---
language: mos
language_name: Mossi
language_family: atlantic_gur
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-atlantic_gur
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: 3.679
  - name: best_isotropy
    type: isotropy
    value: 0.8275
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Mossi** 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** | 3.339x | 3.34 | 0.2504% | 875,853 |
| **16k** | 3.492x | 3.49 | 0.2618% | 837,545 |
| **32k** | 3.594x | 3.59 | 0.2695% | 813,821 |
| **64k** | 3.679x 🏆 | 3.68 | 0.2759% | 794,952 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ne Wẽnd yʋʋre, Nimbaan-zoetb-naaba, Nin-zēnga nimbaan-zoeta`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |
| 16k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |
| 32k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |
| 64k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |

**Sample 2:** `Sɩngda ne Wẽnd yʋʋre, ãndũni Nimbaan-Zoetb-Naaba la laahir Nimbaan-Zoet-Naaba`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sɩngda ▁ne ▁wẽnd ▁yʋʋre , ▁ãndũni ▁nimbaan - zoetb - ... (+8 more)` | 18 |
| 16k | `▁sɩngda ▁ne ▁wẽnd ▁yʋʋre , ▁ãndũni ▁nimbaan - zoetb - ... (+8 more)` | 18 |
| 32k | `▁sɩngda ▁ne ▁wẽnd ▁yʋʋre , ▁ãndũni ▁nimbaan - zoetb - ... (+8 more)` | 18 |
| 64k | `▁sɩngda ▁ne ▁wẽnd ▁yʋʋre , ▁ãndũni ▁nimbaan - zoetb - ... (+8 more)` | 18 |

**Sample 3:** `Ne Wẽnd yʋʋre, Nimbaan-zoetb-naaba, Nin-zēnga nimbaan-zoeta`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |
| 16k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |
| 32k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |
| 64k | `▁ne ▁wẽnd ▁yʋʋre , ▁nimbaan - zoetb - naaba , ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 64k achieves 3.679x compression
- **Lowest UNK Rate:** 8k with 0.2504% 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 | 3,615 | 11.82 | 20,744 | 29.4% | 59.7% |
| **2-gram** | Subword | 273 🏆 | 8.09 | 2,796 | 65.9% | 99.1% |
| **3-gram** | Word | 13,336 | 13.70 | 43,968 | 14.2% | 38.3% |
| **3-gram** | Subword | 1,923 | 10.91 | 21,422 | 32.4% | 73.3% |
| **4-gram** | Word | 40,697 | 15.31 | 90,918 | 7.5% | 22.5% |
| **4-gram** | Subword | 8,329 | 13.02 | 100,573 | 19.4% | 48.8% |
| **5-gram** | Word | 44,157 | 15.43 | 75,214 | 6.3% | 18.6% |
| **5-gram** | Subword | 22,381 | 14.45 | 221,121 | 13.6% | 36.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sẽn yaa` | 13,134 |
| 2 | `b sẽn` | 12,171 |
| 3 | `tɩ b` | 8,032 |
| 4 | `a sẽn` | 6,522 |
| 5 | `na n` | 6,461 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n na n` | 2,771 |
| 2 | `sẽn boond tɩ` | 2,500 |
| 3 | `sẽn na n` | 2,163 |
| 4 | `b sẽn da` | 2,127 |
| 5 | `sẽn wa n` | 1,587 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `b sẽn boond tɩ` | 1,290 |
| 2 | `sẽn na yɩl n` | 905 |
| 3 | `b sẽn na n` | 842 |
| 4 | `a sẽn wa n` | 720 |
| 5 | `sull ning sẽn get` | 574 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `parliament of the 4th republic` | 465 |
| 2 | `of the 4th republic of` | 464 |
| 3 | `the 4th republic of ghana` | 464 |
| 4 | `b sẽn na n maan` | 315 |
| 5 | `sẽn yaa zaalem n yit` | 311 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 226,091 |
| 2 | `n _` | 141,998 |
| 3 | `_ s` | 119,072 |
| 4 | `_ n` | 113,003 |
| 5 | `_ t` | 93,570 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s ẽ n` | 63,951 |
| 2 | `ẽ n _` | 63,904 |
| 3 | `_ s ẽ` | 63,741 |
| 4 | `_ a _` | 59,840 |
| 5 | `_ n _` | 52,363 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s ẽ n _` | 63,824 |
| 2 | `_ s ẽ n` | 63,514 |
| 3 | `_ y a a` | 30,361 |
| 4 | `y a a _` | 29,963 |
| 5 | `_ l a _` | 23,119 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s ẽ n _` | 63,440 |
| 2 | `_ y a a _` | 29,891 |
| 3 | `s ẽ n _ y` | 17,024 |
| 4 | `_ y ʋ ʋ m` | 16,370 |
| 5 | `b _ s ẽ n` | 16,118 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 273
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~36% 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 | 0.7703 | 1.706 | 5.14 | 57,332 | 23.0% |
| **1** | Subword | 0.8648 | 1.821 | 5.86 | 1,399 | 13.5% |
| **2** | Word | 0.3065 | 1.237 | 1.90 | 294,230 | 69.4% |
| **2** | Subword | 0.8276 | 1.775 | 5.18 | 8,196 | 17.2% |
| **3** | Word | 0.1679 | 1.123 | 1.37 | 557,321 | 83.2% |
| **3** | Subword | 0.8333 | 1.782 | 4.05 | 42,425 | 16.7% |
| **4** | Word | 0.0944 🏆 | 1.068 | 1.17 | 763,192 | 90.6% |
| **4** | Subword | 0.6301 | 1.548 | 2.63 | 171,784 | 37.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a dickson sɩnga a sẽn yaa kiris neda log koglgã pʋga neb 0 5 b tall`
2. `sẽn be zĩig a yɩ pipi pipi wã taoor soab a sẽn mik tɩ palmɛtã b`
3. `n pa vɩ ghana karẽn biiga la a yãame tɩ b sẽn wa a piliin sẽn`

