---
language: ay
language_name: Aymara
language_family: american_aymara
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_aymara
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: 4.252
  - name: best_isotropy
    type: isotropy
    value: 0.7572
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Aymara** 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** | 3.398x | 3.40 | 0.2746% | 168,272 |
| **16k** | 3.708x | 3.72 | 0.2996% | 154,209 |
| **32k** | 3.989x | 4.00 | 0.3223% | 143,366 |
| **64k** | 4.252x 🏆 | 4.26 | 0.3435% | 134,499 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Dublin (), nayriri marka Irlandiya Jisk'a t'aqa suyunaka Irpirinaka Wali uñt'at ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁du blin ▁(), ▁nayriri ▁marka ▁ir landiya ▁jisk ' a ... (+14 more)` | 24 |
| 16k | `▁dublin ▁(), ▁nayriri ▁marka ▁irlandiya ▁jisk ' a ▁t ' ... (+11 more)` | 21 |
| 32k | `▁dublin ▁(), ▁nayriri ▁marka ▁irlandiya ▁jisk ' a ▁t ' ... (+11 more)` | 21 |
| 64k | `▁dublin ▁(), ▁nayriri ▁marka ▁irlandiya ▁jisk ' a ▁t ' ... (+11 more)` | 21 |

**Sample 2:** `- mara. Yuriña Jiwaña Uruyaña Payïr Jachʼa Chʼaxwäwi tukuyxäna.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁- ▁mara . ▁yuriña ▁jiwaña ▁uruyaña ▁payïr ▁jach ʼ a ... (+8 more)` | 18 |
| 16k | `▁- ▁mara . ▁yuriña ▁jiwaña ▁uruyaña ▁payïr ▁jach ʼ a ... (+6 more)` | 16 |
| 32k | `▁- ▁mara . ▁yuriña ▁jiwaña ▁uruyaña ▁payïr ▁jach ʼ a ... (+6 more)` | 16 |
| 64k | `▁- ▁mara . ▁yuriña ▁jiwaña ▁uruyaña ▁payïr ▁jach ʼ a ... (+6 more)` | 16 |

**Sample 3:** `Chika uru (), qharatatata ch’amakthapkama uruna taypipa.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁chika ▁uru ▁(), ▁qh ara tata ta ▁ch ’ ama ... (+9 more)` | 19 |
| 16k | `▁chika ▁uru ▁(), ▁qh ara tata ta ▁ch ’ ama ... (+8 more)` | 18 |
| 32k | `▁chika ▁uru ▁(), ▁qhara tatata ▁ch ’ amak thap kama ... (+5 more)` | 15 |
| 64k | `▁chika ▁uru ▁(), ▁qhara tatata ▁ch ’ amakthapkama ▁uruna ▁taypipa ... (+1 more)` | 11 |


