---
language: pam
language_name: Pampanga
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: 4.758
  - name: best_isotropy
    type: isotropy
    value: 0.8287
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Pampanga** 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** | 3.876x | 3.88 | 0.0164% | 341,122 |
| **16k** | 4.216x | 4.22 | 0.0179% | 313,678 |
| **32k** | 4.511x | 4.51 | 0.0191% | 293,138 |
| **64k** | 4.758x 🏆 | 4.76 | 0.0201% | 277,944 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `"The Poet" ensáyu nang Ralph Waldo Emerson "The Poet" kawatásan nang María Teres...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁" the ▁poet " ▁ens áyu ▁nang ▁r al ph ... (+18 more)` | 28 |
| 16k | `▁" the ▁poet " ▁ens áyu ▁nang ▁ralph ▁w aldo ... (+13 more)` | 23 |
| 32k | `▁" the ▁poet " ▁ens áyu ▁nang ▁ralph ▁w aldo ... (+12 more)` | 22 |
| 64k | `▁" the ▁poet " ▁ens áyu ▁nang ▁ralph ▁waldo ▁emerson ... (+10 more)` | 20 |

**Sample 2:** `Ing Antheny metung yang balen at commune king Ardennes département king mauling ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ing ▁ant hen y ▁metung ▁yang ▁balen ▁at ▁commune ▁king ... (+9 more)` | 19 |
| 16k | `▁ing ▁ant hen y ▁metung ▁yang ▁balen ▁at ▁commune ▁king ... (+9 more)` | 19 |
| 32k | `▁ing ▁ant heny ▁metung ▁yang ▁balen ▁at ▁commune ▁king ▁ardennes ... (+8 more)` | 18 |
| 64k | `▁ing ▁ant heny ▁metung ▁yang ▁balen ▁at ▁commune ▁king ▁ardennes ... (+8 more)` | 18 |

**Sample 3:** `I Gonzalo Sta. Maria metung yang Kapampangan watas. Talambie Ding Kayang Kinudta...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁i ▁gonz alo ▁sta . ▁maria ▁metung ▁yang ▁kapampangan ▁watas ... (+9 more)` | 19 |
| 16k | `▁i ▁gonz alo ▁sta . ▁maria ▁metung ▁yang ▁kapampangan ▁watas ... (+9 more)` | 19 |
| 32k | `▁i ▁gonzalo ▁sta . ▁maria ▁metung ▁yang ▁kapampangan ▁watas . ... (+8 more)` | 18 |
| 64k | `▁i ▁gonzalo ▁sta . ▁maria ▁metung ▁yang ▁kapampangan ▁watas . ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.758x compression
- **Lowest UNK Rate:** 8k with 0.0164% 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 | 7,456 | 12.86 | 27,430 | 22.7% | 45.5% |
| **2-gram** | Subword | 264 🏆 | 8.04 | 3,441 | 67.9% | 99.1% |
| **3-gram** | Word | 7,873 | 12.94 | 31,773 | 24.5% | 44.9% |
| **3-gram** | Subword | 2,323 | 11.18 | 27,102 | 27.4% | 69.0% |
| **4-gram** | Word | 11,866 | 13.53 | 55,046 | 24.5% | 41.0% |
| **4-gram** | Subword | 13,207 | 13.69 | 142,685 | 15.3% | 39.7% |
| **5-gram** | Word | 7,287 | 12.83 | 39,747 | 29.4% | 47.0% |
| **5-gram** | Subword | 43,230 | 15.40 | 366,395 | 10.0% | 28.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `metung yang` | 5,374 |
| 2 | `atin yang` | 4,476 |
| 3 | `ya ing` | 4,463 |
| 4 | `of the` | 4,330 |
| 5 | `suglung palwal` | 3,524 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `yang populasyun a` | 1,862 |
| 2 | `atin yang populasyun` | 1,856 |
| 3 | `king lalawigan ning` | 1,836 |
| 4 | `standard geographic code` | 1,739 |
| 5 | `philippine standard geographic` | 1,739 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `atin yang populasyun a` | 1,855 |
| 2 | `philippine standard geographic code` | 1,739 |
| 3 | `governance performance management system` | 1,736 |
| 4 | `local governance performance management` | 1,736 |
| 5 | `standard geographic code local` | 1,731 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `local governance performance management system` | 1,736 |
| 2 | `philippine standard geographic code local` | 1,731 |
| 3 | `philatlas com philippine standard geographic` | 1,731 |
| 4 | `standard geographic code local governance` | 1,731 |
| 5 | `geographic code local governance performance` | 1,731 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g` | 304,553 |
| 2 | `g _` | 266,268 |
| 3 | `a n` | 253,944 |
| 4 | `i n` | 209,259 |
| 5 | `_ a` | 140,744 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n g _` | 258,684 |
| 2 | `i n g` | 127,387 |
| 3 | `a n g` | 89,009 |
| 4 | `a n _` | 61,397 |
| 5 | `_ i n` | 46,327 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i n g _` | 120,149 |
| 2 | `a n g _` | 62,550 |
| 3 | `n g _ p` | 34,131 |
| 4 | `n i n g` | 33,893 |
| 5 | `k i n g` | 33,067 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n i n g _` | 33,478 |
| 2 | `k i n g _` | 32,583 |
| 3 | `_ n i n g` | 32,343 |
| 4 | `_ k i n g` | 32,097 |
| 5 | `_ i n g _` | 26,434 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 264
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.7130 | 1.639 | 4.54 | 146,008 | 28.7% |
| **1** | Subword | 0.8484 | 1.800 | 4.90 | 2,745 | 15.2% |
| **2** | Word | 0.2159 | 1.161 | 1.48 | 660,193 | 78.4% |
| **2** | Subword | 0.6588 | 1.579 | 4.28 | 13,435 | 34.1% |
| **3** | Word | 0.0716 | 1.051 | 1.12 | 975,530 | 92.8% |
| **3** | Subword | 0.8075 | 1.750 | 4.22 | 57,475 | 19.3% |
| **4** | Word | 0.0277 🏆 | 1.019 | 1.04 | 1,090,857 | 97.2% |
| **4** | Subword | 0.7126 | 1.639 | 3.02 | 242,181 | 28.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a lossy lossy lossy data a bangsa king pilatan ning banwang manimunang taluk lon la linto`
2. `ing visa loca biningan callaguip cayubog dolores farm tanaman a new york philharmonic kéng wanan kai...`
3. `ning tsina atyu king maulingalbugan ning bayung variant form the yellow pages isbn vietnam bắc ninhb...`

