README.md

---
language: ca
language_name: Catalan
language_family: romance_galloitalic
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-romance_galloitalic
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: 4.448
  - name: best_isotropy
    type: isotropy
    value: 0.7469
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-08
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Catalan** 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** | 3.608x | 3.61 | 0.1295% | 3,980,202 |
| **16k** | 3.955x | 3.96 | 0.1420% | 3,630,953 |
| **32k** | 4.237x | 4.24 | 0.1521% | 3,389,435 |
| **64k** | 4.448x 🏆 | 4.45 | 0.1597% | 3,228,954 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Llista de topònims (noms propis de lloc) del municipi de Capmany, a l'Alt Empord...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁llista ▁de ▁topònims ▁( nom s ▁propis ▁de ▁lloc ) ... (+13 more)` | 23 |
| 16k | `▁llista ▁de ▁topònims ▁( nom s ▁propis ▁de ▁lloc ) ... (+13 more)` | 23 |
| 32k | `▁llista ▁de ▁topònims ▁( nom s ▁propis ▁de ▁lloc ) ... (+12 more)` | 22 |
| 64k | `▁llista ▁de ▁topònims ▁( noms ▁propis ▁de ▁lloc ) ▁del ... (+10 more)` | 20 |

**Sample 2:** `Trànsportni (Krasnodar), poble del krai de Krasnodar, a Rússia Trànsportni (Maga...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tr àn s port ni ▁( k ras n od ... (+39 more)` | 49 |
| 16k | `▁tràn sport ni ▁( k ras n od ar ), ... (+33 more)` | 43 |
| 32k | `▁tràn sport ni ▁( k ras n odar ), ▁poble ... (+27 more)` | 37 |
| 64k | `▁tràn sport ni ▁( k ras n odar ), ▁poble ... (+25 more)` | 35 |

**Sample 3:** `Torneigs de tennis masculí: Serbia Open (ATP 250) Belgrade Open (ATP 250) Tornei...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁torneig s ▁de ▁ten nis ▁mascul í : ▁ser bia ... (+44 more)` | 54 |
| 16k | `▁torneig s ▁de ▁tennis ▁masculí : ▁ser bia ▁open ▁( ... (+38 more)` | 48 |
| 32k | `▁torneigs ▁de ▁tennis ▁masculí : ▁ser bia ▁open ▁( atp ... (+34 more)` | 44 |
| 64k | `▁torneigs ▁de ▁tennis ▁masculí : ▁ser bia ▁open ▁( atp ... (+33 more)` | 43 |


### Key Findings

- **Best Compression:** 64k achieves 4.448x compression
- **Lowest UNK Rate:** 8k with 0.1295% 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 | 167,717 | 17.36 | 4,576,334 | 10.6% | 23.4% |
| **2-gram** | Subword | 262 🏆 | 8.03 | 41,609 | 69.0% | 98.9% |
| **3-gram** | Word | 1,409,334 | 20.43 | 13,479,698 | 2.7% | 10.3% |
| **3-gram** | Subword | 2,211 | 11.11 | 288,734 | 29.3% | 72.4% |
| **4-gram** | Word | 4,798,593 | 22.19 | 27,616,287 | 1.8% | 7.6% |
| **4-gram** | Subword | 13,232 | 13.69 | 1,676,138 | 14.2% | 40.2% |
| **5-gram** | Word | 4,523,219 | 22.11 | 21,934,897 | 2.3% | 8.8% |
| **5-gram** | Subword | 58,187 | 15.83 | 6,034,155 | 7.7% | 24.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la` | 3,892,352 |
| 2 | `a la` | 1,832,648 |
| 3 | `de l` | 1,806,800 |
| 4 | `a l` | 1,007,338 |
| 5 | `de les` | 998,964 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la seva` | 186,164 |
| 2 | `per a la` | 131,594 |
| 3 | `referències enllaços externs` | 121,418 |
| 4 | `la pel lícula` | 114,682 |
| 5 | `d octubre de` | 112,980 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de kitt peak spacewatch` | 78,569 |
| 2 | `de la universitat de` | 56,957 |
| 3 | `que hi havia el` | 55,303 |
| 4 | `segons el cens del` | 47,569 |
| 5 | `de la família dels` | 44,734 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `el nombre mitjà de persones` | 43,284 |
| 2 | `el següent diagrama mostra les` | 42,548 |
| 3 | `següent diagrama mostra les poblacions` | 42,548 |
| 4 | `diagrama mostra les poblacions més` | 42,542 |
| 5 | `mostra les poblacions més properes` | 42,497 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 65,660,325 |
| 2 | `s _` | 52,744,093 |
| 3 | `_ d` | 49,682,099 |
| 4 | `e _` | 42,364,044 |
| 5 | `d e` | 41,208,775 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 35,468,647 |
| 2 | `d e _` | 24,280,649 |
| 3 | `e s _` | 19,244,620 |
| 4 | `e l _` | 15,094,409 |
| 5 | `l a _` | 14,700,214 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 23,793,570 |
| 2 | `_ l a _` | 12,534,324 |
| 3 | `_ e l _` | 8,556,406 |
| 4 | `s _ d e` | 7,523,945 |
| 5 | `d e _ l` | 7,343,393 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _ l` | 7,323,223 |
| 2 | `_ d e l _` | 5,191,709 |
| 3 | `s _ d e _` | 5,107,850 |
| 4 | `_ q u e _` | 4,821,740 |
| 5 | `a _ d e _` | 4,540,758 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 262
- **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 | 0.9702 | 1.959 | 13.70 | 3,298,751 | 3.0% |
| **1** | Subword | 0.8467 | 1.798 | 7.10 | 30,691 | 15.3% |
| **2** | Word | 0.4478 | 1.364 | 2.95 | 45,099,512 | 55.2% |
| **2** | Subword | 0.5676 | 1.482 | 3.72 | 217,960 | 43.2% |
| **3** | Word | 0.2425 | 1.183 | 1.66 | 133,056,441 | 75.8% |
| **3** | Subword | 0.6293 | 1.547 | 3.86 | 810,473 | 37.1% |
| **4** | Word | 0.1249 🏆 | 1.090 | 1.26 | 221,190,469 | 87.5% |
| **4** | Subword | 0.6563 | 1.576 | 3.56 | 3,128,822 | 34.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de maig de la temporada l acceptació de muntar una muralla i el molí de la`
2. `la població comunicació de encara que alemanya i des de la computació sent l estat substituïda`
3. `i no són esmentats anteriorment icv el símbol del psoe des de guilgameix que un comerç`

