README.md

---
language: br
language_name: Breton
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: 3.787
  - name: best_isotropy
    type: isotropy
    value: 0.8154
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Breton** 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** | 3.238x | 3.24 | 0.4518% | 788,643 |
| **16k** | 3.463x | 3.46 | 0.4832% | 737,391 |
| **32k** | 3.647x | 3.65 | 0.5089% | 700,148 |
| **64k** | 3.787x 🏆 | 3.79 | 0.5284% | 674,255 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Concetta Barra a oa ur ganerez hag un aktourez italian ha dreist-holl napolitane...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁conc etta ▁bar ra ▁a ▁oa ▁ur ▁ganerez ▁hag ▁un ... (+30 more)` | 40 |
| 16k | `▁conc etta ▁barra ▁a ▁oa ▁ur ▁ganerez ▁hag ▁un ▁aktourez ... (+26 more)` | 36 |
| 32k | `▁conc etta ▁barra ▁a ▁oa ▁ur ▁ganerez ▁hag ▁un ▁aktourez ... (+26 more)` | 36 |
| 64k | `▁conc etta ▁barra ▁a ▁oa ▁ur ▁ganerez ▁hag ▁un ▁aktourez ... (+22 more)` | 32 |

**Sample 2:** `Fénis zo ur gumun italian, e rannvro emren Traoñienn Aosta. Notennoù`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁f én is ▁zo ▁ur ▁gumun ▁italian , ▁e ▁rannvro ... (+6 more)` | 16 |
| 16k | `▁f én is ▁zo ▁ur ▁gumun ▁italian , ▁e ▁rannvro ... (+5 more)` | 15 |
| 32k | `▁f én is ▁zo ▁ur ▁gumun ▁italian , ▁e ▁rannvro ... (+5 more)` | 15 |
| 64k | `▁fén is ▁zo ▁ur ▁gumun ▁italian , ▁e ▁rannvro ▁emren ... (+4 more)` | 14 |

**Sample 3:** `Cervera del Río Alhama zo ur gumun e kumuniezh emren La Rioja e Spagn.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁c erv era ▁del ▁río ▁al h ama ▁zo ▁ur ... (+9 more)` | 19 |
| 16k | `▁cerv era ▁del ▁río ▁al h ama ▁zo ▁ur ▁gumun ... (+8 more)` | 18 |
| 32k | `▁cerv era ▁del ▁río ▁al h ama ▁zo ▁ur ▁gumun ... (+8 more)` | 18 |
| 64k | `▁cervera ▁del ▁río ▁alhama ▁zo ▁ur ▁gumun ▁e ▁kumuniezh ▁emren ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 3.787x compression
- **Lowest UNK Rate:** 8k with 0.4518% 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 | 37,064 | 15.18 | 295,690 | 13.7% | 32.1% |
| **2-gram** | Subword | 293 🏆 | 8.19 | 11,777 | 65.4% | 98.9% |
| **3-gram** | Word | 127,942 | 16.97 | 571,162 | 5.9% | 19.5% |
| **3-gram** | Subword | 2,712 | 11.41 | 80,865 | 23.9% | 68.2% |
| **4-gram** | Word | 277,916 | 18.08 | 975,958 | 4.1% | 14.9% |
| **4-gram** | Subword | 17,204 | 14.07 | 420,279 | 10.8% | 35.6% |
| **5-gram** | Word | 202,294 | 17.63 | 684,204 | 4.9% | 16.7% |