**Context Size 2:**

1. `metung yang lakanbalen king hokkaidō prefecture towns king japan bukud pa kareti kayabe no reng luga...`
2. `atin yang 24 a barangay bacnor east bacnor west caliguian catabban cullalabo del norte zamboanga del...`
3. `ya ing septiembre métung yang compositor pianista ampóng compositor a i julian ning norwich c kayaba...`

**Context Size 3:**

1. `yang populasyun a a katau kareng a pamimalemale deng barangay ing tubigon atin yang 34 a barangay ab...`
2. `atin yang populasyun a a katau kareng a pamimalemale ing pasay lakanbalen metung ya kareng pekamagal...`
3. `king lalawigan ning masbate filipinas agpang keng ning sensus atin yang populasyun a a katau kareng ...`

**Context Size 4:**

1. `atin yang populasyun a a katau kareng a pamimalemale deng barangay ing silay lakanbalen atin yang 16...`
2. `philippine standard geographic code local governance performance management system municipality of o...`
3. `local governance performance management system ning negros oriental`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_in,_droras_danc`
2. `ancalguro_pa,_pr`
3. `ndit_nininem_tyi`

**Context Size 2:**

1. `ng_susing_dakover`
2. `g_kaux-pamakang_a`
3. `ang_hictu_ventain`

**Context Size 3:**

1. `ng_kol._ing_pang_s`
2. `ing_ampóng_palwali`
3. `ang_twerte_escus_i`

**Context Size 4:**

1. `ing_ning_banua._míb`
2. `ang_artistandavid_r`
3. `ng_pátaka_ning_anti`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (242,181 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 | 56,109 |
| Total Tokens | 1,253,954 |
| Mean Frequency | 22.35 |
| Median Frequency | 3 |
| Frequency Std Dev | 348.02 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 35,962 |
| 2 | ing | 33,120 |
| 3 | ning | 32,392 |
| 4 | king | 31,916 |
| 5 | of | 18,248 |
| 6 | yang | 17,493 |
| 7 | the | 15,199 |
| 8 | ya | 12,902 |
| 9 | at | 10,686 |
| 10 | metung | 8,722 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | handog | 2 |
| 2 | telatawag | 2 |
| 3 | rason | 2 |
| 4 | halaman | 2 |
| 5 | tatambal | 2 |
| 6 | punso | 2 |
| 7 | bisayang | 2 |
| 8 | itinuturing | 2 |
| 9 | dáyâ | 2 |
| 10 | thoughtco | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0309 |
| R² (Goodness of Fit) | 0.996988 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 37.3% |
| Top 1,000 | 61.5% |
| Top 5,000 | 79.2% |
| Top 10,000 | 86.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9970 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 37.3% of corpus
- **Long Tail:** 46,109 words needed for remaining 14.0% 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 | 0.8287 🏆 | 0.3226 | N/A | N/A |
| **mono_64d** | 64 | 0.6810 | 0.2653 | N/A | N/A |
| **mono_128d** | 128 | 0.3086 | 0.2583 | N/A | N/A |
| **aligned_32d** | 32 | 0.8287 | 0.3246 | 0.0980 | 0.4360 |
| **aligned_64d** | 64 | 0.6810 | 0.2716 | 0.1760 | 0.5740 |
| **aligned_128d** | 128 | 0.3086 | 0.2627 | 0.2700 | 0.6220 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8287 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2842. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 27.0% 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 | **0.634** | 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` | makatyatsat, malútû, maned |
