---
language: tum
language_name: Tumbuka
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: 4.762
  - name: best_isotropy
    type: isotropy
    value: 0.8058
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tumbuka** 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** | 4.090x | 4.09 | 0.1251% | 577,333 |
| **16k** | 4.408x | 4.41 | 0.1348% | 535,662 |
| **32k** | 4.603x | 4.61 | 0.1408% | 512,911 |
| **64k** | 4.762x 🏆 | 4.76 | 0.1456% | 495,791 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Wovwe ni malo agho ghakusangika mu boma la Karonga,chigaŵa cha kumpoto kwa charu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wo v we ▁ni ▁malo ▁agho ▁ghakusangika ▁mu ▁boma ▁la ... (+12 more)` | 22 |
| 16k | `▁wo v we ▁ni ▁malo ▁agho ▁ghakusangika ▁mu ▁boma ▁la ... (+12 more)` | 22 |
| 32k | `▁wo v we ▁ni ▁malo ▁agho ▁ghakusangika ▁mu ▁boma ▁la ... (+12 more)` | 22 |
| 64k | `▁wovwe ▁ni ▁malo ▁agho ▁ghakusangika ▁mu ▁boma ▁la ▁karonga , ... (+10 more)` | 20 |

**Sample 2:** `Manuel Murillo Toro wakawa mlala wa chalo cha Colombia kufuma 1 April mpaka 1 Ap...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁manuel ▁mu ri llo ▁to ro ▁wakawa ▁mlala ▁wa ▁chalo ... (+10 more)` | 20 |
| 16k | `▁manuel ▁mu rillo ▁toro ▁wakawa ▁mlala ▁wa ▁chalo ▁cha ▁colombia ... (+8 more)` | 18 |
| 32k | `▁manuel ▁mu rillo ▁toro ▁wakawa ▁mlala ▁wa ▁chalo ▁cha ▁colombia ... (+8 more)` | 18 |
| 64k | `▁manuel ▁murillo ▁toro ▁wakawa ▁mlala ▁wa ▁chalo ▁cha ▁colombia ▁kufuma ... (+7 more)` | 17 |

**Sample 3:** `Laikipia County, Kenya ni boma ilo likusangika mu charu cha Kenya mukati mwa chi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁la i ki pia ▁county , ▁kenya ▁ni ▁boma ▁ilo ... (+18 more)` | 28 |
| 16k | `▁la iki pia ▁county , ▁kenya ▁ni ▁boma ▁ilo ▁likusangika ... (+17 more)` | 27 |
| 32k | `▁laikipia ▁county , ▁kenya ▁ni ▁boma ▁ilo ▁likusangika ▁mu ▁charu ... (+15 more)` | 25 |
| 64k | `▁laikipia ▁county , ▁kenya ▁ni ▁boma ▁ilo ▁likusangika ▁mu ▁charu ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.762x compression
- **Lowest UNK Rate:** 8k with 0.1251% 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 | 5,474 | 12.42 | 34,661 | 26.6% | 53.6% |
| **2-gram** | Subword | 223 🏆 | 7.80 | 2,837 | 70.7% | 99.6% |
| **3-gram** | Word | 7,258 | 12.83 | 50,253 | 25.2% | 51.5% |
| **3-gram** | Subword | 1,577 | 10.62 | 22,530 | 33.2% | 78.3% |
| **4-gram** | Word | 8,704 | 13.09 | 75,625 | 23.5% | 52.0% |
| **4-gram** | Subword | 6,842 | 12.74 | 113,445 | 19.8% | 51.7% |
| **5-gram** | Word | 5,344 | 12.38 | 48,307 | 25.0% | 58.2% |
| **5-gram** | Subword | 18,567 | 14.18 | 275,747 | 13.9% | 38.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `charu cha` | 18,086 |
| 2 | `mu charu` | 13,923 |
| 3 | `boma la` | 13,289 |
| 4 | `chigaŵa cha` | 11,295 |
| 5 | `mu boma` | 11,014 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mu charu cha` | 13,110 |
| 2 | `mu boma la` | 8,192 |
| 3 | `chilwa chikulu cha` | 6,204 |
| 4 | `mu chigaŵa cha` | 5,908 |
| 5 | `mu chilwa chikulu` | 5,874 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mu chilwa chikulu cha` | 5,874 |
| 2 | `chilwa chikulu cha ulaya` | 5,097 |
| 3 | `ghakusangika mu boma la` | 4,333 |
| 4 | `chikulu cha ulaya europe` | 3,052 |
| 5 | `cha ulaya europe yaku` | 2,824 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mu chilwa chikulu cha ulaya` | 5,062 |
| 2 | `chilwa chikulu cha ulaya europe` | 3,052 |
| 3 | `chikulu cha ulaya europe yaku` | 2,824 |
| 4 | `ni msumba mu boma la` | 2,193 |
| 5 | `malo agho ghakusangika mu boma` | 2,176 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 622,907 |
| 2 | `u _` | 234,729 |
| 3 | `_ m` | 226,843 |
| 4 | `a n` | 215,484 |
| 5 | `_ c` | 199,145 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c h` | 141,906 |
| 2 | `a _ m` | 107,357 |
| 3 | `m u _` | 99,923 |
| 4 | `_ m u` | 99,086 |
| 5 | `_ k u` | 93,801 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c h a` | 81,345 |
| 2 | `_ m u _` | 79,144 |
| 3 | `u _ c h` | 62,069 |
| 4 | `a _ k u` | 61,056 |
| 5 | `_ g h a` | 55,352 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c h a _` | 51,011 |
| 2 | `a _ m u _` | 45,337 |
| 3 | `u _ c h a` | 42,760 |
| 4 | `m u _ c h` | 31,681 |
| 5 | `_ m u _ c` | 29,948 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 223
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~38% 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 | 0.8434 | 1.794 | 5.85 | 97,126 | 15.7% |
| **1** | Subword | 1.1331 | 2.193 | 9.11 | 745 | 0.0% |
| **2** | Word | 0.2898 | 1.223 | 1.75 | 567,037 | 71.0% |
| **2** | Subword | 1.0193 | 2.027 | 6.22 | 6,781 | 0.0% |
| **3** | Word | 0.1172 | 1.085 | 1.22 | 988,755 | 88.3% |
| **3** | Subword | 0.8781 | 1.838 | 4.40 | 42,130 | 12.2% |
| **4** | Word | 0.0476 🏆 | 1.034 | 1.07 | 1,202,229 | 95.2% |
| **4** | Subword | 0.6747 | 1.596 | 2.89 | 185,249 | 32.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `mu boma la karonga chigaŵa cha greece ghakusangika mu austria yulaya austria ghakusangika mu charu c...`
2. `cha kummwela mu catechetical lectures wakaŵa nduna yikuru comene iyo yikusambizga ŵanthu ŵanandi mu ...`
3. `na zina zina la lilongwe mu bunda college ku namibia na mtima pa mndandanda wa ŵanthu`

