README.md

---
language: ln
language_name: Lingala
language_family: bantu_central
tags:
  - wikilangs
  - nlp
  - tokenizer
  - embeddings
  - n-gram
  - markov
  - wikipedia
  - feature-extraction
  - sentence-similarity
  - tokenization
  - n-grams
  - markov-chain
  - text-mining
  - fasttext
  - babelvec
  - vocabulous
  - vocabulary
  - monolingual
  - family-bantu_central
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: 4.485
  - name: best_isotropy
    type: isotropy
    value: 0.7328
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lingala** 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** | 3.555x | 3.56 | 0.4106% | 154,152 |
| **16k** | 3.898x | 3.91 | 0.4502% | 140,596 |
| **32k** | 4.214x | 4.22 | 0.4867% | 130,050 |
| **64k** | 4.485x 🏆 | 4.49 | 0.5181% | 122,181 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Linux ezalí litámbwisi-mokonzi nsɔ́mí na kompíta. Ezalí ofelé. Tála mpé Ubuntu F...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lin ux ▁ezalí ▁litámbwisi - mokonzi ▁nsɔ́ mí ▁na ▁kompíta ... (+12 more)` | 22 |
| 16k | `▁linux ▁ezalí ▁litámbwisi - mokonzi ▁nsɔ́mí ▁na ▁kompíta . ▁ezalí ... (+6 more)` | 16 |
| 32k | `▁linux ▁ezalí ▁litámbwisi - mokonzi ▁nsɔ́mí ▁na ▁kompíta . ▁ezalí ... (+6 more)` | 16 |
| 64k | `▁linux ▁ezalí ▁litámbwisi - mokonzi ▁nsɔ́mí ▁na ▁kompíta . ▁ezalí ... (+6 more)` | 16 |

**Sample 2:** `Bogota ezalí mbóka-mokonzi ya Kolombi. Ekélami Bato ya bwanya Mazita o libanda M...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁bo go ta ▁ezalí ▁mbóka - mokonzi ▁ya ▁kolombi . ... (+12 more)` | 22 |
| 16k | `▁bo gota ▁ezalí ▁mbóka - mokonzi ▁ya ▁kolombi . ▁ekélami ... (+11 more)` | 21 |
| 32k | `▁bogota ▁ezalí ▁mbóka - mokonzi ▁ya ▁kolombi . ▁ekélami ▁bato ... (+10 more)` | 20 |
| 64k | `▁bogota ▁ezalí ▁mbóka - mokonzi ▁ya ▁kolombi . ▁ekélami ▁bato ... (+10 more)` | 20 |

**Sample 3:** `Jean-Claude Kalonji azalí bugumési ya Kalamú. Bapɔnákí yě na mokɔlɔ ya 8 yúli na...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁jean - claude ▁kalonji ▁azalí ▁bugumési ▁ya ▁kalamú . ▁bapɔnákí ... (+13 more)` | 23 |
| 16k | `▁jean - claude ▁kalonji ▁azalí ▁bugumési ▁ya ▁kalamú . ▁bapɔnákí ... (+13 more)` | 23 |
| 32k | `▁jean - claude ▁kalonji ▁azalí ▁bugumési ▁ya ▁kalamú . ▁bapɔnákí ... (+13 more)` | 23 |
| 64k | `▁jean - claude ▁kalonji ▁azalí ▁bugumési ▁ya ▁kalamú . ▁bapɔnákí ... (+13 more)` | 23 |


