README.md

---
language: st
language_name: Southern Sotho
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: 4.418
  - name: best_isotropy
    type: isotropy
    value: 0.5673
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Southern Sotho - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Southern Sotho** 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** | 3.776x | 3.78 | 0.2714% | 231,037 |
| **16k** | 4.068x | 4.07 | 0.2923% | 214,484 |
| **32k** | 4.296x | 4.30 | 0.3087% | 203,079 |
| **64k** | 4.418x 🏆 | 4.42 | 0.3175% | 197,468 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Siphelele Mthembu (ya hlahileng ka la 15 Phato ke sebapadi sa bolo ya maoto Afri...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁si phe lele ▁mthe mbu ▁( ya ▁hlahileng ▁ka ▁la ... (+24 more)` | 34 |
| 16k | `▁siphelele ▁mthembu ▁( ya ▁hlahileng ▁ka ▁la ▁ 1 5 ... (+21 more)` | 31 |
| 32k | `▁siphelele ▁mthembu ▁( ya ▁hlahileng ▁ka ▁la ▁ 1 5 ... (+21 more)` | 31 |
| 64k | `▁siphelele ▁mthembu ▁( ya ▁hlahileng ▁ka ▁la ▁ 1 5 ... (+21 more)` | 31 |

**Sample 2:** `Rafael José Orozco Maestre (Hlakubele 24, – 11 Phupu ne e le sebini, sengoli sa ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ra fa el ▁jo s é ▁o ro z co ... (+26 more)` | 36 |
| 16k | `▁rafa el ▁josé ▁oroz co ▁mae st re ▁( hla ... (+21 more)` | 31 |
| 32k | `▁rafael ▁josé ▁orozco ▁mae st re ▁( hlakubele ▁ 2 ... (+18 more)` | 28 |
| 64k | `▁rafael ▁josé ▁orozco ▁maestre ▁( hlakubele ▁ 2 4 , ... (+16 more)` | 26 |

**Sample 3:** `Mokwallo ke lekeishene le haufi le Vredefort, ka hare ho Masepala wa Ngwathe, po...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mo kwa llo ▁ke ▁lekeishene ▁le ▁haufi ▁le ▁vrede fort ... (+17 more)` | 27 |
| 16k | `▁mo kwa llo ▁ke ▁lekeishene ▁le ▁haufi ▁le ▁vredefort , ... (+16 more)` | 26 |
| 32k | `▁mokwallo ▁ke ▁lekeishene ▁le ▁haufi ▁le ▁vredefort , ▁ka ▁hare ... (+14 more)` | 24 |
| 64k | `▁mokwallo ▁ke ▁lekeishene ▁le ▁haufi ▁le ▁vredefort , ▁ka ▁hare ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 4.418x compression
- **Lowest UNK Rate:** 8k with 0.2714% 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 | 4,147 | 12.02 | 10,524 | 21.0% | 52.2% |
| **2-gram** | Subword | 184 🏆 | 7.52 | 1,683 | 77.1% | 99.6% |
| **3-gram** | Word | 6,664 | 12.70 | 14,321 | 16.6% | 41.7% |
| **3-gram** | Subword | 1,318 | 10.36 | 12,094 | 38.3% | 80.9% |
| **4-gram** | Word | 13,698 | 13.74 | 22,303 | 10.5% | 28.0% |
| **4-gram** | Subword | 6,177 | 12.59 | 50,733 | 19.5% | 52.6% |
| **5-gram** | Word | 10,291 | 13.33 | 14,770 | 10.4% | 28.8% |
| **5-gram** | Subword | 17,540 | 14.10 | 100,714 | 10.4% | 34.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e le` | 2,604 |
| 2 | `ile a` | 2,556 |
| 3 | `o ile` | 2,550 |
| 4 | `afrika borwa` | 1,822 |
| 5 | `ka la` | 1,398 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o ile a` | 2,458 |
| 2 | `e ne e` | 839 |
| 3 | `ne e le` | 639 |
| 4 | `sa afrika borwa` | 459 |
| 5 | `e ile ya` | 458 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e ne e le` | 633 |
| 2 | `sa bolo ya maoto` | 249 |
| 3 | `ka o ile a` | 216 |
| 4 | `bolo ya maoto sa` | 212 |
| 5 | `ka moka afrika borwa` | 179 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sa bolo ya maoto sa` | 211 |
| 2 | `sebapadi sa bolo ya maoto` | 161 |
| 3 | `bolo ya maoto sa afrika` | 156 |
| 4 | `ya maoto sa afrika borwa` | 155 |
| 5 | `ke sebapadi sa bolo ya` | 146 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 129,546 |
| 2 | `e _` | 80,922 |
| 3 | `o _` | 53,695 |
| 4 | `l e` | 48,470 |
| 5 | `_ l` | 37,957 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l e _` | 26,748 |
| 2 | `_ l e` | 23,579 |
| 3 | `n g _` | 22,710 |
| 4 | `k a _` | 18,228 |
| 5 | `h o _` | 18,075 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e _` | 15,451 |
| 2 | `_ h o _` | 13,673 |
| 3 | `_ k a _` | 12,473 |
| 4 | `e n g _` | 11,083 |
| 5 | `_ y a _` | 9,749 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ h o _` | 6,521 |
| 2 | `_ t s a _` | 5,552 |
| 3 | `_ t s e _` | 4,528 |
| 4 | `e _ l e _` | 4,398 |
| 5 | `a _ l e _` | 4,221 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 184
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.7915 | 1.731 | 4.86 | 30,896 | 20.8% |
| **1** | Subword | 0.9659 | 1.953 | 8.17 | 449 | 3.4% |
| **2** | Word | 0.3145 | 1.244 | 1.77 | 149,534 | 68.5% |
| **2** | Subword | 1.0583 | 2.082 | 6.21 | 3,664 | 0.0% |
| **3** | Word | 0.1184 | 1.086 | 1.22 | 264,209 | 88.2% |
| **3** | Subword | 0.8464 | 1.798 | 3.86 | 22,722 | 15.4% |
| **4** | Word | 0.0501 🏆 | 1.035 | 1.08 | 320,187 | 95.0% |
| **4** | Subword | 0.5799 | 1.495 | 2.42 | 87,601 | 42.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `le ka setereke provensing ya hae pele a le phahameng sa setjhaba ba hae la sebaka`
2. `e neng se bapalang e nang le lefapha lefapha bakeng sa bohareng sa boeta pele a`
3. `ho masepala wa bophelo lisebelisoa tsohle tse ling tsa zone 14 qetellong ya latela mokhatlo o`

