README.md

---
language: rn
language_name: Rundi
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: 4.735
  - name: best_isotropy
    type: isotropy
    value: 0.1625
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Rundi** 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** | 3.942x | 3.95 | 0.2846% | 143,361 |
| **16k** | 4.328x | 4.33 | 0.3125% | 130,557 |
| **32k** | 4.735x 🏆 | 4.74 | 0.3419% | 119,347 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Irepuburika y’Ubutariyano ni igihugu kiri m' Uburaya. Umurwa mukuru: Rome Uburin...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁irepuburika ▁y ’ ubu tariyano ▁ni ▁igihugu ▁kiri ▁m ' ... (+19 more)` | 29 |
| 16k | `▁irepuburika ▁y ’ ubutariyano ▁ni ▁igihugu ▁kiri ▁m ' ▁uburaya ... (+18 more)` | 28 |
| 32k | `▁irepuburika ▁y ’ ubutariyano ▁ni ▁igihugu ▁kiri ▁m ' ▁uburaya ... (+18 more)` | 28 |

**Sample 2:** `Ushingiye kuri Bibiliya ni umwana w'Imana. Ko Yesu canke Yezu (Jésus) ari umwana...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁u shingiye ▁kuri ▁bibiliya ▁ni ▁umwana ▁w ' imana . ... (+26 more)` | 36 |
| 16k | `▁u shingiye ▁kuri ▁bibiliya ▁ni ▁umwana ▁w ' imana . ... (+23 more)` | 33 |
| 32k | `▁ushingiye ▁kuri ▁bibiliya ▁ni ▁umwana ▁w ' imana . ▁ko ... (+21 more)` | 31 |

**Sample 3:** `Indonyi (Kobus ellipsiprymnus defassa) ni igikoko gifise amahembe maremare kikam...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁indon yi ▁( ko bu s ▁el lip si p ... (+25 more)` | 35 |
| 16k | `▁indon yi ▁( ko bu s ▁ellip si p ry ... (+24 more)` | 34 |
| 32k | `▁indonyi ▁( kobus ▁ellipsiprymnus ▁defassa ) ▁ni ▁igikoko ▁gifise ▁amahembe ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 32k achieves 4.735x compression
- **Lowest UNK Rate:** 8k with 0.2846% 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 | 1,057 | 10.05 | 1,527 | 29.0% | 84.0% |
| **2-gram** | Subword | 201 🏆 | 7.65 | 1,104 | 75.0% | 99.9% |
| **3-gram** | Word | 1,104 | 10.11 | 1,428 | 25.0% | 84.0% |
| **3-gram** | Subword | 1,386 | 10.44 | 6,340 | 29.6% | 82.8% |
| **4-gram** | Word | 1,786 | 10.80 | 2,222 | 18.3% | 63.5% |
| **4-gram** | Subword | 6,484 | 12.66 | 23,552 | 12.6% | 46.7% |
| **5-gram** | Word | 1,088 | 10.09 | 1,323 | 25.3% | 83.2% |
| **5-gram** | Subword | 17,832 | 14.12 | 46,096 | 7.0% | 28.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ikigabane ca` | 277 |
| 2 | `na we` | 171 |
| 3 | `mu gihugu` | 164 |
| 4 | `avuga ati` | 123 |
| 5 | `mu burundi` | 116 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `uburinganire ibirometero kwadarato` | 87 |
| 2 | `mu ntara ya` | 75 |
| 3 | `mu gihugu ca` | 61 |
| 4 | `ni igisagara kiri` | 53 |
| 5 | `ibintu bifise ubuzima` | 41 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `bw ibintu bifise ubuzima` | 41 |
| 2 | `zunze ubumwe bwa amerika` | 31 |
| 3 | `leta zunze ubumwe bwa` | 31 |
| 4 | `mu gihugu ca kanahani` | 27 |
| 5 | `ni igisagara kiri muri` | 26 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `leta zunze ubumwe bwa amerika` | 31 |
| 2 | `z unze ubumwe za amerika` | 25 |
| 3 | `w ibihumbi bibiri na cumi` | 20 |
| 4 | `ni gutera abavandimwe aa orchidaceae` | 19 |
| 5 | `mumwaka w ibihumbi bibiri na` | 18 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 21,858 |
| 2 | `e _` | 12,255 |
| 3 | `i _` | 10,392 |
| 4 | `a n` | 9,486 |
| 5 | `o _` | 9,301 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m u` | 5,020 |
| 2 | `r a _` | 4,514 |
| 3 | `a r a` | 3,092 |
| 4 | `a b a` | 3,082 |
| 5 | `r i _` | 3,003 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ m u _` | 2,368 |
| 2 | `_ u m u` | 1,634 |
| 3 | `a _ m u` | 1,523 |
| 4 | `i r a _` | 1,469 |
| 5 | `_ n a _` | 1,159 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i h u g u` | 754 |
| 2 | `a _ m u _` | 747 |
| 3 | `g i h u g` | 681 |
| 4 | `_ m u r i` | 654 |
| 5 | `r u n d i` | 653 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 201
- **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 | 0.6054 | 1.521 | 3.16 | 18,741 | 39.5% |
| **1** | Subword | 1.1432 | 2.209 | 8.47 | 307 | 0.0% |
| **2** | Word | 0.1529 | 1.112 | 1.26 | 58,782 | 84.7% |
| **2** | Subword | 0.9964 | 1.995 | 5.12 | 2,593 | 0.4% |
| **3** | Word | 0.0459 | 1.032 | 1.06 | 73,578 | 95.4% |
| **3** | Subword | 0.7791 | 1.716 | 3.27 | 13,247 | 22.1% |
| **4** | Word | 0.0181 🏆 | 1.013 | 1.02 | 77,704 | 98.2% |
| **4** | Subword | 0.5566 | 1.471 | 2.27 | 43,142 | 44.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `mu gihugu cawe c inyoni zose ziguruka imwimwe ku matwi yakobo 29 uwu nyene imbere y`
2. `n ubusho nshoreye n iterambere ry igisagara kiri muri rig veda ibihimbano byatangiye hagati yibiro 4...`
3. `ni gutera abavandimwe acampe nyassana acampe intermedia acampe praemorsa ni we tudaharuye abagore n ...`