| **5-gram** | Subword | 72,650 | 16.15 | 1,308,264 | 6.0% | 21.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e voe` | 60,584 |
| 2 | `ar c` | 55,004 |
| 3 | `a viz` | 53,947 |
| 4 | `e oa` | 52,533 |
| 5 | `d ar` | 48,158 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `zo ur gumun` | 17,679 |
| 2 | `bro c hall` | 15,683 |
| 3 | `a zo ur` | 15,380 |
| 4 | `e oa bet` | 13,023 |
| 5 | `ur gumun eus` | 8,893 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `zo ur gumun eus` | 8,258 |
| 2 | `monumantoù ha traoù heverk` | 5,437 |
| 3 | `a zo ur gumun` | 5,065 |
| 4 | `zo ur gumun e` | 4,316 |
| 5 | `monumant ar re varv` | 3,982 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a zo ur gumun eus` | 3,616 |
| 2 | `ioc world bird list diwar` | 2,760 |
| 3 | `world bird list diwar benn` | 2,760 |
| 4 | `roadennoù ioc world bird list` | 2,759 |
| 5 | `zo ur gumun eus italia` | 2,622 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a` | 1,908,238 |
| 2 | `_ e` | 1,681,083 |
| 3 | `a n` | 1,609,135 |
| 4 | `e _` | 1,599,725 |
| 5 | `r _` | 1,429,762 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a r _` | 641,927 |
| 2 | `_ e _` | 641,853 |
| 3 | `e t _` | 627,577 |
| 4 | `_ a r` | 556,810 |
| 5 | `e n n` | 468,710 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a r _` | 457,578 |
| 2 | `_ a n _` | 280,457 |
| 3 | `a n t _` | 268,610 |
| 4 | `_ g a n` | 228,380 |
| 5 | `_ h a _` | 223,259 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ g a n t` | 202,257 |
| 2 | `g a n t _` | 193,123 |
| 3 | `_ h a g _` | 134,751 |
| 4 | `_ e u s _` | 130,235 |
| 5 | `e t _ e _` | 103,216 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 293
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.8873 | 1.850 | 7.57 | 546,965 | 11.3% |
| **1** | Subword | 0.8951 | 1.860 | 5.84 | 8,419 | 10.5% |
| **2** | Word | 0.3297 | 1.257 | 2.04 | 4,120,028 | 67.0% |
| **2** | Subword | 0.6667 | 1.587 | 4.20 | 49,174 | 33.3% |
| **3** | Word | 0.1564 | 1.115 | 1.35 | 8,357,037 | 84.4% |
| **3** | Subword | 0.6634 | 1.584 | 3.73 | 206,424 | 33.7% |
| **4** | Word | 0.0731 🏆 | 1.052 | 1.13 | 11,199,579 | 92.7% |
| **4** | Subword | 0.6489 | 1.568 | 3.22 | 770,069 | 35.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `e kastell aigneaux kantved merc h kannidi o devoa kemeret hent reter menezioù ezhomm da vont`
2. `ar boblañs melestradurezh tud ar pif gadget de carnac et seigneur isaac baron met breinet gant`
3. `a ra eus bro c haokaz ar fedon ar 25vet rujumant troadegiezhfichenn hiniennel memorial genweb egile`

