---
language: ki
language_name: Kikuyu
language_family: bantu_central
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_central
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: 4.761
  - name: best_isotropy
    type: isotropy
    value: 0.3640
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kikuyu** 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** | 3.740x | 3.76 | 0.1464% | 56,680 |
| **16k** | 4.204x | 4.22 | 0.1646% | 50,431 |
| **32k** | 4.604x | 4.63 | 0.1802% | 46,049 |
| **64k** | 4.761x 🏆 | 4.78 | 0.1864% | 44,531 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Altay City irĩa nene ya China. Altay City irĩ igũrũ mũno ta 887 m. cia China`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁al ta y ▁city ▁irĩa ▁nene ▁ya ▁china . ▁al ... (+15 more)` | 25 |
| 16k | `▁altay ▁city ▁irĩa ▁nene ▁ya ▁china . ▁altay ▁city ▁irĩ ... (+11 more)` | 21 |
| 32k | `▁altay ▁city ▁irĩa ▁nene ▁ya ▁china . ▁altay ▁city ▁irĩ ... (+11 more)` | 21 |
| 64k | `▁altay ▁city ▁irĩa ▁nene ▁ya ▁china . ▁altay ▁city ▁irĩ ... (+11 more)` | 21 |

**Sample 2:** `Ziyodin city irĩa nene ya Uzbekistan. City ya Ziyodin irĩ igũrũ mũno ta 395 m. c...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁zi yo din ▁city ▁irĩa ▁nene ▁ya ▁uzbekistan . ▁city ... (+16 more)` | 26 |
| 16k | `▁ziyodin ▁city ▁irĩa ▁nene ▁ya ▁uzbekistan . ▁city ▁ya ▁ziyodin ... (+12 more)` | 22 |
| 32k | `▁ziyodin ▁city ▁irĩa ▁nene ▁ya ▁uzbekistan . ▁city ▁ya ▁ziyodin ... (+12 more)` | 22 |
| 64k | `▁ziyodin ▁city ▁irĩa ▁nene ▁ya ▁uzbekistan . ▁city ▁ya ▁ziyodin ... (+12 more)` | 22 |

**Sample 3:** `Matekinoronjĩsti me ngumo Bill Gates Everett Rogers Genrich Altshuller Henry For...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mate kinoronjĩ sti ▁me ▁ngumo ▁bill ▁gates ▁e vere tt ... (+26 more)` | 36 |
| 16k | `▁mate kinoronjĩ sti ▁me ▁ngumo ▁bill ▁gates ▁everett ▁rogers ▁genrich ... (+13 more)` | 23 |
| 32k | `▁mate kinoronjĩ sti ▁me ▁ngumo ▁bill ▁gates ▁everett ▁rogers ▁genrich ... (+13 more)` | 23 |
| 64k | `▁mate kinoronjĩsti ▁me ▁ngumo ▁bill ▁gates ▁everett ▁rogers ▁genrich ▁altshuller ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.761x compression
- **Lowest UNK Rate:** 8k with 0.1464% 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 | 1,695 | 10.73 | 3,484 | 29.8% | 67.3% |
| **2-gram** | Subword | 221 🏆 | 7.79 | 1,640 | 72.6% | 99.5% |
| **3-gram** | Word | 2,343 | 11.19 | 4,922 | 26.6% | 51.7% |
| **3-gram** | Subword | 1,638 | 10.68 | 10,992 | 32.8% | 77.3% |
| **4-gram** | Word | 10,195 | 13.32 | 14,421 | 11.0% | 21.2% |
| **4-gram** | Subword | 8,170 | 13.00 | 46,210 | 15.8% | 47.0% |
| **5-gram** | Word | 9,790 | 13.26 | 12,205 | 8.8% | 19.4% |
| **5-gram** | Subword | 23,535 | 14.52 | 90,045 | 8.8% | 30.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nene ya` | 634 |
| 2 | `irĩa nene` | 619 |
| 3 | `city irĩa` | 611 |
| 4 | `mũno ta` | 563 |
| 5 | `igũrũ mũno` | 558 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `irĩa nene ya` | 618 |
| 2 | `city irĩa nene` | 611 |
| 3 | `igũrũ mũno ta` | 554 |
| 4 | `irĩ igũrũ mũno` | 554 |
| 5 | `nene ya china` | 269 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `city irĩa nene ya` | 611 |
| 2 | `irĩ igũrũ mũno ta` | 554 |
| 3 | `irĩa nene ya china` | 268 |
| 4 | `ya china city ya` | 253 |
| 5 | `nene ya china city` | 253 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `city irĩa nene ya china` | 268 |
| 2 | `nene ya china city ya` | 253 |
| 3 | `irĩa nene ya china city` | 252 |
| 4 | `city irĩa nene ya uzbekistan` | 151 |
| 5 | `nene ya uzbekistan city ya` | 103 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 72,286 |
| 2 | `_ m` | 27,852 |
| 3 | `_ n` | 24,566 |
| 4 | `_ k` | 21,508 |
| 5 | `o _` | 20,719 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n a _` | 13,618 |
| 2 | `a _ m` | 12,680 |
| 3 | `a _ k` | 9,647 |
| 4 | `i a _` | 9,237 |
| 5 | `a _ n` | 8,811 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a _` | 7,688 |
| 2 | `_ w a _` | 7,106 |
| 3 | `n d ũ _` | 4,669 |
| 4 | `_ n ĩ _` | 4,466 |
| 5 | `r ĩ a _` | 4,311 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c i a _` | 2,410 |
| 2 | `a _ w a _` | 2,350 |
| 3 | `ũ n d ũ _` | 2,291 |
| 4 | `k a n a _` | 2,253 |
| 5 | `_ k a n a` | 2,082 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 221
- **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 | 0.5880 | 1.503 | 3.26 | 36,290 | 41.2% |
| **1** | Subword | 1.1410 | 2.205 | 8.50 | 464 | 0.0% |
| **2** | Word | 0.1749 | 1.129 | 1.35 | 117,531 | 82.5% |
| **2** | Subword | 1.0027 | 2.004 | 5.54 | 3,943 | 0.0% |
| **3** | Word | 0.0512 | 1.036 | 1.07 | 157,775 | 94.9% |
| **3** | Subword | 0.8396 | 1.790 | 3.66 | 21,830 | 16.0% |
| **4** | Word | 0.0195 🏆 | 1.014 | 1.03 | 168,145 | 98.0% |
| **4** | Subword | 0.6140 | 1.530 | 2.39 | 79,815 | 38.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `na njĩra ya thĩĩ handũ na indo ugĩciganagĩrĩra handu hatugĩru na kĩngeretha concision moigaga atĩ nĩ`
2. `wa mundu e heggy discovery of the anatomy of odinani nĩ ya cinda nĩ maũndũ mothe`
3. `nĩ kĩaringire gĩkaru kĩa njata kana ndamathia apartheid ya kũhũrwo ndwara thita cia mĩhĩrĩga ya keny...`