**Context Size 2:**

1. `ikigabane ca 21 ikigabane ca 7 ikigabane ca 18 ikigabane ca 11 ikigabane ca 23 ikigabane ca`
2. `na we avyara tubari kayini yari nahama 23 rameki abwira abagore biwe babiri umukuru w umugambwe cndd`
3. `mu gihugu benewabo na yozefu ati ehe umuntu yabaye nk umwe mu bantu b urwo rugo yari`

**Context Size 3:**

1. `uburinganire ibirometero kwadarato 840 abanyagihugu 829 677 circus`
2. `mu ntara ya ngozi komine kiremba mu burundi akabizi ni uruzi ruri mu ntara ya makamba mu buseruko`
3. `mu gihugu ca kanahani 19 rabani yari yagiye kumwa ubwoya ubusho bwiwe igihe rakeri yiba ibishusho vy...`

**Context Size 4:**

1. `leta zunze ubumwe bwa amerika abaserukizi 435 34 umuserukizi ashika muri sentare house representativ...`
2. `zunze ubumwe bwa amerika uhimbazwa ryari mu kw indwi mukakaro itariki zine july 4th 10 mur ukwo kwik...`
3. `mu gihugu ca kanahani i kiriyati areba ari ho heburoni aho aburahamu na izahaki bari barabaye 28 imi...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_risiri_kakagi:_`
2. `a_nginko_be_n'in`
3. `isusezi,nandi)_m`

