---
language: nah
language_name: Nahuatl languages
language_family: american_nahuatl
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_nahuatl
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: 4.837
  - name: best_isotropy
    type: isotropy
    value: 0.2842
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Nahuatl languages - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Nahuatl languages** 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** | 3.986x | 4.00 | 0.0238% | 92,310 |
| **16k** | 4.334x | 4.35 | 0.0259% | 84,893 |
| **32k** | 4.614x | 4.63 | 0.0276% | 79,736 |
| **64k** | 4.837x 🏆 | 4.85 | 0.0289% | 76,056 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ītōcā cē xihuitl īpan mācuīlpōhualxihuitl 13 īpan mahtlācxihuitl. Mochīhualiztli...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 3 ▁īpan ... (+7 more)` | 17 |
| 16k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 3 ▁īpan ... (+7 more)` | 17 |
| 32k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 3 ▁īpan ... (+7 more)` | 17 |
| 64k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 3 ▁īpan ... (+7 more)` | 17 |

**Sample 2:** `847 ītōcā cē xihuitl īpan mācuīlpōhualxihuitl 9 īpan 840s mahtlācxihuitl. Mochīh...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 8 4 7 ▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ... (+15 more)` | 25 |
| 16k | `▁ 8 4 7 ▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ... (+15 more)` | 25 |
| 32k | `▁ 8 4 7 ▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ... (+15 more)` | 25 |
| 64k | `▁ 8 4 7 ▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ... (+15 more)` | 25 |

