---
language: wo
language_name: Wolof
language_family: atlantic_other
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_other
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: 3.834
  - name: best_isotropy
    type: isotropy
    value: 0.8649
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Wolof** 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** | 3.486x | 3.49 | 0.1614% | 779,481 |
| **16k** | 3.696x | 3.70 | 0.1711% | 735,134 |
| **32k** | 3.834x 🏆 | 3.84 | 0.1775% | 708,618 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Nuweel Kaledooni : Dun Faraas (Géejpeek u Pacifik)`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁nu w eel ▁k ale dooni ▁: ▁dun ▁faraas ▁( ... (+6 more)` | 16 |
| 16k | `▁nuweel ▁kaledooni ▁: ▁dun ▁faraas ▁( géejpeek ▁u ▁pacifik )` | 10 |
| 32k | `▁nuweel ▁kaledooni ▁: ▁dun ▁faraas ▁( géejpeek ▁u ▁pacifik )` | 10 |

**Sample 2:** `Makaaw (澳門) (澳門特別行政區 , Resiyoŋ u Administaraasioŋ Espesiyaal u Ciin bu Makaaw). ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mak aaw ▁( 澳門 ) ▁( 澳門特別行政區 ▁, ▁res iyoŋ ... (+17 more)` | 27 |
| 16k | `▁makaaw ▁( 澳門 ) ▁( 澳門特別行政區 ▁, ▁res iyoŋ ▁u ... (+11 more)` | 21 |
| 32k | `▁makaaw ▁( 澳門 ) ▁( 澳門特別行政區 ▁, ▁res iyoŋ ▁u ... (+9 more)` | 19 |

**Sample 3:** `Kingisepp (Кингисепп) dëkku di Riisi. Nitñii motnañu 48 488 Riisi`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁k ing is epp ▁( ки н г ис е ... (+17 more)` | 27 |
| 16k | `▁king is epp ▁( ки н г ис е п ... (+16 more)` | 26 |
| 32k | `▁kingisepp ▁( кингисепп ) ▁dëkku ▁di ▁riisi . ▁nitñii ▁motnañu ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 32k achieves 3.834x compression
- **Lowest UNK Rate:** 8k with 0.1614% 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 | 9,913 | 13.28 | 21,313 | 12.7% | 36.9% |
| **2-gram** | Subword | 263 🏆 | 8.04 | 2,618 | 68.3% | 99.2% |
| **3-gram** | Word | 53,177 | 15.70 | 71,583 | 3.9% | 12.9% |
| **3-gram** | Subword | 2,089 | 11.03 | 17,992 | 26.5% | 74.1% |
| **4-gram** | Word | 122,855 | 16.91 | 135,374 | 1.5% | 4.7% |
| **4-gram** | Subword | 11,307 | 13.46 | 78,032 | 12.0% | 38.9% |
| **5-gram** | Word | 127,965 | 16.97 | 134,813 | 0.9% | 3.0% |
| **5-gram** | Subword | 39,248 | 15.26 | 182,915 | 6.0% | 23.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `xam ne` | 1,468 |
| 2 | `na ci` | 1,268 |
| 3 | `yi ci` | 1,216 |
| 4 | `gën a` | 1,163 |
| 5 | `xam xam` | 1,152 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nga xam ne` | 1,027 |
| 2 | `bokk na ci` | 471 |
| 3 | `bu ko defee` | 451 |
| 4 | `yu mag yi` | 235 |
| 5 | `lëkkalekaay yu biti` | 230 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `yi nga xam ne` | 207 |
| 2 | `bi j y m` | 156 |
| 3 | `from the original on` | 125 |
| 4 | `ak delluwaay lëkkalekaay yu` | 119 |
| 5 | `delluwaay lëkkalekaay yu biti` | 119 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `karmat ak delluwaay lëkkalekaay yu` | 119 |
| 2 | `ak delluwaay lëkkalekaay yu biti` | 119 |
| 3 | `archived from the original on` | 103 |
| 4 | `yonnant bi j y m` | 94 |
| 5 | `de wikipédia avec notice d` | 66 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _` | 107,629 |
| 2 | `u _` | 77,269 |
| 3 | `a _` | 63,166 |
| 4 | `_ n` | 58,031 |
| 5 | `a a` | 56,077 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c i` | 35,175 |
| 2 | `c i _` | 33,981 |
| 3 | `_ n a` | 17,142 |
| 4 | `_ a k` | 15,769 |
| 5 | `a k _` | 15,662 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c i _` | 33,053 |
| 2 | `_ a k _` | 14,628 |
| 3 | `o o n _` | 11,321 |
| 4 | `_ k o _` | 9,009 |
| 5 | `_ y i _` | 8,939 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _ c i _` | 3,876 |
| 2 | `_ n e k k` | 3,635 |
| 3 | `_ m o o m` | 3,495 |
| 4 | `_ w o o n` | 3,436 |
| 5 | `m o o y _` | 3,277 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 263
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.8104 | 1.754 | 5.71 | 40,525 | 19.0% |
| **1** | Subword | 1.2572 | 2.390 | 9.28 | 630 | 0.0% |
| **2** | Word | 0.2934 | 1.226 | 1.70 | 230,646 | 70.7% |
| **2** | Subword | 0.9933 | 1.991 | 5.75 | 5,840 | 0.7% |
| **3** | Word | 0.0951 | 1.068 | 1.15 | 392,178 | 90.5% |
| **3** | Subword | 0.8004 | 1.742 | 3.76 | 33,559 | 20.0% |
| **4** | Word | 0.0328 🏆 | 1.023 | 1.04 | 450,681 | 96.7% |
| **4** | Subword | 0.6046 | 1.521 | 2.58 | 126,072 | 39.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ci tariixa xaadiriya ci waxtub xër dafa yem diwam bokk na tudde wenn waxambaane tegi tànkam`
2. `ak yu gàtti dig lu jëkk moo taxoon seex ibraahima mbeng nekkoon seen diggante loolu yërmande`
3. `yi ci wolof mi am ci li moo doon jëfandikoo rawatina nag ag jiital tudd naa`