### Key Findings

- **Best Compression:** 64k achieves 4.252x compression
- **Lowest UNK Rate:** 8k with 0.2746% 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 | 1,093 | 10.09 | 8,159 | 47.5% | 75.3% |
| **2-gram** | Subword | 282 🏆 | 8.14 | 2,432 | 66.7% | 99.2% |
| **3-gram** | Word | 1,711 | 10.74 | 12,666 | 42.2% | 69.1% |
| **3-gram** | Subword | 2,030 | 10.99 | 18,023 | 29.5% | 73.5% |
| **4-gram** | Word | 4,113 | 12.01 | 28,447 | 33.5% | 56.4% |
| **4-gram** | Subword | 8,227 | 13.01 | 79,517 | 19.1% | 48.7% |
| **5-gram** | Word | 4,963 | 12.28 | 27,121 | 30.7% | 52.7% |
| **5-gram** | Subword | 18,419 | 14.17 | 172,494 | 15.5% | 41.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jisk a` | 12,410 |
| 2 | `t aqa` | 10,719 |
| 3 | `aqa suyu` | 8,507 |
| 4 | `a t` | 6,972 |
| 5 | `a suyu` | 5,247 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t aqa suyu` | 8,506 |
| 2 | `a t aqa` | 6,963 |
| 3 | `jisk a t` | 6,951 |
| 4 | `jisk a suyu` | 3,603 |
| 5 | `piruw t aqa` | 2,712 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jisk a t aqa` | 6,950 |
| 2 | `a t aqa suyu` | 4,765 |
| 3 | `piruw t aqa suyu` | 2,712 |
| 4 | `t aqa suyu asu` | 1,947 |
| 5 | `aqa suyu asu jaqinaka` | 1,947 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jisk a t aqa suyu` | 4,757 |
| 2 | `t aqa suyu asu jaqinaka` | 1,947 |
| 3 | `a t aqa suyu asu` | 1,947 |
| 4 | `suyu piruw t aqa suyu` | 1,830 |
| 5 | `t aqa suyu piruw t` | 1,830 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 131,245 |
| 2 | `k a` | 69,413 |
| 3 | `n a` | 64,712 |
| 4 | `a n` | 60,547 |
| 5 | `a r` | 59,718 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a k a` | 37,061 |
| 2 | `n a k` | 33,828 |
| 3 | `a _ s` | 26,955 |
| 4 | `_ m a` | 24,357 |
| 5 | `_ j a` | 23,674 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n a k a` | 32,697 |
| 2 | `s u y u` | 19,816 |
| 3 | `_ s u y` | 19,711 |
| 4 | `a _ s u` | 19,361 |
| 5 | `_ m a r` | 19,102 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s u y u` | 19,654 |
| 2 | `a _ s u y` | 18,833 |
| 3 | `n a k a _` | 16,761 |
| 4 | `a n a k a` | 16,081 |
| 5 | `_ j i s k` | 12,416 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 282
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~41% 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 | 0.6845 | 1.607 | 3.61 | 60,169 | 31.6% |
| **1** | Subword | 0.8600 | 1.815 | 6.42 | 953 | 14.0% |
| **2** | Word | 0.1508 | 1.110 | 1.33 | 216,093 | 84.9% |
| **2** | Subword | 0.9055 | 1.873 | 5.55 | 6,117 | 9.5% |
| **3** | Word | 0.0575 | 1.041 | 1.13 | 286,627 | 94.3% |
| **3** | Subword | 0.8121 | 1.756 | 3.93 | 33,906 | 18.8% |
| **4** | Word | 0.0351 🏆 | 1.025 | 1.08 | 322,229 | 96.5% |
| **4** | Subword | 0.6399 | 1.558 | 2.64 | 133,072 | 36.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a crespo madrid mara fernando belaúnde umalliq uraqipa san huwan bosco giuseppe verdi nabucco italiy...`
2. `suyu asu jaqinaka kurakanaka mario hinostroza ppc carlos milla batres lima jisk a suyupi piruw porta...`
3. `jisk a t aqa suyu wankawillka mons karu puriy sulli phutti charqui kanka champhayna plato paceño`

**Context Size 2:**

1. `jisk a suyuxa wuliwya nayriri marka sport fa šiauliai fc gintra fc šiauliai lituaña marka sport fk`
2. `t aqa suyu piruw t aqa suyu kastilla arupi distrito de chambara na mä jisk a suyu`
3. `aqa suyu bongara jisk a suyu nayra sarnaqawi santa rusa yachay tarpuy yachaychiy asu utanaka huch uy`

**Context Size 3:**

1. `t aqa suyu kurunku jisk a suyu suyu piruw suyu piwra jach a suyu jisk a suyunaka aruskipäwi`
2. `a t aqa suyu asu jaqinaka kurakanaka amílcar gerardo ramos collachagua bloque popular junín jne auto...`
3. `jisk a t aqa suyuxa kastilla aru distrito de bambamarca na mä jisk a t aqa suyu nayriri`

**Context Size 4:**

1. `jisk a t aqa suyu kastilla arupi distrito de pucyura nisqaqa huk jisk a t aqa suyu pallasqa jisk`
2. `a t aqa suyu nayriri marka shanao 270 msnm qullunaka jawiranaka qutanaka qullqinchäwi jaqinaka 9 104...`
3. `piruw t aqa suyu ariqipa jisk a suyupi ariqipa jach a suyupi piruw jach a markapi nayra sarnaqawi qu...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `arererulu_jax_yu`
2. `_ma_uycho_smtera`
3. `i_lorma_-_si_lel`

