---
language: avk
language_name: Kotava
language_family: constructed_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-constructed_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: 4.689
  - name: best_isotropy
    type: isotropy
    value: 0.8768
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kotava** 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** | 3.689x | 3.69 | 0.2370% | 255,266 |
| **16k** | 4.051x | 4.06 | 0.2603% | 232,417 |
| **32k** | 4.380x | 4.39 | 0.2815% | 214,947 |
| **64k** | 4.689x 🏆 | 4.69 | 0.3013% | 200,817 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Victoria tir kelu is lozolonafa widava ke Seycella tigisa valente patecta koe Ma...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁victor ia ▁tir ▁kelu ▁is ▁lozolonafa ▁widava ▁ke ▁s ey ... (+13 more)` | 23 |
| 16k | `▁victoria ▁tir ▁kelu ▁is ▁lozolonafa ▁widava ▁ke ▁sey c ella ... (+10 more)` | 20 |
| 32k | `▁victoria ▁tir ▁kelu ▁is ▁lozolonafa ▁widava ▁ke ▁sey c ella ... (+10 more)` | 20 |
| 64k | `▁victoria ▁tir ▁kelu ▁is ▁lozolonafa ▁widava ▁ke ▁seycella ▁tigisa ▁valente ... (+8 more)` | 18 |

**Sample 2:** `Bifa Afrika Amerika Asia Europa Oceania Koblira Awalkera sanda`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |
| 16k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |
| 32k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |
| 64k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |

**Sample 3:** `Bifa Afrika Amerika Asia Europa Oceania Koblira Awalkera sanda`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |
| 16k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |
| 32k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |
| 64k | `▁bifa ▁afrika ▁amerika ▁asia ▁europa ▁oceania ▁koblira ▁awalkera ▁sanda` | 9 |


### Key Findings

- **Best Compression:** 64k achieves 4.689x compression
- **Lowest UNK Rate:** 8k with 0.2370% 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 | 4,342 | 12.08 | 65,378 | 38.8% | 59.6% |
| **2-gram** | Subword | 284 🏆 | 8.15 | 3,324 | 63.4% | 99.6% |
| **3-gram** | Word | 9,058 | 13.14 | 131,536 | 34.4% | 51.5% |
| **3-gram** | Subword | 1,996 | 10.96 | 24,495 | 26.3% | 74.2% |
| **4-gram** | Word | 16,918 | 14.05 | 222,038 | 30.4% | 44.4% |
| **4-gram** | Subword | 7,464 | 12.87 | 124,607 | 17.4% | 50.9% |
| **5-gram** | Word | 18,754 | 14.19 | 212,819 | 28.7% | 42.2% |
| **5-gram** | Subword | 17,155 | 14.07 | 346,727 | 14.4% | 42.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `en vuest` | 113,005 |
| 2 | `of life` | 25,896 |
| 3 | `of the` | 24,998 |
| 4 | `the world` | 24,670 |
| 5 | `mammal species` | 24,652 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `of the world` | 24,657 |
| 2 | `mammal species of` | 24,652 |
| 3 | `species of the` | 24,652 |
| 4 | `taneon zo pimtayar` | 15,544 |
| 5 | `bak taneon zo` | 15,311 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `species of the world` | 24,652 |
| 2 | `mammal species of the` | 24,652 |
| 3 | `bak taneon zo pimtayar` | 15,309 |
| 4 | `zo pimtayar vexala dem` | 15,226 |
| 5 | `taneon zo pimtayar vexala` | 15,225 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mammal species of the world` | 24,652 |
| 2 | `taneon zo pimtayar vexala dem` | 15,225 |
| 3 | `bak taneon zo pimtayar vexala` | 14,992 |
| 4 | `en vuest animal diversity web` | 14,121 |
| 5 | `en vuest catalogue of life` | 14,116 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 682,687 |
| 2 | `s _` | 476,530 |
| 3 | `_ (` | 458,247 |
| 4 | `e _` | 386,463 |
| 5 | `_ v` | 360,083 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ : _` | 268,658 |
| 2 | `u s _` | 176,817 |
| 3 | `e s t` | 175,950 |
| 4 | `_ v u` | 167,654 |
| 5 | `u e s` | 166,548 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u e s t` | 164,186 |
| 2 | `_ v u e` | 163,879 |
| 3 | `v u e s` | 163,702 |
| 4 | `) _ v u` | 124,953 |
| 5 | `e s t -` | 124,892 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ v u e s` | 163,700 |
| 2 | `v u e s t` | 163,699 |
| 3 | `u e s t -` | 124,886 |
| 4 | `e s t - _` | 124,885 |
| 5 | `) _ v u e` | 124,841 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 284
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~43% 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 | 0.9054 | 1.873 | 5.52 | 115,002 | 9.5% |
| **1** | Subword | 1.0377 | 2.053 | 7.85 | 900 | 0.0% |
| **2** | Word | 0.2492 | 1.189 | 1.63 | 633,477 | 75.1% |
| **2** | Subword | 0.9459 | 1.926 | 5.95 | 7,069 | 5.4% |
| **3** | Word | 0.1398 | 1.102 | 1.31 | 1,026,801 | 86.0% |
| **3** | Subword | 0.7949 | 1.735 | 4.30 | 42,037 | 20.5% |
| **4** | Word | 0.1005 🏆 | 1.072 | 1.21 | 1,342,358 | 89.9% |
| **4** | Subword | 0.6925 | 1.616 | 3.14 | 180,930 | 30.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `en fr vuest paleobiology database dipodomys heermanni heermanni jolonensis grinnell and chiefdom a a...`
2. `vuest paleobiology database xerus erythropus leucoumbrinus rüppell en vuest paleobiology database bu...`
3. `ke otomops johnstonei en vuest itis rusa bak taneon zo bendeyer ewava vuestexa is xantaza en`

