---
language: ff
language_name: Fula
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: 4.156
  - name: best_isotropy
    type: isotropy
    value: 0.8804
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Fula** 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** | 3.290x | 3.29 | 0.2095% | 458,165 |
| **16k** | 3.629x | 3.63 | 0.2311% | 415,362 |
| **32k** | 3.915x | 3.92 | 0.2494% | 384,993 |
| **64k** | 4.156x 🏆 | 4.16 | 0.2647% | 362,620 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Tuobo District is one of 10 districts of River Gee County, Liberia. As of the po...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tu o bo ▁district ▁is ▁one ▁of ▁ 1 0 ... (+23 more)` | 33 |
| 16k | `▁tu o bo ▁district ▁is ▁one ▁of ▁ 1 0 ... (+21 more)` | 31 |
| 32k | `▁tu o bo ▁district ▁is ▁one ▁of ▁ 1 0 ... (+21 more)` | 31 |
| 64k | `▁tu obo ▁district ▁is ▁one ▁of ▁ 1 0 ▁districts ... (+20 more)` | 30 |

**Sample 2:** `Sapele Latake hukuma pamarun Diiwal Delta lysidi Naajeeriya`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sa pe le ▁lat ake ▁hukuma ▁pamarun ▁diiwal ▁delta ▁ly ... (+2 more)` | 12 |
| 16k | `▁sa pe le ▁latake ▁hukuma ▁pamarun ▁diiwal ▁delta ▁lysidi ▁naajeeriya` | 10 |
| 32k | `▁sapele ▁latake ▁hukuma ▁pamarun ▁diiwal ▁delta ▁lysidi ▁naajeeriya` | 8 |
| 64k | `▁sapele ▁latake ▁hukuma ▁pamarun ▁diiwal ▁delta ▁lysidi ▁naajeeriya` | 8 |

**Sample 3:** `Tienie ko wuro e nder diiwaan Grand Cape Mount, to leydi Liberiya.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ti en ie ▁ko ▁wuro ▁e ▁nder ▁diiwaan ▁grand ▁cape ... (+7 more)` | 17 |
| 16k | `▁ti en ie ▁ko ▁wuro ▁e ▁nder ▁diiwaan ▁grand ▁cape ... (+6 more)` | 16 |
| 32k | `▁ti en ie ▁ko ▁wuro ▁e ▁nder ▁diiwaan ▁grand ▁cape ... (+6 more)` | 16 |
| 64k | `▁ti enie ▁ko ▁wuro ▁e ▁nder ▁diiwaan ▁grand ▁cape ▁mount ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.156x compression
- **Lowest UNK Rate:** 8k with 0.2095% 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 | 18,162 | 14.15 | 104,236 | 16.2% | 37.3% |
| **2-gram** | Subword | 296 🏆 | 8.21 | 7,815 | 65.5% | 98.4% |
| **3-gram** | Word | 53,854 | 15.72 | 187,942 | 10.0% | 24.1% |
| **3-gram** | Subword | 2,479 | 11.28 | 53,321 | 26.0% | 70.2% |
| **4-gram** | Word | 183,838 | 17.49 | 408,955 | 5.3% | 14.1% |
| **4-gram** | Subword | 13,282 | 13.70 | 265,846 | 13.1% | 40.8% |
| **5-gram** | Word | 193,974 | 17.57 | 342,827 | 4.9% | 12.3% |
| **5-gram** | Subword | 45,941 | 15.49 | 723,015 | 8.8% | 27.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e nder` | 61,343 |
| 2 | `e hitaande` | 32,860 |
| 3 | `ko e` | 22,642 |
| 4 | `jaaɓi haaɗtirde` | 19,214 |
| 5 | `duɗal jaaɓi` | 17,989 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `duɗal jaaɓi haaɗtirde` | 17,974 |
| 2 | `to duɗal jaaɓi` | 10,218 |
| 3 | `e hitaande o` | 6,335 |
| 4 | `e nder leydi` | 5,945 |
| 5 | `e nder diiwaan` | 4,588 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `to duɗal jaaɓi haaɗtirde` | 10,215 |
| 2 | `e asli mum ñalnde` | 3,566 |
| 3 | `mw parser output reflist` | 3,258 |
| 4 | `ko ɓuri heewde e` | 1,887 |
| 5 | `gila e asli mum` | 1,729 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `gila e asli mum ñalnde` | 1,726 |
| 2 | `ko e asli mum ñalnde` | 1,633 |
| 3 | `mooftaa ko e asli mum` | 1,472 |
| 4 | `moƴƴinaama gila e asli mum` | 1,404 |
| 5 | `mw parser output reflist lower` | 1,396 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 1,192,787 |
| 2 | `o _` | 697,278 |
| 3 | `a a` | 631,137 |
| 4 | `i _` | 590,142 |
| 5 | `d e` | 589,471 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ e _` | 366,386 |
| 2 | `d e _` | 361,065 |
| 3 | `n d e` | 340,092 |
| 4 | `k o _` | 191,527 |
| 5 | `_ k o` | 190,918 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n d e _` | 190,566 |
| 2 | `_ n d e` | 151,153 |
| 3 | `_ k o _` | 147,651 |
| 4 | `n d e r` | 106,570 |
| 5 | `d e r _` | 101,274 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n d e r _` | 100,326 |
| 2 | `_ n d e r` | 99,998 |
| 3 | `e _ n d e` | 89,458 |
| 4 | `_ e _ n d` | 62,590 |
| 5 | `_ i n a _` | 61,992 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 296
- **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 | 0.8658 | 1.822 | 7.09 | 238,209 | 13.4% |
| **1** | Subword | 1.0967 | 2.139 | 6.46 | 4,268 | 0.0% |
| **2** | Word | 0.2953 | 1.227 | 1.86 | 1,682,859 | 70.5% |
| **2** | Subword | 0.7230 | 1.651 | 4.35 | 27,539 | 27.7% |
| **3** | Word | 0.1250 | 1.091 | 1.26 | 3,111,793 | 87.5% |
| **3** | Subword | 0.7226 | 1.650 | 3.82 | 119,629 | 27.7% |
| **4** | Word | 0.0559 🏆 | 1.040 | 1.10 | 3,909,129 | 94.4% |
| **4** | Subword | 0.6523 | 1.572 | 3.00 | 457,157 | 34.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `e fitinaaji gonɗi ɗer daga baro caggal wuro e ganndal paleontologie to tangi tehsil diiwaan lagos`
2. `ko adii aisha halilu akilu winndi e apc mo anndaa e dow dow huutoreeji e nder`
3. `nder cuuɗi 3 nde peeñii e doggol laawɗungol 1 mm 0 m abu muhammadu faade e`

