---
language: ts
language_name: Tsonga
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: 4.757
  - name: best_isotropy
    type: isotropy
    value: 0.4521
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Tsonga** 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** | 4.083x | 4.09 | 0.1543% | 377,103 |
| **16k** | 4.448x | 4.45 | 0.1681% | 346,189 |
| **32k** | 4.757x 🏆 | 4.76 | 0.1798% | 323,678 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ostraliya (Xinghezi: Australia) i tiko ra Oxiyeniya.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ostraliya ▁( xing hezi : ▁australia ) ▁i ▁tiko ▁ra ... (+2 more)` | 12 |
| 16k | `▁ostraliya ▁( xinghezi : ▁australia ) ▁i ▁tiko ▁ra ▁oxiyeniya ... (+1 more)` | 11 |
| 32k | `▁ostraliya ▁( xinghezi : ▁australia ) ▁i ▁tiko ▁ra ▁oxiyeniya ... (+1 more)` | 11 |

**Sample 2:** `E ndhau leyinga le Soweto la ku ngava ni Soweto uprising.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁e ▁ndha u ▁leyin ga ▁le ▁soweto ▁la ▁ku ▁ngava ... (+6 more)` | 16 |
| 16k | `▁e ▁ndha u ▁leyinga ▁le ▁soweto ▁la ▁ku ▁ngava ▁ni ... (+5 more)` | 15 |
| 32k | `▁e ▁ndhau ▁leyinga ▁le ▁soweto ▁la ▁ku ▁ngava ▁ni ▁soweto ... (+2 more)` | 12 |

**Sample 3:** `+Jamhuri ya Kenya 125px 125px (Flag) (Coat of Arms) <small></big> 300px Kenya i ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁+ ja m huri ▁ya ▁kenya ▁ 1 2 5 ... (+30 more)` | 40 |
| 16k | `▁+ jamhuri ▁ya ▁kenya ▁ 1 2 5 px ▁ ... (+28 more)` | 38 |
| 32k | `▁+ jamhuri ▁ya ▁kenya ▁ 1 2 5 px ▁ ... (+28 more)` | 38 |


### Key Findings

- **Best Compression:** 32k achieves 4.757x compression
- **Lowest UNK Rate:** 8k with 0.1543% 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 | 3,674 | 11.84 | 6,696 | 17.5% | 52.9% |
| **2-gram** | Subword | 203 🏆 | 7.66 | 1,426 | 73.8% | 99.8% |
| **3-gram** | Word | 5,300 | 12.37 | 7,866 | 12.8% | 41.5% |
| **3-gram** | Subword | 1,457 | 10.51 | 10,147 | 33.7% | 80.2% |
| **4-gram** | Word | 9,675 | 13.24 | 12,992 | 9.7% | 28.5% |
| **4-gram** | Subword | 6,717 | 12.71 | 42,330 | 16.4% | 49.9% |
| **5-gram** | Word | 6,251 | 12.61 | 8,596 | 13.3% | 34.1% |
| **5-gram** | Subword | 18,231 | 14.15 | 82,731 | 8.9% | 32.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hi ku` | 816 |
| 2 | `na ku` | 518 |
| 3 | `tani hi` | 433 |
| 4 | `lembe ra` | 416 |
| 5 | `hi lembe` | 403 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hi lembe ra` | 342 |
| 2 | `hi siku leri` | 165 |
| 3 | `a ku ri` | 136 |
| 4 | `member of the` | 119 |
| 5 | `ku sukela hi` | 105 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `add text add text` | 103 |
| 2 | `text add text add` | 81 |
| 3 | `flag coat of arms` | 70 |
| 4 | `coat of arms small` | 67 |
| 5 | `hi ku ya hi` | 66 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `add text add text add` | 81 |
| 2 | `text add text add text` | 81 |
| 3 | `flag coat of arms small` | 67 |
| 4 | `life of a south african` | 65 |
| 5 | `of a south african tribe` | 65 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 92,010 |
| 2 | `i _` | 42,197 |
| 3 | `a n` | 25,791 |
| 4 | `_ n` | 22,549 |
| 5 | `u _` | 22,416 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n a _` | 15,155 |
| 2 | `k a _` | 14,105 |
| 3 | `_ k u` | 11,845 |
| 4 | `w a _` | 11,809 |
| 5 | `y a _` | 10,410 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k u _` | 7,542 |
| 2 | `_ y a _` | 7,064 |
| 3 | `_ h i _` | 6,736 |
| 4 | `_ n a _` | 6,398 |
| 5 | `_ w a _` | 5,407 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ e k a _` | 3,747 |
| 2 | `a _ k u _` | 3,382 |
| 3 | `a _ s w i` | 2,884 |
| 4 | `a _ h i _` | 2,861 |
| 5 | `a _ n a _` | 2,635 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 203
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~32% 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 | 0.7323 | 1.661 | 4.40 | 27,675 | 26.8% |
| **1** | Subword | 1.1293 | 2.187 | 8.40 | 380 | 0.0% |
| **2** | Word | 0.2742 | 1.209 | 1.61 | 121,281 | 72.6% |
| **2** | Subword | 1.0411 | 2.058 | 5.99 | 3,190 | 0.0% |
| **3** | Word | 0.0957 | 1.069 | 1.15 | 195,065 | 90.4% |
| **3** | Subword | 0.8570 | 1.811 | 3.83 | 19,088 | 14.3% |
| **4** | Word | 0.0308 🏆 | 1.022 | 1.04 | 223,778 | 96.9% |
| **4** | Subword | 0.5850 | 1.500 | 2.39 | 72,986 | 41.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ku tiyisisa leswaku mati eka buccaneers loko ku betsa timbalelo u tirhile tanihi ntiro wavutshila mi...`
2. `ya siku relero e nkaveni kenya i xirho xa mozambhiki ni moya wun we people amp`
3. `hi maribye ya 70 sangiovese na vasuvuki va a xihlanganisi xa vatsari va minhlangano leyi humesiweke`

