README.md

---
language: ami
language_name: Amis
language_family: austronesian_formosan
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_formosan
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: 3.607
  - name: best_isotropy
    type: isotropy
    value: 0.8437
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Amis** 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** | 3.160x | 3.16 | 0.4656% | 701,501 |
| **16k** | 3.337x | 3.34 | 0.4917% | 664,267 |
| **32k** | 3.486x | 3.49 | 0.5136% | 635,874 |
| **64k** | 3.607x 🏆 | 3.61 | 0.5314% | 614,596 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ising（Kuwaping a sowal：醫生） O maan ko ising? O ising kako. 'Amis`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ising ( kuwaping ▁a ▁sowal : 醫生 ) ▁o ▁maan ... (+9 more)` | 19 |
| 16k | `▁ising ( kuwaping ▁a ▁sowal : 醫生 ) ▁o ▁maan ... (+9 more)` | 19 |
| 32k | `▁ising ( kuwaping ▁a ▁sowal : 醫生 ) ▁o ▁maan ... (+9 more)` | 19 |
| 64k | `▁ising ( kuwaping ▁a ▁sowal : 醫生 ) ▁o ▁maan ... (+9 more)` | 19 |

**Sample 2:** `O Sir James Paul McCartney（kuwaping a sowal：保羅·麥卡尼）`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁o ▁sir ▁j am es ▁paul ▁mc car tn ey ... (+11 more)` | 21 |
| 16k | `▁o ▁sir ▁james ▁paul ▁mccartney ( kuwaping ▁a ▁sowal : ... (+6 more)` | 16 |
| 32k | `▁o ▁sir ▁james ▁paul ▁mccartney ( kuwaping ▁a ▁sowal : ... (+4 more)` | 14 |
| 64k | `▁o ▁sir ▁james ▁paul ▁mccartney ( kuwaping ▁a ▁sowal : ... (+4 more)` | 14 |

**Sample 3:** `hana (花) O mialaan nai Dipong kona sowal. O falo han no roma a niyaro', no roma ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁hana ▁( 花 ) ▁o ▁mi alaan ▁nai ▁dipong ▁kona ... (+15 more)` | 25 |
| 16k | `▁hana ▁( 花 ) ▁o ▁mialaan ▁nai ▁dipong ▁kona ▁sowal ... (+14 more)` | 24 |
| 32k | `▁hana ▁( 花 ) ▁o ▁mialaan ▁nai ▁dipong ▁kona ▁sowal ... (+14 more)` | 24 |
| 64k | `▁hana ▁( 花 ) ▁o ▁mialaan ▁nai ▁dipong ▁kona ▁sowal ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 3.607x compression
- **Lowest UNK Rate:** 8k with 0.4656% 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 | 6,664 | 12.70 | 22,555 | 20.4% | 47.4% |
| **2-gram** | Subword | 206 🏆 | 7.68 | 6,765 | 78.7% | 98.2% |
| **3-gram** | Word | 12,814 | 13.65 | 36,103 | 17.1% | 36.4% |
| **3-gram** | Subword | 1,357 | 10.41 | 25,329 | 37.0% | 81.9% |
| **4-gram** | Word | 30,923 | 14.92 | 77,456 | 15.4% | 26.9% |
| **4-gram** | Subword | 6,313 | 12.62 | 95,308 | 18.3% | 53.9% |
| **5-gram** | Word | 25,903 | 14.66 | 63,935 | 16.8% | 28.0% |
| **5-gram** | Subword | 18,568 | 14.18 | 183,225 | 11.1% | 36.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ira ko` | 5,084 |
| 2 | `romi ad` | 4,077 |
| 3 | `i miheca` | 2,844 |
| 4 | `a tamdaw` | 2,817 |
| 5 | `a sowal` | 2,775 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka aloman no` | 2,123 |
| 2 | `a romi ad` | 1,679 |
| 3 | `ko tamdaw o` | 1,567 |
| 4 | `sa osi no` | 1,535 |
| 5 | `ko ka aloman` | 1,534 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ko sa osi no` | 1,482 |
| 2 | `ko ka aloman no` | 1,395 |
| 3 | `nina angan tilid i` | 853 |
| 4 | `nano nina angan tilid` | 845 |
| 5 | `o roma sato i` | 767 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nano nina angan tilid i` | 820 |
| 2 | `aloman no roma a finacadan` | 737 |
| 3 | `tamdaw o roma sato i` | 737 |
| 4 | `ko sa osi no parod` | 736 |
| 5 | `sa osi no parod no` | 736 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o _` | 201,957 |
| 2 | `a _` | 143,658 |
| 3 | `a n` | 139,880 |
| 4 | `_ k` | 106,844 |
| 5 | `a y` | 96,918 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a y _` | 60,683 |
| 2 | `_ a _` | 59,010 |
| 3 | `n o _` | 54,715 |
| 4 | `a n _` | 54,705 |
| 5 | `t o _` | 54,068 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n o _` | 47,866 |
| 2 | `_ k o _` | 44,431 |
| 3 | `_ t o _` | 37,474 |
| 4 | `o _ k a` | 18,696 |
| 5 | `a y _ a` | 15,406 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _ n o _` | 13,318 |
| 2 | `a y _ a _` | 13,310 |
| 3 | `a n _ n o` | 11,599 |
| 4 | `a m d a w` | 11,462 |
| 5 | `t a m d a` | 11,449 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 206
- **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 | 0.6135 | 1.530 | 4.53 | 72,743 | 38.7% |
| **1** | Subword | 1.5301 | 2.888 | 10.10 | 4,131 | 0.0% |
| **2** | Word | 0.3027 | 1.233 | 1.87 | 329,306 | 69.7% |
| **2** | Subword | 0.4066 | 1.326 | 2.35 | 41,693 | 59.3% |
| **3** | Word | 0.1215 | 1.088 | 1.23 | 614,944 | 87.9% |
| **3** | Subword | 0.3759 | 1.298 | 2.21 | 98,063 | 62.4% |
| **4** | Word | 0.0417 🏆 | 1.029 | 1.07 | 757,884 | 95.8% |
| **4** | Subword | 0.3880 | 1.309 | 2.00 | 216,477 | 61.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a sowal 蝦 hananay ato misalidong i cowacowa a ingiden a misanga an a malasawad ko`
2. `no riyaran ko pico ay koya nitahidangan caay sa osi no pinalengaw a sowal 里約熱內盧 i`
3. `ko wawa i mihecaan malamirotocay to amilika misafa eloh a atapangan rikec saka 8 saka 8`

