---
language: nso
language_name: Northern 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: 4.058
  - name: best_isotropy
    type: isotropy
    value: 0.3848
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Northern 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** | 3.741x | 3.75 | 0.2441% | 110,594 |
| **16k** | 3.926x | 3.94 | 0.2562% | 105,380 |
| **32k** | 4.058x 🏆 | 4.07 | 0.2648% | 101,960 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `This can be one of several places: Ophondweni, Jozini Ophondweni, Mtubatuba Opho...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁this ▁can ▁be ▁one ▁of ▁seve ral ▁places : ▁ophondweni ... (+8 more)` | 18 |
| 16k | `▁this ▁can ▁be ▁one ▁of ▁several ▁places : ▁ophondweni , ... (+7 more)` | 17 |
| 32k | `▁this ▁can ▁be ▁one ▁of ▁several ▁places : ▁ophondweni , ... (+7 more)` | 17 |

**Sample 2:** `(MMXIX)) ke ngwaga wa go thoma ka Labobedi ebile ke ngwaga wa bolešome wa ngwaga...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁( mm xix )) ▁ke ▁ngwaga ▁wa ▁go ▁thoma ▁ka ... (+11 more)` | 21 |
| 16k | `▁( mm xix )) ▁ke ▁ngwaga ▁wa ▁go ▁thoma ▁ka ... (+10 more)` | 20 |
| 32k | `▁( mmxix )) ▁ke ▁ngwaga ▁wa ▁go ▁thoma ▁ka ▁labobedi ... (+8 more)` | 18 |

**Sample 3:** `Mmušôgaê wa Umzumbe ke mmasepala go feta Mmasepala Setereke tša Ugu ka moka Afri...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mmušôgaê ▁wa ▁um zumbe ▁ke ▁mmasepala ▁go ▁feta ▁mmasepala ▁setereke ... (+8 more)` | 18 |
| 16k | `▁mmušôgaê ▁wa ▁umzumbe ▁ke ▁mmasepala ▁go ▁feta ▁mmasepala ▁setereke ▁tša ... (+7 more)` | 17 |
| 32k | `▁mmušôgaê ▁wa ▁umzumbe ▁ke ▁mmasepala ▁go ▁feta ▁mmasepala ▁setereke ▁tša ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 32k achieves 4.058x compression
- **Lowest UNK Rate:** 8k with 0.2441% 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 | 1,877 | 10.87 | 8,796 | 35.8% | 68.5% |
| **2-gram** | Subword | 175 🏆 | 7.45 | 1,382 | 78.3% | 99.9% |
| **3-gram** | Word | 2,747 | 11.42 | 13,343 | 31.7% | 62.0% |
| **3-gram** | Subword | 1,000 | 9.97 | 11,137 | 42.2% | 86.0% |
| **4-gram** | Word | 4,494 | 12.13 | 23,362 | 26.3% | 55.5% |
| **4-gram** | Subword | 3,469 | 11.76 | 44,498 | 26.2% | 64.9% |
| **5-gram** | Word | 4,124 | 12.01 | 17,998 | 24.2% | 56.4% |
| **5-gram** | Subword | 7,565 | 12.89 | 83,147 | 19.5% | 51.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ngwaga wa` | 7,528 |
| 2 | `afrika borwa` | 4,128 |
| 3 | `ka moka` | 3,009 |
| 4 | `yeo e` | 2,782 |
| 5 | `go feta` | 2,753 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka moka afrika` | 2,525 |
| 2 | `moka afrika borwa` | 2,525 |
| 3 | `mmasepala setereke tša` | 2,377 |
| 4 | `afrika borwa ditšhupetšo` | 2,354 |
| 5 | `go thoma ka` | 2,305 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka moka afrika borwa` | 2,525 |
| 2 | `wa go thoma ka` | 2,264 |
| 3 | `moka afrika borwa ditšhupetšo` | 2,034 |
| 4 | `ke nomoro yeo e` | 1,953 |
| 5 | `nomoro yeo e elego` | 1,951 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka moka afrika borwa ditšhupetšo` | 2,034 |
| 2 | `ke nomoro yeo e elego` | 1,951 |
| 3 | `yeo e elego magareng ga` | 1,950 |
| 4 | `nomoro yeo e elego magareng` | 1,950 |
| 5 | `ngwaga wa go thoma ka` | 1,531 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 147,261 |
| 2 | `e _` | 94,060 |
| 3 | `o _` | 75,200 |
| 4 | `w a` | 59,917 |
| 5 | `g o` | 47,431 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `w a _` | 27,531 |
| 2 | `k a _` | 25,523 |
| 3 | `g o _` | 25,104 |
| 4 | `l e _` | 24,070 |
| 5 | `_ w a` | 22,774 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ w a _` | 22,475 |
| 2 | `n g w a` | 20,389 |
| 3 | `g w a g` | 19,806 |
| 4 | `_ n g w` | 19,716 |
| 5 | `_ k a _` | 15,852 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g w a g` | 19,778 |
| 2 | `_ n g w a` | 19,683 |
| 3 | `g w a g a` | 13,412 |
| 4 | `k g o l o` | 12,563 |
| 5 | `a _ w a _` | 8,468 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 175
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~52% 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 | 0.7438 | 1.675 | 4.33 | 27,751 | 25.6% |
| **1** | Subword | 1.1468 | 2.214 | 9.66 | 307 | 0.0% |
| **2** | Word | 0.2865 | 1.220 | 1.70 | 119,289 | 71.4% |
| **2** | Subword | 1.0606 | 2.086 | 6.36 | 2,962 | 0.0% |
| **3** | Word | 0.1248 | 1.090 | 1.23 | 201,609 | 87.5% |
| **3** | Subword | 0.8492 | 1.801 | 3.87 | 18,823 | 15.1% |
| **4** | Word | 0.0569 🏆 | 1.040 | 1.10 | 246,105 | 94.3% |
| **4** | Subword | 0.5827 | 1.498 | 2.38 | 72,828 | 41.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `wa ngwagakete 1 le a kgomaretša afrika borwa ditšhupetšo wa ngwagakgolo 5 213 560 860 gomme`
2. `ka difiliming le koranta ya ferguson ya africa gallery then serving only you never gave us`
3. `go feta mmušôselegae wa bomasomesenyane senyane ke vredendal wellington ke village wa mmušôgaê wa ng...`