**Sample 3:** `ītōcā cē xihuitl īpan mācuīlpōhualxihuitl 12 īpan mahtlācxihuitl. Mochīhualiztli...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 2 ▁īpan ... (+7 more)` | 17 |
| 16k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 2 ▁īpan ... (+7 more)` | 17 |
| 32k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 2 ▁īpan ... (+7 more)` | 17 |
| 64k | `▁ītōcā ▁cē ▁xihuitl ▁īpan ▁mācuīlpōhual xihuitl ▁ 1 2 ▁īpan ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.837x compression
- **Lowest UNK Rate:** 8k with 0.0238% 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 | 582 | 9.18 | 2,574 | 49.8% | 80.2% |
| **2-gram** | Subword | 257 🏆 | 8.00 | 1,917 | 69.1% | 99.1% |
| **3-gram** | Word | 593 | 9.21 | 3,076 | 50.9% | 78.5% |
| **3-gram** | Subword | 1,587 | 10.63 | 12,907 | 37.0% | 75.9% |
| **4-gram** | Word | 1,134 | 10.15 | 5,251 | 42.7% | 69.4% |
| **4-gram** | Subword | 5,857 | 12.52 | 49,857 | 26.7% | 53.4% |
| **5-gram** | Word | 1,235 | 10.27 | 4,148 | 39.7% | 72.1% |
| **5-gram** | Subword | 11,633 | 13.51 | 85,697 | 23.3% | 44.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ītōcā cē` | 2,347 |
| 2 | `īpan mācuīlpōhualxihuitl` | 2,077 |
| 3 | `cē xihuitl` | 2,072 |
| 4 | `xihuitl īpan` | 2,021 |
| 5 | `tlācatiliztli miquiztli` | 1,948 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `cē xihuitl īpan` | 1,988 |
| 2 | `xihuitl īpan mācuīlpōhualxihuitl` | 1,968 |
| 3 | `ītōcā cē xihuitl` | 1,960 |
| 4 | `mochīhualiztli tlācatiliztli miquiztli` | 1,881 |
| 5 | `mahtlācxihuitl mochīhualiztli tlācatiliztli` | 1,500 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `cē xihuitl īpan mācuīlpōhualxihuitl` | 1,968 |
| 2 | `ītōcā cē xihuitl īpan` | 1,960 |
| 3 | `mahtlācxihuitl mochīhualiztli tlācatiliztli miquiztli` | 1,463 |
| 4 | `īpan mahtlācxihuitl mochīhualiztli tlācatiliztli` | 921 |
| 5 | `māhtlacxihuitl mochīhualiztli tlācatiliztli miquiztli` | 399 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ītōcā cē xihuitl īpan mācuīlpōhualxihuitl` | 1,960 |
| 2 | `īpan mahtlācxihuitl mochīhualiztli tlācatiliztli miquiztli` | 884 |
| 3 | `cē xihuitl īpan mācuīlpōhualxihuitl 15` | 170 |
| 4 | `xihuitl īpan mācuīlpōhualxihuitl 15 īpan` | 170 |
| 5 | `īpan mācuīlpōhualxihuitl 15 īpan mahtlācxihuitl` | 170 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t l` | 48,016 |
| 2 | `l i` | 32,159 |
| 3 | `n _` | 26,955 |
| 4 | `h u` | 25,168 |
| 5 | `u i` | 22,921 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l i _` | 14,715 |
| 2 | `t l i` | 13,229 |
| 3 | `t l a` | 12,936 |
| 4 | `a n _` | 11,601 |
| 5 | `z t l` | 11,086 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `t l i _` | 11,323 |
| 2 | `z t l i` | 10,901 |
| 3 | `i z t l` | 10,448 |
| 4 | `u i t l` | 8,705 |
| 5 | `h u i t` | 8,526 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i z t l i` | 10,379 |
| 2 | `z t l i _` | 9,771 |
| 3 | `h u i t l` | 8,254 |
| 4 | `l i z t l` | 7,810 |
| 5 | `i h u i t` | 7,378 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 257
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~44% 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 | 0.5364 | 1.450 | 2.77 | 33,565 | 46.4% |
| **1** | Subword | 1.0165 | 2.023 | 7.61 | 617 | 0.0% |
| **2** | Word | 0.1320 | 1.096 | 1.24 | 92,088 | 86.8% |
| **2** | Subword | 0.9596 | 1.945 | 5.40 | 4,690 | 4.0% |
| **3** | Word | 0.0399 | 1.028 | 1.06 | 112,754 | 96.0% |
| **3** | Subword | 0.8013 | 1.743 | 3.55 | 25,317 | 19.9% |
| **4** | Word | 0.0175 🏆 | 1.012 | 1.03 | 117,889 | 98.3% |
| **4** | Subword | 0.5541 | 1.468 | 2.22 | 89,855 | 44.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `in ompa yeppa conmottiliani 108 centenas de literatura literature littérature āmatlalcāyōtl gramátic...`
2. `īpan 360s māhtlacxihuitl mochīhualiztli tlācatiliztli miquiztli amoxtlahcuilohqueh xiuhpan ītōca in ...`
3. `cē xihuitl īpan 900s mahtlācxihuitl mochīhualiztli tlācatiliztli miquiztli tlamācuīlti 5 la vega alt...`

**Context Size 2:**

1. `ītōcā cē xihuitl īpan mācuīlpōhualxihuitl 14 īpan mahtlācxihuitl mochīhualiztli tlācatiliztli miquiz...`
2. `īpan mācuīlpōhualxihuitl 17 īpan mahtlācxihuitl mochīhualiztli tlācatiliztli miquiztli tlamahtlācti ...`
3. `cē xihuitl īpan mācuīlpōhualxihuitl 1 īpan 50s māhtlacxihuitl mochīhualiztli tlācatiliztli miquiztli...`

**Context Size 3:**

1. `cē xihuitl īpan mācuīlpōhualxihuitl 10 īpan 980s mahtlācxihuitl mochīhualiztli tlācatiliztli miquizt...`
2. `xihuitl īpan mācuīlpōhualxihuitl 1 īpan 40s māhtlacxihuitl mochīhualiztli tlācatiliztli miquiztli tl...`
3. `ītōcā cē xihuitl īpan mācuīlpōhualxihuitl 10 īpan 990s mahtlācxihuitl mochīhualiztli tlācatiliztli m...`