**Context Size 2:**

1. `a_rwo_bangwara_no`
2. `e_17_izi_atai_imb`
3. `i_n'inira_ne_muso`

**Context Size 3:**

1. `_mu_gihe_biwe_ikid`
2. `ra_icendera_cfc1v_`
3. `araso_nimwaka_ngin`

**Context Size 4:**

1. `_mu_nzu_rero_c'aban`
2. `_umunani_gusa_bwint`
3. `a_mu_gushika_iyo_ri`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (43,142 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 | 6,649 |
| Total Tokens | 72,643 |
| Mean Frequency | 10.93 |
| Median Frequency | 3 |
| Frequency Std Dev | 52.83 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mu | 2,396 |
| 2 | n | 1,861 |
| 3 | ni | 1,183 |
| 4 | na | 1,162 |
| 5 | y | 780 |
| 6 | ya | 714 |
| 7 | w | 652 |
| 8 | muri | 611 |
| 9 | ca | 548 |
| 10 | ku | 530 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | umusalaba | 2 |
| 2 | ubutwari | 2 |
| 3 | umukardinali | 2 |
| 4 | bonaventura | 2 |
| 5 | akhenaton | 2 |
| 6 | umukatorika | 2 |
| 7 | ruanda | 2 |
| 8 | stanley | 2 |
| 9 | kirisese | 2 |
| 10 | inyungu | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9786 |
| R² (Goodness of Fit) | 0.986220 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 37.3% |
| Top 1,000 | 72.6% |
| Top 5,000 | 95.5% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9862 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 37.3% of corpus
- **Long Tail:** -3,351 words needed for remaining 100.0% 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 | 0.1625 | 0.5214 | N/A | N/A |
| **mono_64d** | 64 | 0.0296 | 0.5371 | N/A | N/A |
| **mono_128d** | 128 | 0.0040 | 0.5210 | N/A | N/A |
| **aligned_32d** | 32 | 0.1625 🏆 | 0.5232 | 0.0183 | 0.0888 |
| **aligned_64d** | 64 | 0.0296 | 0.5482 | 0.0209 | 0.1384 |
| **aligned_128d** | 128 | 0.0040 | 0.5338 | 0.0235 | 0.1514 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.1625 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.5308. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 2.3% 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 | **1.919** | 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 |
|--------|----------|
| `-i` | imbabazi, imiringa, ishikanwa |
| `-a` | asubira, akoresheje, ashira |
| `-b` | bivugwa, bakomeye, bitungwa |
| `-ba` | bakomeye, baravuga, bahamagara |
| `-m` | marin, mbwira, mumakomine |
| `-mu` | mumakomine, muji, mugitondo |
| `-n` | nzoyiguha, nabantu, ntare |
| `-k` | kumugabane, keza, kampala |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | guhindura, asubira, yumva |
| `-e` | kumugabane, umuhinde, akoresheje |
| `-ra` | guhindura, asubira, ashira |
| `-i` | imbabazi, umushatsi, umutamvyi |
| `-o` | dukoko, ninaho, ivyiyumviro |
| `-ye` | bakomeye, ibaye, ndayizeye |
| `-wa` | bivugwa, ishikanwa, atorwa |
| `-ka` | abasangwabutaka, yubaka, agaruka |

### 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 |
|------|----------|------------------|----------|
| `anga` | 1.62x | 32 contexts | nanga, banga, ibanga |
| `andi` | 1.50x | 23 contexts | bandi, kandi, bandit |
| `nshi` | 1.59x | 18 contexts | menshi, kenshi, benshi |
| `fise` | 1.45x | 23 contexts | afise, ufise, mfise |
| `vuga` | 1.43x | 24 contexts | uvuga, avuga, ivuga |
| `indi` | 1.46x | 20 contexts | zindi, bindi, rindi |
| `gira` | 1.32x | 24 contexts | agira, ugira, igira |
| `kuru` | 1.31x | 21 contexts | nkuru, bikuru, mukuru |
| `anye` | 1.62x | 11 contexts | azanye, ajanye, bazanye |
| `bere` | 1.55x | 12 contexts | mbere, mabere, imbere |
| `mber` | 1.55x | 11 contexts | mbere, ambera, imbere |
| `agar` | 1.43x | 13 contexts | hagari, agaruka, amagara |

### 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 |
|--------|--------|-----------|----------|
| `-a` | `-a` | 289 words | asubira, ashira |
| `-i` | `-a` | 217 words | imiringa, ishikanwa |
| `-b` | `-a` | 208 words | bivugwa, bitungwa |
| `-k` | `-a` | 183 words | keza, kampala |
| `-i` | `-o` | 152 words | ivyiyumviro, ikirago |
| `-u` | `-a` | 142 words | umwuga, ushobora |
| `-u` | `-i` | 117 words | umushatsi, umutamvyi |
| `-b` | `-e` | 109 words | bakomeye, bahejeje |
| `-a` | `-ra` | 107 words | asubira, ashira |
| `-i` | `-e` | 104 words | itikize, ibaye |

### 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 |
|------|-----------------|------------|------|
| shineyari | **`shiney-a-ri`** | 7.5 | `a` |
| bahamagara | **`bahamag-a-ra`** | 7.5 | `a` |
| iyondwara | **`iyondw-a-ra`** | 7.5 | `a` |
| umupfakazi | **`umupfa-ka-zi`** | 7.5 | `ka` |
| yaramuhaye | **`yaramu-ha-ye`** | 7.5 | `ha` |
| colombiana | **`colombi-a-na`** | 7.5 | `a` |
| inyambaro | **`inyamb-a-ro`** | 7.5 | `a` |
| abahanuzi | **`abahan-u-zi`** | 7.5 | `u` |
| umuganuro | **`umugan-u-ro`** | 7.5 | `u` |
| ikibiribiri | **`ikibirib-i-ri`** | 7.5 | `i` |
| ahagaragara | **`ahagarag-a-ra`** | 7.5 | `a` |
| nyamukuru | **`n-ya-mukuru`** | 7.5 | `mukuru` |
| yagaragaye | **`yagarag-a-ye`** | 7.5 | `a` |
| ahamagara | **`ahamag-a-ra`** | 7.5 | `a` |
| intambara | **`intamb-a-ra`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Rundi 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 | **32k BPE** | Best compression (4.73x) |
| N-gram | **2-gram** | Lowest perplexity (201) |
| Markov | **Context-4** | Highest predictability (98.2%) |
| 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: 2026-01-10 18:46:39*