**Context Size 2:**

1. `ngwaga wa go thoma ka 1 pherekgong 320 ya fela ka morago letšatšing lona leo la sesotho`
2. `afrika borwa toropo kgolo wa letsemeng go feta mmušôselegae wa fetakgomo tubatse mmasepala setereke ...`
3. `ka moka porofense gauteng afrika borwa louis trichardt yeo pele e be e le kereke e fa`

**Context Size 3:**

1. `ka moka afrika borwa wepener ke 84 km borwa bodikela la bloemfontein ditšhupetšo`
2. `moka afrika borwa ditšhupetšo mmusogae mmusogae`
3. `mmasepala setereke tša nkangala wa porofense mpumalanga ka moka afrika borwa e bontšha se 587 154 85...`

**Context Size 4:**

1. `ka moka afrika borwa ditšhupetšo mmusogae history ka mokopane e be e bitšwa yunibesithi ya bophuthat...`
2. `wa go thoma ka 1 pherekgong ya fela ka 31 manthole ngwagasome o wela ngwagengkgolo wa 12`
3. `ke nomoro yeo e elego magareng ga sekete makgolosenyane masomeseswai tshela ke nomoro yeo e elego ma...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ya_ma_hlego_di,`
2. `a_maga_ka_fenapa`
3. `eoladegagwa_gomu`

