---
language: cy
language_name: Welsh
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: 4.109
  - name: best_isotropy
    type: isotropy
    value: 0.8420
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Welsh** 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** | 3.346x | 3.35 | 0.0427% | 894,556 |
| **16k** | 3.678x | 3.68 | 0.0469% | 813,770 |
| **32k** | 3.925x | 3.93 | 0.0501% | 762,670 |
| **64k** | 4.109x 🏆 | 4.11 | 0.0524% | 728,422 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Canwr opera o Ganada oedd Jonathan Stewart Vickers, CC (29 Hydref – 10 Gorffenna...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁canwr ▁opera ▁o ▁ganada ▁oedd ▁jonathan ▁stewart ▁v ick ers ... (+30 more)` | 40 |
| 16k | `▁canwr ▁opera ▁o ▁ganada ▁oedd ▁jonathan ▁stewart ▁vick ers , ... (+27 more)` | 37 |
| 32k | `▁canwr ▁opera ▁o ▁ganada ▁oedd ▁jonathan ▁stewart ▁vick ers , ... (+26 more)` | 36 |
| 64k | `▁canwr ▁opera ▁o ▁ganada ▁oedd ▁jonathan ▁stewart ▁vickers , ▁cc ... (+22 more)` | 32 |

**Sample 2:** `Pêl-droediwr o Japan yw (ganed 11 Rhagfyr Tîm Cenedlaethol Tîm cenedlaethol Dole...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pêl - droediwr ▁o ▁japan ▁yw ▁( ganed ▁ 1 ... (+15 more)` | 25 |
| 16k | `▁pêl - droediwr ▁o ▁japan ▁yw ▁( ganed ▁ 1 ... (+15 more)` | 25 |
| 32k | `▁pêl - droediwr ▁o ▁japan ▁yw ▁( ganed ▁ 1 ... (+15 more)` | 25 |
| 64k | `▁pêl - droediwr ▁o ▁japan ▁yw ▁( ganed ▁ 1 ... (+15 more)` | 25 |

**Sample 3:** `Clostridium tetani yw'r bacteria sy'n achosi Tetanws.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cl ost rid ium ▁t et ani ▁yw ' r ... (+13 more)` | 23 |
| 16k | `▁cl ost rid ium ▁t et ani ▁yw ' r ... (+12 more)` | 22 |
| 32k | `▁cl ost rid ium ▁tet ani ▁yw ' r ▁bacteria ... (+8 more)` | 18 |
| 64k | `▁cl ost rid ium ▁tet ani ▁yw ' r ▁bacteria ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.109x compression
- **Lowest UNK Rate:** 8k with 0.0427% 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 | 17,960 | 14.13 | 742,720 | 26.5% | 49.5% |
| **2-gram** | Subword | 266 🏆 | 8.05 | 14,977 | 67.6% | 99.3% |
| **3-gram** | Word | 34,403 | 15.07 | 1,470,847 | 23.6% | 43.7% |
| **3-gram** | Subword | 2,056 | 11.01 | 96,402 | 28.1% | 74.0% |
| **4-gram** | Word | 58,140 | 15.83 | 2,520,966 | 20.5% | 39.2% |
| **4-gram** | Subword | 9,573 | 13.22 | 505,960 | 17.0% | 48.0% |
| **5-gram** | Word | 66,270 | 16.02 | 2,303,277 | 18.6% | 36.6% |
| **5-gram** | Subword | 29,179 | 14.83 | 1,685,188 | 12.7% | 38.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `unol daleithiau` | 486,479 |
| 2 | `daleithiau america` | 459,399 |
| 3 | `y ffilm` | 330,346 |
| 4 | `y cyfarwyddwr` | 255,174 |
| 5 | `o ffilmiau` | 249,770 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `unol daleithiau america` | 447,977 |
| 2 | `daleithiau america saesneg` | 189,392 |
| 3 | `gan y cyfarwyddwr` | 147,806 |
| 4 | `gan gynnwys y` | 143,480 |
| 5 | `gynnwys y canlynol` | 142,458 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `unol daleithiau america saesneg` | 183,879 |
| 2 | `gan gynnwys y canlynol` | 142,457 |
| 3 | `o ffilmiau gan gynnwys` | 141,034 |
| 4 | `nifer o ffilmiau gan` | 141,018 |
| 5 | `ffilmiau gan gynnwys y` | 141,004 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nifer o ffilmiau gan gynnwys` | 141,016 |
| 2 | `o ffilmiau gan gynnwys y` | 141,003 |
| 3 | `ffilmiau gan gynnwys y canlynol` | 140,997 |
| 4 | `y nodwyd cyhoeddwyd y ffilm` | 140,932 |
| 5 | `fel y nodwyd cyhoeddwyd y` | 140,932 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 6,965,988 |
| 2 | `d _` | 6,143,531 |
| 3 | `_ y` | 5,977,485 |
| 4 | `d d` | 5,740,307 |
| 5 | `_ a` | 5,232,448 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `y n _` | 2,646,508 |
| 2 | `d d _` | 2,490,077 |
| 3 | `_ y n` | 2,304,841 |
| 4 | `w y d` | 2,285,145 |
| 5 | `_ y _` | 2,240,041 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ y n _` | 2,171,280 |
| 2 | `f i l m` | 1,586,546 |
| 3 | `f f i l` | 1,571,751 |
| 4 | `_ f f i` | 1,455,954 |
| 5 | `i l m _` | 1,222,896 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `f f i l m` | 1,569,304 |
| 2 | `_ f f i l` | 1,419,063 |
| 3 | `f i l m _` | 1,222,863 |
| 4 | `_ g a n _` | 924,207 |
| 5 | `w y d _ y` | 781,315 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 266
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~38% 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 | 0.9977 | 1.997 | 9.84 | 671,269 | 0.2% |
| **1** | Subword | 1.0862 | 2.123 | 6.65 | 8,673 | 0.0% |
| **2** | Word | 0.3690 | 1.291 | 2.18 | 6,591,949 | 63.1% |
| **2** | Subword | 0.6157 | 1.532 | 3.90 | 57,679 | 38.4% |
| **3** | Word | 0.1502 | 1.110 | 1.34 | 14,351,859 | 85.0% |
| **3** | Subword | 0.6340 | 1.552 | 3.78 | 225,011 | 36.6% |
| **4** | Word | 0.0687 🏆 | 1.049 | 1.14 | 19,154,889 | 93.1% |
| **4** | Subword | 0.6561 | 1.576 | 3.40 | 850,309 | 34.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `y ffindir gweler hefyd cyhoeddodd nifer o r almaen almaenegno unknown value the white ship mutiny`
2. `yn ystod eang derbyniad gweler hefyd rhestr goch yr enw tacson delwedd gwlad dyddiad a 22`
3. `o leiaf 1 050 o ffilmiau gan nifer o fariau cul o awstria almaeneg cyfeiriadau gan`

