---
language: sw
language_name: Swahili
language_family: bantu_eastern
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_eastern
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: 4.845
  - name: best_isotropy
    type: isotropy
    value: 0.8185
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Swahili** 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** | 4.023x | 4.02 | 0.1861% | 762,689 |
| **16k** | 4.373x | 4.37 | 0.2022% | 701,655 |
| **32k** | 4.646x | 4.65 | 0.2149% | 660,356 |
| **64k** | 4.845x 🏆 | 4.85 | 0.2241% | 633,306 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Eduardo Cerda (1 Januari – 19 Februari alikuwa mwanasiasa kutoka Chile aliyehudu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁edu ar do ▁cer da ▁( 1 ▁januari ▁– ▁ ... (+15 more)` | 25 |
| 16k | `▁edu ardo ▁cer da ▁( 1 ▁januari ▁– ▁ 1 ... (+13 more)` | 23 |
| 32k | `▁eduardo ▁cer da ▁( 1 ▁januari ▁– ▁ 1 9 ... (+12 more)` | 22 |
| 64k | `▁eduardo ▁cer da ▁( 1 ▁januari ▁– ▁ 1 9 ... (+12 more)` | 22 |

**Sample 2:** `ni mji wa Afrika Kusini katika jimbo la Limpopo. Mwaka ulikuwa na wakazi 150,637...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ni ▁mji ▁wa ▁afrika ▁kusini ▁katika ▁jimbo ▁la ▁li mpo ... (+27 more)` | 37 |
| 16k | `▁ni ▁mji ▁wa ▁afrika ▁kusini ▁katika ▁jimbo ▁la ▁limpopo . ... (+25 more)` | 35 |
| 32k | `▁ni ▁mji ▁wa ▁afrika ▁kusini ▁katika ▁jimbo ▁la ▁limpopo . ... (+25 more)` | 35 |
| 64k | `▁ni ▁mji ▁wa ▁afrika ▁kusini ▁katika ▁jimbo ▁la ▁limpopo . ... (+25 more)` | 35 |

**Sample 3:** `Calvados ni département au department la Basse-Normandie ya Ufaransa. Mji mkuu w...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cal va dos ▁ni ▁dé partement ▁au ▁department ▁la ▁ba ... (+22 more)` | 32 |
| 16k | `▁cal va dos ▁ni ▁département ▁au ▁department ▁la ▁ba sse ... (+21 more)` | 31 |
| 32k | `▁cal va dos ▁ni ▁département ▁au ▁department ▁la ▁basse - ... (+20 more)` | 30 |
| 64k | `▁calva dos ▁ni ▁département ▁au ▁department ▁la ▁basse - normandie ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 64k achieves 4.845x compression
- **Lowest UNK Rate:** 8k with 0.1861% 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 | 32,577 | 14.99 | 236,638 | 11.9% | 32.7% |
| **2-gram** | Subword | 217 🏆 | 7.76 | 8,173 | 70.6% | 99.4% |
| **3-gram** | Word | 76,791 | 16.23 | 451,861 | 10.5% | 26.1% |
| **3-gram** | Subword | 1,772 | 10.79 | 58,649 | 33.0% | 75.0% |
| **4-gram** | Word | 139,824 | 17.09 | 795,817 | 10.4% | 23.7% |
| **4-gram** | Subword | 9,836 | 13.26 | 327,130 | 17.7% | 45.5% |
| **5-gram** | Word | 100,216 | 16.61 | 591,148 | 11.6% | 26.1% |
| **5-gram** | Subword | 36,485 | 15.15 | 1,045,354 | 10.1% | 30.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `orodha ya` | 42,976 |
| 2 | `viungo vya` | 33,564 |
| 3 | `vya nje` | 33,274 |
| 4 | `mkoa wa` | 28,247 |
| 5 | `mwaka wa` | 26,864 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `viungo vya nje` | 33,145 |
| 2 | `ya mito ya` | 18,487 |
| 3 | `orodha ya mito` | 16,786 |
| 4 | `orodha ya watakatifu` | 13,847 |
| 5 | `pia orodha ya` | 13,762 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `orodha ya mito ya` | 16,782 |
| 2 | `tanbihi viungo vya nje` | 13,442 |
| 3 | `tazama pia orodha ya` | 13,414 |
| 4 | `viungo vya nje geonames` | 11,683 |
| 5 | `vya nje geonames org` | 11,683 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `viungo vya nje geonames org` | 11,683 |
| 2 | `tanbihi viungo vya nje geonames` | 11,453 |
| 3 | `vya nje geonames org ya` | 8,508 |
| 4 | `pia orodha ya mito ya` | 5,727 |
| 5 | `tazama pia orodha ya mito` | 5,721 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 5,814,475 |
| 2 | `w a` | 2,144,347 |
| 3 | `i _` | 1,912,486 |
| 4 | `_ k` | 1,852,377 |
| 5 | `_ m` | 1,569,760 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `w a _` | 1,284,455 |
| 2 | `a _ k` | 1,094,934 |
| 3 | `_ w a` | 1,053,327 |
| 4 | `y a _` | 1,017,628 |
| 5 | `_ y a` | 970,536 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ y a _` | 848,634 |
| 2 | `_ w a _` | 582,979 |
| 3 | `_ n a _` | 505,684 |
| 4 | `a _ w a` | 409,317 |
| 5 | `a _ y a` | 354,524 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ y a _` | 321,570 |
| 2 | `i _ y a _` | 263,973 |
| 3 | `_ k a t i` | 252,483 |
| 4 | `a _ n a _` | 243,482 |
| 5 | `a t i k a` | 235,918 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 217
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.8924 | 1.856 | 8.08 | 460,401 | 10.8% |
| **1** | Subword | 1.0657 | 2.093 | 6.66 | 3,978 | 0.0% |
| **2** | Word | 0.2982 | 1.230 | 1.99 | 3,713,903 | 70.2% |
| **2** | Subword | 0.8028 | 1.745 | 4.94 | 26,486 | 19.7% |
| **3** | Word | 0.1311 | 1.095 | 1.29 | 7,371,068 | 86.9% |
| **3** | Subword | 0.7744 | 1.710 | 4.25 | 130,800 | 22.6% |
| **4** | Word | 0.0548 🏆 | 1.039 | 1.10 | 9,467,105 | 94.5% |
| **4** | Subword | 0.7269 | 1.655 | 3.45 | 556,331 | 27.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ya afrika asia william watson alijiunga baada ya kati ya kwimba katika ziwa victoria msaada wa`
2. `wa uzo august anthony gonsalvez filamu mwanamitindo na uchovu dalili wakati wa ii wa kisayansi anaan...`
3. `na kinanda trevor grace ni kifaa kinachotumika hasa sindhi rasool gangi marejeo walio na mama yake`

