---
language: kw
language_name: Cornish
language_family: celtic_brythonic
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-celtic_brythonic
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: 4.173
  - name: best_isotropy
    type: isotropy
    value: 0.8337
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Cornish** 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** | 3.429x | 3.43 | 0.1065% | 186,869 |
| **16k** | 3.721x | 3.73 | 0.1156% | 172,217 |
| **32k** | 3.977x | 3.98 | 0.1235% | 161,115 |
| **64k** | 4.173x 🏆 | 4.18 | 0.1296% | 153,552 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Arthur Ian Lavender (genys 16 mis Hwevrer yw gwarier sowsnek. bellwolok sowsnek ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁arthur ▁ian ▁lav ender ▁( genys ▁ 1 6 ▁mis ... (+8 more)` | 18 |
| 16k | `▁arthur ▁ian ▁lav ender ▁( genys ▁ 1 6 ▁mis ... (+8 more)` | 18 |
| 32k | `▁arthur ▁ian ▁lav ender ▁( genys ▁ 1 6 ▁mis ... (+8 more)` | 18 |
| 64k | `▁arthur ▁ian ▁lavender ▁( genys ▁ 1 6 ▁mis ▁hwevrer ... (+7 more)` | 17 |

**Sample 2:** `Christoph Waltz (genys 4 a vis Hedra yn Wien) yw gwarier almaynek hag ostrian. b...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁christ oph ▁walt z ▁( genys ▁ 4 ▁a ▁vis ... (+18 more)` | 28 |
| 16k | `▁christ oph ▁walt z ▁( genys ▁ 4 ▁a ▁vis ... (+18 more)` | 28 |
| 32k | `▁christoph ▁waltz ▁( genys ▁ 4 ▁a ▁vis ▁hedra ▁yn ... (+15 more)` | 25 |
| 64k | `▁christoph ▁waltz ▁( genys ▁ 4 ▁a ▁vis ▁hedra ▁yn ... (+15 more)` | 25 |

**Sample 3:** `Sergei Pavlovich Korolev (12 mis Genver - 14 mis Genver o ynjynor fusen sovietek...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ser g ei ▁pav l ovich ▁kor ol ev ▁( ... (+16 more)` | 26 |
| 16k | `▁serg ei ▁pav l ovich ▁kor ol ev ▁( 1 ... (+14 more)` | 24 |
| 32k | `▁sergei ▁pavl ovich ▁kor ol ev ▁( 1 2 ▁mis ... (+12 more)` | 22 |
| 64k | `▁sergei ▁pavlovich ▁korolev ▁( 1 2 ▁mis ▁genver ▁- ▁ ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 64k achieves 4.173x compression
- **Lowest UNK Rate:** 8k with 0.1065% 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 | 6,140 | 12.58 | 17,327 | 19.9% | 47.0% |
| **2-gram** | Subword | 280 🏆 | 8.13 | 3,069 | 65.7% | 99.2% |
| **3-gram** | Word | 8,636 | 13.08 | 20,020 | 16.7% | 39.2% |
| **3-gram** | Subword | 2,413 | 11.24 | 20,195 | 25.0% | 69.6% |
| **4-gram** | Word | 12,101 | 13.56 | 28,809 | 15.8% | 36.0% |
| **4-gram** | Subword | 13,333 | 13.70 | 96,993 | 11.0% | 37.3% |
| **5-gram** | Word | 7,437 | 12.86 | 18,240 | 18.7% | 42.6% |
| **5-gram** | Subword | 42,511 | 15.38 | 221,084 | 6.2% | 23.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `y n` | 3,849 |
| 2 | `a n` | 3,256 |
| 3 | `dhe n` | 2,209 |
| 4 | `a veu` | 1,834 |
| 5 | `ev a` | 1,712 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a dro dhe` | 1,033 |
| 2 | `yw tre yn` | 711 |
| 3 | `a wodhya kewsel` | 679 |
| 4 | `wodhya kewsel kembrek` | 678 |
| 5 | `km dhiworth loundres` | 677 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a wodhya kewsel kembrek` | 678 |
| 2 | `kembra lleoedd canolfan bedwyr` | 676 |
| 3 | `km dhiworth kardydh ha` | 676 |
| 4 | `lleoedd canolfan bedwyr yma` | 675 |
| 5 | `canolfan bedwyr yma hi` | 675 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kembra lleoedd canolfan bedwyr yma` | 675 |
| 2 | `lleoedd canolfan bedwyr yma hi` | 675 |
| 3 | `a wodhya kewsel kembrek pednventydnyow` | 674 |
| 4 | `braster an poblans yn ha` | 643 |
| 5 | `o braster an poblans yn` | 638 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 116,444 |
| 2 | `s _` | 97,434 |
| 3 | `_ a` | 94,959 |
| 4 | `a _` | 91,201 |
| 5 | `a n` | 89,956 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n _` | 39,084 |
| 2 | `_ a n` | 33,267 |
| 3 | `o w _` | 30,057 |
| 4 | `_ a _` | 27,654 |
| 5 | `_ h a` | 26,523 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a n _` | 30,039 |
| 2 | `_ y n _` | 20,330 |
| 3 | `a n s _` | 16,203 |
| 4 | `_ h a _` | 16,012 |
| 5 | `_ d h e` | 13,152 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d h e _` | 8,088 |
| 2 | `s _ a n _` | 5,747 |
| 3 | `s _ y n _` | 5,446 |
| 4 | `_ g a n s` | 5,365 |
| 5 | `g a n s _` | 5,220 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 280
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.8579 | 1.812 | 5.27 | 68,677 | 14.2% |
| **1** | Subword | 0.8370 | 1.786 | 6.02 | 1,609 | 16.3% |
| **2** | Word | 0.2604 | 1.198 | 1.60 | 359,874 | 74.0% |
| **2** | Subword | 0.8174 | 1.762 | 4.63 | 9,678 | 18.3% |
| **3** | Word | 0.0856 | 1.061 | 1.14 | 570,742 | 91.4% |
| **3** | Subword | 0.7769 | 1.713 | 3.81 | 44,741 | 22.3% |
| **4** | Word | 0.0299 🏆 | 1.021 | 1.05 | 648,256 | 97.0% |
| **4** | Subword | 0.6461 | 1.565 | 2.69 | 170,507 | 35.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a lettyas nebes is ha tornyaseth yw šiprage map devy buhez mab nechtan cenél ngabráin dre`
2. `an poblans an brassa niver a dro dhe rutheniom niver a wra medhogyon heb fugieth amerikanek`
3. `yn asi yn afrika keskreunys a wra an ordinalia ha radn a melbost o 6 mis`