### Key Findings

- **Best Compression:** 64k achieves 4.485x compression
- **Lowest UNK Rate:** 8k with 0.4106% 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 | 5,174 | 12.34 | 14,092 | 19.7% | 50.0% |
| **2-gram** | Subword | 245 🏆 | 7.94 | 2,735 | 70.5% | 98.9% |
| **3-gram** | Word | 10,269 | 13.33 | 21,481 | 13.0% | 36.2% |
| **3-gram** | Subword | 1,757 | 10.78 | 18,976 | 33.9% | 74.6% |
| **4-gram** | Word | 25,188 | 14.62 | 42,798 | 8.7% | 23.1% |
| **4-gram** | Subword | 8,040 | 12.97 | 81,004 | 19.5% | 48.2% |
| **5-gram** | Word | 20,070 | 14.29 | 32,202 | 9.6% | 24.7% |
| **5-gram** | Subword | 22,299 | 14.44 | 167,515 | 12.5% | 34.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mpo na` | 3,151 |
| 2 | `na ye` | 2,560 |
| 3 | `ya ba` | 1,630 |
| 4 | `ezali na` | 1,494 |
| 5 | `kongó kinsásá` | 1,464 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `na mokolo ya` | 659 |
| 2 | `ya kongó kinsásá` | 654 |
| 3 | `na ye ya` | 586 |
| 4 | `démocratique du congo` | 541 |
| 5 | `na kati ya` | 531 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `république démocratique du congo` | 515 |
| 2 | `ya bomoi ya bato` | 441 |
| 3 | `biografi ya bomoi ya` | 415 |
| 4 | `moto ya politiki ya` | 263 |
| 5 | `banote mpe ba références` | 244 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `biografi ya bomoi ya bato` | 411 |
| 2 | `ya république démocratique du congo` | 234 |
| 3 | `azali moto ya politiki ya` | 210 |
| 4 | `mbúla na manáka ya glégwalè` | 191 |
| 5 | `tǒ mbúla na manáka ya` | 191 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 195,411 |
| 2 | `_ m` | 88,286 |
| 3 | `y a` | 72,891 |
| 4 | `_ y` | 72,395 |
| 5 | `_ n` | 71,895 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ y a` | 66,739 |
| 2 | `y a _` | 65,868 |
| 3 | `n a _` | 53,277 |
| 4 | `_ n a` | 50,800 |
| 5 | `a _ m` | 37,316 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ y a _` | 62,045 |
| 2 | `_ n a _` | 48,326 |
| 3 | `a _ y a` | 15,957 |
| 4 | `y a _ m` | 13,666 |
| 5 | `i _ y a` | 12,708 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ y a _` | 13,303 |
| 2 | `_ y a _ m` | 12,930 |
| 3 | `i _ y a _` | 12,251 |
| 4 | `i _ n a _` | 12,016 |
| 5 | `o _ y a _` | 11,394 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 245
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.7987 | 1.740 | 4.74 | 49,624 | 20.1% |
| **1** | Subword | 1.2616 | 2.398 | 11.18 | 493 | 0.0% |
| **2** | Word | 0.2666 | 1.203 | 1.67 | 234,159 | 73.3% |
| **2** | Subword | 1.0538 | 2.076 | 6.33 | 5,503 | 0.0% |
| **3** | Word | 0.1127 | 1.081 | 1.21 | 389,544 | 88.7% |
| **3** | Subword | 0.8061 | 1.748 | 3.86 | 34,806 | 19.4% |
| **4** | Word | 0.0501 🏆 | 1.035 | 1.07 | 468,155 | 95.0% |
| **4** | Subword | 0.5954 | 1.511 | 2.51 | 134,153 | 40.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ya kinsásá bokúli bonganga diacre hermès fɛ́tí 9 yúli 7 décembre na yango col de france`
2. `na molongo ya moto botángi bapu m conservatoire et les autres mouvements de boeck larcier départemen...`
3. `mpe photographies mosala na akendaki kotala bakonzi ya bobandisi lingomba ya kongó kinsásá o mobu az...`

**Context Size 2:**

1. `mpo na ba congolais lokola azali député national ya microfinance ya droit na université libre ya kin...`
2. `na ye laurence ndong aponamaki directeur adjoint ya assemblée constituante oyo azali na mbongo ya mo...`
3. `ya ba saisons mibale azalaki ministre ya république démocratique ya congo ya franc ya congo kinshasa...`

**Context Size 3:**

1. `na mokolo ya 12 sanza ya minéi mobu ya bomoyi ya lucie eyenga mituya ya miké wa kongó`
2. `na ye ya mwasi lokola mama na ye mpo na koluka ekimelo na crète lokola esanga yango ezalaki`
3. `na kati ya relation na ye ntango vidéo moko na ba provinces oyo ezwami naino te na mokili`

**Context Size 4:**

1. `république démocratique du congo wuta mobu mpe aponamaki ministre d etat ya bilenge mpe bana 5 na nk...`
2. `ya bomoi ya bato libota mpe bomwana anita mwarabu abotami o mokɔlɔ 30 sanza ya zomi na moko console`
3. `biografi ya bomoi ya bato mosala ya politiki banote mpe ba références wa kongó kinsásá na na kinsásá...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_o_yaswe_ya_mi_p`
2. `ai_na_catuvi_wol`
3. `ouve_kilazangiom`