**Context Size 4:**

1. `cē xihuitl īpan mācuīlpōhualxihuitl 18 īpan mahtlācxihuitl mochīhualiztli tlācatiliztli miquiztli tl...`
2. `ītōcā cē xihuitl īpan mācuīlpōhualxihuitl 6 īpan 550s mahtlācxihuitl mochīhualiztli tlācatiliztli mi...`
3. `īpan mahtlācxihuitl mochīhualiztli tlācatiliztli miquiztli nō xiquitta cuīcapan`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_xitlāhīpalih._s`
2. `ia,_ztiztliuil_(`
3. `a_molahcahīlizcô`

**Context Size 2:**

1. `tlathayotliztli_j`
2. `liztli_*_*_*_*_*_`
3. `n_tl_4,40%_san_ma`

**Context Size 3:**

1. `li_tlanēci_uikalil`
2. `tli_mammakandrealt`
3. `tlahtoznequichtlat`

**Context Size 4:**

1. `tli_tlacatlahkuitl_`
2. `ztli._in_tlacatiliz`
3. `iztli_(yēm_+_pōhual`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (89,855 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 | 11,901 |
| Total Tokens | 139,625 |
| Mean Frequency | 11.73 |
| Median Frequency | 3 |
| Frequency Std Dev | 116.70 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | in | 8,302 |
| 2 | īpan | 5,152 |
| 3 | cē | 2,961 |
| 4 | xihuitl | 2,907 |
| 5 | ītōcā | 2,782 |
| 6 | miquiztli | 2,512 |
| 7 | mācuīlpōhualxihuitl | 2,216 |
| 8 | tlācatiliztli | 2,123 |
| 9 | mochīhualiztli | 2,005 |
| 10 | mahtlācxihuitl | 1,706 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | polanco | 2 |
| 2 | tepochcalli | 2 |
| 3 | tenis | 2 |
| 4 | mapatoltiliztli | 2 |
| 5 | panohco | 2 |
| 6 | ichcacuatitlan | 2 |
| 7 | tepetzintlah | 2 |
| 8 | itlachijchiualis | 2 |
| 9 | vehículos | 2 |
| 10 | vehículo | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9414 |
| R² (Goodness of Fit) | 0.992093 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 46.5% |
| Top 1,000 | 69.8% |
| Top 5,000 | 88.7% |
| Top 10,000 | 97.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9921 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 46.5% of corpus
- **Long Tail:** 1,901 words needed for remaining 2.7% 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 | 0.2842 🏆 | 0.4247 | N/A | N/A |
| **mono_64d** | 64 | 0.0571 | 0.4200 | N/A | N/A |
| **mono_128d** | 128 | 0.0070 | 0.4306 | N/A | N/A |
| **aligned_32d** | 32 | 0.2842 | 0.4337 | 0.0200 | 0.1680 |
| **aligned_64d** | 64 | 0.0571 | 0.4188 | 0.0260 | 0.2000 |
| **aligned_128d** | 128 | 0.0070 | 0.4318 | 0.0580 | 0.2360 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.2842 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4266. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.8% 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 | **0.627** | 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 |
|--------|----------|
| `-t` | texohtic, teyaotlacah, tecpanchantli |
| `-c` | connor, conihcuāniliā, carochi |
| `-m` | momotlalistli, motzololoc, marcelo |
| `-a` | azul, amoxchihualiztli, azz |
| `-i` | indígena, itzcuintli, ixeliuhcayo |
| `-p` | política, proceso, peuh |
| `-te` | texohtic, teyaotlacah, tecpanchantli |
| `-s` | square, sandoval, sombra |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-li` | momotlalistli, tecpanchantli, tubartlahtōlli |
| `-i` | momotlalistli, tecpanchantli, omonamicti |
| `-a` | niquelehuia, sombra, indígena |
| `-tl` | zāzotepozmalacatl, tepozohtlamalacatl, pipincāyōtl |
| `-l` | sandoval, zāzotepozmalacatl, tepozohtlamalacatl |
| `-n` | harrison, īhuan, jesutzin |
| `-o` | oro, dentado, ixeliuhcayo |
| `-h` | teyaotlacah, quihualquixtih, ōquitzintih |