**Context Size 2:**

1. `e le puo yaa bahatelli e le toropo ea ypres setsi sa setso sa sekgowa`
2. `ile a fumana diploma ya hae le ka leboya ho noka ya elands ka histori sebaka sena`
3. `o ile a khethwa sehlopheng sa gauteng afrika borwa u23 ha a hopola mabaka a mang a`

**Context Size 3:**

1. `o ile a latelwa ke moprofesa daya reddy ka la 13 phuptjane ke senokwane sa afrika borwa dipina`
2. `e ne e le ya hae ya independence day dipina bahale ba hosane ho hong ho maafrika borwa`
3. `ne e le karolo ea sehlopha se neng se nahana hore se utlwa likhohlano tsa lelapa le ho`

**Context Size 4:**

1. `e ne e le moruti mme seo sa etsa hore a be le maqhama hodima dijo le meetlo letsatsing`
2. `sa bolo ya maoto sa afrika borwa se bapalang e le sebapadi sa bohareng ba sehlopha sa ts galaxy`
3. `ka o ile a hlaha nakong ea papali ea papadi eo afrika borwa e ileng ya e ba ngaka`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_sts'erie_pa_pha`
2. `a_lesora_me._ya_`
3. `ent_afumapa_kabi`

**Context Size 2:**

1. `a_tliaha_ka_bo_o_`
2. `e_mohlo,_tlo_b_'m`
3. `o_kemini_wa_mang_`

**Context Size 3:**

1. `le_swa_bokgatang_e`
2. `_le_mabotjoalonyan`
3. `ng_ba_yuniteremira`

**Context Size 4:**

1. `_le_45_000_ka_e_mpe`
2. `_ho_bua_kang_jwalo_`
3. `_ka_nation_boydelli`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (87,601 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 | 14,659 |
| Total Tokens | 368,067 |
| Mean Frequency | 25.11 |
| Median Frequency | 4 |
| Frequency Std Dev | 312.16 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | le | 15,561 |
| 2 | e | 14,132 |
| 3 | ho | 13,814 |
| 4 | ka | 12,570 |
| 5 | a | 10,894 |
| 6 | ya | 10,066 |
| 7 | ba | 7,883 |
| 8 | sa | 7,305 |
| 9 | o | 6,830 |
| 10 | ea | 5,887 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | baker | 2 |
| 2 | navorsingsentrum | 2 |
| 3 | afrikanerbakens | 2 |
| 4 | federasie | 2 |
| 5 | kultuurvereniginge | 2 |
| 6 | 112 | 2 |
| 7 | ntlokgolo | 2 |
| 8 | lingoli | 2 |
| 9 | moiloa | 2 |
| 10 | trelawny | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1072 |
| R² (Goodness of Fit) | 0.991733 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 53.1% |
| Top 1,000 | 76.3% |
| Top 5,000 | 92.1% |
| Top 10,000 | 97.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9917 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 53.1% of corpus
- **Long Tail:** 4,659 words needed for remaining 2.5% 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 | 0.5673 🏆 | 0.3940 | N/A | N/A |
| **mono_64d** | 64 | 0.1528 | 0.3621 | N/A | N/A |
| **mono_128d** | 128 | 0.0222 | 0.3760 | N/A | N/A |
| **aligned_32d** | 32 | 0.5673 | 0.3806 | 0.0140 | 0.2000 |
| **aligned_64d** | 64 | 0.1528 | 0.3683 | 0.0300 | 0.2140 |
| **aligned_128d** | 128 | 0.0222 | 0.3775 | 0.0460 | 0.2040 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.5673 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3764. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.6% 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 | **-0.169** | 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` | menyabuketso, motorsports, makhooa |
| `-ma` | makhooa, maiteko, makhadzi |
