---
language: pag
language_name: Pangasinan
language_family: austronesian_philippine_northern
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-austronesian_philippine_northern
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: 4.912
  - name: best_isotropy
    type: isotropy
    value: 0.0888
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Pangasinan** Wikipedia data.
We analyze tokenizers, n-gram models, Markov chains, vocabulary statistics, and word embeddings.

## 📋 Repository Contents

### Models & Assets

- Tokenizers (8k, 16k, 32k, 64k)
- N-gram models (2, 3, 4, 5-gram)
- Markov chains (context of 1, 2, 3, 4 and 5)
- Subword N-gram and Markov chains
- Embeddings in various sizes and dimensions (aligned and unaligned)
- Language Vocabulary
- Language Statistics

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

### Analysis and Evaluation

- [1. Tokenizer Evaluation](#1-tokenizer-evaluation)
- [2. N-gram Model Evaluation](#2-n-gram-model-evaluation)
- [3. Markov Chain Evaluation](#3-markov-chain-evaluation)
- [4. Vocabulary Analysis](#4-vocabulary-analysis)
- [5. Word Embeddings Evaluation](#5-word-embeddings-evaluation)
- [6. Morphological Analysis (Experimental)](#6--morphological-analysis-experimental)
- [7. Summary & Recommendations](#7-summary--recommendations)
- [Metrics Glossary](#appendix-metrics-glossary--interpretation-guide)
- [Visualizations Index](#visualizations-index)

---
## 1. Tokenizer Evaluation

![Tokenizer Compression](visualizations/tokenizer_compression.png)

![Tokenizer Fertility](visualizations/tokenizer_fertility.png)

![Tokenizer OOV](visualizations/tokenizer_oov.png)

![Total Tokens](visualizations/tokenizer_total_tokens.png)

### Results

| Vocab Size | Compression | Avg Token Len | UNK Rate | Total Tokens |
|------------|-------------|---------------|----------|--------------|
| **8k** | 4.339x | 4.35 | 0.7127% | 96,109 |
| **16k** | 4.639x | 4.65 | 0.7621% | 89,884 |
| **32k** | 4.912x 🏆 | 4.92 | 0.8069% | 84,898 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Category: Listaan na Nakaukulan ya Artikulo ed Pangasinan`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁category : ▁listaan ▁na ▁nakaukulan ▁ya ▁artikulo ▁ed ▁pangasinan` | 9 |
| 16k | `▁category : ▁listaan ▁na ▁nakaukulan ▁ya ▁artikulo ▁ed ▁pangasinan` | 9 |
| 32k | `▁category : ▁listaan ▁na ▁nakaukulan ▁ya ▁artikulo ▁ed ▁pangasinan` | 9 |

**Sample 2:** `Say C sakey arapan ya letra diad alpabeto ya Romano. 3`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁say ▁c ▁sakey ▁arapan ▁ya ▁letra ▁diad ▁alpabeto ▁ya ▁romano ... (+3 more)` | 13 |
| 16k | `▁say ▁c ▁sakey ▁arapan ▁ya ▁letra ▁diad ▁alpabeto ▁ya ▁romano ... (+3 more)` | 13 |
| 32k | `▁say ▁c ▁sakey ▁arapan ▁ya ▁letra ▁diad ▁alpabeto ▁ya ▁romano ... (+3 more)` | 13 |