**Context Size 2:**

1. `unol daleithiau america rhamantaidd gyda llai na 10 o actorion lleisiol a olygwyd gan mogens skot ha...`
2. `daleithiau america cyfeiriadau gan gyfarwyddwyr ffilm gwrywaidd saesneg du a gwyn o japan mud sydd a...`
3. `y ffilm hon yw warner baxter stuart erwin edmund lowe cafodd ei ddanfon gan fyddin a adwaenid`

**Context Size 3:**

1. `unol daleithiau america in every womans life unol daleithiau america saesneg the boys from brazil a ...`
2. `daleithiau america saesneg cyfeiriadau gan gyfarwyddwyr ffilm gwrywaidd tsieceg o tsiecoslofacia gyd...`
3. `gan y cyfarwyddwr kevin billington yw the rise of the nazis stalingrad fernsehepisode y deyrnas uned...`

**Context Size 4:**

1. `unol daleithiau america saesneg o unol daleithiau america arswyd o unol daleithiau america comedi gy...`
2. `gan gynnwys y canlynol cyfeiriadau lliw lliw o sbaen rhamantaidd o sbaen sbaeneg o sbaen comedi gyda...`
3. `o ffilmiau gan gynnwys y canlynol ffilm delwedd gwlad iaith wreiddiol dyddiad coyote summer unol dal...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_o/uchomau_dcolm`
2. `adankeegoeei'cho`
3. `elm_seratir,_pae`