**Context Size 2:**

1. `sẽn yaa rap sẽn be volta tẽnga ghana a keem soaba ra yii na baooda taaba yuuya`
2. `b sẽn tõe n lebg n wa ne yell sẽn boond tɩ segã b sẽn paam n`
3. `tɩ b pa bas tɩ b ra boond b lame tɩ pa yɩ sõma n tõe n`

**Context Size 3:**

1. `n na n sõng ghana tẽnga neb tɩ b yũ a ne fɩɩmã zĩig buud wʋsg na n`
2. `sẽn boond tɩ étni wã wɛɛngẽ kamã rutenberg yɩɩ tẽn zẽms taab karen saamb hekima university college s...`
3. `sẽn na n zĩnd afcon sẽn zĩnd kameroõ wãpʋgẽ b vɩɩmã a oteng gyasi yaa kiris ned 1`

**Context Size 4:**

1. `b sẽn boond tɩ fõndã yaa fõnd sẽn yaa bẽnd sẽn yaa agaricales tɩ b yaa bẽnda la b`
2. `sẽn na yɩl n bas a jin ganggang n kẽng a kang ganggangã ye b sẽn maan tʋʋm teedã`
3. `b sẽn na n tõog a zabrã yʋʋm a yiib sẽn zĩnd senegal tẽnga tʋʋm kaoodbã taoor soaba sẽn`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_oorvo-bã,_wĩ-br`
2. `amulg_b_rinee_r_`
3. `n_tẽngerorẽn_nan`

