---
language: ve
language_name: Venda
language_family: bantu_southern
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_southern
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: 4.989
  - name: best_isotropy
    type: isotropy
    value: 0.0347
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Venda** 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** | 4.573x | 4.58 | 0.1398% | 90,147 |
| **16k** | 4.989x 🏆 | 5.00 | 0.1525% | 82,635 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Azwihangwisi Faith Muthambi o bebwa nga la fumitahe la Luhuhi Ndi ndi muthu wa b...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁azwi hangwi si ▁fa ith ▁mutha mbi ▁o ▁bebwa ▁nga ... (+20 more)` | 30 |
| 16k | `▁azwihangwisi ▁faith ▁muthambi ▁o ▁bebwa ▁nga ▁la ▁fumitahe ▁la ▁luhuhi ... (+15 more)` | 25 |

**Sample 2:** `Maswiakae ndi ḓorobo, ino wanala Makhuduthamaga Local Municipality, Limpopo kha ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁maswi akae ▁ndi ▁ḓorobo , ▁ino ▁wanala ▁makhuduthamaga ▁local ▁municipality ... (+8 more)` | 18 |
| 16k | `▁maswiakae ▁ndi ▁ḓorobo , ▁ino ▁wanala ▁makhuduthamaga ▁local ▁municipality , ... (+7 more)` | 17 |

**Sample 3:** `Mogorwane ndi ḓorobo, ino wanala Makhuduthamaga Local Municipality, Limpopo kha ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mogo rwa ne ▁ndi ▁ḓorobo , ▁ino ▁wanala ▁makhuduthamaga ▁local ... (+9 more)` | 19 |
| 16k | `▁mogorwane ▁ndi ▁ḓorobo , ▁ino ▁wanala ▁makhuduthamaga ▁local ▁municipality , ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 16k achieves 4.989x compression
- **Lowest UNK Rate:** 8k with 0.1398% 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 | 553 | 9.11 | 1,442 | 48.8% | 91.2% |
| **2-gram** | Subword | 170 🏆 | 7.41 | 892 | 77.7% | 100.0% |
| **3-gram** | Word | 370 | 8.53 | 1,366 | 58.6% | 92.9% |
| **3-gram** | Subword | 929 | 9.86 | 5,199 | 41.7% | 86.8% |
| **4-gram** | Word | 577 | 9.17 | 2,528 | 55.0% | 78.6% |
| **4-gram** | Subword | 3,239 | 11.66 | 17,351 | 26.0% | 62.5% |
| **5-gram** | Word | 445 | 8.80 | 1,799 | 59.6% | 86.1% |
| **5-gram** | Subword | 6,856 | 12.74 | 28,611 | 19.4% | 48.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `afurika tshipembe` | 744 |
| 2 | `kha la` | 599 |
| 3 | `la afurika` | 578 |
| 4 | `ino wanala` | 553 |
| 5 | `ndi ḓorobo` | 538 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `la afurika tshipembe` | 575 |
| 2 | `kha la afurika` | 568 |
| 3 | `ḓorobo ino wanala` | 530 |
| 4 | `ndi ḓorobo ino` | 527 |
| 5 | `limpopo kha la` | 469 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kha la afurika tshipembe` | 568 |
| 2 | `ndi ḓorobo ino wanala` | 527 |
| 3 | `limpopo kha la afurika` | 468 |
| 4 | `local municipality limpopo kha` | 456 |
| 5 | `municipality limpopo kha la` | 452 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `limpopo kha la afurika tshipembe` | 468 |
| 2 | `local municipality limpopo kha la` | 452 |
| 3 | `municipality limpopo kha la afurika` | 452 |
| 4 | `henefha hu na vhadzulapo vha` | 261 |
| 5 | `kha la afurika tshipembe dza` | 256 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 28,563 |
| 2 | `h a` | 11,957 |
| 3 | `v h` | 9,459 |
| 4 | `i _` | 9,304 |
| 5 | `o _` | 8,161 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ v h` | 7,128 |
| 2 | `h a _` | 6,686 |
| 3 | `v h a` | 5,533 |
| 4 | `t s h` | 4,409 |
| 5 | `_ t s` | 3,991 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ v h a` | 4,614 |
| 2 | `_ t s h` | 3,640 |
| 3 | `a _ v h` | 3,320 |
| 4 | `t s h i` | 3,188 |
| 5 | `v h a _` | 2,961 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t s h i` | 2,846 |
| 2 | `_ v h a _` | 2,451 |
| 3 | `a _ t s h` | 2,354 |
| 4 | `a _ v h a` | 2,049 |
| 5 | `_ n d i _` | 1,599 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 170
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~48% 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 | 0.6638 | 1.584 | 3.61 | 9,716 | 33.6% |
| **1** | Subword | 1.3289 | 2.512 | 10.31 | 162 | 0.0% |
| **2** | Word | 0.2215 | 1.166 | 1.43 | 34,846 | 77.9% |
| **2** | Subword | 1.2039 | 2.304 | 6.12 | 1,665 | 0.0% |
| **3** | Word | 0.0671 | 1.048 | 1.10 | 49,273 | 93.3% |
| **3** | Subword | 0.7757 | 1.712 | 3.17 | 10,158 | 22.4% |
| **4** | Word | 0.0208 🏆 | 1.015 | 1.03 | 53,626 | 97.9% |
| **4** | Subword | 0.4655 | 1.381 | 2.00 | 32,136 | 53.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `vha no mametja vha vha vho kavhiwa nga itshi vhathu vha tshisimani fet college publishers zwi`
2. `u bvisa tshilonda tshi kha vhutshilo ha zwiila zwa pfunzo ya nga vhahulwane na kunwalele kwa`
3. `na vhashumeli vha mbo ḓi tambela tshanda ha ngo tea u kona u anzela u dzhenelela`

