---
language: so
language_name: Somali
language_family: cushitic
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-cushitic
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: 4.804
  - name: best_isotropy
    type: isotropy
    value: 0.8622
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Somali** 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** | 3.863x | 3.86 | 0.0648% | 951,080 |
| **16k** | 4.234x | 4.23 | 0.0710% | 867,649 |
| **32k** | 4.560x | 4.56 | 0.0765% | 805,556 |
| **64k** | 4.804x 🏆 | 4.80 | 0.0806% | 764,706 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Korean Broadcasting System (KBS) waa shabakad raadiye iyo telefishan Kuuriyada K...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kor ean ▁bro ad cas ting ▁system ▁( k bs ... (+12 more)` | 22 |
| 16k | `▁korean ▁broad cas ting ▁system ▁( k bs ) ▁waa ... (+10 more)` | 20 |
| 32k | `▁korean ▁broadcasting ▁system ▁( k bs ) ▁waa ▁shabakad ▁raadiye ... (+7 more)` | 17 |
| 64k | `▁korean ▁broadcasting ▁system ▁( kbs ) ▁waa ▁shabakad ▁raadiye ▁iyo ... (+6 more)` | 16 |

**Sample 2:** `Universidade Federal do Recôncavo da Bahia (UFRB) waxa ay ku taala magaalada Cru...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁univer sida de ▁federal ▁do ▁rec ô n ca vo ... (+32 more)` | 42 |
| 16k | `▁univer sida de ▁federal ▁do ▁rec ô n ca vo ... (+28 more)` | 38 |
| 32k | `▁universidade ▁federal ▁do ▁rec ô n ca vo ▁da ▁bahia ... (+21 more)` | 31 |
| 64k | `▁universidade ▁federal ▁do ▁rec ô n ca vo ▁da ▁bahia ... (+20 more)` | 30 |

**Sample 3:** `Camar bin Hishaam al-Makhzuumi "abuu jahal" waa gaal weyn oo cadaw ku ahaa islaa...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cam ar ▁bin ▁h ish aam ▁al - ma kh ... (+19 more)` | 29 |
| 16k | `▁camar ▁bin ▁hishaam ▁al - ma kh z uu mi ... (+15 more)` | 25 |
| 32k | `▁camar ▁bin ▁hishaam ▁al - ma kh z uu mi ... (+13 more)` | 23 |
| 64k | `▁camar ▁bin ▁hishaam ▁al - makh z uu mi ▁" ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.804x compression
- **Lowest UNK Rate:** 8k with 0.0648% 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 | 18,941 | 14.21 | 69,253 | 15.3% | 34.5% |
| **2-gram** | Subword | 235 🏆 | 7.88 | 6,710 | 73.0% | 98.7% |
| **3-gram** | Word | 47,961 | 15.55 | 102,689 | 7.8% | 19.8% |
| **3-gram** | Subword | 1,924 | 10.91 | 42,349 | 30.9% | 75.9% |
| **4-gram** | Word | 131,970 | 17.01 | 198,378 | 3.3% | 9.4% |
| **4-gram** | Subword | 10,789 | 13.40 | 193,486 | 14.2% | 43.9% |
| **5-gram** | Word | 119,528 | 16.87 | 156,118 | 2.1% | 7.4% |
| **5-gram** | Subword | 39,683 | 15.28 | 478,214 | 7.8% | 26.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka mid` | 9,808 |
| 2 | `ah oo` | 8,183 |
| 3 | `mid ah` | 8,058 |
| 4 | `waxa uu` | 7,173 |
| 5 | `sidoo kale` | 6,685 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka mid ah` | 7,046 |
| 2 | `oo ay ku` | 1,827 |
| 3 | `waxaa ka mid` | 1,557 |
| 4 | `mid ka mid` | 1,546 |
| 5 | `ka dib markii` | 1,252 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mid ka mid ah` | 1,525 |
| 2 | `waxaa ka mid ah` | 1,268 |
| 3 | `oo ay ku jiraan` | 939 |
| 4 | `oo ka mid ah` | 887 |
| 5 | `si kastaba ha ahaatee` | 800 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `waa mid ka mid ah` | 381 |
| 2 | `badan oo ka mid ah` | 232 |
| 3 | `oo ay ka mid yihiin` | 222 |
| 4 | `kani waa maqaal ku saabsan` | 204 |
| 5 | `ah oo ay ku jiraan` | 193 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 785,129 |
| 2 | `a a` | 551,833 |
| 3 | `a y` | 314,106 |
| 4 | `d a` | 311,005 |
| 5 | `a d` | 306,639 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k a _` | 191,283 |
| 2 | `a y _` | 182,234 |
| 3 | `_ w a` | 154,920 |
| 4 | `a d a` | 139,571 |
| 5 | `o o _` | 132,027 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ w a x` | 83,580 |
| 2 | `_ o o _` | 75,106 |
| 3 | `w a x a` | 72,968 |
| 4 | `a d a _` | 69,414 |
| 5 | `i y o _` | 65,977 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ w a x a` | 71,618 |
| 2 | `_ i y o _` | 60,073 |
| 3 | `w a x a a` | 28,120 |
| 4 | `w a x a y` | 27,648 |
| 5 | `a x a y _` | 26,222 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 235
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.8636 | 1.820 | 6.47 | 196,962 | 13.6% |
| **1** | Subword | 1.0789 | 2.112 | 6.98 | 3,275 | 0.0% |
| **2** | Word | 0.2528 | 1.192 | 1.66 | 1,269,511 | 74.7% |
| **2** | Subword | 0.7113 | 1.637 | 4.28 | 22,823 | 28.9% |
| **3** | Word | 0.0936 | 1.067 | 1.18 | 2,096,777 | 90.6% |
| **3** | Subword | 0.6878 | 1.611 | 3.58 | 97,500 | 31.2% |
| **4** | Word | 0.0360 🏆 | 1.025 | 1.06 | 2,465,103 | 96.4% |
| **4** | Subword | 0.5986 | 1.514 | 2.75 | 349,170 | 40.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `oo ahaa 165 595 in ay direen askar guutaale abadiaziiz maxamuud yaxye bin cumeyr si walboo`
2. `ee dibedda soomaaliya siyaasadda siyaasadda codsadayaasha maxaliga ah oo dhanna guurti la silciyey s...`
3. `iyo kuwa la dhaho wacaysmoge degmada dayniile muqdisho guddoomiyaha ururka waxaa lala yeeshay warbaa...`

