---
language: kus
language_name: Kusaal
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: 3.674
  - name: best_isotropy
    type: isotropy
    value: 0.8088
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kusaal** 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** | 3.399x | 3.40 | 0.0986% | 862,718 |
| **16k** | 3.563x | 3.56 | 0.1034% | 823,082 |
| **32k** | 3.674x 🏆 | 3.68 | 0.1066% | 798,260 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Wadmaan anɛ zi’eni tisi o sʋ’ʋlim dim wadmaanib yin. O anɛ onɛ paasi gɔsid wada ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wadmaan ▁anɛ ▁zi ’ eni ▁tisi ▁o ▁sʋ ’ ʋlim ... (+19 more)` | 29 |
| 16k | `▁wadmaan ▁anɛ ▁zi ’ eni ▁tisi ▁o ▁sʋ ’ ʋlim ... (+19 more)` | 29 |
| 32k | `▁wadmaan ▁anɛ ▁zi ’ eni ▁tisi ▁o ▁sʋ ’ ʋlim ... (+18 more)` | 28 |

**Sample 2:** `Nɔraŋ anɛ yin bunkɔnbid la yinne. Buudi There several types cockerels Nyɔɔd ther...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁nɔ ra ŋ ▁anɛ ▁yin ▁bun kɔn bid ▁la ▁yinne ... (+29 more)` | 39 |
| 16k | `▁nɔ ra ŋ ▁anɛ ▁yin ▁bun kɔnbid ▁la ▁yinne . ... (+22 more)` | 32 |
| 32k | `▁nɔ ra ŋ ▁anɛ ▁yin ▁bunkɔnbid ▁la ▁yinne . ▁buudi ... (+13 more)` | 23 |

**Sample 3:** `Ndebugri Akparipoka Patience anɛ pu'a kanɛ yit Zebilla su'ulum. o anɛ karinsaam ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ndebugri ▁ak p ari po ka ▁pa ti ence ▁anɛ ... (+26 more)` | 36 |
| 16k | `▁ndebugri ▁ak p ari poka ▁pati ence ▁anɛ ▁pu ' ... (+22 more)` | 32 |
| 32k | `▁ndebugri ▁akparipoka ▁patience ▁anɛ ▁pu ' a ▁kanɛ ▁yit ▁zebilla ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 32k achieves 3.674x compression
- **Lowest UNK Rate:** 8k with 0.0986% 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 | 7,522 | 12.88 | 26,351 | 18.4% | 46.2% |
| **2-gram** | Subword | 293 🏆 | 8.20 | 2,565 | 64.8% | 99.0% |
| **3-gram** | Word | 23,120 | 14.50 | 51,608 | 10.0% | 27.1% |
| **3-gram** | Subword | 2,318 | 11.18 | 22,043 | 27.6% | 70.2% |
| **4-gram** | Word | 53,599 | 15.71 | 91,269 | 6.5% | 17.1% |
| **4-gram** | Subword | 11,494 | 13.49 | 102,940 | 13.6% | 41.9% |
| **5-gram** | Word | 48,864 | 15.58 | 71,111 | 5.8% | 15.3% |
| **5-gram** | Subword | 35,256 | 15.11 | 239,430 | 7.9% | 28.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka ba` | 6,977 |
| 2 | `la ni` | 5,343 |
| 3 | `ka o` | 4,336 |
| 4 | `o da` | 3,608 |
| 5 | `la ka` | 3,126 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tusa ayi nɛ` | 1,924 |
| 2 | `yʋʋm tusa ayi` | 1,743 |
| 3 | `from the original` | 1,206 |
| 4 | `the original on` | 1,172 |
| 5 | `archived from the` | 1,171 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `yʋʋm tusa ayi nɛ` | 1,517 |
| 2 | `archived from the original` | 1,171 |
| 3 | `from the original on` | 1,167 |
| 4 | `yʋʋm tusir kɔbiswai nɛ` | 792 |
| 5 | `tusa ayi nɛ piinɛ` | 526 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `archived from the original on` | 1,132 |
| 2 | `yʋʋm tusa ayi nɛ piinɛ` | 501 |
| 3 | `ma asim tiig na adɔɔg` | 369 |
| 4 | `yʋʋm tusa ayi nɛ pisi` | 323 |
| 5 | `parliament of the 4th republic` | 287 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 206,888 |
| 2 | `a n` | 104,100 |
| 3 | `_ n` | 103,608 |
| 4 | `_ k` | 87,930 |
| 5 | `ɛ _` | 84,875 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n ɛ _` | 65,600 |
| 2 | `_ k a` | 52,937 |
| 3 | `_ l a` | 49,510 |
| 4 | `k a _` | 42,042 |
| 5 | `_ b a` | 38,532 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a _` | 41,238 |
| 2 | `_ l a _` | 32,031 |
| 3 | `_ n ɛ _` | 28,130 |
| 4 | `a n ɛ _` | 21,450 |
| 5 | `_ b a _` | 20,894 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a _ b` | 9,122 |
| 2 | `_ l a _ n` | 9,113 |
| 3 | `k a _ b a` | 8,038 |
| 4 | `i _ n ɛ _` | 7,949 |
| 5 | `a _ b a _` | 7,848 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 293
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.8171 | 1.762 | 5.91 | 58,990 | 18.3% |
| **1** | Subword | 0.8560 | 1.810 | 7.50 | 727 | 14.4% |
| **2** | Word | 0.3267 | 1.254 | 1.89 | 348,345 | 67.3% |
| **2** | Subword | 1.0600 | 2.085 | 6.97 | 5,454 | 0.0% |
| **3** | Word | 0.1478 | 1.108 | 1.28 | 656,351 | 85.2% |
| **3** | Subword | 0.9345 | 1.911 | 4.45 | 37,990 | 6.6% |
| **4** | Word | 0.0633 🏆 | 1.045 | 1.10 | 839,904 | 93.7% |
| **4** | Subword | 0.6543 | 1.574 | 2.76 | 169,223 | 34.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `la linɛ kɛ ka ba wadmaan kʋk daan ka nintaŋ wʋsa dʋ ʋs nɛ atan la`
2. `ka biig yesu ken ninsabilis pua bɔɔd saʋŋ nɛ ka ba bʋgʋdnɛ wʋʋ bahamas nɛ sigir`
3. `nɛ widi tɛŋ da gaŋi o nɛ saam la tisif la as dim yinne la pigisid`

