---
language: qu
language_name: Quechua
language_family: american_quechua
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-american_quechua
license: mit
library_name: wikilangs
pipeline_tag: text-generation
datasets:
  - omarkamali/wikipedia-monthly
dataset_info:
  name: wikipedia-monthly
  description: Monthly snapshots of Wikipedia articles across 300+ languages
metrics:
  - name: best_compression_ratio
    type: compression
    value: 3.814
  - name: best_isotropy
    type: isotropy
    value: 0.8810
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Quechua** 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** | 3.075x | 3.08 | 0.1752% | 308,239 |
| **16k** | 3.341x | 3.34 | 0.1903% | 283,718 |
| **32k** | 3.587x | 3.59 | 0.2043% | 264,268 |
| **64k** | 3.814x 🏆 | 3.82 | 0.2173% | 248,495 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Kawitu, Puñuna icha Kama nisqaqa tawantin chakiyuq kuyuyllam, puñunapaq. Hawa t'...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁k awi tu , ▁puñ una ▁icha ▁kama ▁nisqaqa ▁tawantin ... (+12 more)` | 22 |
| 16k | `▁k awi tu , ▁puñuna ▁icha ▁kama ▁nisqaqa ▁tawantin ▁chakiyuq ... (+10 more)` | 20 |
| 32k | `▁k awitu , ▁puñuna ▁icha ▁kama ▁nisqaqa ▁tawantin ▁chakiyuq ▁kuyuy ... (+9 more)` | 19 |
| 64k | `▁kawitu , ▁puñuna ▁icha ▁kama ▁nisqaqa ▁tawantin ▁chakiyuq ▁kuyuyllam , ... (+6 more)` | 16 |

**Sample 2:** `544 wataqa Hulyanu kalindaryukama ch'askachawwan qallarisqa wakllanwatam karqan....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 5 4 4 ▁wataqa ▁hulyanu ▁kalindaryukama ▁ch ' askachawwan ... (+8 more)` | 18 |
| 16k | `▁ 5 4 4 ▁wataqa ▁hulyanu ▁kalindaryukama ▁ch ' askachawwan ... (+8 more)` | 18 |
| 32k | `▁ 5 4 4 ▁wataqa ▁hulyanu ▁kalindaryukama ▁ch ' askachawwan ... (+8 more)` | 18 |
| 64k | `▁ 5 4 4 ▁wataqa ▁hulyanu ▁kalindaryukama ▁ch ' askachawwan ... (+8 more)` | 18 |