**Context Size 2:**

1. `a_tɩ_tõnd_zãgd_wa`
2. `n_yʋʋmd_wã_yaa_n_`
3. `_scul_ham_sẽngané`

**Context Size 3:**

1. `sẽn_da_gov.gh._yʋʋ`
2. `ẽn_tãag_anda_zĩis_`
3. `_sẽn_na_sã_la_sẽn_`

**Context Size 4:**

1. `sẽn_yɩɩl_n_to-to_no`
2. `_sẽn_da_tẽnga_la_ki`
3. `_yaa_woto_lisga_a_t`


### Key Findings

- **Best Predictability:** Context-4 (word) with 90.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (171,784 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 | 25,483 |
| Total Tokens | 1,059,645 |
| Mean Frequency | 41.58 |
| Median Frequency | 4 |
| Frequency Std Dev | 835.14 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 70,107 |
| 2 | sẽn | 63,849 |
| 3 | n | 55,318 |
| 4 | b | 41,576 |
| 5 | yaa | 30,095 |
| 6 | wã | 26,687 |
| 7 | la | 24,541 |
| 8 | tɩ | 18,168 |
| 9 | ne | 14,910 |
| 10 | be | 10,303 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | grup | 2 |
| 2 | pamiat | 2 |
| 3 | kɛlẽ | 2 |
| 4 | geroy | 2 |
| 5 | yɛlm | 2 |
| 6 | ayensu | 2 |
| 7 | folu | 2 |
| 8 | storms | 2 |
| 9 | kabah | 2 |
| 10 | ayirevire | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2282 |
| R² (Goodness of Fit) | 0.997023 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 57.5% |
| Top 1,000 | 81.7% |
| Top 5,000 | 92.6% |
| Top 10,000 | 96.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9970 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 57.5% of corpus
- **Long Tail:** 15,483 words needed for remaining 3.9% 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 | 0.8275 🏆 | 0.3352 | N/A | N/A |
| **mono_64d** | 64 | 0.6882 | 0.2965 | N/A | N/A |
| **mono_128d** | 128 | 0.2573 | 0.2728 | N/A | N/A |
| **aligned_32d** | 32 | 0.8275 | 0.3501 | 0.0400 | 0.2040 |
| **aligned_64d** | 64 | 0.6882 | 0.2969 | 0.0880 | 0.3240 |
| **aligned_128d** | 128 | 0.2573 | 0.2710 | 0.1100 | 0.3980 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8275 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3037. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 11.0% 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 | **-0.486** | 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 |
|--------|----------|
| `-s` | supreme, spaans, svētki |
| `-a` | adiku, artiste, ampem |
| `-k` | kʋʋlem, kʋgs, karshon |
| `-b` | buginese, blige, brobby |
| `-t` | tuud, tradition, tre |
| `-p` | pseudostem, parlamentã, ppiri |
| `-m` | micronesia, mate, molard |
| `-ma` | mate, malɛɛzi, mante |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | citifmonline, supreme, artiste |
| `-a` | micronesia, natalia, zaba |
| `-s` | kʋgs, laws, earphones |
| `-n` | oleson, tradition, văn |
| `-ã` | lillã, parlamentã, baoobã |
| `-i` | yendi, ppiri, malɛɛzi |
| `-r` | görenler, glamour, tõor |
| `-o` | folklórico, instituto, klymenko |

### 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 |
|------|----------|------------------|----------|
| `aand` | 2.29x | 31 contexts | maand, naand, vaand |
| `inis` | 1.96x | 27 contexts | minisr, pinisi, phinis |
| `aren` | 2.46x | 12 contexts | karen, arena, kareng |
| `oore` | 1.97x | 16 contexts | boore, poore, moore |
| `kãse` | 1.95x | 15 contexts | kãsem, kãseng, kãsems |
| `akat` | 2.23x | 10 contexts | wakat, wakato, wakatã |
| `tame` | 2.15x | 11 contexts | votame, kɩtame, getame |
| `atio` | 1.95x | 14 contexts | nation, nations, station |
| `poli` | 1.90x | 15 contexts | polis, politk, police |
| `oond` | 1.96x | 13 contexts | moond, boond, boondd |
| `olit` | 2.06x | 10 contexts | politk, polity, politic |
| `amen` | 2.30x | 7 contexts | ameng, amenfi, amenga |

### 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` | `-s` | 53 words | alfreds, anas |
| `-a` | `-e` | 52 words | ascultare, atske |
| `-s` | `-e` | 46 words | sokre, suzanne |
| `-m` | `-s` | 44 words | marsalis, morris |
| `-s` | `-s` | 43 words | sɩns, seychelles |
| `-m` | `-a` | 42 words | moroccoa, menga |
| `-a` | `-n` | 42 words | abelian, agyeman |
| `-p` | `-s` | 40 words | poems, pʋʋs |
| `-a` | `-a` | 39 words | arzɛka, adisa |
| `-k` | `-a` | 37 words | koata, kõta |

### 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 |
|------|-----------------|------------|------|
| nicholson | **`nichol-s-on`** | 7.5 | `s` |
| neuigkeiten | **`neuigkeit-e-n`** | 7.5 | `e` |
| geleneksel | **`geleneks-e-l`** | 7.5 | `e` |
| charreadas | **`charread-a-s`** | 7.5 | `a` |
| ekonomiya | **`ekonomi-y-a`** | 7.5 | `y` |
| ukrainien | **`ukraini-e-n`** | 7.5 | `e` |
| condiment | **`condi-me-nt`** | 7.5 | `me` |
| unopposed | **`unoppo-s-ed`** | 7.5 | `s` |
| sertipikat | **`sertipik-a-t`** | 7.5 | `a` |
| valensians | **`valensi-an-s`** | 6.0 | `valensi` |
| ecoregions | **`e-co-regions`** | 6.0 | `regions` |
| karẽnsaamb | **`ka-r-ẽnsaamb`** | 4.5 | `ẽnsaamb` |
| laureates | **`laureat-es`** | 4.5 | `laureat` |
| koordinatɛɛr | **`ko-ordinatɛɛr`** | 4.5 | `ordinatɛɛr` |
| monographs | **`monograph-s`** | 4.5 | `monograph` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Mossi 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 (3.68x) |
| N-gram | **2-gram** | Lowest perplexity (273) |
| Markov | **Context-4** | Highest predictability (90.6%) |
| 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 12:34:58*