**Context Size 2:**

1. `ka ba gban e ye o an wadmaan la yɛl o ye reggae na ab la asʋg`
2. `la ni unesco intangible cultural heritage gbaʋŋin list gⴢsim nɛŋa ya as 23 enok yʋma wʋsa da`
3. `ka o tiraan alhassan abdul majeed waris abu danladi adama fofana bismark adjei boateng clinton antwi...`

**Context Size 3:**

1. `tusa ayi nɛ kɔbisnaasi nɛ pisyuobʋ nɛ ayuobʋ mɛ da bɛ ndc ka da maal ka alim la`
2. `yʋʋm tusa ayi nε ayuobu la ni nε an dinε an yiiga mʋ asʋg dinε ka on mεŋ`
3. `from the original on 24 june retrieved 23 june o da diya ka bas onɛ da zin i`

**Context Size 4:**

1. `yʋʋm tusa ayi nɛ piinɛ nii la emelia brobbey at 3g awards primenewsghana 14 november retrieved 1 dec...`
2. `archived from the original on 17 february retrieved 24 october ga nɛ akan mɔr nwɛnɛm di anɛ pian ʋk`
3. `from the original on november 26 retrieved june 9 ceres da paas nwɛn ɛ nwɛn ɛdib sama banɛ nam`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_da_y),_bɛɛ_za_p`
2. `a_pa_zum_demboct`
3. `i_bɛ_an_wʋʋʋŋ_mo`