**Context Size 2:**

1. `e voe azoet an oferenn rak miret eo bet troet e galleg a 346 pajennad a zeuas`
2. `ar c haner en deus kumuniezhioù kumunioù beg ar skeul mañ zo levezonet gant friedrich dürrenmatt d`
3. `a viz eost e departamant il ha gwilen bro roazhon bet ganet d ar mare se e`

**Context Size 3:**

1. `zo ur gumun e spagn e kumuniezh valencia spagn pennadoù kar carlo ii charlez iañ karl iañ carlo`
2. `a zo ur sammad a stennadur a en em astenn a ra erv kourland eus ledenez sambia lec`
3. `bro c hall société des amis de benjamin péret pour un second manifeste communiste gant grandizo muni...`

**Context Size 4:**

1. `zo ur gumun eus departamant calvados e bro c hall douaroniezh armerzh emdroadur ar boblañs melestrad...`
2. `monumantoù ha traoù heverk iliz katolik sant albin ners douaroniezh emdroadur ar boblañs cassini hag...`
3. `a zo ur gumun eus departamant pas de calais bro c hall istor armerzh kompagnunezh mengleuzioù bruay ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_cheunoù_wez:_be`
2. `ere_zharndütren_`
3. `añs_t.lalel_da_k`

**Context Size 2:**

1. `_amm_da_gant_ges_`
2. `_evez._marezal_pe`
3. `annoù_art,_pag_ga`

**Context Size 3:**

1. `ar_senner._levelet`
2. `_e_rout_-_bloareku`
3. `et_en_affarink_d’a`

**Context Size 4:**

1. `_ar_solinago,_mab_s`
2. `_an_ilizoù_sir_krei`
3. `ant_bet_kemeret_an_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (770,069 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 | 241,991 |
| Total Tokens | 15,343,130 |
| Mean Frequency | 63.40 |
| Median Frequency | 4 |
| Frequency Std Dev | 2509.84 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | e | 703,890 |
| 2 | ar | 518,682 |
| 3 | a | 468,243 |
| 4 | an | 326,691 |
| 5 | ha | 229,662 |
| 6 | gant | 189,178 |
| 7 | c | 187,433 |
| 8 | en | 180,997 |
| 9 | da | 171,218 |
| 10 | ur | 158,920 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | veyne | 2 |
| 2 | wga | 2 |
| 3 | codreanu | 2 |
| 4 | dumitru | 2 |
| 5 | maghrebonkoud | 2 |
| 6 | fidefide | 2 |
| 7 | ougandachess | 2 |
| 8 | cytonn | 2 |
| 9 | malinga | 2 |
| 10 | ablainville | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1114 |
| R² (Goodness of Fit) | 0.996756 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.9% |
| Top 1,000 | 65.8% |
| Top 5,000 | 80.5% |
| Top 10,000 | 85.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9968 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.9% of corpus
- **Long Tail:** 231,991 words needed for remaining 14.3% 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 | 0.8117 | 0.3810 | N/A | N/A |
| **mono_64d** | 64 | 0.8154 🏆 | 0.2792 | N/A | N/A |
| **mono_128d** | 128 | 0.8010 | 0.2076 | N/A | N/A |
| **aligned_32d** | 32 | 0.8117 | 0.3700 | 0.2440 | 0.6460 |
| **aligned_64d** | 64 | 0.8154 | 0.2752 | 0.3920 | 0.7600 |
| **aligned_128d** | 128 | 0.8010 | 0.2094 | 0.5340 | 0.8640 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.8154 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2871. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 53.4% 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 | **-0.232** | 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 |
|--------|----------|
| `-s` | wolves, hobbs, cassis |
| `-où` | gwallzarvoudoù, emstummoù, pellgomzioù |
| `-us` | tarphonomus, benildus, gigantorhinus |
| `-er` | hompozer, siger, geschwister |
| `-es` | wolves, béssèges, fontenailles |

### 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 |
|------|----------|------------------|----------|
| `tion` | 2.41x | 78 contexts | tione, eetion, motion |
| `adoù` | 2.03x | 74 contexts | tadoù, padoù, hadoù |
| `emba` | 2.26x | 40 contexts | emban, pemba, bemba |
| `iamm` | 2.35x | 24 contexts | liamm, fiamma, fiamme |
| `ouar` | 1.52x | 126 contexts | mouar, zouar, bouar |
| `nnet` | 1.68x | 71 contexts | annet, rannet, rennet |
| `nnad` | 1.53x | 98 contexts | mennad, gannad, vennad |
| `zhañ` | 1.96x | 35 contexts | ezhañ, tizhañ, dizhañ |
| `reze` | 1.52x | 94 contexts | rezet, dreze, breze |
| `ntañ` | 1.75x | 51 contexts | antaño, vontañ, wintañ |
| `nnoù` | 1.87x | 38 contexts | vannoù, gennoù, pennoù |
| `iwar` | 2.55x | 13 contexts | diwar, ziwar, siward |

### 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 |
|------|-----------------|------------|------|
| heureuses | **`heure-us-es`** | 6.0 | `heure` |
| burzhudoù | **`burzhud-où`** | 4.5 | `burzhud` |
| ziarbennoù | **`ziarbenn-où`** | 4.5 | `ziarbenn` |
| goudeskridoù | **`goudeskrid-où`** | 4.5 | `goudeskrid` |
| nijadegoù | **`nijadeg-où`** | 4.5 | `nijadeg` |
| ziskoulmoù | **`ziskoulm-où`** | 4.5 | `ziskoulm` |
| dasprenus | **`daspren-us`** | 4.5 | `daspren` |
| tradutores | **`tradutor-es`** | 4.5 | `tradutor` |
| drubuilhoù | **`drubuilh-où`** | 4.5 | `drubuilh` |
| reichsmarkoù | **`reichsmark-où`** | 4.5 | `reichsmark` |
| variantennoù | **`variantenn-où`** | 4.5 | `variantenn` |
| livuzennoù | **`livuzenn-où`** | 4.5 | `livuzenn` |
| kompozadoù | **`kompozad-où`** | 4.5 | `kompozad` |
| viñsaskelloù | **`viñsaskell-où`** | 4.5 | `viñsaskell` |
| kellennoù | **`kellenn-où`** | 4.5 | `kellenn` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Breton 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 (3.79x) |
| N-gram | **2-gram** | Lowest perplexity (293) |
| Markov | **Context-4** | Highest predictability (92.7%) |
| 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 20:37:28*