**Context Size 2:**

1. `a_mujisqa_34_300_`
2. `ka_jisk'aqäwiru)_`
3. `nayrin_jisychérro`

**Context Size 3:**

1. `aka_nayriri_irpiru`
2. `nakapi._maraka_-_l`
3. `a_sasa_uywa_baldi_`

**Context Size 4:**

1. `naka:_musampïmwa._j`
2. `suyu;_(kasti_wat'ay`
3. `_suyuwa,_209,12_km2`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (133,072 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 | 24,208 |
| Total Tokens | 520,495 |
| Mean Frequency | 21.50 |
| Median Frequency | 3 |
| Frequency Std Dev | 253.66 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 19,357 |
| 2 | suyu | 14,560 |
| 3 | jisk | 12,473 |
| 4 | t | 11,844 |
| 5 | de | 11,521 |
| 6 | aqa | 10,723 |
| 7 | jach | 6,951 |
| 8 | jaqinaka | 5,107 |
| 9 | piruw | 5,076 |
| 10 | la | 4,233 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | lunisa | 2 |
| 2 | sawaru | 2 |
| 3 | tuminku | 2 |
| 4 | urupawa | 2 |
| 5 | capitalapawa | 2 |
| 6 | kurunawirus | 2 |
| 7 | uttar | 2 |
| 8 | pradesh | 2 |
| 9 | quqanakampi | 2 |
| 10 | jawiranakat | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0705 |
| R² (Goodness of Fit) | 0.996948 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 47.7% |
| Top 1,000 | 73.0% |
| Top 5,000 | 87.2% |
| Top 10,000 | 93.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9969 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 47.7% of corpus
- **Long Tail:** 14,208 words needed for remaining 7.0% 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 | 0.7572 🏆 | 0.3779 | N/A | N/A |
| **mono_64d** | 64 | 0.4924 | 0.3361 | N/A | N/A |
| **mono_128d** | 128 | 0.1272 | 0.3426 | N/A | N/A |
| **aligned_32d** | 32 | 0.7572 | 0.3748 | 0.0400 | 0.2060 |
| **aligned_64d** | 64 | 0.4924 | 0.3390 | 0.0480 | 0.2520 |
| **aligned_128d** | 128 | 0.1272 | 0.3283 | 0.0740 | 0.3280 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7572 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3498. 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 | **0.285** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

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

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-ma` | mayura, manon, marcona |
| `-pa` | pallasqa, palestina, pachakutiq |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | horadnia, enlacenaka, pukllaykuna |
| `-as` | cotabambas, caritas, chinapas |
| `-na` | pukllaykuna, pukyukuna, amasuna |
| `-es` | desapariciones, regiones, crueles |

### 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 |
|------|----------|------------------|----------|
| `kana` | 2.06x | 39 contexts | ukana, kanal, akana |
| `arka` | 2.00x | 39 contexts | arkañ, marka, markaq |
| `qull` | 1.97x | 27 contexts | qulla, qullu, qullq |
| `raqi` | 2.19x | 19 contexts | uraqi, uraqiw, saraqi |
| `hach` | 1.91x | 29 contexts | hacha, qhach, chacha |
| `hana` | 1.93x | 25 contexts | chana, hanaq, ghana |
| `tana` | 1.88x | 26 contexts | utana, utanak, patana |
| `aqin` | 2.00x | 19 contexts | taqin, jaqin, jaqinx |
| `rkan` | 2.10x | 15 contexts | hirkan, markan, markani |
| `ista` | 1.57x | 31 contexts | vista, lista, wista |
| `irin` | 1.96x | 14 contexts | irina, irinak, irineo |
| `arus` | 1.90x | 15 contexts | arusa, larus, arust |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-ma` | `-a` | 66 words | maceda, marakama |
| `-pa` | `-a` | 52 words | patunka, paulina |
| `-ma` | `-na` | 11 words | maradona, martina |
| `-pa` | `-na` | 9 words | paulina, pagina |
| `-pa` | `-es` | 8 words | patrones, pacajes |
| `-ma` | `-as` | 5 words | matorras, maravillas |
| `-ma` | `-es` | 4 words | marques, mayores |
| `-pa` | `-as` | 2 words | palabras, pachas |

### 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 |
|------|-----------------|------------|------|
| populares | **`popular-es`** | 4.5 | `popular` |
| ceremoniales | **`ceremonial-es`** | 4.5 | `ceremonial` |
| apóstoles | **`apóstol-es`** | 4.5 | `apóstol` |
| uywanakana | **`uywanaka-na`** | 4.5 | `uywanaka` |
| funerales | **`funeral-es`** | 4.5 | `funeral` |
| christies | **`christi-es`** | 4.5 | `christi` |
| regulares | **`regular-es`** | 4.5 | `regular` |
| familiares | **`familiar-es`** | 4.5 | `familiar` |
| wawanakana | **`wawanaka-na`** | 4.5 | `wawanaka` |
| australiana | **`australia-na`** | 4.5 | `australia` |
| magisteriales | **`ma-gisterial-es`** | 3.0 | `gisterial` |
| pacoricona | **`pa-corico-na`** | 3.0 | `corico` |
| maranakana | **`ma-ranaka-na`** | 3.0 | `ranaka` |
| partituras | **`pa-rtitur-as`** | 3.0 | `rtitur` |
| pallaytas | **`pa-llayt-as`** | 3.0 | `llayt` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Aymara shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.25x) |
| N-gram | **2-gram** | Lowest perplexity (282) |
| Markov | **Context-4** | Highest predictability (96.5%) |
| 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: 2026-01-03 18:29:39*