**Context Size 2:**

1. `ka mid yihiin marc jacobs hervé léger hugo boss giorgio armani beauty 3 xilli ciyaareed ee royal`
2. `ah oo la wadaago 70 80 in wakhtigaas ku dhawaaqay inay yihiin qaybo ka mida gobolka jarar`
3. `mid ah 1dii janaayo bisha janaayo musk wuxuu ku laabtay magrib wuxuu ka kooban yihiin lix milyan`

**Context Size 3:**

1. `ka mid ah ciidankiisa waran sumeysan ibni cumar oo qabay walaashiis safiya bniti cubeyd ayuu u qoray...`
2. `oo ay ku jiraan majaladda sheekada dodge artful vinyl poetry prairie schooner iyo rhino gabayadeeda ...`
3. `waxaa ka mid ah geela maraykanka ah oo heesta kana shaqeeysa filimada hindiga waxay ka soo muuqatay ...`

**Context Size 4:**

1. `mid ka mid ah kuwa ugu bandhiga badan hollywood spoto p 221 churchwell pp 61 65 lev p 168`
2. `waxaa ka mid ah sheikh ibraahim yalale oo xilka xildhibannimo hayay inta u dhexeysay doorkii uu shie...`
3. `oo ay ku jiraan ashoka arab world africa action sinnaanta hadda golaha la talinta ee sanduuqa caalam...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `aminun_d_btoraqa`
2. `_u_da_caxigleeri`
3. `ita_o_gadid_b_1.`

**Context Size 2:**

1. `a_gooxdan_dagu_ta`
2. `aadkally_gobad_we`
3. `aysabiiyo_maga_sa`

**Context Size 3:**

1. `ka_ka_ay_qur’aano_`
2. `ay_waxay_damaada_s`
3. `_waqooyiga_dhaba._`

**Context Size 4:**

1. `_wax_ka_socota_waxa`
2. `_oo_ka_oo_maamulka_`
3. `waxay_u_aroor_ayaa_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (349,170 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 | 88,887 |
| Total Tokens | 2,839,359 |
| Mean Frequency | 31.94 |
| Median Frequency | 4 |
| Frequency Std Dev | 606.37 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | oo | 75,907 |
| 2 | ee | 62,003 |
| 3 | iyo | 60,594 |
| 4 | ah | 59,190 |
| 5 | ka | 58,938 |
| 6 | ku | 47,129 |
| 7 | u | 33,969 |
| 8 | ay | 27,872 |
| 9 | la | 26,142 |
| 10 | waxay | 24,810 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | abdulsalam | 2 |
| 2 | jamilu | 2 |
| 3 | ruggedman | 2 |
| 4 | rraz | 2 |
| 5 | inetimi | 2 |
| 6 | odon | 2 |
| 7 | eedris | 2 |
| 8 | foston | 2 |
| 9 | lanky | 2 |
| 10 | rhythmz | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0134 |
| R² (Goodness of Fit) | 0.995365 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 37.0% |
| Top 1,000 | 59.8% |
| Top 5,000 | 77.9% |
| Top 10,000 | 84.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9954 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 37.0% of corpus
- **Long Tail:** 78,887 words needed for remaining 15.1% 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 | 0.8622 | 0.3506 | N/A | N/A |
| **mono_64d** | 64 | 0.8393 | 0.2541 | N/A | N/A |
| **mono_128d** | 128 | 0.8150 | 0.1899 | N/A | N/A |
| **aligned_32d** | 32 | 0.8622 🏆 | 0.3423 | 0.0460 | 0.2720 |
| **aligned_64d** | 64 | 0.8393 | 0.2570 | 0.0880 | 0.3940 |
| **aligned_128d** | 128 | 0.8150 | 0.1956 | 0.1480 | 0.4820 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8622 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2649. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 14.8% 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 | **-0.717** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

