famire ye jyavaamu baddamu ebigambo bye baba balowozaako h wewale okuka...`
2. `mu uganda judith babirye obuto bwe n okusoma kwe kakoma yazaalibwa mu buganda nga tewanabaawo kyefan...`
3. `y e makerere ayongerako nti yalina ekisanja kye ekyokubiri nga enkambi yamaje era essomero lino lwal...`

**Context Size 3:**

1. `disitulikiti y e buhweju olukalala lw abakyala abawandiisi mu uganda eka femrite era abadde muwandii...`
2. `mu mwaka gwa okutuuka mu yakomawo mu uganda mu n alondebwa okuba omusumba mu n awummula mu joseph`
3. `mu disitulikiti y e kayunga mu paalamenti ey omwenda mwalimu edward katumba wamala yazaalibwa ng enn...`

**Context Size 4:**

1. `mu disitulikiti y e ibanda siniya eyokuna yagimaliririza mu immaculate heart nyakibale secondary sch...`
2. `okuva mu okutuuka mu oluvannyuma yakola ng omukulu w essomero mu yalondebwa nga ssentebe w ekibiina ...`
3. `mu ssaza ly e texas mu nsi ya united states of america g e kentucky united states ebisangibwa mu`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ddenndeti_e_ngo`
2. `a_kulizyokamu_ku`
3. `erokokin’o_ebake`

**Context Size 2:**

1. `a_n'ebyasootard,_`
2. `mu_neba_kiri_aba_`
3. `u_mmu_binovera_co`

**Context Size 3:**

1. `mu_kino_okwe_yatal`
2. `_mu_ugaziko_emisom`
3. `okutender,_mu_gulu`

**Context Size 4:**

1. `_mu_by'amateekera_e`
2. `a_mu_mabuvo_bwe_mu_`
3. `_okuva_mu_luguumiro`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (154,616 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 | 51,479 |
| Total Tokens | 1,503,057 |
| Mean Frequency | 29.20 |
| Median Frequency | 4 |
| Frequency Std Dev | 508.71 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mu | 89,527 |
| 2 | ku | 30,386 |
| 3 | nga | 29,634 |
| 4 | n | 29,585 |
| 5 | uganda | 17,006 |
| 6 | ne | 15,431 |
| 7 | era | 14,238 |
| 8 | y | 12,890 |
| 9 | e | 10,819 |
| 10 | ya | 10,765 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | leku | 2 |
| 2 | agataalimu | 2 |
| 3 | gyebafuna | 2 |
| 4 | omuwuubi | 2 |
| 5 | baakyalira | 2 |
| 6 | eturude | 2 |
| 7 | bannanyinimu | 2 |
| 8 | obusoose | 2 |
| 9 | abanyanya | 2 |
| 10 | kalogo | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0794 |
| R² (Goodness of Fit) | 0.993590 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 36.5% |
| Top 1,000 | 63.8% |
| Top 5,000 | 82.3% |
| Top 10,000 | 88.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9936 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 36.5% of corpus
- **Long Tail:** 41,479 words needed for remaining 11.1% 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 | 0.8731 | 0.3015 | N/A | N/A |
| **mono_64d** | 64 | 0.8603 | 0.2214 | N/A | N/A |
| **mono_128d** | 128 | 0.6513 | 0.2031 | N/A | N/A |
| **aligned_32d** | 32 | 0.8731 🏆 | 0.2999 | 0.0840 | 0.3380 |
| **aligned_64d** | 64 | 0.8603 | 0.2236 | 0.0980 | 0.3860 |
| **aligned_128d** | 128 | 0.6513 | 0.2073 | 0.1800 | 0.5160 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8731 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2428. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 18.0% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.474** | 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` | atuzibwa, abafirosoofa, amazze |
| `-e` | ekifuula, enschede, ebisonjola |
| `-ba` | banabyamizannyo, bazanye, babonabona |
| `-b` | banabyamizannyo, bazanye, braun |
| `-m` | musambi, miracle, margret |
| `-k` | kyaleetera, kikungiri, kipande |
| `-ka` | kabwegyere, kaweefube, kagoma |
| `-o` | okwefuula, omugate, okulinnyisibwa |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | atuzibwa, lwawangula, okwefuula |
| `-wa` | atuzibwa, okulinnyisibwa, obubwa |
| `-o` | banabyamizannyo, luweero, ssonko |
| `-e` | enschede, omugate, kipande |
| `-ra` | kyaleetera, yakyogera, luddirira |
| `-i` | musambi, kikungiri, ppulaani |
| `-u` | ekizungu, ntenjeru, gyawulwamu |
| `-za` | awezezza, byanjigiriza, kulowooza |