**Context Size 2:**

1. `xam ne day leeral li waa espaañ ak holand ànd ak xol asaf naa nag ñu doon`
2. `na ci diggante askan yeek seeni goornamaa loolu tam dooleel bennoo gu almaañ gi ñu dugal ko`
3. `yi ci tugal bu yees bii tay goornamaay tugal yi ci ngérum tàggat dajale leen du nu`

**Context Size 3:**

1. `nga xam ne danuy sukkandiku ci li nekk ci ginnaaw tawaaful qudoom te jokk ci su dee ajkat`
2. `bokk na ci mbootaay yu bari oif au cedeao ak ñoom seen te jumtukaay yi muy jëfandikoo amuñu`
3. `bu ko defee mu song ko ca tripoli gu soww ga atum daal di fas kollareg litofski gi`

**Context Size 4:**

1. `yi nga xam ne xareb adduna bu njëkk bi yëgoon nanu ne danu leen a xañoon itaali ca ndajem`
2. `bi j y m mas naa teew bis kenn ci boroom xam xam yi nag li gën a lëng`
3. `from the original on retrieved bu ci melni bu polio bi bobu wane na ni ay ndaw mën nañ`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_tonnde_m_jiy_cà`
2. `aakonckku_ko_ten`
3. `i,_amen_ci-jëmee`