**Sample 3:** `Saray Inianak Birthday Niduman Agew Special Day Agew na Letnegan Foundation Day ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁saray ▁inianak ▁birthday ▁niduman ▁agew ▁special ▁day ▁agew ▁na ▁letnegan ... (+5 more)` | 15 |
| 16k | `▁saray ▁inianak ▁birthday ▁niduman ▁agew ▁special ▁day ▁agew ▁na ▁letnegan ... (+5 more)` | 15 |
| 32k | `▁saray ▁inianak ▁birthday ▁niduman ▁agew ▁special ▁day ▁agew ▁na ▁letnegan ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 32k achieves 4.912x compression
- **Lowest UNK Rate:** 8k with 0.7127% 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 | 205 | 7.68 | 2,255 | 79.7% | 93.6% |
| **2-gram** | Subword | 213 | 7.74 | 1,452 | 73.2% | 99.8% |
| **3-gram** | Word | 147 | 7.20 | 2,427 | 86.2% | 95.5% |
| **3-gram** | Subword | 1,197 | 10.23 | 9,027 | 35.3% | 83.0% |
| **4-gram** | Word | 152 | 7.25 | 3,955 | 86.3% | 93.7% |
| **4-gram** | Subword | 3,558 | 11.80 | 37,136 | 23.9% | 64.7% |
| **5-gram** | Word | 121 🏆 | 6.91 | 2,812 | 89.3% | 96.1% |
| **5-gram** | Subword | 5,759 | 12.49 | 68,453 | 19.6% | 59.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `to et` | 3,500 |
| 2 | `na filipinas` | 2,001 |
| 3 | `saray reperensiya` | 1,826 |
| 4 | `to ya` | 1,774 |
| 5 | `luyag na` | 1,769 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `gawing ed labas` | 1,757 |
| 2 | `saray gawing ed` | 1,753 |
| 3 | `philippine standard geographic` | 1,738 |
| 4 | `saray reperensiya saray` | 1,738 |
| 5 | `standard geographic code` | 1,738 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `saray gawing ed labas` | 1,752 |
| 2 | `philippine standard geographic code` | 1,738 |
| 3 | `saray reperensiya saray gawing` | 1,735 |
| 4 | `reperensiya saray gawing ed` | 1,735 |
| 5 | `tan sukat to ya` | 1,733 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `reperensiya saray gawing ed labas` | 1,735 |
| 2 | `saray reperensiya saray gawing ed` | 1,735 |
| 3 | `kabaleg tan sukat to ya` | 1,733 |
| 4 | `walay kabaleg tan sukat to` | 1,733 |
| 5 | `local governance performance management system` | 1,731 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n` | 31,807 |
| 2 | `_ s` | 28,468 |
| 3 | `y _` | 25,578 |
| 4 | `a _` | 23,919 |
| 5 | `a y` | 21,692 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a y _` | 19,505 |
| 2 | `_ s a` | 14,577 |
| 3 | `a n _` | 10,573 |
| 4 | `a r a` | 10,005 |
| 5 | `e d _` | 8,979 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ e d _` | 8,348 |
| 2 | `_ n a _` | 7,570 |
| 3 | `r a y _` | 7,012 |
| 4 | `s a r a` | 6,954 |
| 5 | `a r a y` | 6,936 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s a r a y` | 6,895 |
| 2 | `a r a y _` | 6,892 |
| 3 | `_ s a r a` | 6,692 |
| 4 | `_ t a n _` | 4,954 |
| 5 | `_ s a y _` | 4,849 |


### Key Findings

- **Best Perplexity:** 5-gram (word) with 121
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~60% 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 | 0.6201 | 1.537 | 3.30 | 21,681 | 38.0% |
| **1** | Subword | 0.9010 | 1.867 | 5.17 | 994 | 9.9% |
| **2** | Word | 0.1693 | 1.124 | 1.30 | 71,109 | 83.1% |
| **2** | Subword | 0.6653 | 1.586 | 3.95 | 5,133 | 33.5% |
| **3** | Word | 0.0511 | 1.036 | 1.08 | 91,940 | 94.9% |
| **3** | Subword | 0.7224 | 1.650 | 3.38 | 20,253 | 27.8% |
| **4** | Word | 0.0195 🏆 | 1.014 | 1.03 | 98,208 | 98.1% |
| **4** | Subword | 0.5566 | 1.471 | 2.28 | 68,355 | 44.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ed labas philatlas com philippine standard geographic code to ya barangay demograpiko saray siyudad ...`
2. `na filipinas unong ed saray alahas pati angga ed europa tan abong walay kabaleg tan abong`
3. `say zip code local governance performance by transporting warm gun kayari na oriental mindoro garcia...`

**Context Size 2:**

1. `to et totoo tan abong walay kabaleg tan sukat to ya sq km say zip code to`
2. `saray reperensiya saray gawing ed labas philatlas com philippine standard geographic code local gove...`
3. `to ya sq km say zip code to et saray barangay demograpiko saray reperensiya saray gawing ed`

**Context Size 3:**

1. `gawing ed labas philatlas com philippine standard geographic code local governance performance manag...`
2. `saray gawing ed labas philatlas com philippine standard geographic code local governance performance...`
3. `saray reperensiya saray gawing ed labas philatlas com philippine standard geographic code local gove...`

**Context Size 4:**

1. `saray gawing ed labas philatlas com philippine standard geographic code local governance performance...`
2. `philippine standard geographic code local governance performance management system baley na quezon`
3. `reperensiya saray gawing ed labas philatlas com philippine standard geographic code local governance...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_kanderan_n_anay`
2. `a_vay_ssta_sakis`
3. `ninilayara_y_sq.`

