README.md

---
language: nia
language_name: Nias
language_family: austronesian_other
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_other
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: 4.014
  - name: best_isotropy
    type: isotropy
    value: 0.5991
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Nias** 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** | 3.685x | 3.69 | 0.1179% | 377,555 |
| **16k** | 3.874x | 3.88 | 0.1239% | 359,160 |
| **32k** | 4.014x 🏆 | 4.02 | 0.1284% | 346,649 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Mo'awö no töi mbanua ba Danö Niha: Mo'awö, Kecamatan Gunungsitoli, Kota Gunungsi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mo ' awö ▁no ▁töi ▁mbanua ▁ba ▁danö ▁niha : ... (+19 more)` | 29 |
| 16k | `▁mo ' awö ▁no ▁töi ▁mbanua ▁ba ▁danö ▁niha : ... (+19 more)` | 29 |
| 32k | `▁mo ' awö ▁no ▁töi ▁mbanua ▁ba ▁danö ▁niha : ... (+19 more)` | 29 |

**Sample 2:** `Do ya'ia da'ö si hulö nidanö sola'a-la'a oyo ba sofanö-fanö bakha ba mboto sanör...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁do ▁ya ' ia ▁da ' ö ▁si ▁hulö ▁nidanö ... (+20 more)` | 30 |
| 16k | `▁do ▁ya ' ia ▁da ' ö ▁si ▁hulö ▁nidanö ... (+20 more)` | 30 |
| 32k | `▁do ▁ya ' ia ▁da ' ö ▁si ▁hulö ▁nidanö ... (+20 more)` | 30 |

**Sample 3:** `Baruzö no töi mbanua ba Danö Niha: Baruzö, Kecamatan Idanögawo, Kabupaten Nias B...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁baruzö ▁no ▁töi ▁mbanua ▁ba ▁danö ▁niha : ▁baruzö , ... (+14 more)` | 24 |
| 16k | `▁baruzö ▁no ▁töi ▁mbanua ▁ba ▁danö ▁niha : ▁baruzö , ... (+14 more)` | 24 |
| 32k | `▁baruzö ▁no ▁töi ▁mbanua ▁ba ▁danö ▁niha : ▁baruzö , ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 32k achieves 4.014x compression
- **Lowest UNK Rate:** 8k with 0.1179% 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 | 2,758 | 11.43 | 10,121 | 32.1% | 59.9% |
| **2-gram** | Subword | 217 🏆 | 7.76 | 1,534 | 71.6% | 99.7% |
| **3-gram** | Word | 4,344 | 12.08 | 14,140 | 28.0% | 49.1% |
| **3-gram** | Subword | 1,588 | 10.63 | 12,306 | 31.9% | 78.5% |
| **4-gram** | Word | 6,308 | 12.62 | 20,991 | 25.9% | 43.0% |
| **4-gram** | Subword | 7,212 | 12.82 | 54,669 | 16.4% | 49.8% |
| **5-gram** | Word | 3,712 | 11.86 | 13,231 | 30.4% | 51.6% |
| **5-gram** | Subword | 19,478 | 14.25 | 118,364 | 11.4% | 35.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `da ö` | 3,555 |
| 2 | `moroi ba` | 2,755 |
| 3 | `ba danö` | 2,721 |
| 4 | `ya ia` | 2,653 |
| 5 | `danö niha` | 2,149 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ba danö niha` | 2,084 |
| 2 | `ya ia da` | 1,571 |
| 3 | `ia da ö` | 1,561 |
| 4 | `menteri dalam negeri` | 1,033 |
| 5 | `dalam negeri no` | 1,028 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ya ia da ö` | 1,558 |
| 2 | `menteri dalam negeri no` | 1,028 |
| 3 | `dalam negeri no 72` | 1,027 |
| 4 | `negeri no 72 tahun` | 1,027 |
| 5 | `kodenia ba wamatörö indonesia` | 1,025 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dalam negeri no 72 tahun` | 1,027 |
| 2 | `menteri dalam negeri no 72` | 1,027 |
| 3 | `negeri no 72 tahun pdf` | 992 |
| 4 | `no sambua desa ba kecamatan` | 924 |
| 5 | `peraturan menteri dalam negeri no` | 890 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 125,464 |
| 2 | `b a` | 51,774 |
| 3 | `i _` | 51,062 |
| 4 | `a n` | 49,901 |
| 5 | `_ b` | 48,112 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ b a` | 40,895 |
| 2 | `b a _` | 35,312 |
| 3 | `i a _` | 16,399 |
| 4 | `_ n i` | 15,214 |
| 5 | `a _ b` | 15,172 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ b a _` | 34,789 |
| 2 | `a _ b a` | 13,160 |
| 3 | `n i h a` | 7,319 |
| 4 | `_ n i h` | 7,204 |
| 5 | `a _ d a` | 7,113 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _ b a _` | 11,657 |
| 2 | `_ n i h a` | 7,150 |
| 3 | `i _ b a _` | 6,034 |
| 4 | `_ b a _ w` | 5,169 |
| 5 | `n i h a _` | 4,502 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 217
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~36% 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 | 0.8816 | 1.842 | 5.55 | 31,686 | 11.8% |
| **1** | Subword | 1.1187 | 2.172 | 7.98 | 442 | 0.0% |
| **2** | Word | 0.2829 | 1.217 | 1.70 | 175,623 | 71.7% |
| **2** | Subword | 1.0534 | 2.075 | 6.37 | 3,528 | 0.0% |
| **3** | Word | 0.1113 | 1.080 | 1.20 | 297,898 | 88.9% |
| **3** | Subword | 0.8852 | 1.847 | 4.09 | 22,462 | 11.5% |
| **4** | Word | 0.0413 🏆 | 1.029 | 1.06 | 356,990 | 95.9% |
| **4** | Subword | 0.6276 | 1.545 | 2.58 | 91,854 | 37.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ba da ö papias moroi ba wa anumana la a ira ma suku logika teologi ba`
2. `ö fa auri mazauwu nitötöi faoma lakue fa ebua aruzö ruzö bua wangera ngerania zi lalö`
3. `no 72 tahun pdf nga örö 491 umbu ba tradisi nifotöi keynesian ya ia tsunami tehalö`