**Context Size 2:**

1. `de la guerra di mario tronti i no solament va trobar que era del 5è al 16è`
2. `a la taula de composició amb la seva història general del magistrat monetari c cassi a la`
3. `de l expedició del virrei un germà gran del poble ulldeconencs o ulldeconins són coneguts com a`

**Context Size 3:**

1. `de la seva carrera periodística escrivint col laboracions a joves intel lectuals pertanyents a l alt...`
2. `per a la secció de filosofia i ciències socials en les seves obligacions amb la seguretat i el`
3. `referències enllaços externs fira festa de la pasqua hayivky el casament vessilia o ladkannya de la ...`

**Context Size 4:**

1. `de kitt peak spacewatch 8 de novembre de parcak i mumford del 8 de novembre de militants del flec`
2. `de la universitat de salamanca honoris causa per la universitat christian albrecht de kiel de la uni...`
3. `que hi havia el 1 era una gran superfície de material de bricolatge 1 una botiga de congelats 1`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_daral_euílere_s`
2. `eivinde_ditel'hi`
3. `agraweros._ome_2`

**Context Size 2:**

1. `a_ses_va_únivenci`
2. `s_als_(rdor_reu_d`
3. `_d'ofegria_amb_o_`

**Context Size 3:**

1. `_de_bre_seteodent_`
2. `de_la_de_col·locia`
3. `es_pres,_nastorals`

**Context Size 4:**

1. `_de_doble_(a_−_batx`
2. `_la_de_fan_es_va_ca`
3. `_el_donar_les_si_es`


### Key Findings

- **Best Predictability:** Context-4 (word) with 87.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (3,128,822 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 | 1,490,582 |
| Total Tokens | 372,231,757 |
| Mean Frequency | 249.72 |
| Median Frequency | 4 |
| Frequency Std Dev | 29623.92 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 23,862,515 |
| 2 | la | 12,874,088 |
| 3 | i | 9,923,035 |
| 4 | a | 9,593,194 |
| 5 | el | 8,820,173 |
| 6 | l | 6,195,164 |
| 7 | d | 5,995,004 |
| 8 | en | 5,534,785 |
| 9 | del | 5,257,995 |
| 10 | que | 4,926,945 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | binaritruncat | 2 |
| 2 | fanerozoiques | 2 |
| 3 | biòmers | 2 |
| 4 | nianzhi | 2 |
| 5 | fuching | 2 |
| 6 | mndm | 2 |
| 7 | cpsf | 2 |
| 8 | preestàndard | 2 |
| 9 | sweetshop | 2 |
| 10 | whakaata | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0222 |
| R² (Goodness of Fit) | 0.996032 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 45.0% |
| Top 1,000 | 63.8% |
| Top 5,000 | 78.5% |
| Top 10,000 | 84.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9960 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 45.0% of corpus
- **Long Tail:** 1,480,582 words needed for remaining 15.8% 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 | 0.7469 🏆 | 0.3896 | N/A | N/A |
| **mono_64d** | 64 | 0.7390 | 0.2972 | N/A | N/A |
| **mono_128d** | 128 | 0.6902 | 0.2374 | N/A | N/A |
| **aligned_32d** | 32 | 0.7469 | 0.3696 | 0.4960 | 0.8360 |
| **aligned_64d** | 64 | 0.7390 | 0.3068 | 0.7200 | 0.9380 |
| **aligned_128d** | 128 | 0.6902 | 0.2443 | 0.8320 | 0.9720 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7469 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3075. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 83.2% 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 | **-0.637** | 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 |
