---
language: rw
language_name: Kinyarwanda
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: 4.330
  - name: best_isotropy
    type: isotropy
    value: 0.8846
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kinyarwanda** 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** | 3.440x | 3.44 | 0.7778% | 231,049 |
| **16k** | 3.758x | 3.76 | 0.8498% | 211,461 |
| **32k** | 4.054x | 4.06 | 0.9168% | 196,016 |
| **64k** | 4.330x 🏆 | 4.34 | 0.9791% | 183,531 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Jibuti (izina mu cyarabu : جيبوتي ‎ ; izina mu gifaransa : Djibouti ) n’igihugu ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁j ibu ti ▁( izina ▁mu ▁cyarabu ▁: ▁ج ي ... (+20 more)` | 30 |
| 16k | `▁jibu ti ▁( izina ▁mu ▁cyarabu ▁: ▁ج ي ب ... (+19 more)` | 29 |
| 32k | `▁jibuti ▁( izina ▁mu ▁cyarabu ▁: ▁ج ي بو ت ... (+17 more)` | 27 |
| 64k | `▁jibuti ▁( izina ▁mu ▁cyarabu ▁: ▁ج ي بو تي ... (+16 more)` | 26 |

**Sample 2:** `Bizimana Abdu uzwi nka Bekeni wari umutoza wa Etincelles FC, akayibera umuyobozi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁bi zimana ▁abdu ▁uzwi ▁nka ▁be ke ni ▁wari ▁umutoza ... (+18 more)` | 28 |
| 16k | `▁bizimana ▁abdu ▁uzwi ▁nka ▁be ke ni ▁wari ▁umutoza ▁wa ... (+15 more)` | 25 |
| 32k | `▁bizimana ▁abdu ▁uzwi ▁nka ▁be ke ni ▁wari ▁umutoza ▁wa ... (+12 more)` | 22 |
| 64k | `▁bizimana ▁abdu ▁uzwi ▁nka ▁be ke ni ▁wari ▁umutoza ▁wa ... (+12 more)` | 22 |

**Sample 3:** `thumb Umusigiti wa mukuru muri Dubai (izina mu cyarabu: مسجد دبي الكبير) ni umus...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁thumb ▁umusigiti ▁wa ▁mukuru ▁muri ▁du bai ▁( izina ▁mu ... (+29 more)` | 39 |
| 16k | `▁thumb ▁umusigiti ▁wa ▁mukuru ▁muri ▁dubai ▁( izina ▁mu ▁cyarabu ... (+24 more)` | 34 |
| 32k | `▁thumb ▁umusigiti ▁wa ▁mukuru ▁muri ▁dubai ▁( izina ▁mu ▁cyarabu ... (+19 more)` | 29 |
| 64k | `▁thumb ▁umusigiti ▁wa ▁mukuru ▁muri ▁dubai ▁( izina ▁mu ▁cyarabu ... (+19 more)` | 29 |


### Key Findings

- **Best Compression:** 64k achieves 4.330x compression
- **Lowest UNK Rate:** 8k with 0.7778% 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 | 18,987 | 14.21 | 53,674 | 10.8% | 31.0% |
| **2-gram** | Subword | 211 🏆 | 7.72 | 3,711 | 74.0% | 99.6% |
| **3-gram** | Word | 34,739 | 15.08 | 72,467 | 7.4% | 22.2% |
| **3-gram** | Subword | 1,627 | 10.67 | 26,865 | 29.4% | 80.4% |
| **4-gram** | Word | 91,637 | 16.48 | 141,823 | 3.7% | 12.2% |
| **4-gram** | Subword | 8,816 | 13.11 | 136,860 | 12.5% | 45.0% |
| **5-gram** | Word | 80,915 | 16.30 | 108,276 | 3.1% | 10.7% |
| **5-gram** | Subword | 31,538 | 14.94 | 354,876 | 6.7% | 26.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mu rwanda` | 5,463 |
| 2 | `u rwanda` | 4,916 |
| 3 | `ku ya` | 3,826 |
| 4 | `mu mwaka` | 3,035 |
| 5 | `ndetse n` | 2,749 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mu mwaka wa` | 2,056 |
| 2 | `y u rwanda` | 1,711 |
| 3 | `mu karere ka` | 1,652 |
| 4 | `umupira w amaguru` | 1,081 |
| 5 | `ihuza ryo hanze` | 917 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `repubulika iharanira demokarasi ya` | 738 |
| 2 | `iharanira demokarasi ya kongo` | 731 |
| 3 | `reba ihuza ryo hanze` | 632 |
| 4 | `muri afurika y epfo` | 365 |
| 5 | `ukina umupira w amaguru` | 346 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `repubulika iharanira demokarasi ya kongo` | 686 |
| 2 | `umukinnyi ukina umupira w amaguru` | 271 |
| 3 | `ni umukinnyi ukina umupira w` | 248 |
| 4 | `izina ry ubumenyi mu kilatini` | 240 |
| 5 | `leta zunze ubumwe z amerika` | 203 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 625,374 |
| 2 | `e _` | 368,094 |
| 3 | `i _` | 293,023 |
| 4 | `a n` | 290,094 |
| 5 | `o _` | 286,827 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m u` | 160,364 |
| 2 | `r i _` | 100,543 |
| 3 | `_ k u` | 99,022 |
| 4 | `r a _` | 93,428 |
| 5 | `m u _` | 88,869 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m u _` | 84,002 |
| 2 | `u r i _` | 57,539 |
| 3 | `a _ m u` | 45,538 |
| 4 | `_ m u r` | 43,557 |
| 5 | `m u r i` | 42,556 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m u r i` | 39,861 |
| 2 | `m u r i _` | 39,743 |
| 3 | `a _ m u _` | 25,873 |
| 4 | `e _ m u _` | 22,150 |
| 5 | `_ m u _ m` | 20,415 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 211
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.8463 | 1.798 | 6.38 | 163,621 | 15.4% |
| **1** | Subword | 0.8435 | 1.794 | 6.17 | 1,743 | 15.7% |
| **2** | Word | 0.2628 | 1.200 | 1.68 | 1,040,519 | 73.7% |
| **2** | Subword | 0.8424 | 1.793 | 5.13 | 10,741 | 15.8% |
| **3** | Word | 0.0947 | 1.068 | 1.17 | 1,737,932 | 90.5% |
| **3** | Subword | 0.8178 | 1.763 | 4.19 | 55,059 | 18.2% |
| **4** | Word | 0.0364 🏆 | 1.026 | 1.06 | 2,027,315 | 96.4% |
| **4** | Subword | 0.6852 | 1.608 | 2.97 | 230,427 | 31.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `mu buryo ababukora batabukora neza 2 n umuryango w ukwezi kwa muganga cyangwa bashyizeho amakaro gif...`
2. `n imwe iyo mibare ari umukunzi we washinze kandi ifite umukara amaguru bakiri mu kugabanya ubutaka`
3. `muri na dabby chimere muriyi filime nibwo yambitswe ikamba agaciro no muri drc ubuzima n imyumbati`