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

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-a` | ankka, a6, aruuriyeen |
| `-s` | simay, sharab, sucuudiyyah |
| `-ma` | markiisii, masaxaya, markaas |
| `-ال` | التربية, المستطاب, الخندق |
| `-m` | markiisii, masaxaya, muxadis |
| `-d` | dayi, dhadhanku, doobka |
| `-b` | beyoncés, buuloburde, bulshadan |
| `-ba` | badbaadiyo, baasna, baangad |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | tula, qaahira, masaxaya |
| `-n` | kirsten, concepción, nasreen |
| `-da` | cabbirkeeda, metelida, hijrada |
| `-i` | markiisii, lari, dayi |
| `-an` | bulshadan, laaban, aaadan |
| `-o` | istuudiyoo, dhaqasho, amico |
| `-y` | yaqanay, simay, wacdiyay |
| `-ii` | markiisii, halkoodii, khaliifkii |

### 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 |
|------|----------|------------------|----------|
| `ooyi` | 2.19x | 64 contexts | mooyi, woqooyi, waqooyi |
| `iisa` | 2.08x | 69 contexts | hiisa, xiisa, ciisa |
| `aank` | 1.83x | 108 contexts | aanku, aanka, baanka |
| `yaas` | 2.16x | 47 contexts | iyaas, yaase, ilyaas |
| `agaa` | 1.76x | 114 contexts | dagaa, lagaa, tagaa |
| `eeya` | 1.68x | 136 contexts | geeya, geeyay, beeyay |
| `eeda` | 1.99x | 61 contexts | eeday, teeda, keeda |
| `aara` | 1.49x | 206 contexts | aaran, baara, faara |
| `alka` | 1.69x | 109 contexts | halka, jalka, xalka |
| `soom` | 2.59x | 20 contexts | soomi, soomo, sooma |
| `ooma` | 1.94x | 57 contexts | rooma, looma, nooma |
| `rkii` | 1.76x | 72 contexts | uurkii, jirkii, markii |

### 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 |
|--------|--------|-----------|----------|
| `-d` | `-a` | 218 words | dhinaciisa, dhigma |
| `-s` | `-a` | 172 words | shaqaynaya, sperma |
| `-a` | `-a` | 129 words | arrintiina, aadaya |
| `-b` | `-a` | 125 words | bataaxa, balaraba |
| `-k` | `-a` | 123 words | kaashanaysaa, koofiga |
| `-ma` | `-a` | 99 words | majaajiliistayaasha, maqaarka |
| `-d` | `-n` | 90 words | dhacsan, daadejin |
| `-s` | `-n` | 70 words | soojireen, suuxdin |
| `-d` | `-o` | 69 words | dhawaaqo, duqeymo |
| `-m` | `-a` | 68 words | midigta, moodaa |

### 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 |
|------|-----------------|------------|------|
| martigeliyaan | **`martigeliy-a-an`** | 7.5 | `a` |
| fadhiistaa | **`fadhiist-a-a`** | 7.5 | `a` |
| diiddanaa | **`diiddan-a-a`** | 7.5 | `a` |
| wakiiladu | **`wakiil-a-du`** | 7.5 | `a` |
| itoobiyada | **`itoobiy-a-da`** | 7.5 | `a` |
| amxaarada | **`amxaar-a-da`** | 7.5 | `a` |
| nimankani | **`niman-ka-ni`** | 7.5 | `ka` |
| filosofiyada | **`filosofiy-a-da`** | 7.5 | `a` |
| afduubeen | **`afduub-e-en`** | 7.5 | `e` |
| ilaahaaga | **`ilaaha-a-ga`** | 7.5 | `a` |
| aqoontaas | **`aqoonta-a-s`** | 7.5 | `a` |
| kumbuyuutar | **`kumbuyuut-a-r`** | 7.5 | `a` |
| ceelxagar | **`ceelxag-a-r`** | 7.5 | `a` |
| hadalkisii | **`hadalki-s-ii`** | 7.5 | `s` |
| diidnimada | **`diidnim-a-da`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Somali 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 (4.80x) |
| N-gram | **2-gram** | Lowest perplexity (235) |
| Markov | **Context-4** | Highest predictability (96.4%) |
| 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: 2026-01-10 21:47:10*