**Sample 3:** `wataqa Hulyanu kalindaryukama illapachawwan qallarisqa chhasku watam karqan. Ima...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wataqa ▁hulyanu ▁kalindaryukama ▁illapachawwan ▁qallarisqa ▁chhasku ▁watam ▁karqan . ▁ima ... (+7 more)` | 17 |
| 16k | `▁wataqa ▁hulyanu ▁kalindaryukama ▁illapachawwan ▁qallarisqa ▁chhasku ▁watam ▁karqan . ▁ima ... (+7 more)` | 17 |
| 32k | `▁wataqa ▁hulyanu ▁kalindaryukama ▁illapachawwan ▁qallarisqa ▁chhasku ▁watam ▁karqan . ▁ima ... (+7 more)` | 17 |
| 64k | `▁wataqa ▁hulyanu ▁kalindaryukama ▁illapachawwan ▁qallarisqa ▁chhasku ▁watam ▁karqan . ▁ima ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 3.814x compression
- **Lowest UNK Rate:** 8k with 0.1752% 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 | 7,264 | 12.83 | 39,330 | 23.8% | 50.0% |
| **2-gram** | Subword | 298 🏆 | 8.22 | 5,423 | 66.9% | 98.9% |
| **3-gram** | Word | 12,773 | 13.64 | 62,529 | 19.2% | 42.6% |
| **3-gram** | Subword | 2,472 | 11.27 | 36,562 | 26.4% | 70.3% |
| **4-gram** | Word | 28,198 | 14.78 | 122,111 | 14.8% | 33.9% |
| **4-gram** | Subword | 12,905 | 13.66 | 188,362 | 14.8% | 42.6% |
| **5-gram** | Word | 27,683 | 14.76 | 106,668 | 14.4% | 32.7% |
| **5-gram** | Subword | 40,481 | 15.30 | 509,294 | 11.4% | 31.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hawa t` | 15,166 |
| 2 | `t inkikuna` | 15,101 |
| 3 | `kaypipas qhaway` | 12,266 |
| 4 | `kastilla simipi` | 7,981 |
| 5 | `llaqtapi huk` | 6,598 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hawa t inkikuna` | 15,077 |
| 2 | `simita rimaqkuna 1` | 3,117 |
| 3 | `t inkikuna saywitu` | 3,010 |
| 4 | `mama llaqtapi huk` | 2,896 |
| 5 | `allpa saywachi urqukuna` | 2,757 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `hawa t inkikuna saywitu` | 3,010 |
| 2 | `ima tukusqakuna yurisqakuna wañusqakuna` | 2,681 |
| 3 | `llaqtapi huk mama llaqtayuq` | 2,246 |
| 4 | `pukyukuna hawa t inkikuna` | 2,135 |
| 5 | `kastilla simipi distrito de` | 1,872 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `karqan ima tukusqakuna yurisqakuna wañusqakuna` | 1,708 |
| 2 | `rimaqkuna 1 indihina simita rimaqkuna` | 1,538 |
| 3 | `1 indihina simita rimaqkuna 1` | 1,538 |
| 4 | `indihina simita rimaqkuna 1 2` | 1,538 |
| 5 | `simita rimaqkuna 1 indihina simita` | 1,533 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 517,514 |
| 2 | `a n` | 245,957 |
| 3 | `n a` | 225,941 |
| 4 | `u n` | 213,735 |
| 5 | `m a` | 197,596 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u n a` | 147,282 |
| 2 | `k u n` | 125,343 |
| 3 | `l l a` | 114,842 |
| 4 | `n a _` | 101,812 |
| 5 | `c h a` | 85,994 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k u n a` | 120,434 |
| 2 | `u n a _` | 72,857 |
| 3 | `l l a q` | 53,527 |
| 4 | `_ l l a` | 53,050 |
| 5 | `a q t a` | 51,662 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k u n a _` | 67,038 |
| 2 | `l a q t a` | 50,837 |
| 3 | `l l a q t` | 50,836 |
| 4 | `_ l l a q` | 47,933 |
| 5 | `_ s i m i` | 38,886 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 298
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~32% 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 | 0.7310 | 1.660 | 4.55 | 204,902 | 26.9% |
| **1** | Subword | 0.6430 | 1.562 | 4.45 | 5,037 | 35.7% |
| **2** | Word | 0.1782 | 1.131 | 1.39 | 928,009 | 82.2% |
| **2** | Subword | 0.6244 | 1.542 | 3.91 | 22,429 | 37.6% |
| **3** | Word | 0.0678 | 1.048 | 1.13 | 1,281,917 | 93.2% |
| **3** | Subword | 0.6945 | 1.618 | 3.75 | 87,652 | 30.6% |
| **4** | Word | 0.0377 🏆 | 1.026 | 1.07 | 1,441,549 | 96.2% |
| **4** | Subword | 0.6763 | 1.598 | 3.03 | 328,292 | 32.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de velázquez barcelona qori medalla de oliveira guterres uralan runasimillapi t inkikuna www ine gov...`
2. `huk mamá me again by country dance single haley bill his comets jun sheng zhan feng`
3. `t inkikuna www inei gob pe kaypipas qhaway piluta hayt aqmi pinchikilla killikachap facultad qa paqa...`