**Context Size 2:**

1. `angemol_gew_so_ph`
2. `_siya_barchrivers`
3. `y_geograp-le_to_e`

**Context Size 3:**

1. `ay_et_ed_labangay_`
2. `_say_gawing_ed_met`
3. `an_to_et_kids'_pan`

**Context Size 4:**

1. `_ed_et_totoo_a_dapi`
2. `_na_,_filipinas._un`
3. `ray_repúblic_oceano`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (68,355 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 | 8,492 |
| Total Tokens | 189,672 |
| Mean Frequency | 22.34 |
| Median Frequency | 3 |
| Frequency Std Dev | 233.09 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ed | 8,364 |
| 2 | na | 7,609 |
| 3 | say | 6,874 |
| 4 | saray | 6,859 |
| 5 | et | 6,059 |
| 6 | to | 5,969 |
| 7 | ya | 5,232 |
| 8 | tan | 4,961 |
| 9 | code | 3,372 |
| 10 | filipinas | 2,140 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kabisera | 2 |
| 2 | wiesbaden | 2 |
| 3 | lento | 2 |
| 4 | lacrimoso | 2 |
| 5 | ceremonial | 2 |
| 6 | seremonyal | 2 |
| 7 | chikvaidze | 2 |
| 8 | kanlurang | 2 |
| 9 | soan | 2 |
| 10 | makiabay | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0335 |
| R² (Goodness of Fit) | 0.985808 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 67.4% |
| Top 1,000 | 84.3% |
| Top 5,000 | 96.2% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9858 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 67.4% of corpus
- **Long Tail:** -1,508 words needed for remaining 100.0% 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 | 0.0888 | 0.4796 | N/A | N/A |
| **mono_64d** | 64 | 0.0147 | 0.4928 | N/A | N/A |
| **mono_128d** | 128 | 0.0021 | 0.5047 | N/A | N/A |
| **aligned_32d** | 32 | 0.0888 🏆 | 0.4864 | 0.0120 | 0.1220 |
| **aligned_64d** | 64 | 0.0147 | 0.4907 | 0.0180 | 0.1620 |
| **aligned_128d** | 128 | 0.0021 | 0.5245 | 0.0220 | 0.1900 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.0888 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4964. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 2.2% 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 | **3.984** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **0.605** | 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 |
|--------|----------|
| `-a` | argel, achievement, administrasyon |
| `-s` | shounen, streisands, sebastian |
| `-ma` | marijuana, magasin, malaysia |
| `-b` | basel, bonifacio, buendia |
| `-p` | pati, paraan, partner |
| `-m` | marijuana, magasin, malaysia |
| `-d` | diverse, diskograpiya, derby |
| `-t` | teritorya, tanom, tango |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | jefferson, shounen, paraan |
| `-a` | teritorya, halina, republika |
| `-an` | paraan, sebastian, sankamaimpluensyan |
| `-s` | wikimedians, streisands, basbas |
| `-o` | bonifacio, wario, tango |
| `-e` | diverse, bustamante, save |
| `-on` | jefferson, generation, terminon |
| `-g` | nyog, trung, gandang |

### 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 |
|------|----------|------------------|----------|
| `anga` | 1.40x | 35 contexts | banga, angat, sanga |
| `pana` | 1.68x | 13 contexts | panag, espana, panaon |
| `ngga` | 1.51x | 16 contexts | angga, anggan, anggad |
| `angg` | 1.51x | 15 contexts | angga, anggan, anggad |
| `angi` | 1.62x | 12 contexts | sangi, angie, mangi |
| `anla` | 1.67x | 10 contexts | kanlaon, nanlapu, nanlapo |
| `kaba` | 1.51x | 12 contexts | kabay, kabat, akabat |
| `tion` | 1.33x | 14 contexts | action, nation, motion |
| `laba` | 1.50x | 10 contexts | labay, labat, labas |
| `nter` | 1.37x | 12 contexts | inter, hunter, center |
| `inte` | 1.45x | 10 contexts | inter, intero, winter |
| `bale` | 1.43x | 10 contexts | baley, baler, baleg |

### 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 |
|--------|--------|-----------|----------|
| `-ka` | `-n` | 94 words | kayon, kareenan |
| `-p` | `-n` | 91 words | paraan, panguman |
| `-ka` | `-an` | 83 words | kareenan, kayamanan |
| `-s` | `-n` | 81 words | shounen, sebastian |
| `-a` | `-n` | 60 words | administrasyon, aviation |
| `-p` | `-an` | 57 words | paraan, panguman |
| `-p` | `-a` | 56 words | probinsiya, pampanga |
| `-s` | `-an` | 54 words | sebastian, sankamaimpluensyan |
| `-a` | `-o` | 51 words | apo, apolinario |
| `-p` | `-s` | 48 words | productions, posadas |

### 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 |
|------|-----------------|------------|------|
| wonderland | **`wonderl-an-d`** | 7.5 | `an` |
| ipakitana | **`ipakit-an-a`** | 7.5 | `an` |
| kayamanan | **`kayam-an-an`** | 7.5 | `an` |
| relihyoson | **`relihyo-s-on`** | 7.5 | `s` |
| josephine | **`joseph-in-e`** | 7.5 | `in` |
| angadanan | **`angad-an-an`** | 7.5 | `an` |
| metropolitano | **`metropolit-an-o`** | 7.5 | `an` |
| masaganan | **`masag-an-an`** | 7.5 | `an` |
| awstralyano | **`awstraly-an-o`** | 7.5 | `an` |
| michigans | **`michig-an-s`** | 7.5 | `an` |
| lithuania | **`lithu-an-ia`** | 7.5 | `an` |
| baranggay | **`barang-g-ay`** | 7.5 | `g` |
| ginampanan | **`ginamp-an-an`** | 7.5 | `an` |
| manngaran | **`ma-n-ngaran`** | 7.5 | `ngaran` |
| agtrabaho | **`a-g-trabaho`** | 7.5 | `trabaho` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Pangasinan 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 | **32k BPE** | Best compression (4.91x) |
| N-gram | **5-gram** | Lowest perplexity (121) |
| Markov | **Context-4** | Highest predictability (98.1%) |
| 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 17:16:06*