**Context Size 2:**

1. `a_peditina_to_50s`
2. `e_to_makgole_na_m`
3. `o_moka_jo_1,_go_w`

**Context Size 3:**

1. `wa_ndlovu_go_feme.`
2. `ka_bodikete_wa_go_`
3. `go_thatobo_ngwaga_`

**Context Size 4:**

1. `_wa_ngwaga_wa_boith`
2. `ngwagengkete_2.1_pi`
3. `gwaga_wa_blue_whole`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (72,828 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 | 12,853 |
| Total Tokens | 414,233 |
| Mean Frequency | 32.23 |
| Median Frequency | 4 |
| Frequency Std Dev | 392.25 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | wa | 22,490 |
| 2 | ka | 15,960 |
| 3 | go | 15,871 |
| 4 | le | 14,392 |
| 5 | ya | 10,575 |
| 6 | ke | 9,273 |
| 7 | e | 9,250 |
| 8 | ngwaga | 7,952 |
| 9 | a | 7,812 |
| 10 | tša | 5,967 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | discipline | 2 |
| 2 | coach | 2 |
| 3 | drills | 2 |
| 4 | mentorship | 2 |
| 5 | accuracy | 2 |
| 6 | leagues | 2 |
| 7 | save | 2 |
| 8 | rekhotso | 2 |
| 9 | uttar | 2 |
| 10 | pradesh | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1658 |
| R² (Goodness of Fit) | 0.993219 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 62.1% |
| Top 1,000 | 83.7% |
| Top 5,000 | 94.7% |
| Top 10,000 | 98.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9932 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 62.1% of corpus
- **Long Tail:** 2,853 words needed for remaining 1.4% 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 | 0.3848 🏆 | 0.4271 | N/A | N/A |
| **mono_64d** | 64 | 0.0854 | 0.4240 | N/A | N/A |
| **mono_128d** | 128 | 0.0110 | 0.4112 | N/A | N/A |
| **aligned_32d** | 32 | 0.3848 | 0.4278 | 0.0160 | 0.1360 |
| **aligned_64d** | 64 | 0.0854 | 0.4247 | 0.0140 | 0.1520 |
| **aligned_128d** | 128 | 0.0110 | 0.4306 | 0.0300 | 0.1500 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.3848 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4242. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.0% 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 | **0.087** | 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` | mural, marope, msukaligwa |
| `-ma` | marope, mahlo, max |
| `-di` | dikete, diketekete, diakone |
| `-b` | balega, baile, barwarre |
| `-mo` | molato, moeti, mosweu |
| `-s` | sutherland, syncerus, senyane |
| `-se` | senyane, sehlare, sedibeng |
| `-bo` | bophara, botša, botala |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | balega, latofatšwa, kgethwa |
| `-e` | baile, marope, barwarre |
| `-o` | tiro, do, molato |
| `-ng` | tšoanang, kgang, tirišong |
| `-go` | lemorago, makatšago, paletšwego |
| `-g` | tšoanang, kgang, tirišong |
| `-i` | zweli, moeti, dzanani |
| `-le` | baile, lepelle, edenville |

### 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 |
|------|----------|------------------|----------|
| `ditš` | 1.75x | 14 contexts | ditšo, ditšie, ditšong |
| `nyan` | 1.43x | 23 contexts | nyane, nyana, nnyane |
| `ngwa` | 1.33x | 29 contexts | ngwana, ngwale, mongwa |
| `etšo` | 1.76x | 12 contexts | metšo, setšo, letšo |
| `thom` | 1.49x | 18 contexts | thome, thoma, thomo |
| `akgo` | 1.57x | 15 contexts | akgofa, makgolo, makgomo |
| `makg` | 1.67x | 11 contexts | makga, makgolo, makgabo |
| `hlan` | 1.40x | 16 contexts | hlano, hlangwa, mahlano |
| `tshe` | 1.43x | 14 contexts | tshepo, tshela, tsheko |
| `enya` | 1.31x | 14 contexts | fenya, kenya, senya |
| `yane` | 1.47x | 10 contexts | nyane, moyane, nnyane |
| `lano` | 1.56x | 8 contexts | hlano, mahlano, bohlano |

### 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` | 176 words | moima, mohlakola |
| `-di` | `-o` | 169 words | dihlaloso, ditumelo |
| `-t` | `-o` | 143 words | tšewego, tshwarelo |
| `-m` | `-e` | 133 words | meferefere, molatswanene |
| `-m` | `-o` | 128 words | madondo, motsotso |
| `-m` | `-i` | 127 words | mesebetsi, mlangeni |
| `-m` | `-g` | 113 words | meetsing, madireng |
| `-m` | `-ng` | 107 words | meetsing, madireng |
| `-b` | `-o` | 107 words | boso, butšwego |
| `-b` | `-i` | 102 words | bofokodi, bisi |

### 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 |
|------|-----------------|------------|------|
| producing | **`produc-i-ng`** | 7.5 | `i` |
| dintlhakgolo | **`dintlhak-go-lo`** | 7.5 | `go` |
| koringberg | **`koringb-e-rg`** | 7.5 | `e` |
| tšhišinyego | **`tšhišiny-e-go`** | 7.5 | `e` |
| sepetlele | **`sepet-le-le`** | 7.5 | `le` |
| riversdale | **`riversd-a-le`** | 7.5 | `a` |
| madingoane | **`madingo-a-ne`** | 7.5 | `a` |
| kolokotela | **`kolokot-e-la`** | 7.5 | `e` |
| bohlabani | **`bohlab-a-ni`** | 7.5 | `a` |
| christiana | **`christi-a-na`** | 7.5 | `a` |
| ditšhabeng | **`ditšhab-e-ng`** | 7.5 | `e` |
| pherekgong | **`pherek-go-ng`** | 7.5 | `go` |
| bolekgolo | **`bo-le-kgolo`** | 7.5 | `kgolo` |
| lokologile | **`lokolog-i-le`** | 7.5 | `i` |
| fihlellwa | **`fihlel-l-wa`** | 7.5 | `l` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Northern 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 | **32k BPE** | Best compression (4.06x) |
| N-gram | **2-gram** | Lowest perplexity (175) |
| Markov | **Context-4** | Highest predictability (94.3%) |
| 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 16:13:47*