### 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 |
|------|----------|------------------|----------|
| `teek` | 2.29x | 104 contexts | teeka, ateeka, eteeka |
| `tion` | 2.59x | 28 contexts | action, motion, cation |
| `wang` | 1.81x | 117 contexts | wangu, wangi, lwang |
| `gand` | 2.28x | 38 contexts | ganda, ugand, nganda |
| `anny` | 1.99x | 62 contexts | danny, zannya, zannyi |
| `atio` | 2.45x | 26 contexts | ratio, cation, nation |
| `embe` | 2.09x | 37 contexts | ember, dembe, ddembe |
| `ugan` | 1.97x | 46 contexts | ugand, uganda, ugandas |
| `erez` | 2.01x | 30 contexts | perez, tereza, wereza |
| `omuk` | 1.90x | 34 contexts | omuko, omuka, omukka |
| `okus` | 1.82x | 37 contexts | okusa, okussa, okusiba |
| `okuk` | 1.97x | 26 contexts | okuka, okukka, okukuu |

### 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 |
|--------|--------|-----------|----------|
| `-o` | `-a` | 720 words | okukiikirirwa, okumusaba |
| `-e` | `-a` | 516 words | eyonooneddwa, entakyuuka |
| `-k` | `-a` | 384 words | kuvuganya, kubula |
| `-a` | `-a` | 376 words | atea, akomererwa |
| `-e` | `-o` | 230 words | ebipapajjo, ekigattikakibabiro |
| `-ba` | `-a` | 197 words | bamerika, balumbagana |
| `-b` | `-a` | 185 words | bamerika, balumbagana |
| `-o` | `-o` | 147 words | ogwomukwano, okuzaawo |
| `-e` | `-wa` | 138 words | eyonooneddwa, egizannyirwa |
| `-o` | `-u` | 116 words | ogusibukamu, ogirimu |

### 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 |
|------|-----------------|------------|------|
| baamatwale | **`baamat-wa-le`** | 7.5 | `wa` |
| ebikwatibwako | **`ebikwatib-wa-ko`** | 7.5 | `wa` |
| okuyisaawo | **`okuyisa-a-wo`** | 7.5 | `a` |
| ekisingamu | **`ekising-a-mu`** | 7.5 | `a` |
| obusingirayo | **`obusingir-a-yo`** | 7.5 | `a` |
| kumuyamba | **`ku-mu-yamba`** | 7.5 | `yamba` |
| kwatuukibwako | **`kwatuukib-wa-ko`** | 7.5 | `wa` |
| mukungaaniramu | **`mukungaanir-a-mu`** | 7.5 | `a` |
| ekitangaala | **`ekitanga-a-la`** | 7.5 | `a` |
| batandikawo | **`batandik-a-wo`** | 7.5 | `a` |
| bannyonyola | **`bannyony-o-la`** | 7.5 | `o` |
| obunakuwavu | **`obunaku-wa-vu`** | 7.5 | `wa` |
| akaateekebwawo | **`akaateekeb-wa-wo`** | 7.5 | `wa` |
| okwetuusaako | **`okwetuusa-a-ko`** | 7.5 | `a` |
| ekwatibwako | **`ekwatib-wa-ko`** | 7.5 | `wa` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ganda 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 (4.75x) |
| N-gram | **2-gram** | Lowest perplexity (219) |
| Markov | **Context-4** | Highest predictability (95.7%) |
| 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: 2026-01-10 10:45:52*