**Context Size 2:**

1. `orodha ya mito ya wilaya ya kwimba za mkoa wa manyara nchini tanzania kilele kina urefu wa`
2. `viungo vya nje lugha ya kuhispania lilirekodiwa tar 21 juni ni mtamgazaji wa runinga na hali mbalimb...`
3. `vya nje lugha ya kiduke katika glottolog lugha ya kilatini ingawa kuna makundi ya madawa yaliyodhami...`

**Context Size 3:**

1. `viungo vya nje geonames org vya tanzania vya bahari ya hindi ya kwale`
2. `ya mito ya mkoa wa mara tanzania kaskazini ambao maji yake yanaingia katika ziwa viktoria na hatimay...`
3. `orodha ya mito ya burundi mito mirefu ya afrika tanbihi viungo vya nje ya uholanzi wa groningen`

**Context Size 4:**

1. `orodha ya mito ya kaunti ya makueni tanbihi viungo vya nje kuhusu papa telesphorus katika kamusi ele...`
2. `tazama pia orodha ya mito ya uganda orodha ya mito ya wilaya ya kyenjojo tanbihi viungo vya nje geon...`
3. `tanbihi viungo vya nje geonames org wa bururi n tanganyika kongo`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `a_an,7593_naakwa`
2. `_kaje_zar._maadu`
3. `i_5_fa_lahife_hi`