**Context Size 2:**

1. `hawa t inkikuna saywitu kashamarka suyu piruw kuntisuyus pruwinsya chichas pruwinsya buliwya chuqiya...`
2. `t inkikuna ñawpaqnin kaq barack obama rodolfo castillo hawa t inkikuna nobel prize in literature en ...`
3. `kaypipas qhaway pulitika rakiy uma llaqtanqa el porvenir distritup uma llaqtanmi rikchakuna hawa t i...`

**Context Size 3:**

1. `hawa t inkikuna saywitu chapari pruwinsya buliwya quchapampa suyu killaqullu pruwinsya`
2. `simita rimaqkuna 1 indihina simita rimaqkuna 1 indihina simita rimaqkuna 1 indihina simita rimaqkuna...`
3. `t inkikuna saywitu san martin suyu san martin suyu piruw san martin suyu piruw san martin suyu quris...`

**Context Size 4:**

1. `hawa t inkikuna saywitu daniel campos pruwinsya buliwya p utuqsi suyu bustillo pruwinsya buliwya`
2. `llaqtapi huk mama llaqtayuq taripay amachaq wan pulitiku qarqan watamanta watakama ñawpaq kuti ispañ...`
3. `pukyukuna hawa t inkikuna saywitu hunin suyu hunin suyu pruwinsya pruwinsya pruwinsya fajardo pruwin...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `acorukutaqma)_ch`
2. `_alan.4_obo_stol`
3. `ia_quñi)_stivest`

**Context Size 2:**

1. `a_suttie_forescor`
2. `anovive_puk_mi:_q`
3. `na_ruwitina_ñayta`

**Context Size 3:**

1. `una:_5_/_qunturpak`
2. `kuna_el_no_•_the_m`
3. `lla_suyuya_manqa_p`

**Context Size 4:**

1. `kuna:_chichwamaqa_t`
2. `una_kang_朝阳市_chén_p`
3. `llaqtap_uma_llar_fe`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (328,292 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 | 84,317 |
| Total Tokens | 2,026,402 |
| Mean Frequency | 24.03 |
| Median Frequency | 4 |
| Frequency Std Dev | 301.31 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 36,630 |
| 2 | huk | 21,274 |
| 3 | t | 18,029 |
| 4 | hawa | 17,411 |
| 5 | llaqtapi | 17,307 |
| 6 | simi | 16,544 |
| 7 | mama | 16,041 |
| 8 | inkikuna | 15,101 |
| 9 | la | 15,098 |
| 10 | kastilla | 13,320 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | lluqsinankupaq | 2 |
| 2 | argentinamanta | 2 |
| 3 | puchuchkaptin | 2 |
| 4 | aplikasyun | 2 |
| 5 | hillap | 2 |
| 6 | siqhikunata | 2 |
| 7 | aramco | 2 |
| 8 | asml | 2 |
| 9 | tarhitan | 2 |
| 10 | tarhita | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0224 |
| R² (Goodness of Fit) | 0.997655 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 33.2% |
| Top 1,000 | 59.9% |
| Top 5,000 | 76.0% |
| Top 10,000 | 82.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9977 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 33.2% of corpus
- **Long Tail:** 74,317 words needed for remaining 17.1% 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 | 0.8810 🏆 | 0.3426 | N/A | N/A |
| **mono_64d** | 64 | 0.8340 | 0.2733 | N/A | N/A |
| **mono_128d** | 128 | 0.5721 | 0.2442 | N/A | N/A |
| **aligned_32d** | 32 | 0.8810 | 0.3377 | 0.0680 | 0.3340 |
| **aligned_64d** | 64 | 0.8340 | 0.2731 | 0.0960 | 0.4220 |
| **aligned_128d** | 128 | 0.5721 | 0.2474 | 0.1720 | 0.5500 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8810 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2864. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 17.2% 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 | **0.035** | 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` | anapaqmi, antauta, amore |
| `-s` | suriname, swanson, semo |
| `-ma` | mayta, masiykip, mawrisyu |
| `-p` | pers, próximo, planas |
| `-c` | cuál, constelaciones, cayubaba |
| `-m` | música, mayta, montoya |
| `-t` | taming, trivial, traviata |
| `-pa` | pawsirna, pakaran, panicum |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | quriwayrachina, negociokunata, encendida |
| `-s` | pers, planas, humanas |
| `-n` | garrison, danon, swanson |
| `-ta` | negociokunata, infanta, mayta |
| `-i` | sagnasti, qhuyakunapi, nazi |
| `-o` | próximo, semo, fisiográfico |
| `-e` | suriname, neue, amore |
| `-na` | quriwayrachina, ispañulkuna, imiratukuna |