**Context Size 2:**

1. `ira ko sakowan no po o kakeridan no tadamaanay lisin mapatiko tayra i anpin 9 miheca 7`
2. `romi ad tahira i miheca oni pacomodan a dafong 經濟 縮圖 niyaro gitega flickr dave proffer ato`
3. `i miheca 希臘應借鑑愛爾蘭 實事求是由奢入儉 miheca lacemcem ko kohecalay tamdaw no ikiris a sowal formula ona kala ed...`

**Context Size 3:**

1. `ka aloman no yincomin polong han i 821 ko tamdaw o roma sato saheto i manikaway a kaliomahan`
2. `a romi ad o mihayiay 49 77 o minaayay ira ko 50 ko madengaay to nia aids 23`
3. `ko tamdaw o poay li i miheca a new hebrides palapa lira ko 45 000 a month reuters`

**Context Size 4:**

1. `ko sa osi no tamdaw 97 ko ka aloman no roma a finacadan polong 全部 han i 11 ko`
2. `ko ka aloman no roma a finacadan polong han i 53 ko tamdaw o roma sato i 7 ko`
3. `nina angan tilid i 522 south africa tona ci mandela ato kalalaed no finacadan mala likisiay to new y...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `afidawapafoco_ip`
2. `_巴哥維茨·穆罕默西亞灣基追思的`
3. `o’ena_mu_no_safi`

**Context Size 2:**

1. `o_samday_a_i_lont`
2. `a_cifetatating_a_`
3. `an._ci_jinceca,_s`

**Context Size 3:**

1. `ay_lals_mata._ikir`
2. `_a_mital,_tangos_n`
3. `no_kasapipankos_of`

**Context Size 4:**

1. `_no_nina’angra_to,_`
2. `_ko_tamdaw;_o_romi’`
3. `_to_i,_caay_ko_i_ta`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (216,477 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 | 29,904 |
| Total Tokens | 912,858 |
| Mean Frequency | 30.53 |
| Median Frequency | 3 |
| Frequency Std Dev | 654.44 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 59,833 |
| 2 | no | 48,143 |
| 3 | ko | 44,598 |
| 4 | to | 39,959 |
| 5 | i | 38,034 |
| 6 | o | 30,294 |
| 7 | ato | 10,833 |
| 8 | tamdaw | 10,726 |
| 9 | miheca | 6,785 |
| 10 | sa | 6,742 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | hiay | 2 |
| 2 | 牡丹社事件 | 2 |
| 3 | pasitenokay | 2 |
| 4 | satsuma | 2 |
| 5 | pisamawmaw | 2 |
| 6 | saigo | 2 |
| 7 | tsumoru | 2 |
| 8 | vetoma | 2 |
| 9 | mitingting | 2 |
| 10 | kalosaasik | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1692 |
| R² (Goodness of Fit) | 0.995283 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 53.0% |
| Top 1,000 | 76.7% |
| Top 5,000 | 89.9% |
| Top 10,000 | 94.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9953 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 53.0% of corpus
- **Long Tail:** 19,904 words needed for remaining 5.9% 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 | 0.8437 | 0.3356 | N/A | N/A |
| **mono_64d** | 64 | 0.8007 | 0.2526 | N/A | N/A |
| **mono_128d** | 128 | 0.4818 | 0.2214 | N/A | N/A |
| **aligned_32d** | 32 | 0.8437 🏆 | 0.3313 | 0.0340 | 0.2100 |
| **aligned_64d** | 64 | 0.8007 | 0.2560 | 0.0540 | 0.2540 |
| **aligned_128d** | 128 | 0.4818 | 0.2213 | 0.1040 | 0.3400 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8437 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2697. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.4% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

---
## 6.  Morphological Analysis (Experimental)

This section presents an automated morphological analysis derived from the statistical divergence between word-level and subword-level models. By analyzing where subword predictability spikes and where word-level coverage fails, we can infer linguistic structures without supervised data.