**Context Size 2:**

1. `y n seson segh hir hirder an kensa 10 perfydh besketh en istori amerika ̺ kansvledhen a`
2. `a n omsav kregys veu parson korlan wosa omsav kethyon afrikan erbynn aga mesters frynkek an wlas`
3. `dhe n golanes ev ew broder cy davyth fear skrifednyas an orsedh dyllys gans pab leo x`

**Context Size 3:**

1. `a dro dhe vewnans teylu rag ensampel demedhi a ji dhe n goos ankebmyn ew dhe n virus`
2. `yw tre yn sir ddinbych kembra lleoedd canolfan bedwyr yma hi 47 9 mildir 77 km dhiworth kardydh`
3. `a wodhya kewsel kembrek pednventydnyow yn kembra kembra`

**Context Size 4:**

1. `a wodhya kewsel kembrek pednventydnyow yn kembra kembra`
2. `km dhiworth kardydh ha 150 7 m 242 6 km dhiworth loundres 235 o braster an poblans yn ha`
3. `kembra lleoedd canolfan bedwyr yma hi 47 3 mildir 76 1 km dhiworth kardydh ha 153 8 m 247`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_owa_aglkedhabur`
2. `erdyn_nten)_s_do`
3. `aiem_ow,_y_46_au`

**Context Size 2:**

1. `n_miskriusys_ra_e`
2. `s_ani_hballs_gans`
3. `_ascrott_en:_που,`

**Context Size 3:**

1. `an_a_bys_o_an_sewy`
2. `_an_mygydnyow_dory`
3. `ow_boosdhe_dhe_dhe`

**Context Size 4:**

1. `_an_dowr_e'n_esel_s`
2. `_yn_kodhasow_bygh_1`
3. `ans_doemm_an_rebel.`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (170,507 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 | 30,471 |
| Total Tokens | 725,474 |
| Mean Frequency | 23.81 |
| Median Frequency | 4 |
| Frequency Std Dev | 361.46 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 35,840 |
| 2 | an | 30,880 |
| 3 | yn | 21,945 |
| 4 | ha | 18,075 |
| 5 | n | 12,791 |
| 6 | yw | 12,421 |
| 7 | dhe | 10,462 |
| 8 | y | 10,232 |
| 9 | o | 6,009 |
| 10 | gans | 5,241 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | tinethy | 2 |
| 2 | chislehurst | 2 |
| 3 | pensions | 2 |
| 4 | gluthys | 2 |
| 5 | recayt | 2 |
| 6 | aunt | 2 |
| 7 | lyasow | 2 |
| 8 | calabresi | 2 |
| 9 | prinsipya | 2 |
| 10 | romanzo | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0615 |
| R² (Goodness of Fit) | 0.995825 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.6% |
| Top 1,000 | 67.7% |
| Top 5,000 | 85.0% |
| Top 10,000 | 91.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9958 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.6% of corpus
- **Long Tail:** 20,471 words needed for remaining 8.5% 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 | 0.8337 | 0.3251 | N/A | N/A |
| **mono_64d** | 64 | 0.5460 | 0.2971 | N/A | N/A |
| **mono_128d** | 128 | 0.1358 | 0.2890 | N/A | N/A |
| **aligned_32d** | 32 | 0.8337 🏆 | 0.3307 | 0.0380 | 0.2340 |
| **aligned_64d** | 64 | 0.5460 | 0.2936 | 0.0580 | 0.2660 |
| **aligned_128d** | 128 | 0.1358 | 0.2812 | 0.0940 | 0.3220 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8337 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3028. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 9.4% 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 | **0.802** | 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` | sufi, sempelhes, surhe |
| `-d` | dolly, doeg, diskargans |
