---
language: ny
language_name: Nyanja
language_family: bantu_eastern
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-bantu_eastern
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 5.373
  - name: best_isotropy
    type: isotropy
    value: 0.5144
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Nyanja** 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** | 4.350x | 4.35 | 0.1091% | 362,203 |
| **16k** | 4.804x | 4.81 | 0.1204% | 328,020 |
| **32k** | 5.168x | 5.17 | 0.1296% | 304,892 |
| **64k** | 5.373x 🏆 | 5.38 | 0.1347% | 293,232 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Shanghai ndi mzinda ku dziko la China. Chiwerengero cha anthu: Link Shanghai`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sh ang ha i ▁ndi ▁mzinda ▁ku ▁dziko ▁la ▁china ... (+10 more)` | 20 |
| 16k | `▁sh anghai ▁ndi ▁mzinda ▁ku ▁dziko ▁la ▁china . ▁chiwerengero ... (+6 more)` | 16 |
| 32k | `▁shanghai ▁ndi ▁mzinda ▁ku ▁dziko ▁la ▁china . ▁chiwerengero ▁cha ... (+4 more)` | 14 |
| 64k | `▁shanghai ▁ndi ▁mzinda ▁ku ▁dziko ▁la ▁china . ▁chiwerengero ▁cha ... (+4 more)` | 14 |

**Sample 2:** `Maseru ndi boma lina la dziko la Lesotho. Chiwerengero cha anthu: 227.880 Maonek...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mas er u ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁le ... (+37 more)` | 47 |
| 16k | `▁mas er u ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁lesotho ... (+36 more)` | 46 |
| 32k | `▁maseru ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁lesotho . ▁chiwerengero ... (+34 more)` | 44 |
| 64k | `▁maseru ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁lesotho . ▁chiwerengero ... (+34 more)` | 44 |

**Sample 3:** `Vientiane ndi boma lina la dziko la Laos. Chiwerengero cha anthu: 783.000 *`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁vi enti ane ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁laos ... (+14 more)` | 24 |
| 16k | `▁vi entiane ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁laos . ... (+13 more)` | 23 |
| 32k | `▁vientiane ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁laos . ▁chiwerengero ... (+12 more)` | 22 |
| 64k | `▁vientiane ▁ndi ▁boma ▁lina ▁la ▁dziko ▁la ▁laos . ▁chiwerengero ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 5.373x compression
- **Lowest UNK Rate:** 8k with 0.1091% 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 | 3,188 | 11.64 | 5,338 | 18.6% | 54.3% |
| **2-gram** | Subword | 222 🏆 | 7.80 | 1,757 | 71.7% | 99.6% |
| **3-gram** | Word | 2,902 | 11.50 | 4,515 | 20.6% | 52.6% |
| **3-gram** | Subword | 1,621 | 10.66 | 11,412 | 31.1% | 78.1% |
| **4-gram** | Word | 6,438 | 12.65 | 8,970 | 13.8% | 31.5% |
| **4-gram** | Subword | 7,327 | 12.84 | 47,179 | 16.6% | 47.7% |
| **5-gram** | Word | 4,770 | 12.22 | 6,620 | 15.4% | 32.5% |
| **5-gram** | Subword | 19,229 | 14.23 | 93,564 | 9.9% | 32.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dziko la` | 584 |
| 2 | `ali ndi` | 414 |
| 3 | `pakati pa` | 361 |
| 4 | `boma la` | 312 |
| 5 | `chifukwa cha` | 292 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dziko la malawi` | 171 |
| 2 | `chiwerengero cha anthu` | 168 |
| 3 | `mu boma la` | 155 |
| 4 | `boma la machinga` | 149 |
| 5 | `opezeka mu boma` | 148 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `opezeka mu boma la` | 148 |
| 2 | `mu boma la machinga` | 148 |
| 3 | `zaka za m ma` | 95 |
| 4 | `lina la dziko la` | 82 |
| 5 | `mu dziko la malawi` | 80 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `opezeka mu boma la machinga` | 148 |
| 2 | `boma lina la dziko la` | 78 |
| 3 | `ndi boma lina la dziko` | 78 |
| 4 | `kummwela mu dziko la malawi` | 74 |
| 5 | `chigawo cha kummwela mu dziko` | 74 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 80,308 |
| 2 | `i _` | 34,728 |
| 3 | `a n` | 31,578 |
| 4 | `_ a` | 29,553 |
| 5 | `_ k` | 28,762 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k u` | 17,718 |
| 2 | `n d i` | 16,188 |
| 3 | `_ n d` | 15,022 |
| 4 | `a _ k` | 14,184 |
| 5 | `w a _` | 12,745 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n d i` | 14,282 |
| 2 | `n d i _` | 11,297 |
| 3 | `a _ k u` | 9,196 |
| 4 | `a _ n d` | 5,294 |
| 5 | `i r a _` | 5,286 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n d i _` | 11,171 |
| 2 | `a _ n d i` | 4,899 |
| 3 | `o m w e _` | 3,617 |
| 4 | `a m b i r` | 3,093 |
| 5 | `k u t i _` | 2,955 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 222
- **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 | 0.7721 | 1.708 | 4.40 | 34,588 | 22.8% |
| **1** | Subword | 0.9317 | 1.908 | 6.79 | 717 | 6.8% |
| **2** | Word | 0.2103 | 1.157 | 1.42 | 151,862 | 79.0% |
| **2** | Subword | 0.9054 | 1.873 | 4.91 | 4,864 | 9.5% |
| **3** | Word | 0.0558 | 1.039 | 1.08 | 214,433 | 94.4% |
| **3** | Subword | 0.7819 | 1.719 | 3.55 | 23,858 | 21.8% |
| **4** | Word | 0.0163 🏆 | 1.011 | 1.02 | 230,882 | 98.4% |
| **4** | Subword | 0.5693 | 1.484 | 2.37 | 84,707 | 43.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ndi shinar babuloia malinga ndi ogwira sitimayo ndi ku asia oceanian byzantine ndi kupewa kutayika n...`
2. `ku 6 mitundu yosiyanasiyana ya loya komanso mwadzidzidzi adachoka patatha milungu ingapo muulamuliro...`
3. `a bézier triangle ya zachuma ndi positi ndi kubwelela komwe amakhala ngati m madzi akumwa masikelo`