**Context Size 2:**

1. `n_gannwyddyd_gwed`
2. `d_rasalanc_wr_pon`
3. `_y_faraithia_cymg`

**Context Size 3:**

1. `yn_wreidd_gwyn_cyh`
2. `dd_a_10,700_strwyd`
3. `_yn_coln,_sy'n_alm`

**Context Size 4:**

1. `_yn_sydd_('cyfarwyd`
2. `filmio_oeddwyd,_cyh`
3. `ffilm_hon_walter,_j`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (850,309 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 | 360,120 |
| Total Tokens | 54,213,529 |
| Mean Frequency | 150.54 |
| Median Frequency | 5 |
| Frequency Std Dev | 7791.16 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | y | 2,261,654 |
| 2 | yn | 2,177,991 |
| 3 | o | 1,594,538 |
| 4 | a | 1,391,156 |
| 5 | ffilm | 1,218,819 |
| 6 | gan | 925,486 |
| 7 | r | 723,127 |
| 8 | i | 650,709 |
| 9 | yr | 521,021 |
| 10 | daleithiau | 501,348 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | geirfaoedd | 2 |
| 2 | volcabulaire | 2 |
| 3 | ethnolog | 2 |
| 4 | siculu | 2 |
| 5 | metafonetig | 2 |
| 6 | prano | 2 |
| 7 | defynydd | 2 |
| 8 | clwsterau | 2 |
| 9 | ŋm | 2 |
| 10 | ŋw | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1638 |
| R² (Goodness of Fit) | 0.998189 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.6% |
| Top 1,000 | 72.6% |
| Top 5,000 | 84.6% |
| Top 10,000 | 88.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9982 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.6% of corpus
- **Long Tail:** 350,120 words needed for remaining 11.3% 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 | 0.8420 🏆 | 0.3264 | N/A | N/A |
| **mono_64d** | 64 | 0.8198 | 0.2681 | N/A | N/A |
| **mono_128d** | 128 | 0.7807 | 0.2230 | N/A | N/A |
| **aligned_32d** | 32 | 0.8420 | 0.3314 | 0.2180 | 0.6520 |
| **aligned_64d** | 64 | 0.8198 | 0.2651 | 0.3480 | 0.7540 |
| **aligned_128d** | 128 | 0.7807 | 0.2238 | 0.5000 | 0.8640 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8420 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2730. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 50.0% R@1 in cross-lingual retrieval.
- **Recommendation:** 128d aligned for best cross-lingual performance

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

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

### 6.1 Productivity & Complexity

| Metric | Value | Interpretation | Recommendation |
|--------|-------|----------------|----------------|
| Productivity Index | **5.000** | High morphological productivity | Reliable analysis |
| Idiomaticity Gap | **-0.043** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-er` | menschenfresser, spengler, giessler |
| `-dd` | cwmnioedd, ailysgrifennodd, maswedd |
| `-on` | cenawon, pittston, dimson |
| `-au` | llinachau, rygiau, halennau |
| `-en` | vorsitzenden, misshandlingen, ddiacen |

### 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 |
|------|----------|------------------|----------|
| `iada` | 2.24x | 67 contexts | riada, viada, diada |
| `efyd` | 2.21x | 69 contexts | hefyd, lefyd, efydd |
| `ddio` | 1.98x | 84 contexts | addio, ddiog, ddios |
| `feir` | 2.03x | 69 contexts | feiro, feira, sfeir |
| `nnwy` | 2.19x | 46 contexts | annwyl, annwyd, gynnwy |
| `leit` | 2.36x | 32 contexts | leite, fleit, leith |
| `yddi` | 1.71x | 121 contexts | fyddi, byddi, dyddio |
| `dwyd` | 2.14x | 43 contexts | nodwyd, ildwyd, codwyd |
| `ithi` | 1.55x | 152 contexts | deithi, teithi, rithio |
| `alei` | 2.30x | 26 contexts | dalei, malei, maleia |
| `adau` | 2.02x | 40 contexts | badau, gadau, fadau |
| `eddw` | 1.67x | 49 contexts | feddw, weddw, meddw |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| deiamwntau | **`deiamwnt-au`** | 4.5 | `deiamwnt` |
| croniclau | **`cronicl-au`** | 4.5 | `cronicl` |
| komödianten | **`komödiant-en`** | 4.5 | `komödiant` |
| recruiter | **`recruit-er`** | 4.5 | `recruit` |
| diffiniodd | **`diffinio-dd`** | 4.5 | `diffinio` |
| catholicon | **`catholic-on`** | 4.5 | `catholic` |
| telesgopau | **`telesgop-au`** | 4.5 | `telesgop` |
| canlyniadau | **`canlyniad-au`** | 4.5 | `canlyniad` |
| lluswydden | **`lluswy-dd-en`** | 3.0 | `lluswy` |
| organeddau | **`organe-dd-au`** | 3.0 | `organe` |
| chynffonau | **`chynff-on-au`** | 3.0 | `chynff` |
| wastadeddau | **`wastade-dd-au`** | 3.0 | `wastade` |
| ffilmymgyrchydd | **`ffilmymgyrchy-dd`** | 1.5 | `ffilmymgyrchy` |
| stabilizer | **`stabiliz-er`** | 1.5 | `stabiliz` |
| effeithiolrwydd | **`effeithiolrwy-dd`** | 1.5 | `effeithiolrwy` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Welsh 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 (4.11x) |
| N-gram | **2-gram** | Lowest perplexity (266) |
| Markov | **Context-4** | Highest predictability (93.1%) |
| 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: 2026-01-04 02:01:49*