**Context Size 2:**

1. `a_natricat_nal_sɔ`
2. `anbi_yinni._aceas`
3. `_nε_ka_sʋŋinɛ_ba_`

**Context Size 3:**

1. `nɛ_piinsaal_ni_lig`
2. `_ka_gɔsidib_nwa_dɔ`
3. `_lationsowusa_pamm`

**Context Size 4:**

1. `_ka_pa'ali_onɛ_bɛ_k`
2. `_la_pʋʋgin_(at_sɔ’_`
3. `_nɛ_o_tis_winstitue`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (169,223 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 | 27,663 |
| Total Tokens | 1,043,706 |
| Mean Frequency | 37.73 |
| Median Frequency | 4 |
| Frequency Std Dev | 541.33 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | la | 45,978 |
| 2 | ka | 42,536 |
| 3 | nɛ | 29,431 |
| 4 | o | 23,467 |
| 5 | ba | 22,327 |
| 6 | da | 21,036 |
| 7 | na | 12,286 |
| 8 | an | 11,857 |
| 9 | ye | 11,591 |
| 10 | ni | 10,171 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | coursera | 2 |
| 2 | udacity | 2 |
| 3 | unib | 2 |
| 4 | abʋ | 2 |
| 5 | samnya | 2 |
| 6 | din1 | 2 |
| 7 | giinlbanɛ | 2 |
| 8 | luosi | 2 |
| 9 | kᴐnba | 2 |
| 10 | gbilifʋ | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2228 |
| R² (Goodness of Fit) | 0.996032 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 48.3% |
| Top 1,000 | 77.8% |
| Top 5,000 | 91.0% |
| Top 10,000 | 95.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9960 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 48.3% of corpus
- **Long Tail:** 17,663 words needed for remaining 4.8% 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 | 0.8088 | 0.3514 | N/A | N/A |
| **mono_64d** | 64 | 0.6903 | 0.3126 | N/A | N/A |
| **mono_128d** | 128 | 0.2166 | 0.2849 | N/A | N/A |
| **aligned_32d** | 32 | 0.8088 🏆 | 0.3494 | 0.0500 | 0.2260 |
| **aligned_64d** | 64 | 0.6903 | 0.3077 | 0.0700 | 0.2960 |
| **aligned_128d** | 128 | 0.2166 | 0.2779 | 0.1000 | 0.3960 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8088 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3140. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.0% 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 | **-0.455** | 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 |
|--------|----------|
| `-a` | adazum, adviser, aimee |
| `-s` | saae, sakurasokore, stroke |
| `-b` | bugur, bit, bʋʋsi |
| `-t` | title, trichiasis, tɛŋzʋŋ |
| `-k` | karibiig, kalbelias, kumiodori |
| `-d` | donkornpptano, districts, dudley |
| `-m` | mclellan, mahamanational, mט |
| `-p` | pastor, palami, paamim |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | kalbelias, gerklaus, bars |
| `-n` | mclellan, fɔn, gbedemahjun |
| `-a` | xia, lʋgkaŋa, flea |
| `-e` | saae, sakurasokore, title |
| `-i` | bʋʋsi, kumiodori, palami |
| `-d` | bond, dʋgʋd, kirid |
| `-m` | zaam, paamim, adazum |
| `-r` | bugur, pastor, hamburger |

### 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 |
|------|----------|------------------|----------|
| `ligi` | 1.64x | 96 contexts | aligi, ligid, iligi |
| `atio` | 2.07x | 20 contexts | spatio, nation, nations |
| `akur` | 2.29x | 13 contexts | sakur, sakuri, sakura |
| `ieba` | 2.16x | 15 contexts | sieba, isieba, ɛsieba |
| `ʋʋgi` | 1.87x | 21 contexts | yʋʋgi, bʋʋgi, tʋʋgi |
| `dmaa` | 2.33x | 9 contexts | wadmaan, wadmaanɛ, wadmaani |
| `ɔbis` | 2.37x | 8 contexts | kɔbis, bɔbis, kɔbisa |
| `tion` | 1.81x | 16 contexts | option, nation, motion |
| `yinn` | 1.89x | 14 contexts | yinni, yinna, yinnɛ |
| `aasi` | 1.42x | 35 contexts | baasi, laasi, kaasi |
| `iswa` | 2.21x | 7 contexts | piswai, piiswai, kↄbiswai |
| `istr` | 1.76x | 12 contexts | listra, distric, distrit |

### 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` | 58 words | antoa, andrea |
| `-p` | `-s` | 51 words | pancras, photographers |
| `-s` | `-a` | 48 words | sakurwinneba, starsdormaa |
| `-s` | `-n` | 48 words | southwestern, singaporean |
| `-s` | `-s` | 45 words | scientists, situations |
| `-a` | `-e` | 44 words | alangde, agree |
| `-a` | `-s` | 42 words | afʋtis, addis |
| `-a` | `-n` | 38 words | asaallin, aan |
| `-s` | `-e` | 37 words | samme, sakureffiduase |
| `-n` | `-a` | 37 words | nwama, nifa |

### 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 |
|------|-----------------|------------|------|
| inbaanlim | **`i-n-baanlim`** | 7.5 | `baanlim` |
| cleveland | **`clevel-an-d`** | 7.5 | `an` |
| organising | **`organis-i-ng`** | 7.5 | `i` |
| tempʋʋdin | **`tempʋʋ-d-in`** | 7.5 | `d` |
| sanpielig | **`sa-n-pielig`** | 7.5 | `pielig` |
| summalisim | **`su-m-malisim`** | 7.5 | `malisim` |
| kugbaanlig | **`ku-g-baanlig`** | 7.5 | `baanlig` |
| constituencies | **`constituenc-i-es`** | 7.5 | `i` |
| governing | **`govern-i-ng`** | 7.5 | `i` |
| officially | **`official-l-y`** | 7.5 | `l` |
| anastasia | **`anasta-s-ia`** | 7.5 | `s` |
| oxherding | **`oxher-di-ng`** | 7.5 | `di` |
| sʋnpɛɛnni | **`sʋnpɛɛn-n-i`** | 7.5 | `n` |
| wadmaannam | **`wadmaan-n-am`** | 7.5 | `n` |
| regionnam | **`region-n-am`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kusaal 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 (3.67x) |
| N-gram | **2-gram** | Lowest perplexity (293) |
| Markov | **Context-4** | Highest predictability (93.7%) |
| 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 08:44:17*