**Context Size 2:**

1. `hi ku angarhela va vuriwa vatatana ntirho wa vukorhokeri mati na chukele leswi bakiweke hi mahiselo ...`
2. `na ku thyakisiwa vito hi nandzu wa ku tihlanganisa na swilo kumbe swiendlakalo swin wana leswi a`
3. `tani hi psitjemba kambe a va swi dyaka swinene mapa lawa ya nyiketeriweke eka hosi kheto uve`

**Context Size 3:**

1. `hi lembe ra huvo leyi ku hlanganisa na swihlawulekisi swa yona xivutiso lexi saleke hi ta mihleketo ...`
2. `hi siku leri lava tswariweke hi siku leri nelson mandela khale ka phresidenti ya afrika dzonga hinkw...`
3. `a ku ri xihaha mpfhuka lexi na xona kutani va famba va cela makhele ehenhla ka xona lomu`

**Context Size 4:**

1. `add text add text add text add text add text add text jkl add text add text add text`
2. `text add text add text add text add text m add text add text add text xyz add text`
3. `flag coat of arms small big 300px mauritius i tiko ra afrika leri kumekaka exikhari ka afrika dzonga...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_keka_yowi._nya_`
2. `awambo_lo_yana_h`
3. `i_ncavu_mananatl`

**Context Size 2:**

1. `a_mpito_yi_ntso_h`
2. `i_tioatimisi._mu_`
3. `anitsof_tiwa_hezi`

**Context Size 3:**

1. `na_le_ealt=blackso`
2. `ka_mbana_e_tala_nh`
3. `_ku_andla_kufiketo`

**Context Size 4:**

1. `_ku_tirho_leyintirh`
2. `_ya_le_makarta)_abu`
3. `_hi_fambia_nelsprud`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (72,986 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 | 11,975 |
| Total Tokens | 236,184 |
| Mean Frequency | 19.72 |
| Median Frequency | 4 |
| Frequency Std Dev | 174.31 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ku | 7,660 |
| 2 | ya | 7,078 |
| 3 | hi | 6,805 |
| 4 | na | 6,438 |
| 5 | wa | 5,468 |
| 6 | a | 4,111 |
| 7 | eka | 3,768 |
| 8 | va | 3,734 |
| 9 | ka | 3,663 |
| 10 | ra | 2,819 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | übersetzerinnen | 2 |
| 2 | übersetzern | 2 |
| 3 | allgemeinen | 2 |
| 4 | digitalisierung | 2 |
| 5 | linguistische | 2 |
| 6 | übersetzungsdienstleistungen | 2 |
| 7 | elektronischer | 2 |
| 8 | literarischen | 2 |
| 9 | übersetzungssektor | 2 |
| 10 | erfolgt | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1100 |
| R² (Goodness of Fit) | 0.990922 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.2% |
| Top 1,000 | 75.0% |
| Top 5,000 | 92.4% |
| Top 10,000 | 98.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9909 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.2% of corpus
- **Long Tail:** 1,975 words needed for remaining 1.7% 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 | 0.4521 | 0.4099 | N/A | N/A |
| **mono_64d** | 64 | 0.0928 | 0.3968 | N/A | N/A |
| **mono_128d** | 128 | 0.0116 | 0.4051 | N/A | N/A |
| **aligned_32d** | 32 | 0.4521 🏆 | 0.3983 | 0.0120 | 0.0800 |
| **aligned_64d** | 64 | 0.0928 | 0.4034 | 0.0220 | 0.1360 |
| **aligned_128d** | 128 | 0.0116 | 0.4050 | 0.0220 | 0.1020 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.4521 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4031. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 2.2% 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 | **0.051** | 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` | mavulavulelo, mankweng, mindzhuti |
| `-ma` | mavulavulelo, mankweng, makumekaka |
| `-xi` | xitanga, xiendla, xiximiwa |
| `-s` | swisaka, switereka, siku |
| `-t` | thoveriwa, tiviwaka, tise |
| `-ti` | tiviwaka, tise, tikonkulu |
| `-n` | ntlambi, nwaka, ngoni |
| `-e` | endliwa, evuhlongeni, endyangwini |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | thoveriwa, rhandziwa, vitana |
| `-i` | ntlambi, wansati, imini |
| `-e` | gewünschte, have, compare |
| `-o` | hikwalaho, mavulavulelo, ko |
| `-ni` | imini, koroni, evuhlongeni |
| `-le` | fuwile, uyile, chukele |
| `-wa` | thoveriwa, rhandziwa, endliwa |
| `-ka` | nwaka, swisaka, switereka |