**Context Size 2:**

1. `e nder eɓɓoore jaŋde coodguuli o siftorii e hitaande opitaal oo ina rokka kadi batte e peewnugol`
2. `e hitaande nde martin timmini mbaydi ndii ɗuuɗal ngal heewaani ina maantiniree aksan grave yeru helm...`
3. `ko e jannginde sosiyoloji 18 4 158 168 issn s2cid politik e jamaanu koloñaal ko adii hitaande`

**Context Size 3:**

1. `duɗal jaaɓi haaɗtirde makerere mooftaa ko e asli mum ñalnde 13 lewru abriil o arti e galle makko`
2. `to duɗal jaaɓi haaɗtirde wharton to duɗal jaaɓi haaɗtirde madrasa islamia buxi bazar to leydi kuttak...`
3. `e hitaande o joofni e 7 056 woote afolami suɓiima heddaade e celibateer e nder tikkere e ko`

**Context Size 4:**

1. `to duɗal jaaɓi haaɗtirde williams college e hitaande o heɓi ba e jaŋde ƴellitaare kuuɓtidinnde e jaŋ...`
2. `e asli mum ñalnde keɓtinaa ko jaaynde duɗal jaaɓi haaɗtirde columbia to duɗal jaaɓi haaɗtirde bagdaa...`
3. `mw parser output reflist reflist columns ol margin top 0 mw parser output reflist lower greek list s...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_mpabileɓe_mwor_`
2. `a_lita,_ошкараки`
3. `edimeye_fo_wi_kk`