**Context Size 2:**

1. `mu rwanda nka kaminuza ifunguye mu bwongereza agakingirizo ni uburyo abanyarwanda bo hambere bateka ...`
2. `u rwanda rugeze rwiyubaka ndetse akishimira icyerekezo igihugu gifite abaturage 6 kwigisha ubuhanga ...`
3. `ku ya 7 nyakanga itangira ku mwanya wa gatandatu mu mikino olempike mu gihugu akatirwa igifungo kire...`

**Context Size 3:**

1. `mu mwaka wa na padiri hitimana waje kucyirukanwamo bivugwa ko byagizwemo uruhare n uwitwa musonera f...`
2. `mu karere ka bugesera haboneka inamaz ihariye zirebana no guhangana nicyo kibazo cya abana mu miirya...`
3. `y u rwanda gutera busongora kuko yatekerezaga ko kamaliza akiri muto agikeneye umuntu ujya mu kimbo ...`

**Context Size 4:**

1. `repubulika iharanira demokarasi ya kongo afite imyaka 13 yaje mu bubiligi bitewe nuko nyina yashakan...`
2. `iharanira demokarasi ya kongo mu mukino wa gicuti 0 0 imibare reba wa congo`
3. `reba ihuza ryo hanze u rwanda mu gutanga amasoko atandukanye u rwanda rwabonye amashanyarazi ya mber...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_yangit'd_uge,_n`
2. `ano_kwa_ranga_gs`
3. `i_ma_kure_mu_ne_`