**Context Size 2:**

1. `da ö zikala na la aturai wama ema hadia kabarata nösi gosali sifakhai ba dalö cina fananö`
2. `moroi ba provinsi bengkulu indonesia kota bandung göi no faola sibai ia ba iklim pegunungan sokafu k...`
3. `ba danö niha ma abölö sökhi ba si lö sökhi kreeft nga örö 361 umbu ba danö`

**Context Size 3:**

1. `ya ia da ö labe e khönia dandra ya ia da ö kecoak lipas mazui coro sambua moroi`
2. `ia da ö cabai ma lombok hiza lada no fao ia ba wamasindro mbolo gu ö facebook awö`
3. `ba danö niha ma ono niha sangarato ba danö misiyefo asala niha si onarai danö niha böi sofu`

**Context Size 4:**

1. `ya ia da ö öröba si öli ma baru wasuwöta nihaogö moroi ba zi öli so göi wondraru moroi`
2. `menteri dalam negeri no 72 tahun pdf kementerian dalam negeri nga örö 492 umbu ba danö niha mufareso`
3. `dalam negeri no 72 tahun pdf nga örö 581 umbu ba danö niha ba hiza sukhoi nisura andre ya`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_falewabu-_ma_8.`
2. `a_kseca_pani_bö_`
3. `in_fa-3172,_ikha`