**Context Size 2:**

1. `afurika tshipembe vhathu vhunzhi ha vhathu vha u bva asia dzinwe thoro dzine dza vha uri zwo`
2. `kha la afurika tshipembe dza limpopo dza limpopo dza dze dza vh dzi thamumbuloni ya muvhuso wa`
3. `la afurika tshipembe dorobo dza tsini ndi thohoyandou na tzaneen i tsini na muserenga tondo dzingi d...`

**Context Size 3:**

1. `la afurika tshipembe henefha hu na vhadzulapo vha 1 265 dza limpopo`
2. `kha la afurika tshipembe henefha hu na vhadzulapo vha 4 452 ka xikundu references dza limpopo`
3. `ḓorobo ino wanala limpopo kha la afurika tshipembe dza limpopo`

**Context Size 4:**

1. `kha la afurika tshipembe dza limpopo`
2. `ndi ḓorobo ino wanala greater tzaneen local municipality limpopo kha la afurika tshipembe dza limpop...`
3. `limpopo kha la afurika tshipembe dza limpopo`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ḓi._ali_ts_l_e_`
2. `alaipophiavho_na`
3. `hi_hwafhamufso_v`

**Context Size 2:**

1. `a_zwina_me_kwa_kh`
2. `ha_ha_jerendi_no_`
3. `vhou_vha_vha_ya_v`

**Context Size 3:**

1. `_vho_90px_27.934_d`
2. `ha_la_a_i_wana._mu`
3. `vha_lipida_vha_kha`

**Context Size 4:**

1. `_vha_mitshedzo_nga_`
2. `_tsha_sovengo_la_af`
3. `a_vhaisimane_na_kal`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (32,136 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 | 4,057 |
| Total Tokens | 63,019 |
| Mean Frequency | 15.53 |
| Median Frequency | 3 |
| Frequency Std Dev | 95.58 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | vha | 2,496 |
| 2 | u | 2,148 |
| 3 | na | 2,117 |
| 4 | ndi | 1,632 |
| 5 | kha | 1,576 |
| 6 | nga | 1,426 |
| 7 | ya | 1,347 |
| 8 | a | 1,211 |
| 9 | dza | 1,085 |
| 10 | limpopo | 1,062 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | out | 2 |
| 2 | ḽihoro | 2 |
| 3 | stanley | 2 |
| 4 | announces | 2 |
| 5 | tells | 2 |
| 6 | open | 2 |
| 7 | books | 2 |
| 8 | close | 2 |
| 9 | your | 2 |
| 10 | hourlyhits | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0307 |
| R² (Goodness of Fit) | 0.989758 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 59.5% |
| Top 1,000 | 85.1% |
| Top 5,000 | 0.0% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9898 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 59.5% of corpus
- **Long Tail:** -5,943 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 | 0.0347 🏆 | 0.7804 | N/A | N/A |
| **mono_64d** | 64 | 0.0065 | 0.7768 | N/A | N/A |
| **mono_128d** | 128 | 0.0015 | 0.7951 | N/A | N/A |
| **aligned_32d** | 32 | 0.0347 | 0.7762 | 0.0096 | 0.0927 |
| **aligned_64d** | 64 | 0.0065 | 0.8086 | 0.0096 | 0.0831 |