**Context Size 2:**

1. `e_ng_"gelloyɗe_e_`
2. `o_wuuɓɓe_ɗaaweddi`
3. `aayya._dogina_mu_`

**Context Size 3:**

1. `_e_kosa_tuugii_haa`
2. `de_17_famɗam_huun,`
3. `nde_8_oktooɓe_ype:`

**Context Size 4:**

1. `nde_dingirde_batte_`
2. `_nde_23_lewru_ut_ha`
3. `_ko_ñawɓe_22_mars_k`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (457,157 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 | 109,082 |
| Total Tokens | 4,968,136 |
| Mean Frequency | 45.54 |
| Median Frequency | 4 |
| Frequency Std Dev | 1398.20 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | e | 374,881 |
| 2 | ko | 151,825 |
| 3 | nder | 99,826 |
| 4 | o | 93,579 |
| 5 | to | 65,456 |
| 6 | ina | 62,692 |
| 7 | hitaande | 48,933 |
| 8 | ngam | 37,608 |
| 9 | leydi | 35,673 |
| 10 | nde | 31,552 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | delee | 2 |
| 2 | trokanter | 2 |
| 3 | casteeji | 2 |
| 4 | hoffa | 2 |
| 5 | hallux | 2 |
| 6 | falannde | 2 |
| 7 | calthorpe | 2 |
| 8 | stopes | 2 |
| 9 | trokleer | 2 |
| 10 | mortons | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1660 |
| R² (Goodness of Fit) | 0.992989 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.8% |
| Top 1,000 | 67.8% |
| Top 5,000 | 83.4% |
| Top 10,000 | 88.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9930 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.8% of corpus
- **Long Tail:** 99,082 words needed for remaining 11.6% 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 | 0.8735 | 0.3675 | N/A | N/A |
| **mono_64d** | 64 | 0.8804 🏆 | 0.2760 | N/A | N/A |
| **mono_128d** | 128 | 0.8690 | 0.2101 | N/A | N/A |
| **aligned_32d** | 32 | 0.8735 | 0.3540 | 0.1020 | 0.3900 |
| **aligned_64d** | 64 | 0.8804 | 0.2806 | 0.1860 | 0.5660 |
| **aligned_128d** | 128 | 0.8690 | 0.2018 | 0.2480 | 0.6620 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.8804 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2817. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 24.8% 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 | **-0.556** | 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 |
|--------|----------|
| `-ma` | mallihemre, madaaw, mariam |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | mallihemre, olive, 9ice |
| `-ji` | notifikaaji, cedeeji, reenngooji |
| `-de` | koɗorde, wiyde, nuunɗude |

### 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 |
|------|----------|------------------|----------|
| `anng` | 1.65x | 80 contexts | anngu, manngu, mannga |
| `annd` | 1.37x | 157 contexts | annde, anndi, annda |
| `innd` | 1.61x | 67 contexts | inndo, innde, inndi |
| `ooji` | 1.58x | 72 contexts | sooji, jooji, booji |
| `ande` | 1.39x | 126 contexts | ɓande, andes, wande |
| `riya` | 1.51x | 75 contexts | riyaz, oriya, uriya |
| `nnde` | 1.48x | 76 contexts | annde, innde, wonnde |
| `goll` | 1.88x | 27 contexts | gollo, gollu, golla |
| `hita` | 1.91x | 21 contexts | chita, shita, ichita |
| `itaa` | 1.40x | 62 contexts | kitaa, gitaar, kitaab |
| `aand` | 1.30x | 65 contexts | aande, aandi, naande |
| `lnde` | 1.58x | 25 contexts | nalnde, jolnde, falnde |

### 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 |
|--------|--------|-----------|----------|
| `-ma` | `-e` | 24 words | marylise, mahde |
| `-ma` | `-de` | 7 words | mahde, mahaande |
| `-ma` | `-ji` | 3 words | mabboji, mahngooji |

### 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 |
|------|-----------------|------------|------|
| jottoriide | **`jottorii-de`** | 4.5 | `jottorii` |
| afrikaaji | **`afrikaa-ji`** | 4.5 | `afrikaa` |
| hawtaagoji | **`hawtaago-ji`** | 4.5 | `hawtaago` |
| jaaynooji | **`jaaynoo-ji`** | 4.5 | `jaaynoo` |
| ajiboyede | **`ajiboye-de`** | 4.5 | `ajiboye` |
| sungullaji | **`sungulla-ji`** | 4.5 | `sungulla` |
| maagiyaŋkooji | **`ma-agiyaŋkoo-ji`** | 3.0 | `agiyaŋkoo` |
| matsumoridate | **`ma-tsumoridate`** | 1.5 | `tsumoridate` |
| makambako | **`ma-kambako`** | 1.5 | `kambako` |
| temperaaji | **`temperaa-ji`** | 1.5 | `temperaa` |
| telefoŋaaji | **`telefoŋaa-ji`** | 1.5 | `telefoŋaa` |
| hangaruuji | **`hangaruu-ji`** | 1.5 | `hangaruu` |
| mangeshkar | **`ma-ngeshkar`** | 1.5 | `ngeshkar` |
| maldivian | **`ma-ldivian`** | 1.5 | `ldivian` |
| datadowlaaji | **`datadowlaa-ji`** | 1.5 | `datadowlaa` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Fula 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 (4.16x) |
| N-gram | **2-gram** | Lowest perplexity (296) |
| Markov | **Context-4** | Highest predictability (94.4%) |
| 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: 2026-01-04 15:09:43*