**Context Size 2:**

1. `charu cha malaŵi la dowa ghakusangika mu mangochi mu ŵamalonda ŵanandi ŵa ku zimbabwe sumu iyo yinga...`
2. `mu charu cha turkey mu chilwa chikulu cha adana mu charu cha malaŵi la chiradzulu cha kummwela`
3. `boma la libya ŵakakana ivyo ŵakayowoya kale kufika mu mafuko gha rozvi changamire dombo wakaparanya ...`

**Context Size 3:**

1. `mu charu cha united states of america ndipouli mu vyaka vyasonosono apa ukuchepa wupu wa zimbabwe el...`
2. `mu boma la ceyhan mu chigaŵa chikulu cha kwazulu natal ku south africa ilo likususkana na wagner gro...`
3. `chilwa chikulu cha ulaya ikulu na idoko yamu germany ghamu germany wa misumba na matauni ghachoko gh...`

**Context Size 4:**

1. `mu chilwa chikulu cha ulaya ikulu na idoko yamu germany ghamu germany wa misumba na matauni ghachoko...`
2. `chilwa chikulu cha ulaya europe yaku austria ghakusangika mu austria yulaya austria austria`
3. `ghakusangika mu boma la machinga cha kummwela ndi dela limene limapezeka anthu awulemu ndi ozichepet...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ptef_muna_kiper`
2. `amulo,_tedo_gwu_`
3. `ichinapermse_ŵik`