### 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 |
|------|----------|------------------|----------|
| `rqan` | 2.15x | 37 contexts | irqan, arqan, ñirqan |
| `naku` | 1.90x | 56 contexts | unaku, anaku, inakuy |
| `aqta` | 1.65x | 78 contexts | maqta, saqta, laqta |
| `trit` | 2.25x | 21 contexts | trita, matrit, triticum |
| `llaq` | 1.68x | 55 contexts | illaq, llaqa, llaqi |
| `qtap` | 1.98x | 22 contexts | llaqtap, waqtapi, waqtapim |
| `tapi` | 1.67x | 40 contexts | tapia, tapis, watapi |
| `stri` | 1.64x | 36 contexts | strip, string, nostri |
| `laqt` | 1.97x | 19 contexts | laqta, llaqta, llaqtap |
| `istr` | 1.63x | 33 contexts | maistre, mistral, oistrach |
| `uwin` | 2.30x | 11 contexts | uwina, luwin, quwinqa |
| `imip` | 2.12x | 13 contexts | simip, simipa, simipi |

### 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` | 194 words | agrupa, ariola |
| `-p` | `-a` | 178 words | peninsula, pakasqa |
| `-c` | `-a` | 173 words | columbia, cutuglahua |
| `-t` | `-a` | 108 words | thuxlla, teologia |
| `-s` | `-a` | 100 words | saruma, sharma |
| `-c` | `-s` | 98 words | cargas, circulares |
| `-p` | `-s` | 85 words | phaseolus, peplus |
| `-c` | `-o` | 74 words | comparativo, consorcio |
| `-s` | `-s` | 73 words | standards, sonchus |
| `-l` | `-a` | 71 words | la, lamolina |

### 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 |
|------|-----------------|------------|------|
| illaykikunata | **`illaykikun-a-ta`** | 7.5 | `a` |
| sitiomanta | **`sitiom-an-ta`** | 7.5 | `an` |
| arkitiktu | **`arkitik-t-u`** | 7.5 | `t` |
| intervista | **`intervi-s-ta`** | 7.5 | `s` |
| llaqtantas | **`llaqtan-ta-s`** | 7.5 | `ta` |
| diskunpas | **`diskun-pa-s`** | 7.5 | `pa` |
| unchulpiqa | **`unchul-pi-qa`** | 7.5 | `pi` |
| imayaykunata | **`imayaykun-a-ta`** | 7.5 | `a` |
| ruwayninkunata | **`ruwayninkun-a-ta`** | 7.5 | `a` |
| puriqchana | **`puriqc-ha-na`** | 7.5 | `ha` |
| kawsaykuna | **`kawsay-ku-na`** | 7.5 | `ku` |
| correspondências | **`correspondênc-i-as`** | 7.5 | `i` |
| qallariqanku | **`qallariq-an-ku`** | 7.5 | `an` |
| chinkachin | **`ch-in-kachin`** | 7.5 | `kachin` |
| novelakuna | **`novela-ku-na`** | 7.5 | `ku` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Quechua 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 (3.81x) |
| N-gram | **2-gram** | Lowest perplexity (298) |
| Markov | **Context-4** | Highest predictability (96.2%) |
| 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 18:27:46*