### 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 |
|------|----------|------------------|----------|
| `ungu` | 1.62x | 54 contexts | hungu, kungu, lungu |
| `andz` | 1.52x | 54 contexts | andza, pandza, kandza |
| `hamb` | 1.74x | 27 contexts | hamba, hambi, rhambu |
| `isiw` | 1.56x | 36 contexts | yisiwa, hisiwa, nwisiwa |
| `tirh` | 1.54x | 35 contexts | tirha, tirhe, tirhi |
| `karh` | 1.70x | 24 contexts | karhi, nkarhi, mikarhi |
| `ngan` | 1.52x | 34 contexts | ngana, ngani, angana |
| `lela` | 1.62x | 26 contexts | hlela, fulela, leland |
| `riwa` | 1.61x | 25 contexts | siriwa, mariwa, soriwa |
| `tson` | 1.68x | 21 contexts | watson, tsongo, tsonga |
| `arhi` | 1.66x | 16 contexts | harhi, karhi, marhi |
| `ngul` | 1.66x | 15 contexts | angula, nguluve, sungule |

### 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` | 253 words | titimela, tivekaka |
| `-m` | `-a` | 207 words | mfukuzana, mintlwa |
| `-v` | `-i` | 187 words | vulavisisi, vukarhi |
| `-m` | `-i` | 177 words | mthombheni, mimiti |
| `-v` | `-a` | 141 words | vona, vatshila |
| `-e` | `-i` | 138 words | ematini, enyameni |
| `-m` | `-o` | 133 words | mikomiso, minxaxamelo |
| `-t` | `-i` | 129 words | tshuri, tihanyi |
| `-s` | `-a` | 128 words | swekeriwa, swokoma |
| `-t` | `-e` | 125 words | tumbuluxe, tshahiwile |

### 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 |
|------|-----------------|------------|------|
| tumbuluxiweke | **`tumbuluxiw-e-ke`** | 7.5 | `e` |
| chavisaka | **`chavis-a-ka`** | 7.5 | `a` |
| mudyandhzaka | **`mudyandhz-a-ka`** | 7.5 | `a` |
| swivulavulelo | **`swivulavu-le-lo`** | 7.5 | `le` |
| xirimbyati | **`xirimby-a-ti`** | 7.5 | `a` |
| wusunguleke | **`wusungu-le-ke`** | 7.5 | `le` |
| okmalumkoolkat | **`okmalumkoolk-a-t`** | 7.5 | `a` |
| nyangweni | **`nyangw-e-ni`** | 7.5 | `e` |
| fikeleleke | **`fikele-le-ke`** | 7.5 | `le` |
| xikalanga | **`xi-ka-langa`** | 7.5 | `langa` |
| nhlengani | **`nhleng-a-ni`** | 7.5 | `a` |
| leswivulaka | **`leswivu-la-ka`** | 7.5 | `la` |
| robertson | **`robert-s-on`** | 7.5 | `s` |
| exihlaleni | **`exihla-le-ni`** | 7.5 | `le` |
| hlanganani | **`hlangan-a-ni`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Tsonga 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 | **32k BPE** | Best compression (4.76x) |
| N-gram | **2-gram** | Lowest perplexity (203) |
| Markov | **Context-4** | Highest predictability (96.9%) |
| 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 01:42:25*