|--------|----------|
| `-ca` | canadàwilliam, cancells, callissot |
| `-co` | compsopogon, corlea, constitutionem |
| `-ma` | matricarina, masaraga, massai |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | pomacèntrids, pentalobulars, quiotas |
| `-a` | matricarina, arduinna, yarima |
| `-es` | asfèriques, biomatemàtiques, quies |
| `-en` | grieneisen, robien, tensionen |
| `-is` | rufistrigalis, reaccionaris, catàrsis |
| `-ia` | praskóvia, llògia, orogenia |
| `-ta` | lucasta, samudragupta, lisetita |

### 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 |
|------|----------|------------------|----------|
| `nter` | 1.39x | 729 contexts | inter, anter, únter |
| `efer` | 1.66x | 177 contexts | kefer, lefer, defer |
| `uerr` | 1.61x | 153 contexts | uerra, guerr, duerr |
| `espr` | 1.73x | 95 contexts | esprî, despr, esprai |
| `stru` | 1.32x | 389 contexts | strum, struk, strus |
| `rson` | 1.46x | 205 contexts | rsona, arson, urson |
| `ient` | 1.31x | 364 contexts | rient, oient, lient |
| `lmen` | 1.57x | 122 contexts | ulmen, ilmen, olmen |
| `rinc` | 1.48x | 147 contexts | rinck, rincó, rinca |
| `ènci` | 1.57x | 107 contexts | ència, mència, lència |
| `embr` | 1.33x | 234 contexts | membr, embre, embry |
| `onst` | 1.42x | 159 contexts | onsta, konst, const |

### 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 |
|--------|--------|-----------|----------|
| `-co` | `-s` | 48 words | conventos, conservadors |
| `-ma` | `-a` | 45 words | masicka, macclureana |
| `-ca` | `-s` | 40 words | callolepis, cambyses |
| `-co` | `-a` | 35 words | comunera, costanzana |
| `-ma` | `-s` | 33 words | mahates, maktens |
| `-ca` | `-a` | 30 words | camborda, cardellina |
| `-co` | `-es` | 14 words | congoatlàntiques, colomates |
| `-ca` | `-es` | 11 words | cambyses, calcídies |
| `-ma` | `-es` | 9 words | mahates, masies |
| `-ma` | `-ta` | 9 words | magnesiodumortierita, malwatta |

### 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 |
|------|-----------------|------------|------|
| guerrista | **`guerr-is-ta`** | 6.0 | `guerr` |
| whitlockita | **`whitlocki-ta`** | 4.5 | `whitlocki` |
| assumptionis | **`assumption-is`** | 4.5 | `assumption` |
| zumacales | **`zumacal-es`** | 4.5 | `zumacal` |
| raperswilen | **`raperswil-en`** | 4.5 | `raperswil` |
| antinomies | **`antinomi-es`** | 4.5 | `antinomi` |
| reglamentaren | **`reglamentar-en`** | 4.5 | `reglamentar` |
| remarcaria | **`remarcar-ia`** | 4.5 | `remarcar` |
| reichsfürsten | **`reichsfürst-en`** | 4.5 | `reichsfürst` |
| deflectores | **`deflector-es`** | 4.5 | `deflector` |
| produeixen | **`produeix-en`** | 4.5 | `produeix` |
| autoadjuntes | **`autoadjunt-es`** | 4.5 | `autoadjunt` |
| subministraria | **`subministrar-ia`** | 4.5 | `subministrar` |
| barbertonita | **`barbertoni-ta`** | 4.5 | `barbertoni` |
| balsameres | **`balsamer-es`** | 4.5 | `balsamer` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Catalan 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 (4.45x) |
| N-gram | **2-gram** | Lowest perplexity (262) |
| Markov | **Context-4** | Highest predictability (87.5%) |
| 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: 2026-01-08 03:10:53*