**Context Size 2:**

1. `a_vinee_li_ghakaŵ`
2. `u_anthen,_mulies,`
3. `_matricassanne_ŵa`

**Context Size 3:**

1. `_chigaŵa_maland_so`
2. `a_magazi_milira_ro`
3. `mu_boma_zakwa_mwap`

**Context Size 4:**

1. `_charu_cha_gandambo`
2. `_mu_chilwa_yikakhum`
3. `u_cha_germanyuma_pa`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (185,249 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 | 45,104 |
| Total Tokens | 1,805,602 |
| Mean Frequency | 40.03 |
| Median Frequency | 4 |
| Frequency Std Dev | 678.44 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mu | 81,954 |
| 2 | cha | 51,027 |
| 3 | na | 50,305 |
| 4 | ku | 29,094 |
| 5 | la | 26,744 |
| 6 | ni | 25,502 |
| 7 | wa | 23,621 |
| 8 | boma | 21,934 |
| 9 | charu | 21,617 |
| 10 | pa | 21,122 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | vyakuseŵera | 2 |
| 2 | hypervisor | 2 |
| 3 | kuzima | 2 |
| 4 | muzakaŵe | 2 |
| 5 | maloboti | 2 |
| 6 | lichitira | 2 |
| 7 | chindale | 2 |
| 8 | tum_latntum_latntum_latn | 2 |
| 9 | yikupangikira | 2 |
| 10 | sae | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2067 |
| R² (Goodness of Fit) | 0.995267 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 47.4% |
| Top 1,000 | 74.5% |
| Top 5,000 | 88.7% |
| Top 10,000 | 93.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9953 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 47.4% of corpus
- **Long Tail:** 35,104 words needed for remaining 7.0% 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 | 0.8058 | 0.3384 | N/A | N/A |
| **mono_64d** | 64 | 0.7416 | 0.2724 | N/A | N/A |
| **mono_128d** | 128 | 0.4731 | 0.2502 | N/A | N/A |
| **aligned_32d** | 32 | 0.8058 🏆 | 0.3446 | 0.1300 | 0.4640 |
| **aligned_64d** | 64 | 0.7416 | 0.2694 | 0.1620 | 0.5160 |
| **aligned_128d** | 128 | 0.4731 | 0.2503 | 0.2340 | 0.6120 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8058 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2875. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 23.4% 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 | **0.520** | High formulaic/idiomatic 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` | mutesi, mikhail, mtimabi |
| `-ma` | mandinka, masheke, mafinga |
| `-s` | sexagesimal, soviet, sirte |
| `-a` | amelika, apr, achikulire |
| `-c` | chakukolerana, chitambo, cigaŵa |
| `-k` | kununkhira, kukhazikiska, kumanyuma |
| `-b` | bantus, barrios, beach |
| `-ku` | kununkhira, kukhazikiska, kumanyuma |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | pakutonda, chakukolerana, wakadangilira |
| `-ka` | wakabapatizika, ghakusinthiska, amelika |
| `-e` | ŵayowoyanenge, dale, charlottesville |
| `-ra` | wakadangilira, ghangaŵawovwira, ukuyendera |
| `-s` | bantus, iranians, prestigious |
| `-o` | chitambo, chigaŵo, too |
| `-ga` | wakawoneseskanga, wakachenjezga, ŵakalenga |
| `-n` | traunstein, nastätten, lahnstein |

### 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 |
|------|----------|------------------|----------|
| `tion` | 2.51x | 41 contexts | notion, option, motion |
| `stri` | 2.63x | 23 contexts | strip, strife, strict |
| `chik` | 2.04x | 38 contexts | chiku, chika, chikwi |
| `umba` | 1.94x | 43 contexts | sumba, rumba, tumba |
| `angi` | 1.73x | 51 contexts | bangi, ubangi, tangier |
| `haku` | 2.13x | 22 contexts | chaku, ghaku, chakum |
| `hiku` | 2.25x | 17 contexts | chiku, chikulu, chikung |
| `chil` | 1.86x | 28 contexts | child, chili, chile |
| `ghak` | 2.03x | 20 contexts | ghake, ghaku, ghakhe |
| `anth` | 1.72x | 35 contexts | anthu, kanthu, anthus |
| `chig` | 2.05x | 17 contexts | chigha, chigez, chigwa |
| `higa` | 2.09x | 14 contexts | shiga, vihiga, chigaŵo |

### 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 |
|--------|--------|-----------|----------|
| `-ŵa` | `-a` | 285 words | ŵakwimikika, ŵakucitira |
| `-k` | `-a` | 284 words | kakoma, kulekeka |
| `-c` | `-a` | 202 words | cafika, chikazura |
| `-m` | `-a` | 153 words | mawema, mataka |
| `-ŵa` | `-ga` | 100 words | ŵakafikanga, ŵakawonekanga |
| `-k` | `-ka` | 92 words | kulekeka, kupokeka |
| `-c` | `-s` | 83 words | circles, credentials |
| `-ŵa` | `-e` | 73 words | ŵasande, ŵandaŵathereske |
| `-m` | `-o` | 70 words | mulatho, mphalamuko |
| `-k` | `-ra` | 70 words | kuzunura, kuchokera |

### 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 |
|------|-----------------|------------|------|
| accipitridae | **`accipitrid-a-e`** | 7.5 | `a` |
| ŵakavwara | **`ŵakavw-a-ra`** | 7.5 | `a` |
| ghakuperekeka | **`ghakuperek-e-ka`** | 7.5 | `e` |
| wachiŵili | **`wachiŵi-l-i`** | 7.5 | `l` |
| pakacitikaso | **`pakaciti-ka-so`** | 7.5 | `ka` |
| landkreis | **`landkre-i-s`** | 7.5 | `i` |
| yikawonekaso | **`yikawone-ka-so`** | 7.5 | `ka` |
| wakunyang | **`wakuny-a-ng`** | 7.5 | `a` |
| expressway | **`express-wa-y`** | 7.5 | `wa` |
| ghakatora | **`ghakat-o-ra`** | 7.5 | `o` |
| kupambanako | **`kupamban-a-ko`** | 7.5 | `a` |
| wakuphika | **`wakuph-i-ka`** | 7.5 | `i` |
| ghakwambukira | **`ghakwambuk-i-ra`** | 7.5 | `i` |
| ŵakasamira | **`ŵakasam-i-ra`** | 7.5 | `i` |
| treasuries | **`treasur-i-es`** | 7.5 | `i` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tumbuka shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 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 (223) |
| Markov | **Context-4** | Highest predictability (95.2%) |
| 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: 2026-01-11 01:51:59*