**Context Size 2:**

1. `a_a_wuge_yumu_bya`
2. `e_kwicingarerandi`
3. `i_ko_(kuza_mya_ir`

**Context Size 3:**

1. `_mu_bara:_munta_ic`
2. `ri_ebya_kare_bushy`
3. `_kubakororidageneg`

**Context Size 4:**

1. `_mu_rwanyarwaye_mu_`
2. `uri_ndijk_africa_pr`
3. `a_muri_w'ama_imye_a`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (230,427 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 | 71,439 |
| Total Tokens | 2,285,892 |
| Mean Frequency | 32.00 |
| Median Frequency | 4 |
| Frequency Std Dev | 512.25 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mu | 84,764 |
| 2 | n | 44,189 |
| 3 | muri | 39,306 |
| 4 | y | 32,989 |
| 5 | ya | 31,781 |
| 6 | ku | 30,372 |
| 7 | na | 26,704 |
| 8 | wa | 20,501 |
| 9 | ni | 18,825 |
| 10 | kandi | 14,981 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | faddis | 2 |
| 2 | twiganye | 2 |
| 3 | pierson | 2 |
| 4 | whitehead | 2 |
| 5 | imposing | 2 |
| 6 | whirlwind | 2 |
| 7 | abwire | 2 |
| 8 | verve | 2 |
| 9 | bassiste | 2 |
| 10 | pinderhughes | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1070 |
| R² (Goodness of Fit) | 0.990401 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 33.8% |
| Top 1,000 | 62.0% |
| Top 5,000 | 81.1% |
| Top 10,000 | 87.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9904 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 33.8% of corpus
- **Long Tail:** 61,439 words needed for remaining 12.6% 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 | 0.8846 | 0.3598 | N/A | N/A |
| **mono_64d** | 64 | 0.8628 | 0.2440 | N/A | N/A |
| **mono_128d** | 128 | 0.8154 | 0.1705 | N/A | N/A |
| **aligned_32d** | 32 | 0.8846 🏆 | 0.3561 | 0.0400 | 0.2600 |
| **aligned_64d** | 64 | 0.8628 | 0.2297 | 0.1180 | 0.3800 |
| **aligned_128d** | 128 | 0.8154 | 0.1717 | 0.1600 | 0.4620 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8846 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2553. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 16.0% 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 | **-0.590** | 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` | azitandukanya, agbada, anitta |
| `-ba` | bariciwe, batisimu, barware |
| `-b` | bwakorwaga, bubarizwa, bonnaterre |
| `-m` | marked, moi, mtb |
| `-i` | ikurikiyeho, ibyinitse, influenced |
| `-n` | ninini, ntacyananira, niño |
| `-s` | strigiformes, santa, slowakiya |
| `-ma` | marked, malagarasi, makossa |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | azitandukanya, agbada, anitta |
| `-e` | kubagore, tubakunde, rugwe |
| `-o` | ukorerwamo, cyigo, zubuhumekero |
| `-ra` | byinzara, ntacyananira, banywera |
| `-ye` | twakagombye, bikoranye, cyicaye |
| `-i` | ubukanishi, umusesenguzi, funji |
| `-wa` | hagashyirwa, bubarizwa, bigikorwa |
| `-we` | rugwe, abimuwe, bariciwe |

### 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 |
|------|----------|------------------|----------|
| `ores` | 2.61x | 62 contexts | forest, flores, scores |
| `anga` | 1.61x | 275 contexts | banga, langa, zanga |
| `mber` | 2.03x | 60 contexts | mbera, imber, amber |
| `atan` | 1.63x | 165 contexts | atanu, zlatan, satani |
| `ngan` | 1.73x | 120 contexts | ngano, ngange, ungana |
| `ihug` | 2.53x | 25 contexts | ihugu, bihugu, gihugu |
| `aban` | 1.54x | 200 contexts | abana, abanu, yabana |
| `ikor` | 1.64x | 138 contexts | ikora, ikoro, ikore |
| `amas` | 1.96x | 56 contexts | damas, amaso, amase |
| `anda` | 1.67x | 114 contexts | andam, randa, panda |
| `shin` | 1.67x | 112 contexts | shina, oshin, shine |
| `ubur` | 1.73x | 84 contexts | ubura, uburo, rubura |

### 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 |
|--------|--------|-----------|----------|
| `-k` | `-a` | 297 words | kuzenguruka, kudaha |
| `-a` | `-a` | 252 words | azerubayija, atarahabwa |
| `-b` | `-a` | 240 words | bwanwa, baha |
| `-b` | `-e` | 230 words | bristlecone, barateye |
| `-i` | `-a` | 226 words | izitera, iyihanganira |
| `-ba` | `-a` | 170 words | baha, bahashinga |
| `-i` | `-e` | 136 words | inshinge, ikingiye |
| `-a` | `-e` | 133 words | abaturajye, ardenne |
| `-ba` | `-e` | 119 words | barateye, babonye |
| `-i` | `-o` | 119 words | ihitamo, ikirushijeho |

### 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 |
|------|-----------------|------------|------|
| yoherezayo | **`yohereza-y-o`** | 7.5 | `y` |
| wimibereho | **`wimiber-e-ho`** | 7.5 | `e` |
| bakamujya | **`ba-ka-mujya`** | 7.5 | `mujya` |
| porofeseri | **`porofes-e-ri`** | 7.5 | `e` |
| umurynago | **`umury-na-go`** | 7.5 | `na` |
| yiyumvagamo | **`yiyumvag-a-mo`** | 7.5 | `a` |
| byanditseho | **`byandits-e-ho`** | 7.5 | `e` |
| byakongera | **`byakong-e-ra`** | 7.5 | `e` |
| karidinari | **`karidin-a-ri`** | 7.5 | `a` |
| ashushanyijeho | **`ashushanyij-e-ho`** | 7.5 | `e` |
| accessories | **`accesso-ri-es`** | 7.5 | `ri` |
| kwerekera | **`kwerek-e-ra`** | 7.5 | `e` |
| ikigabiro | **`ikigab-i-ro`** | 7.5 | `i` |
| akanyamasyo | **`akanyamas-y-o`** | 7.5 | `y` |
| rwagennye | **`rwagen-n-ye`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kinyarwanda 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 (4.33x) |
| N-gram | **2-gram** | Lowest perplexity (211) |
| Markov | **Context-4** | Highest predictability (96.4%) |
| 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: 2026-01-10 19:15:41*