**Context Size 2:**

1. `i_de_we_doon_saak`
2. `u_aki_aji_lu_mu_m`
3. `a_konaal_nekk_ye_`

**Context Size 3:**

1. `_ci_na_bindikoonan`
2. `ci_niou,_lool_bind`
3. `_na_bi_ci_seere_ni`

**Context Size 4:**

1. `_ci_jii_nag_mbëj,_m`
2. `_ak_wu_jéggi,nekk_c`
3. `oon_à_l'emmeel_bi,_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (126,072 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 | 21,320 |
| Total Tokens | 669,546 |
| Mean Frequency | 31.40 |
| Median Frequency | 4 |
| Frequency Std Dev | 356.08 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ci | 34,235 |
| 2 | ak | 15,534 |
| 3 | yi | 12,854 |
| 4 | ko | 10,384 |
| 5 | bi | 10,094 |
| 6 | di | 8,275 |
| 7 | mu | 7,957 |
| 8 | bu | 7,472 |
| 9 | na | 7,210 |
| 10 | yu | 6,832 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kapi | 2 |
| 2 | aicha | 2 |
| 3 | fassou | 2 |
| 4 | sagno | 2 |
| 5 | rugby | 2 |
| 6 | souaré | 2 |
| 7 | yéro | 2 |
| 8 | guinéenne | 2 |
| 9 | kandet | 2 |
| 10 | diawara | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2143 |
| R² (Goodness of Fit) | 0.993629 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 46.2% |
| Top 1,000 | 76.0% |
| Top 5,000 | 91.1% |
| Top 10,000 | 95.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9936 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 46.2% of corpus
- **Long Tail:** 11,320 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 | 0.8649 🏆 | 0.3602 | N/A | N/A |
| **mono_64d** | 64 | 0.7358 | 0.2985 | N/A | N/A |
| **mono_128d** | 128 | 0.2553 | 0.2614 | N/A | N/A |
| **aligned_32d** | 32 | 0.8649 | 0.3643 | 0.0160 | 0.1220 |
| **aligned_64d** | 64 | 0.7358 | 0.3085 | 0.0280 | 0.2040 |
| **aligned_128d** | 128 | 0.2553 | 0.2646 | 0.0560 | 0.2420 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8649 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3096. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.6% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.871** | 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` | saytuloo, saws, sayyidimaa |
| `-a` | andis, afc, aamustrong |
| `-m` | magellan, mujjam, médecine |
| `-b` | bërëp, bàyyiwoon, bashiir |
| `-d` | dammte, dadi, dimbale |
| `-n` | natoo, notee, nationale |
| `-t` | tv, tenqam, tóoru |
| `-ma` | magellan, mar, maritime |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | xiirtalante, relatée, notee |
| `-n` | bàyyiwoon, chemin, magellan |
| `-i` | lakkati, rakki, parti |
| `-l` | wiccal, ñenteel, jërul |
| `-a` | jola, keita, sayyidimaa |
| `-u` | gondiku, tóoru, sosu |
| `-s` | andis, saws, joxees |
| `-on` | bàyyiwoon, àndutoon, interprétation |

### 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 |
|------|----------|------------------|----------|
| `tion` | 2.39x | 17 contexts | nation, notion, option |
| `oroo` | 1.98x | 29 contexts | loroo, joroom, woroom |
| `enee` | 2.00x | 26 contexts | benee, weneen, yéenee |
| `ante` | 1.77x | 39 contexts | dante, kante, wante |
| `maan` | 1.65x | 41 contexts | maang, maane, maana |
| `araa` | 1.42x | 65 contexts | araab, saraa, araam |
| `raan` | 1.70x | 29 contexts | iraan, xiraan, fraans |
| `àlla` | 1.77x | 25 contexts | yàlla, wàlla, àllaa |
| `oole` | 1.66x | 27 contexts | doole, boole, xoole |
| `aari` | 1.56x | 33 contexts | yaari, naari, baari |
| `afri` | 2.06x | 13 contexts | afric, afrig, afrik |
| `kkoo` | 1.52x | 34 contexts | dàkkoo, jokkoo, sàkkoo |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-e` | 55 words | secondaire, seete |
| `-m` | `-e` | 46 words | mbusóobe, matiere |
| `-d` | `-e` | 43 words | dofe, dikke |
| `-m` | `-a` | 42 words | miimiya, maginta |
| `-t` | `-e` | 40 words | toogee, tëjee |
| `-m` | `-i` | 39 words | maymooni, mai |
| `-m` | `-n` | 38 words | mbàmbullaan, muttaquun |
| `-t` | `-n` | 36 words | telefon, tëjoon |
| `-a` | `-i` | 35 words | asi, almeeri |
| `-m` | `-m` | 34 words | mycobacterium, muurum |

### 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 |
|------|-----------------|------------|------|
| mokkalloo | **`mokkal-l-oo`** | 7.5 | `l` |
| ulaayikal | **`ulaayi-k-al`** | 7.5 | `k` |
| politigkat | **`politig-k-at`** | 7.5 | `k` |
| ndokkeelsi | **`ndokkeel-s-i`** | 7.5 | `s` |
| endustreem | **`endustr-e-em`** | 7.5 | `e` |
| rafetatul | **`rafet-at-ul`** | 6.0 | `rafet` |
| terewuloon | **`terewul-o-on`** | 6.0 | `terewul` |
| serigneum | **`serigne-u-m`** | 6.0 | `serigne` |
| ahmadubnu | **`ahmad-ub-nu`** | 6.0 | `ahmad` |
| séddaleeb | **`séddalee-b`** | 4.5 | `séddalee` |
| siyaareem | **`siyaaree-m`** | 4.5 | `siyaaree` |
| kolombiya | **`kolombi-ya`** | 4.5 | `kolombi` |
| detection | **`de-te-ction`** | 4.5 | `ction` |
| jubluwunu | **`jubluwu-nu`** | 4.5 | `jubluwu` |
| melosuufug | **`melosuuf-ug`** | 4.5 | `melosuuf` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Wolof 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 (3.83x) |
| N-gram | **2-gram** | Lowest perplexity (263) |
| Markov | **Context-4** | Highest predictability (96.7%) |
| 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: 2026-01-11 04:34:19*