**Context Size 2:**

1. `nene ya uzbekistan city ya karachi irĩ igũrũ mũno ta 1 270 m cia china`
2. `irĩa nene ya uzbekistan city ya liuyang irĩ igũrũ mũno ta 162 279 m links poznań cia`
3. `city irĩa nene ya uzbekistan city ya malindi irĩ igũrũ mũno ta 12 0 m 39 4`

**Context Size 3:**

1. `irĩa nene ya china city ya guigang irĩ igũrũ mũno ta 1 779 m cia china`
2. `city irĩa nene ya japan city ya sakai irĩ igũrũ mũno ta 757 m cia uzbekistan`
3. `igũrũ mũno ta 61 m cia uzbekistan`

**Context Size 4:**

1. `city irĩa nene ya uzbekistan cia uzbekistan`
2. `irĩ igũrũ mũno ta 12 m cia china`
3. `irĩa nene ya china city ya baotou irĩ igũrũ mũno ta 1 084 m cia china`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ma_gh_rwerĩ_ara`
2. `a_mwty_rigo_rerî`
3. `ntha_fegabu_rĩna`

**Context Size 2:**

1. `a_ungĩte_ũgĩthĩ'.`
2. `_mo_gö_·_agwĩngo-`
3. `_nĩa_igikamũthead`

**Context Size 3:**

1. `na_kagwo_ata_7.3.2`
2. `a_mahũ_ya_nĩ_ndu_w`
3. `a_kũthonal_koretwo`

**Context Size 4:**

1. `_na_kwĩrutaga_rtngt`
2. `_wa_kũhiti_(deducat`
3. `ndũ_matho_wa_ũtihoy`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (79,815 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 | 15,538 |
| Total Tokens | 176,023 |
| Mean Frequency | 11.33 |
| Median Frequency | 3 |
| Frequency Std Dev | 112.81 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | na | 7,738 |
| 2 | wa | 7,198 |
| 3 | nĩ | 4,567 |
| 4 | ya | 4,306 |
| 5 | cia | 2,416 |
| 6 | kana | 2,104 |
| 7 | ta | 1,979 |
| 8 | inĩ | 1,613 |
| 9 | kĩa | 1,218 |
| 10 | city | 1,195 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | bisosa | 2 |
| 2 | biela | 2 |
| 3 | nzeba | 2 |
| 4 | mitshi | 2 |
| 5 | ikuama | 2 |
| 6 | bimuma | 2 |
| 7 | muikale | 2 |
| 8 | bujima | 2 |
| 9 | ngondu | 2 |
| 10 | kumonaye | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9723 |
| R² (Goodness of Fit) | 0.992255 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 43.1% |
| Top 1,000 | 67.4% |
| Top 5,000 | 85.5% |
| Top 10,000 | 93.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9923 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 43.1% of corpus
- **Long Tail:** 5,538 words needed for remaining 6.3% coverage