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.226** | Low formulaic 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` | mamakari, mapasifana, mamisarocod |
| `-mi` | mipaliwalay, micowatan, mipadangay |
| `-ka` | kasasolsol, kasasiked, katulagan |
| `-sa` | sacipaysoay, sakararamod, sapifelih |
| `-pa` | pataminaan, pawalian, paliwalan |
| `-pi` | pidafo, pirnato, pisaepahan |
| `-ta` | tatangangay, taypa, taipingjing |
| `-mal` | maliyangay, malawidangay, malikiday |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | cayin, napirmaan, komian |
| `-y` | mipaliwalay, ccayay, nanomay |
| `-ay` | mipaliwalay, ccayay, nanomay |
| `-an` | napirmaan, komian, pataminaan |
| `-ng` | popatireng, intuyang, awsiyong |
| `-en` | cecayen, iloen, pakilacen |

### 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 |
|------|----------|------------------|----------|
| `emak` | 2.37x | 36 contexts | demak, hemak, ademak |
| `alom` | 2.07x | 51 contexts | aloma, alomi, naloma |
| `ilid` | 2.25x | 32 contexts | tilid, atilid, mililid |
| `dema` | 2.16x | 33 contexts | demak, ademak, odemak |
| `olon` | 1.93x | 46 contexts | tolon, olong, polon |
| `iren` | 2.24x | 25 contexts | ireng, yiren, sairen |
| `ihec` | 2.13x | 28 contexts | niheca, miheca, ciheci |
| `onga` | 1.54x | 55 contexts | ongay, conga, songa |
| `taki` | 2.19x | 15 contexts | takid, takimi, kitaki |
| `ngra` | 1.98x | 19 contexts | ingra, cngra, angra |
| `mihe` | 2.08x | 14 contexts | mihea, miheca, miheaan |
| `ngan` | 1.37x | 52 contexts | ngani, ingan, angan |

### 6.4 Affix Compatibility (Co-occurrence)

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

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-ma` | `-y` | 212 words | mafalicay, mapatodongay |
| `-ma` | `-ay` | 210 words | mafalicay, mapatodongay |
| `-mi` | `-y` | 196 words | mitekeday, mihinomay |
| `-mi` | `-ay` | 190 words | mitekeday, mihinomay |
| `-ka` | `-n` | 187 words | kasakapingan, kamaomahan |
| `-ka` | `-an` | 168 words | kasakapingan, kamaomahan |
| `-pa` | `-n` | 119 words | pasitaywan, palinkaan |
| `-pi` | `-n` | 113 words | pisiyakayan, pidemakan |
| `-pi` | `-an` | 105 words | pisiyakayan, pidemakan |
| `-pa` | `-y` | 91 words | pacarcaray, pahay |

### 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 |
|------|-----------------|------------|------|
| pipalafangan | **`pi-pa-lafa-ng-an`** | 9.0 | `lafa` |
| masataporoay | **`ma-sa-ta-poro-ay`** | 9.0 | `poro` |
| kasatatelekan | **`ka-sa-ta-telek-an`** | 9.0 | `telek` |
| masapinangay | **`ma-sa-pi-nang-ay`** | 9.0 | `nang` |
| pipanganganan | **`pi-pa-ngang-an-an`** | 9.0 | `ngang` |
| tatefingen | **`ta-tefi-ng-en`** | 7.5 | `tefi` |
| masawawaay | **`ma-sa-wawa-ay`** | 7.5 | `wawa` |
| mikowananay | **`mi-kowan-an-ay`** | 7.5 | `kowan` |
| papinanamen | **`pa-pi-nanam-en`** | 7.5 | `nanam` |
| kakakilimen | **`ka-ka-kilim-en`** | 7.5 | `kilim` |
| mipatenakay | **`mi-pa-tenak-ay`** | 7.5 | `tenak` |
| masamaciay | **`ma-sa-ma-ciay`** | 7.5 | `ciay` |
| pakalayapay | **`pa-ka-layap-ay`** | 7.5 | `layap` |
| pisadingkian | **`pi-sa-dingki-an`** | 7.5 | `dingki` |
| sakapilowid | **`sa-ka-pi-lowid`** | 7.5 | `lowid` |

### 6.6 Linguistic Interpretation

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (3.61x) |
| N-gram | **2-gram** | Lowest perplexity (206) |
| Markov | **Context-4** | Highest predictability (95.8%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-03 18:29:47*