| `-s` | sahesu, sammy, silila |
| `-b` | blaq, bruce, behile |
| `-mo` | motorsports, mopalami, motona |
| `-t` | tlalehilwe, toit, tsebahatsoa |
| `-bo` | bonahetse, bomampodi, bohahlauli |
| `-di` | diporesente, dikarabello, dienjini |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-ng` | iponahatsang, thahasellang, liking |
| `-a` | ginwala, elella, makhooa |
| `-e` | tlalehilwe, ujeqe, vlamertinge |
| `-g` | iponahatsang, thahasellang, liking |
| `-o` | menyabuketso, pablo, alebamo |
| `-i` | giovanni, makhadzi, mopalami |
| `-s` | motorsports, countries, bioethics |
| `-n` | in, upington, chan |

### 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 |
|------|----------|------------------|----------|
| `ilen` | 1.60x | 35 contexts | ileng, bileng, nileng |
| `tswe` | 1.62x | 27 contexts | etswe, entswe, tswela |
| `tsoe` | 1.70x | 21 contexts | etsoe, tsoelo, tsoela |
| `etso` | 1.32x | 45 contexts | ketso, setso, etsoa |
| `tsen` | 1.63x | 21 contexts | tsena, etseng, itseng |
| `lang` | 1.46x | 29 contexts | tlang, slang, lange |
| `elet` | 1.45x | 26 contexts | eletsa, leleti, keletso |
| `bapa` | 1.77x | 13 contexts | bapapa, bapale, bapala |
| `etsi` | 1.53x | 17 contexts | wetsi, setsi, metsi |
| `bets` | 1.58x | 15 contexts | betsa, ebetso, sebetse |
| `otho` | 1.41x | 20 contexts | motho, botho, sotho |
| `ehlo` | 1.48x | 14 contexts | lehloyo, lehloeo, lefehlo |

### 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 |
|--------|--------|-----------|----------|
| `-m` | `-a` | 170 words | maphalla, masilela |
| `-m` | `-i` | 128 words | multi, moletsi |
| `-m` | `-e` | 128 words | mohurutshe, millione |
| `-l` | `-o` | 125 words | lechato, likoloto |
| `-t` | `-g` | 120 words | tsejweng, tswelang |
| `-m` | `-o` | 120 words | mosiamo, meipiletso |
| `-t` | `-ng` | 118 words | tsejweng, tswelang |
| `-m` | `-g` | 108 words | maropeng, moelelong |
| `-b` | `-i` | 108 words | babuelli, bolepi |
| `-m` | `-ng` | 106 words | maropeng, moelelong |

### 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 |
|------|-----------------|------------|------|
| lithaoleng | **`lithaol-e-ng`** | 7.5 | `e` |
| lokolohile | **`lokoloh-i-le`** | 7.5 | `i` |
| hammanskraal | **`hammanskr-a-al`** | 7.5 | `a` |
| phetohelo | **`phetoh-e-lo`** | 7.5 | `e` |
| performing | **`perform-i-ng`** | 7.5 | `i` |
| matšeliso | **`matše-li-so`** | 7.5 | `li` |
| mangaliso | **`manga-li-so`** | 7.5 | `li` |
| tsamaisana | **`tsamais-a-na`** | 7.5 | `a` |
| nathaniel | **`nathani-e-l`** | 7.5 | `e` |
| dihlabeng | **`dihlab-e-ng`** | 7.5 | `e` |
| litlhaselo | **`litlha-se-lo`** | 7.5 | `se` |
| macroalga | **`macroal-g-a`** | 7.5 | `g` |
| hlahisang | **`hlahi-sa-ng`** | 7.5 | `sa` |
| moloisane | **`moloi-sa-ne`** | 7.5 | `sa` |
| batlileng | **`batli-le-ng`** | 7.5 | `le` |

### 6.6 Linguistic Interpretation

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

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.42x) |
| N-gram | **2-gram** | Lowest perplexity (184) |
| Markov | **Context-4** | Highest predictability (95.0%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 22:42:51*