| **aligned_128d** | 128 | 0.0015 | 0.7992 | 0.0128 | 0.0767 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.0347 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.7894. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.3% 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 | **0.784** | 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` | marema, minisța, maṱo |
| `-ma` | marema, maṱo, mahosi |
| `-vh` | vhudifari, vhudzekani, vhengiwa |
| `-mu` | muṅwe, muvhilini, mueni |
| `-t` | tshenetshi, tea, teya |
| `-n` | nkhumbela, ngavha, north |
| `-s` | springer, stellenbosch, shandukani |
| `-k` | kongomisa, khirikhete, kamakosha |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | kongomisa, marema, wina |
| `-i` | vhudifari, vhudzekani, zwavhuḓi |
| `-o` | dzinyambo, petro, onoyo |
| `-e` | khirikhete, jane, gude |
| `-wa` | vhengiwa, vuswa, livhuwa |
| `-ni` | vhudzekani, lifhasini, vhukonani |
| `-la` | nkhumbela, ambelela, dalela |
| `-ho` | ḓivheaho, henefho, fanaho |

### 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.

*No significant bound stems detected.*


### 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 |
|--------|--------|-----------|----------|
| `-t` | `-a` | 131 words | tea, teya |
| `-m` | `-a` | 125 words | marema, minisța |
| `-m` | `-o` | 88 words | maṱo, mbuno |
| `-m` | `-i` | 86 words | mahosi, mathomoni |
| `-vh` | `-i` | 82 words | vhudifari, vhudzekani |
| `-vh` | `-a` | 68 words | vhengiwa, vhovha |
| `-t` | `-o` | 58 words | tshumisano, thendelano |
| `-t` | `-i` | 51 words | tshenetshi, takalani |
| `-m` | `-e` | 50 words | muṅwe, marriage |
| `-k` | `-a` | 48 words | kongomisa, kamakosha |

### 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 |
|------|-----------------|------------|------|
| tshinnani | **`tshin-na-ni`** | 7.5 | `na` |
| bvelesisa | **`bvele-si-sa`** | 7.5 | `si` |
| ramabindu | **`ra-ma-bindu`** | 7.5 | `bindu` |
| tshikhala | **`tshik-ha-la`** | 7.5 | `ha` |
| swikelela | **`swike-le-la`** | 7.5 | `le` |
| tshiphani | **`tship-ha-ni`** | 7.5 | `ha` |
| humbulela | **`humbu-le-la`** | 7.5 | `le` |
| vhonalaho | **`vhona-la-ho`** | 6.0 | `vhona` |
| vhatshini | **`vh-atshi-ni`** | 6.0 | `atshi` |
| maḓuvhani | **`ma-ḓuvha-ni`** | 6.0 | `ḓuvha` |
| mashangoni | **`ma-shango-ni`** | 6.0 | `shango` |
| mavhulani | **`ma-vhula-ni`** | 6.0 | `vhula` |
| tshikoloni | **`tshikolo-ni`** | 4.5 | `tshikolo` |
| muhulwane | **`mu-hulwane`** | 4.5 | `hulwane` |
| mashuvhuru | **`ma-shuvhuru`** | 4.5 | `shuvhuru` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Venda 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 | **16k BPE** | Best compression (4.99x) |
| N-gram | **2-gram** | Lowest perplexity (170) |
| Markov | **Context-4** | Highest predictability (97.9%) |
| 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 02:39:50*