### 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 |
|------|----------|------------------|----------|
| `tlac` | 1.49x | 22 contexts | itlac, tlacah, tlacat |
| `iliz` | 1.76x | 11 contexts | inemiliz, iyoliliz, īnemiliz |
| `chīh` | 1.76x | 10 contexts | chīhua, mochīhua, chīhualo |
| `uitl` | 1.52x | 14 contexts | xiuitl, tequitl, ilhuitl |
| `iqui` | 1.46x | 14 contexts | iquin, miqui, triqui |
| `laht` | 1.43x | 12 contexts | tlahtōl, tlahtec, tlahtic |
| `hīhu` | 1.76x | 7 contexts | chīhua, mochīhua, chīhualo |
| `lizt` | 1.88x | 6 contexts | yoliztli, yeliztli, axiliztli |
| `ztli` | 1.65x | 8 contexts | eztli, otztli, meztli |
| `aliz` | 1.63x | 8 contexts | alizée, ihcaliz, icealiz |
| `lāca` | 1.55x | 9 contexts | tlācah, tlācati, otlācat |
| `huit` | 1.54x | 9 contexts | huitz, ilhuitl, xiuhuit |

### 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 |
|--------|--------|-----------|----------|
| `-t` | `-i` | 494 words | tonameyocaquizcopinaloni, tlateōmahuiztiliztli |
| `-t` | `-li` | 377 words | tlateōmahuiztiliztli, tlakxitoktli |
| `-t` | `-l` | 183 words | thumbnail, tlacuīcalizpal |
| `-t` | `-tl` | 172 words | tepozyōllōtl, tlacetilīllahtohcāyōtēcatl |
| `-c` | `-i` | 161 words | capuli, cempohualli |
| `-n` | `-i` | 119 words | nōncuahquīzaliztli, neehēcanāmictiliztli |
| `-c` | `-l` | 117 words | chiucnauhtetl, cacallotl |
| `-t` | `-n` | 114 words | tzintzontzan, tomín |
| `-c` | `-li` | 109 words | capuli, cempohualli |
| `-n` | `-li` | 102 words | nōncuahquīzaliztli, neehēcanāmictiliztli |

### 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 |
|------|-----------------|------------|------|
| mācuīlxōchitl | **`mācuīlxōch-i-tl`** | 7.5 | `i` |
| itlahtollaliz | **`itlahtoll-al-iz`** | 7.5 | `al` |
| octacatia | **`octacat-i-a`** | 7.5 | `i` |
| mihcuanih | **`mihcuan-i-h`** | 7.5 | `i` |
| oyuhquimottili | **`oyuhquimott-i-li`** | 7.5 | `i` |
| tlahtolcopa | **`tlahtol-co-pa`** | 7.5 | `co` |
| atlāntico | **`atlānt-i-co`** | 7.5 | `i` |
| tlahcalli | **`tlahc-al-li`** | 7.5 | `al` |
| huehcaīxipcaxitl | **`huehcaīxipcax-i-tl`** | 7.5 | `i` |
| huitztlan | **`huitz-tl-an`** | 7.5 | `tl` |
| cihuātlān | **`cihuā-tl-ān`** | 7.5 | `tl` |
| chālchihuitl | **`chālchihu-i-tl`** | 7.5 | `i` |
| desgracia | **`desgrac-i-a`** | 7.5 | `i` |
| quipanahuia | **`quipanahu-i-a`** | 7.5 | `i` |
| tlazoxochitl | **`tlazoxoch-i-tl`** | 7.5 | `i` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Nahuatl languages 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 (4.84x) |
| N-gram | **2-gram** | Lowest perplexity (257) |
| Markov | **Context-4** | Highest predictability (98.3%) |
| 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 14:41:15*