**Context Size 2:**

1. `a_mei_ina_perifak`
2. `bai_da'a_dalö'örö`
3. `i_pate'ogu_i,_no_`

**Context Size 3:**

1. `_ba_pencos,_pdf),_`
2. `ba_goia_ba_world_s`
3. `ia_bukoroi_bau,_in`

**Context Size 4:**

1. `_ba_zi_töi-töra_wa'`
2. `a_ba_lalau_bible_in`
3. `_niha,_niha_ya'ia_d`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (91,854 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 | 15,228 |
| Total Tokens | 420,205 |
| Mean Frequency | 27.59 |
| Median Frequency | 4 |
| Frequency Std Dev | 348.05 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ba | 34,969 |
| 2 | ö | 11,724 |
| 3 | no | 7,652 |
| 4 | niha | 6,922 |
| 5 | ia | 6,234 |
| 6 | si | 6,090 |
| 7 | da | 5,122 |
| 8 | so | 4,824 |
| 9 | ma | 4,273 |
| 10 | a | 3,856 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | faustina | 2 |
| 2 | kowalska | 2 |
| 3 | margaret | 2 |
| 4 | keynote | 2 |
| 5 | sondröi | 2 |
| 6 | penanggulangan | 2 |
| 7 | bnpb | 2 |
| 8 | risks | 2 |
| 9 | maenamölö | 2 |
| 10 | sadaŵa | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1818 |
| R² (Goodness of Fit) | 0.992823 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.9% |
| Top 1,000 | 77.0% |
| Top 5,000 | 92.6% |
| Top 10,000 | 97.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9928 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.9% of corpus
- **Long Tail:** 5,228 words needed for remaining 2.5% 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 | 0.5991 🏆 | 0.3687 | N/A | N/A |
| **mono_64d** | 64 | 0.2083 | 0.3585 | N/A | N/A |
| **mono_128d** | 128 | 0.0338 | 0.3754 | N/A | N/A |
| **aligned_32d** | 32 | 0.5991 | 0.3706 | 0.0080 | 0.1460 |
| **aligned_64d** | 64 | 0.2083 | 0.3741 | 0.0360 | 0.2220 |
| **aligned_128d** | 128 | 0.0338 | 0.3809 | 0.0660 | 0.2520 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.5991 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3714. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 6.6% 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 | **0.441** | 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 |
|--------|----------|
| `-s` | samaria, sifaudu, sanadrösa |
| `-a` | annual, april, asimola |
| `-m` | mealu, musa, maharaja |
| `-fa` | fakhögusa, famakiko, fanemali |
| `-la` | lagundri, law, labuan |
| `-ma` | maharaja, mangebua, mangolombu |
| `-t` | tafo, tebözi, terletak |
| `-b` | bawaslu, boyo, bela |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | fakhögusa, gahulua, kelera |
| `-i` | orahuahili, nifaböbözi, tebözi |
| `-n` | cablin, pembibitan, linn |
| `-an` | pembibitan, labuan, saluran |
| `-ia` | samaria, furinia, norwegia |
| `-ö` | tö, wurugö, awögö |
| `-s` | teoretis, cardinals, habis |
| `-e` | dete, carmelite, importance |

### 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 |
|------|----------|------------------|----------|
| `andr` | 1.62x | 63 contexts | andrö, andre, andré |
| `anga` | 1.46x | 86 contexts | zanga, fanga, tanga |
| `wang` | 1.76x | 29 contexts | wango, wanga, wangi |
| `amat` | 1.56x | 40 contexts | amate, camat, zamati |
| `akha` | 1.53x | 43 contexts | lakha, bakha, fakha |
| `atör` | 1.93x | 18 contexts | atöra, atörö, tatörö |
| `ndrö` | 1.54x | 36 contexts | andrö, indrö, ndröni |
| `ambu` | 1.57x | 30 contexts | sambu, tambu, hambu |
| `anua` | 1.77x | 20 contexts | wanua, banua, manual |
| `ndre` | 1.63x | 18 contexts | andre, undre, ndrela |
| `nötö` | 1.60x | 19 contexts | inötö, ginötö, sanötö |
| `ogun` | 1.94x | 10 contexts | oguna, ogunaö, moguna |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-a` | 115 words | samuza, siraha |
| `-a` | `-a` | 99 words | abölönia, alawenia |
| `-m` | `-a` | 87 words | morena, manila |
| `-s` | `-i` | 77 words | samaehusi, solakhömi |
| `-k` | `-n` | 75 words | kelaparan, keputusan |
| `-b` | `-a` | 73 words | bersabda, bawanguma |
| `-fa` | `-a` | 70 words | fangöhöna, fadekha |
| `-m` | `-i` | 66 words | manöi, molakhömi |
| `-k` | `-an` | 64 words | kelaparan, keputusan |
| `-t` | `-a` | 60 words | terpena, timna |

### 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 |
|------|-----------------|------------|------|
| whitehead | **`whitehe-a-d`** | 7.5 | `a` |
| mangomasi | **`mangom-a-si`** | 7.5 | `a` |
| tandraigö | **`tandra-i-gö`** | 7.5 | `i` |
| mengenang | **`mengen-a-ng`** | 7.5 | `a` |
| hikayania | **`hikay-an-ia`** | 7.5 | `an` |
| hilibanua | **`hilib-an-ua`** | 7.5 | `an` |
| nifahaönia | **`nifahaö-n-ia`** | 7.5 | `n` |
| ahuluania | **`ahulu-an-ia`** | 7.5 | `an` |
| mangalani | **`mangal-an-i`** | 7.5 | `an` |
| nituriaigö | **`nituria-i-gö`** | 7.5 | `i` |
| proposisi | **`propo-si-si`** | 7.5 | `si` |
| galadanga | **`ga-la-danga`** | 7.5 | `danga` |
| sangosili | **`sango-si-li`** | 7.5 | `si` |
| hilimböwöma | **`hilimböwö-m-a`** | 7.5 | `m` |
| nifaduhusira | **`nifaduhu-si-ra`** | 7.5 | `si` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Nias 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 (4.01x) |
| N-gram | **2-gram** | Lowest perplexity (217) |
| Markov | **Context-4** | Highest predictability (95.9%) |
| 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 14:55:14*