**Context Size 2:**

1. `a_na_ncina_wann_y`
2. `wat)"_afuanteadem`
3. `i_gui_vike_la_mag`

**Context Size 3:**

1. `wa_katikation_hola`
2. `a_kufu_wa_kice_ana`
3. `_walihus_tolea_,_1`

**Context Size 4:**

1. `_ya_cha_jina_wa_tan`
2. `_wa_kenya_ya_alihes`
3. `_na_kuwa_matolikio_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (556,331 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 | 215,305 |
| Total Tokens | 13,265,910 |
| Mean Frequency | 61.61 |
| Median Frequency | 4 |
| Frequency Std Dev | 2704.96 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ya | 849,701 |
| 2 | wa | 583,407 |
| 3 | na | 508,022 |
| 4 | katika | 214,000 |
| 5 | kwa | 192,923 |
| 6 | ni | 157,481 |
| 7 | za | 140,350 |
| 8 | la | 133,736 |
| 9 | mwaka | 92,204 |
| 10 | kama | 74,978 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | xqc | 2 |
| 2 | cenat | 2 |
| 3 | thandiwe | 2 |
| 4 | msimango | 2 |
| 5 | technocrats | 2 |
| 6 | explosively | 2 |
| 7 | paracinema | 2 |
| 8 | sphingonotus | 2 |
| 9 | tmetonota | 2 |
| 10 | vosseleriana | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1454 |
| R² (Goodness of Fit) | 0.992293 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.6% |
| Top 1,000 | 66.1% |
| Top 5,000 | 81.9% |
| Top 10,000 | 87.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9923 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.6% of corpus
- **Long Tail:** 205,305 words needed for remaining 13.0% 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 | 0.8185 | 0.3407 | N/A | N/A |
| **mono_64d** | 64 | 0.8034 | 0.2947 | N/A | N/A |
| **mono_128d** | 128 | 0.7557 | 0.2285 | N/A | N/A |
| **aligned_32d** | 32 | 0.8185 🏆 | 0.3482 | 0.2100 | 0.6260 |
| **aligned_64d** | 64 | 0.8034 | 0.2933 | 0.3440 | 0.7440 |
| **aligned_128d** | 128 | 0.7557 | 0.2305 | 0.4480 | 0.7880 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8185 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2893. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 44.8% 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 | **-0.139** | 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 |
|--------|----------|
| `-ki` | kimuru, kievant, kinachoaminiwa |
| `-a` | akisomea, alipoumia, amino |
| `-ma` | markazi, mabingwadurufile, matuidi |
| `-m` | mukato, markazi, mabingwadurufile |
| `-wa` | wanaodaiwa, wanazozitumia, wanaokoma |
| `-s` | seann, stepfather, sosi |
| `-k` | kujengewa, kimuru, kievant |
| `-ka` | kamwene, kapitolias, kakora |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | zilianguka, kujengewa, akisomea |
| `-i` | pokezi, dodati, markazi |
| `-wa` | kujengewa, imechanganywa, wanaodaiwa |
| `-e` | kamwene, hue, kikwere |
| `-s` | ldcs, kimarangis, wells |
| `-ia` | alipoumia, wanazozitumia, alimhakikishia |
| `-o` | mukato, amino, khutso |
| `-n` | gybrian, liberalization, grindin |

### 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 |
|------|----------|------------------|----------|
| `ikuw` | 2.17x | 92 contexts | ikuwo, ikuwa, uikuwa |
| `fany` | 1.88x | 165 contexts | fanya, mfanya, fanywa |
| `iung` | 2.05x | 86 contexts | viung, viungu, jiunge |
| `akat` | 1.78x | 160 contexts | akate, akata, zakat |
| `liku` | 1.97x | 96 contexts | aliku, likud, likuyu |
| `mwan` | 2.14x | 62 contexts | mwang, mwana, mwano |
| `ikan` | 1.98x | 82 contexts | ikana, kikanu, onikan |
| `reje` | 1.87x | 74 contexts | rejeo, rejea, arejee |
| `kwen` | 2.07x | 44 contexts | nkwen, kwenu, kweny |
| `ekan` | 2.00x | 45 contexts | lekan, dekan, kekana |
| `lish` | 1.67x | 93 contexts | lisha, lisht, lishe |
| `utok` | 2.04x | 38 contexts | utoke, kutok, utoka |

### 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` | 407 words | ameendesha, akoma |
| `-wa` | `-a` | 277 words | waliwaita, wakisukumwa |
| `-k` | `-a` | 272 words | kutotulia, kilichofunganishwa |
| `-ki` | `-a` | 136 words | kilichofunganishwa, kipama |
| `-ki` | `-i` | 103 words | kifupifupi, kichaudangsi |
| `-m` | `-i` | 90 words | mwambaoni, msanidi |
| `-wa` | `-i` | 78 words | walivyoishi, wamamaluki |
| `-a` | `-wa` | 78 words | akahifadhiwa, ahesabiwa |
| `-m` | `-a` | 73 words | mkesia, magaia |
| `-a` | `-i` | 71 words | akipoi, amkabidhi |

### 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 |
|------|-----------------|------------|------|
| charleroi | **`charler-o-i`** | 7.5 | `o` |
| wamebaini | **`wameba-i-ni`** | 7.5 | `i` |
| srilankan | **`srilank-a-n`** | 7.5 | `a` |
| anisopliae | **`anisopli-a-e`** | 7.5 | `a` |
| amcharrat | **`amcharr-a-t`** | 7.5 | `a` |
| vegetarian | **`vegetari-a-n`** | 7.5 | `a` |
| nyamashishi | **`nyamashi-s-hi`** | 7.5 | `s` |
| fregatidae | **`fregatid-a-e`** | 7.5 | `a` |
| tunapandanet | **`tunapandan-e-t`** | 7.5 | `e` |
| alioutaka | **`aliout-a-ka`** | 7.5 | `a` |
| humheshimu | **`hu-m-heshimu`** | 7.5 | `heshimu` |
| inayopaswa | **`inayopa-s-wa`** | 7.5 | `s` |
| ametawala | **`ameta-wa-la`** | 7.5 | `wa` |
| chillianwala | **`chillian-wa-la`** | 7.5 | `wa` |
| anchietas | **`anchie-ta-s`** | 7.5 | `ta` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Swahili 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 (4.84x) |
| N-gram | **2-gram** | Lowest perplexity (217) |
| Markov | **Context-4** | Highest predictability (94.5%) |
| 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 00:35:41*