**Context Size 2:**

1. `dziko la china chiwerengero cha anthu pafupifupi 483 628 monga census makamaka ndi achibale awo kuka...`
2. `ali ndi ana asukulu ndi ophunzira ena kusukulu adathamangitsidwa atapereka mpando kwa aphunzitsi ake...`
3. `pakati pa aroma omwe ankaima m mawa kwambiri pa nkhondo yachiwiri yapadziko lonse lapansi kuphatikiz...`

**Context Size 3:**

1. `dziko la malawi la machinga opezeka mu boma la machinga chigawo cha kummwela mu dziko la united stat...`
2. `mu boma la machinga chigawo cha kummwela mu dziko la malawi litalandira ufulu wodzilamulira lidakuma...`
3. `boma la machinga chigawo cha kummwela mu dziko la malawi kukhala pa udindowu poyankhula pamene amala...`

**Context Size 4:**

1. `opezeka mu boma la machinga chigawo cha kummwela mu dziko la malawi la machinga opezeka mu boma la m...`
2. `mu boma la machinga cha kummwela`
3. `zaka za m ma ndi koyambirira kwa kusintha kwa chiyukireniya ndi nkhondo pambuyo pa masabata angapo a...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_o_wa_ata_gwe_15`
2. `anje_uchi_nti_wi`
3. `ikelanagangwotum`