**Context Size 2:**

1. `en vuest walvedeyafa zveriopafa aba 2 2 siatos 5 katca oxi phonygammus 1 katca proklano philemon pro...`
2. `of life dicerorhinus sumatrensis lasiotis en vuest ncbi campicoloides fr en vuest mammal species of ...`
3. `of the world siatos ke konakara apta dere tid ke mila veyafa katca vesnol nycticeius humeralis humer...`

**Context Size 3:**

1. `of the world v 3 petrogale purpureicollis le souef en vuest cites ctenomys colburni en vuest uicn ka...`
2. `species of the world v 3 isolobodon portoricensis j a allen vesnol myotis yumanensis sociabilis h w ...`
3. `mammal species of the world siatos ke konakara apta dere tid ke mila veyafa katca vesnol lonchorhina...`

**Context Size 4:**

1. `species of the world siatos ke bata katca tir aptiskafa dere rupel pulasa vuestexa is xantaza en vue...`
2. `mammal species of the world siatos ke bata katca tir aptiskafa pulasa vuestexa is xantaza en vuest m...`
3. `bak taneon zo pimtayar vexala dem katceem sedme vuestesa pulara ke walvedeyafa zveriopafa aba 2 2 si...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ves_wirtis_cada`
2. `aldronururuda_a,`
3. `e_oe_s_ta_tcimot`