**Context Size 2:**

1. `a_na_miteyelselá-`
2. `_mabili_lotdi._._`
3. `ya_na_lo_ya_2h2o_`

**Context Size 3:**

1. `_ya_basi_o_kabimin`
2. `ya_baye_bazalí_na_`
3. `na_ezalí_engango:_`

**Context Size 4:**

1. `_ya_12_sɛtɛ́mbɛ_na_b`
2. `_na_kongo:_dick_mpe`
3. `a_yangomba_na_commi`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (134,153 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 | 23,757 |
| Total Tokens | 563,773 |
| Mean Frequency | 23.73 |
| Median Frequency | 4 |
| Frequency Std Dev | 530.15 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ya | 62,155 |
| 2 | na | 48,882 |
| 3 | mpe | 9,425 |
| 4 | oyo | 6,953 |
| 5 | ba | 6,454 |
| 6 | ezali | 4,114 |
| 7 | o | 4,086 |
| 8 | mpé | 3,857 |
| 9 | ye | 3,508 |
| 10 | mpo | 3,484 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | utroque | 2 |
| 2 | iure | 2 |
| 3 | latran | 2 |
| 4 | nyon | 2 |
| 5 | buvandji | 2 |
| 6 | buvanji | 2 |
| 7 | g10 | 2 |
| 8 | mboulignaoh | 2 |
| 9 | onkô | 2 |
| 10 | jula | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0891 |
| R² (Goodness of Fit) | 0.993943 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 44.8% |
| Top 1,000 | 71.3% |
| Top 5,000 | 87.8% |
| Top 10,000 | 93.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9939 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 44.8% of corpus
- **Long Tail:** 13,757 words needed for remaining 6.3% 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 | 0.7328 🏆 | 0.3467 | N/A | N/A |
| **mono_64d** | 64 | 0.3440 | 0.3258 | N/A | N/A |
| **mono_128d** | 128 | 0.0954 | 0.3221 | N/A | N/A |
| **aligned_32d** | 32 | 0.7328 | 0.3472 | 0.0340 | 0.2280 |
| **aligned_64d** | 64 | 0.3440 | 0.3261 | 0.0520 | 0.2520 |
| **aligned_128d** | 128 | 0.0954 | 0.3189 | 0.0740 | 0.3160 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7328 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3312. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 7.4% 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 | **-0.290** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-m` | musées, mes, monani |
| `-b` | bilelo, balapolo, balaboratware |
| `-ba` | balapolo, balaboratware, bazwá |
| `-ma` | mayelemaya, madívi, malonga |
| `-a` | above, attention, apparition |
| `-s` | spectre, spekilos, statut |
| `-mo` | monani, mokɛle, mondúle |
| `-e` | entrepreneuriat, ekɛ́sɛ́ní, empompo |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | above, diarrhee, spectre |
| `-a` | libóta, kimbanda, kopelisa |
| `-i` | fpi, pulutugɛ́shi, katalani |
| `-s` | peintures, musées, mes |
| `-es` | peintures, musées, mes |
| `-ki` | ekokisaki, ebandamaki, mbeki |
| `-n` | attention, girkin, apparition |
| `-o` | bilelo, kopo, balapolo |

### 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 |
|------|----------|------------------|----------|
| `ongo` | 1.65x | 88 contexts | yongo, bongo, mongo |
| `anga` | 1.49x | 126 contexts | banga, vanga, kanga |
| `anda` | 1.40x | 106 contexts | manda, sanda, fanda |
| `tion` | 1.88x | 28 contexts | nation, action, option |
| `zalí` | 2.10x | 19 contexts | azalí, ézalí, izalí |
| `enge` | 1.67x | 41 contexts | wenge, kenge, penge |
| `ambo` | 1.61x | 46 contexts | yambo, mambo, tambo |
| `bong` | 1.62x | 44 contexts | bongo, bongó, bongò |
| `alak` | 1.45x | 66 contexts | alakí, salaka, palaki |
| `atio` | 2.02x | 19 contexts | nation, ization, station |
| `osal` | 1.76x | 28 contexts | tosala, mosala, kosala |
| `maka` | 1.72x | 30 contexts | makau, makasi, makabo |

### 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 |
|--------|--------|-----------|----------|
| `-b` | `-i` | 222 words | bomanyoli, bowéi |
| `-ko` | `-a` | 196 words | komilakisa, kopusa |
| `-b` | `-a` | 159 words | bakáa, bulambemba |
| `-e` | `-i` | 157 words | emonaneli, eyebisamaki |
| `-a` | `-i` | 129 words | aluki, atalelami |
| `-m` | `-i` | 123 words | minéyi, musuni |
| `-e` | `-a` | 122 words | etika, esálaka |
| `-m` | `-a` | 102 words | madeira, makota |
| `-a` | `-ki` | 83 words | aluki, atombolaki |
| `-m` | `-e` | 82 words | mwange, michelle |

### 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 |
|------|-----------------|------------|------|
| publicité | **`public-i-té`** | 7.5 | `i` |
| esengelaka | **`esengel-a-ka`** | 7.5 | `a` |
| moipolitik | **`mo-i-politik`** | 7.5 | `politik` |
| présidentiel | **`présidenti-e-l`** | 7.5 | `e` |
| quasiment | **`quasim-e-nt`** | 7.5 | `e` |
| kominanola | **`kominan-o-la`** | 7.5 | `o` |
| elandamaki | **`elandam-a-ki`** | 7.5 | `a` |
| électricité | **`électric-i-té`** | 7.5 | `i` |
| millettia | **`millett-i-a`** | 7.5 | `i` |
| débarquement | **`débarquem-e-nt`** | 7.5 | `e` |
| heuvelmans | **`heuvelm-a-ns`** | 7.5 | `a` |
| balandelaki | **`balandel-a-ki`** | 7.5 | `a` |
| continent | **`contin-e-nt`** | 7.5 | `e` |
| epesameli | **`epesam-e-li`** | 7.5 | `e` |
| balingaki | **`ba-linga-ki`** | 6.0 | `linga` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lingala 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 (4.49x) |
| N-gram | **2-gram** | Lowest perplexity (245) |
| Markov | **Context-4** | Highest predictability (95.0%) |
| 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 11:16:42*