---
## 5. Word Embeddings Evaluation

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

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

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

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


### 5.1 Cross-Lingual Alignment

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

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


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.3640 🏆 | 0.4073 | N/A | N/A |
| **mono_64d** | 64 | 0.0941 | 0.3880 | N/A | N/A |
| **mono_128d** | 128 | 0.0139 | 0.4127 | N/A | N/A |
| **aligned_32d** | 32 | 0.3640 | 0.4033 | 0.0120 | 0.0680 |
| **aligned_64d** | 64 | 0.0941 | 0.3956 | 0.0080 | 0.0980 |
| **aligned_128d** | 128 | 0.0139 | 0.4268 | 0.0140 | 0.1120 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.3640 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4056. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.4% 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 | **-0.354** | 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 |
|--------|----------|
| `-m` | maarutaga, mahiu, mathondekaga |
| `-ma` | maarutaga, mahiu, mathondekaga |
| `-k` | kindũ, kũmuunda, kumenereria |
| `-kĩ` | kĩhumo, kĩna, kĩũteti |
| `-n` | nĩũĩ, ndangĩciara, ndĩra |
| `-a` | athĩni, athĩrĩria, ahingagia |
| `-t` | tũothe, tehũka, thĩiniĩ |
| `-g` | gacui, game, gũũcia |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | kũmuunda, maarutaga, bora |
| `-o` | marotero, hatonyagĩrwo, mĩako |
| `-e` | ohĩgĩrĩire, game, médiatique |
| `-ia` | henereria, athĩrĩria, kumenereria |
| `-wo` | hatonyagĩrwo, gĩakĩtwo, angikorwo |
| `-i` | hanini, athĩni, woneki |
| `-ra` | bora, ciura, ndangĩciara |
| `-re` | ohĩgĩrĩire, ũndũire, inyitanĩire |

### 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 |
|------|----------|------------------|----------|
| `gĩrĩ` | 1.60x | 39 contexts | igĩrĩ, ĩgĩrĩ, gĩrĩma |
| `orag` | 1.77x | 27 contexts | groraga, ĩroraga, űkoragwo |
| `ĩrĩr` | 1.54x | 44 contexts | kĩrĩrĩ, hĩrĩre, kĩrĩro |
| `ũthi` | 1.56x | 40 contexts | ũthii, ũthiĩ, ũthiũ |
| `ithi` | 1.49x | 47 contexts | ithia, nithi, ithii |
| `gĩth` | 1.57x | 35 contexts | gĩthĩ, gĩthu, gĩthũ |
| `agwo` | 1.59x | 31 contexts | nagwo, wagwo, magwo |
| `thia` | 1.45x | 41 contexts | ithia, ethia, athia |
| `mũth` | 1.67x | 22 contexts | mũthĩ, mũthiu, mũthee |
| `hũth` | 1.59x | 25 contexts | hũthũ, ũhũthe, hũthia |
| `math` | 1.57x | 25 contexts | matha, ũmatho, mathaa |
| `rĩri` | 1.63x | 21 contexts | rĩria, irĩria, arĩria |

### 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` | 424 words | kũrota, kĩorotaga |
| `-m` | `-a` | 271 words | mĩanga, matagathira |
| `-g` | `-a` | 266 words | gĩakinya, gĩrima |
| `-m` | `-o` | 222 words | mũmero, mehumbĩtwo |
| `-k` | `-o` | 150 words | kĩroho, kĩnyitithanagio |
| `-t` | `-a` | 149 words | tga, thĩgia |
| `-m` | `-e` | 145 words | maruanĩire, mbage |
| `-k` | `-ia` | 127 words | kũnyiihia, kĩgiragĩrĩria |
| `-a` | `-a` | 119 words | athamia, arara |
| `-m` | `-i` | 117 words | mũthũũri, muti |

### 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 |
|------|-----------------|------------|------|
| kũgathimĩra | **`kũgathim-ĩ-ra`** | 7.5 | `ĩ` |
| rĩtingĩrora | **`rĩtingĩr-o-ra`** | 7.5 | `o` |
| athomeire | **`athome-i-re`** | 7.5 | `i` |
| uzbekistan | **`uzbekist-a-n`** | 7.5 | `a` |
| inyanjara | **`inyanj-a-ra`** | 7.5 | `a` |
| ĩhũthĩkaga | **`ĩhũthĩk-a-ga`** | 7.5 | `a` |
| ndaragarara | **`ndaragar-a-ra`** | 7.5 | `a` |
| kũharahara | **`kũharah-a-ra`** | 7.5 | `a` |
| kĩhũthikaga | **`kĩhũthik-a-ga`** | 7.5 | `a` |
| ateretaga | **`ateret-a-ga`** | 7.5 | `a` |
| tengchong | **`tengch-o-ng`** | 7.5 | `o` |
| mũthigari | **`mũthi-ga-ri`** | 7.5 | `ga` |
| kĩhũthĩkaga | **`kĩhũthĩk-a-ga`** | 7.5 | `a` |
| hakundeeru | **`hakunde-e-ru`** | 7.5 | `e` |
| matikoragwo | **`ma-t-ikoragwo`** | 7.5 | `ikoragwo` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kikuyu 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 (4.76x) |
| N-gram | **2-gram** | Lowest perplexity (221) |
| Markov | **Context-4** | Highest predictability (98.0%) |
| 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 07:41:12*