| `-a` | aliste, anc, ayaring |
| `-s` | salmbach, sorcy, sang |
| `-m` | mormon, murphy, makatyatsat |
| `-b` | brée, belfort, basilisa |
| `-p` | phú, pekamaluat, pamiugne |
| `-pa` | pamiugne, pareung, pasantingan |
| `-c` | crest, chesnois, circuit |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | mormon, pirinan, gaillon |
| `-s` | chesnois, magellans, runners |
| `-ng` | lilung, pareung, tanikalang |
| `-g` | lilung, pareung, tanikalang |
| `-e` | desire, laye, aliste |
| `-an` | pirinan, disnan, kapupusan |
| `-a` | villalonga, ruspolia, basilisa |
| `-t` | crest, feat, circuit |

### 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 |
|------|----------|------------------|----------|
| `aman` | 2.30x | 108 contexts | amanu, daman, raman |
| `ling` | 1.84x | 113 contexts | úling, aling, lingo |
| `tion` | 1.94x | 41 contexts | potion, motion, action |
| `atio` | 2.04x | 30 contexts | ratio, nation, babatio |
| `aren` | 1.80x | 45 contexts | yaren, arena, areni |
| `alaw` | 2.02x | 25 contexts | kalaw, lalawe, malawi |
| `ment` | 1.61x | 44 contexts | mental, cement, moment |
| `laka` | 1.80x | 25 contexts | lakan, plaka, lakay |
| `akan` | 1.61x | 37 contexts | lakan, yakan, bakan |
| `niba` | 1.84x | 23 contexts | aniban, mánibat, nibaliw |
| `kare` | 2.12x | 14 contexts | karen, karel, kareti |
| `alen` | 1.63x | 32 contexts | balen, halen, aalen |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-n` | 137 words | pigagamitan, pangadapun |
| `-p` | `-an` | 104 words | pigagamitan, panlalawigan |
| `-c` | `-s` | 90 words | camarines, cultures |
| `-c` | `-n` | 85 words | caingin, chairwoman |
| `-p` | `-g` | 82 words | paútang, pangmaluatang |
| `-p` | `-s` | 82 words | patents, paparazzis |
| `-b` | `-n` | 78 words | bléquin, binawian |
| `-p` | `-ng` | 74 words | paútang, pangmaluatang |
| `-ma` | `-g` | 74 words | macalang, mag |
| `-p` | `-a` | 74 words | panga, pamagparla |

### 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 |
|------|-----------------|------------|------|
| communism | **`communi-s-m`** | 7.5 | `s` |
| inglesang | **`ingles-an-g`** | 7.5 | `an` |
| cabiasnan | **`cabias-n-an`** | 7.5 | `n` |
| kilalanan | **`kilal-an-an`** | 7.5 | `an` |
| kapamiltan | **`kapamil-t-an`** | 7.5 | `t` |
| makatukang | **`makatuk-an-g`** | 7.5 | `an` |
| dramaturga | **`dramatur-g-a`** | 7.5 | `g` |
| thüringen | **`thüring-e-n`** | 7.5 | `e` |
| gravenhage | **`gravenha-g-e`** | 7.5 | `g` |
| pampangans | **`pampang-an-s`** | 7.5 | `an` |
| paliwasan | **`paliwa-s-an`** | 7.5 | `s` |
| migsamantala | **`mi-g-samantala`** | 7.5 | `samantala` |
| intertwined | **`intertwi-n-ed`** | 7.5 | `n` |
| fouesnant | **`fouesn-an-t`** | 7.5 | `an` |
| pamanalto | **`pamanal-t-o`** | 7.5 | `t` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Pampanga 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 (4.76x) |
| N-gram | **2-gram** | Lowest perplexity (264) |
| Markov | **Context-4** | Highest predictability (97.2%) |
| 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 17:28:27*