| `-a` | andy, amstyryus, aghskrifer |
| `-g` | gwiska, group, gwedhek |
| `-b` | bual, baronetage, barjavel |
| `-k` | kuršių, krestennogyon, keshevelyans |
| `-p` | peblys, provyans, pygmaea |
| `-t` | trohag, troha, tyghtya |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | peblys, iseldiryekdedhyas, norvys |
| `-n` | chinkapin, elfyn, krestennogyon |
| `-ow` | megyansow, filmow, posow |
| `-w` | megyansow, filmow, wiw |
| `-a` | gwiska, bianna, wosa |
| `-k` | unnek, gwedhek, vywoniethek |
| `-on` | krestennogyon, menystroryon, kwarton |
| `-h` | babergh, bouddydh, priweyth |

### 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 |
|------|----------|------------------|----------|
| `skri` | 1.99x | 54 contexts | skrif, skrij, skrin |
| `yans` | 1.73x | 71 contexts | usyans, unyans, wayans |
| `krif` | 1.92x | 27 contexts | skrif, skrift, skrifa |
| `eyth` | 1.53x | 57 contexts | neyth, leyth, seyth |
| `anso` | 2.04x | 20 contexts | ganso, kansow, sansom |
| `edhy` | 1.53x | 54 contexts | hedhys, dedhya, anedhy |
| `nnow` | 2.01x | 20 contexts | lynnow, donnow, vonnow |
| `nsow` | 2.05x | 18 contexts | vynsow, kansow, ponsow |
| `ened` | 1.92x | 17 contexts | wened, senedd, venedh |
| `edhe` | 1.37x | 52 contexts | edhen, hedhew, wedhen |
| `lans` | 1.65x | 26 contexts | plans, blans, kalans |
| `dhya` | 1.53x | 32 contexts | dedhya, tydhya, tedhya |

### 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 |
|--------|--------|-----------|----------|
| `-d` | `-s` | 189 words | definys, dielvednans |
| `-g` | `-s` | 98 words | gevres, glaucoides |
| `-k` | `-s` | 90 words | kows, kerwys |
| `-k` | `-w` | 80 words | krow, kalenderyow |
| `-p` | `-s` | 79 words | pleasants, porpos |
| `-k` | `-ow` | 78 words | krow, kalenderyow |
| `-d` | `-ns` | 75 words | dielvednans, dhielvennans |
| `-a` | `-s` | 73 words | antarcticus, arvreusyas |
| `-s` | `-s` | 70 words | skwattys, shackys |
| `-t` | `-s` | 69 words | tredhinas, trehevis |

### 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 |
|------|-----------------|------------|------|
| politikel | **`politi-k-el`** | 7.5 | `k` |
| lanndreth | **`lannd-re-th`** | 7.5 | `re` |
| degvledhen | **`de-g-vledhen`** | 7.5 | `vledhen` |
| anserhogath | **`anserhog-a-th`** | 7.5 | `a` |
| harryhausen | **`harryhau-s-en`** | 7.5 | `s` |
| haakonsson | **`haakons-s-on`** | 7.5 | `s` |
| klavjiores | **`klavjio-r-es`** | 7.5 | `r` |
| daskorrys | **`da-skorr-ys`** | 6.0 | `skorr` |
| sewyansow | **`sewya-ns-ow`** | 6.0 | `sewya` |
| fondyansow | **`fondya-ns-ow`** | 6.0 | `fondya` |
| tetroksid | **`te-tr-oksid`** | 6.0 | `oksid` |
| wordhonek | **`wordh-on-ek`** | 6.0 | `wordh` |
| gonisogethel | **`gonisogeth-el`** | 4.5 | `gonisogeth` |
| delinyans | **`delinya-ns`** | 4.5 | `delinya` |
| guntellas | **`guntella-s`** | 4.5 | `guntella` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Cornish 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 (4.17x) |
| N-gram | **2-gram** | Lowest perplexity (280) |
| Markov | **Context-4** | Highest predictability (97.0%) |
| 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 08:58:14*