**Context Size 2:**

1. `a_:_cathirojunafa`
2. `s_:_le="vey_tazne`
3. `_(heropanelterifo`

**Context Size 3:**

1. `_:_burnata_kuksa_(`
2. `us_paleobiologue_o`
3. `ested_nudingus_vor`

**Context Size 4:**

1. `uest-_:_uicn_:_acom`
2. `_vuestesa_vaticus_p`
3. `vuest-_:_mephitis_:`


### Key Findings

- **Best Predictability:** Context-4 (word) with 89.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (180,930 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 | 58,045 |
| Total Tokens | 3,510,675 |
| Mean Frequency | 60.48 |
| Median Frequency | 5 |
| Frequency Std Dev | 1080.85 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | en | 127,527 |
| 2 | vuest | 124,885 |
| 3 | ke | 85,172 |
| 4 | of | 52,509 |
| 5 | tir | 40,501 |
| 6 | is | 37,459 |
| 7 | katca | 36,160 |
| 8 | va | 35,241 |
| 9 | bak | 28,713 |
| 10 | koe | 28,499 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | medotegalaf | 2 |
| 2 | j1 | 2 |
| 3 | tageltaf | 2 |
| 4 | l4 | 2 |
| 5 | l5 | 2 |
| 6 | l6 | 2 |
| 7 | l8 | 2 |
| 8 | fakaf | 2 |
| 9 | rozuxa | 2 |
| 10 | eaksat | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1330 |
| R² (Goodness of Fit) | 0.996896 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 48.9% |
| Top 1,000 | 72.2% |
| Top 5,000 | 86.2% |
| Top 10,000 | 91.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9969 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 48.9% of corpus
- **Long Tail:** 48,045 words needed for remaining 9.0% 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 | 0.8768 🏆 | 0.3464 | N/A | N/A |
| **mono_64d** | 64 | 0.8339 | 0.2956 | N/A | N/A |
| **mono_128d** | 128 | 0.6767 | 0.2580 | N/A | N/A |
| **aligned_32d** | 32 | 0.8768 | 0.3495 | 0.0440 | 0.2440 |
| **aligned_64d** | 64 | 0.8339 | 0.2976 | 0.0760 | 0.3520 |
| **aligned_128d** | 128 | 0.6767 | 0.2493 | 0.1320 | 0.4720 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8768 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2994. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 13.2% 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 | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.015** | 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` | maltadleks, marnatum, marco |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | teguina, coa, klaba |
| `-s` | verticalis, mees, tellus |
| `-us` | tellus, scapanulus, catagonus |
| `-ra` | tara, aliera, mallanira |
| `-er` | edobeyer, walzer, palliser |
| `-is` | verticalis, anhuiensis, quitensis |
| `-on` | goreston, styron, laizon |
| `-fa` | kaikifa, isteamerikafa, lopinafa |

### 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 |
|------|----------|------------------|----------|
| `ayar` | 2.06x | 93 contexts | vayar, wayar, iayar |
| `ensi` | 2.30x | 45 contexts | pensil, owensi, hensies |
| `anta` | 1.76x | 73 contexts | canta, tanta, xanta |
| `urus` | 2.30x | 23 contexts | purus, urusí, myurus |
| `imta` | 2.02x | 22 contexts | pimtas, pimtad, pimtan |
| `tava` | 1.80x | 25 contexts | stava, kotava, poltava |
| `atca` | 1.64x | 31 contexts | zatca, datca, catca |
| `pimt` | 2.34x | 8 contexts | pimtas, pimtad, pimtan |
| `stes` | 1.71x | 16 contexts | lestes, wastes, restes |
| `xant` | 1.51x | 19 contexts | xanta, xanto, xantik |
| `neon` | 2.03x | 8 contexts | deneon, keneon, roneon |
| `ukol` | 1.51x | 14 contexts | bukol, stukol, moukol |

### 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` | `-a` | 34 words | mafia, malaya |
| `-ma` | `-s` | 29 words | maculicollis, mangas |
| `-ma` | `-is` | 13 words | maculicollis, managuensis |
| `-ma` | `-us` | 8 words | macrocephalicus, mastus |
| `-ma` | `-ra` | 7 words | malyerara, mallapira |
| `-ma` | `-on` | 5 words | maubuisson, malsaveson |
| `-ma` | `-er` | 5 words | malgruper, mayasquer |
| `-ma` | `-es` | 4 words | manzanares, macropodiformes |
| `-ma` | `-fa` | 4 words | magyarafa, malyoparafa |
| `-ma` | `-afa` | 4 words | magyarafa, malyoparafa |

### 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 |
|------|-----------------|------------|------|
| balumarafa | **`balumar-afa`** | 4.5 | `balumar` |
| vageroneon | **`vagerone-on`** | 4.5 | `vagerone` |
| koridanikafa | **`koridanik-afa`** | 4.5 | `koridanik` |
| lidarotifa | **`lidaroti-fa`** | 4.5 | `lidaroti` |
| pacificus | **`pacific-us`** | 4.5 | `pacific` |
| yambikafa | **`yambik-afa`** | 4.5 | `yambik` |
| zimmerius | **`zimmeri-us`** | 4.5 | `zimmeri` |
| christies | **`christi-es`** | 4.5 | `christi` |
| bristutuson | **`bristut-us-on`** | 3.0 | `bristut` |
| aultoveson | **`aultov-es-on`** | 3.0 | `aultov` |
| promeneuses | **`promene-us-es`** | 3.0 | `promene` |
| stakseson | **`staks-es-on`** | 3.0 | `staks` |
| atlantoxerus | **`atlantox-er-us`** | 3.0 | `atlantox` |
| mantukafa | **`ma-ntuk-afa`** | 3.0 | `ntuk` |
| ruyatakoler | **`ruyatakol-er`** | 1.5 | `ruyatakol` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kotava 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 (4.69x) |
| N-gram | **2-gram** | Lowest perplexity (284) |
| Markov | **Context-4** | Highest predictability (89.9%) |
| 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: 2026-01-03 17:46:55*