**Context Size 2:**

1. `a_315_5.5_4026_(p`
2. `i_zi_yayamayakabi`
3. `anthukwa_ko_kutir`

**Context Size 3:**

1. `_ku_lakwirira_ku_f`
2. `ndi_lembera_ndi_wa`
3. `_ndi_tshugona_kwa_`

**Context Size 4:**

1. `_ndi_mamembara_atol`
2. `ndi_mchilipoti_woya`
3. `a_kumweratic_frog_l`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (84,707 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 | 14,912 |
| Total Tokens | 230,602 |
| Mean Frequency | 15.46 |
| Median Frequency | 3 |
| Frequency Std Dev | 131.83 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ndi | 11,197 |
| 2 | ku | 4,331 |
| 3 | a | 3,486 |
| 4 | mu | 3,150 |
| 5 | wa | 3,051 |
| 6 | pa | 3,037 |
| 7 | la | 2,805 |
| 8 | kuti | 2,778 |
| 9 | ya | 2,515 |
| 10 | m | 2,353 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | koshi | 2 |
| 2 | álex | 2 |
| 3 | speedway | 2 |
| 4 | adagwetsa | 2 |
| 5 | tomiko | 2 |
| 6 | itooka | 2 |
| 7 | lanata | 2 |
| 8 | henri | 2 |
| 9 | routledge | 2 |
| 10 | run | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0440 |
| R² (Goodness of Fit) | 0.989912 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 38.8% |
| Top 1,000 | 67.1% |
| Top 5,000 | 88.0% |
| Top 10,000 | 95.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9899 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 38.8% of corpus
- **Long Tail:** 4,912 words needed for remaining 4.3% 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 | 0.5144 | 0.3662 | N/A | N/A |
| **mono_64d** | 64 | 0.1254 | 0.3698 | N/A | N/A |
| **mono_128d** | 128 | 0.0173 | 0.3726 | N/A | N/A |
| **aligned_32d** | 32 | 0.5144 🏆 | 0.3731 | 0.0360 | 0.2220 |
| **aligned_64d** | 64 | 0.1254 | 0.3661 | 0.0540 | 0.2760 |
| **aligned_128d** | 128 | 0.0173 | 0.3812 | 0.0600 | 0.2640 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.5144 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3715. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 6.0% 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 | **0.002** | 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` | mitembo, makampeni, manyazi |
| `-a` | asanasankhidwe, adatumiza, amalamulira |
| `-ma` | makampeni, manyazi, mabafa |
| `-ku` | kuvomera, kuwala, kuno |
| `-ch` | cheers, chikhumbo, cholimbikitsa |
| `-k` | kuvomera, kuwala, kuno |
| `-s` | sayansi, sibwera, sp |
| `-c` | cov, carbonate, cheers |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | yoberekera, adatumiza, zipatsidwa |
| `-ra` | yoberekera, ofiira, amalamulira |
| `-wa` | zipatsidwa, wowongoleredwa, agonekedwa |
| `-o` | iwo, mitembo, bwato |
| `-e` | asanasankhidwe, ge, carbonate |
| `-i` | dongosololi, makampeni, manyazi |
| `-sa` | inagwiritsa, adagonjetsa, cholimbikitsa |
| `-ka` | ndikuika, umapezeka, anadziwika |

### 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 |
|------|----------|------------------|----------|
| `khal` | 1.55x | 67 contexts | ikhala, ukhala, akhala |
| `chit` | 1.40x | 67 contexts | chitha, ochita, nchito |
| `yamb` | 1.49x | 44 contexts | ayambe, oyamba, ayamba |
| `akha` | 1.41x | 53 contexts | akhala, akhale, yakhala |
| `ambi` | 1.48x | 38 contexts | mwambi, zambia, ambili |
| `hala` | 1.61x | 28 contexts | ikhala, ukhala, akhala |
| `dzik` | 1.76x | 19 contexts | dziko, adziko, mdziko |
| `ziko` | 1.75x | 19 contexts | dziko, adziko, zikomo |
| `nali` | 1.47x | 27 contexts | anali, inali, unali |
| `tchi` | 1.72x | 13 contexts | tchire, wotchi, ritchie |
| `ntha` | 1.45x | 20 contexts | nthawo, nthaŵi, nthawi |
| `mbir` | 1.55x | 15 contexts | mbira, mbiri, ambiri |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-a` | `-a` | 733 words | adagundidwa, anauka |
| `-ku` | `-a` | 424 words | kuvutitsidwa, kuchepetsedwa |
| `-ch` | `-a` | 195 words | choopsa, chona |
| `-a` | `-wa` | 185 words | adagundidwa, amaphatikizidwa |
| `-a` | `-ra` | 145 words | akummwera, akuchitira |
| `-a` | `-e` | 136 words | agawane, angalandire |
| `-m` | `-a` | 130 words | manja, mabala |
| `-p` | `-a` | 123 words | pizza, pascha |
| `-ch` | `-o` | 109 words | chisindikizo, chicago |
| `-m` | `-i` | 103 words | mwangozi, mampi |

### 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 |
|------|-----------------|------------|------|
| opezekapo | **`opezek-a-po`** | 7.5 | `a` |
| pamaulendo | **`pa-ma-ulendo`** | 7.5 | `ulendo` |
| abdirahman | **`abdirahm-a-n`** | 7.5 | `a` |
| lachipani | **`lachip-a-ni`** | 7.5 | `a` |
| kwamphamvu | **`k-wa-mphamvu`** | 7.5 | `mphamvu` |
| masewerowa | **`masewer-o-wa`** | 7.5 | `o` |
| sebastian | **`sebasti-a-n`** | 7.5 | `a` |
| okhudzana | **`okhudz-a-na`** | 7.5 | `a` |
| malingana | **`maling-a-na`** | 7.5 | `a` |
| shakespeare | **`shakespe-a-re`** | 7.5 | `a` |
| presbyterian | **`presbyteri-a-n`** | 7.5 | `a` |
| ntchitozaka | **`ntchito-za-ka`** | 7.5 | `za` |
| yosakwana | **`yosak-wa-na`** | 7.5 | `wa` |
| tinalowapo | **`tinalo-wa-po`** | 7.5 | `wa` |
| loyandikana | **`loyandik-a-na`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Nyanja 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 (5.37x) |
| N-gram | **2-gram** | Lowest perplexity (222) |
| Markov | **Context-4** | Highest predictability (98.4%) |
| 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 16:28:22*