README.md

---
language: lld
language_name: Ladin
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: 3.871
  - name: best_isotropy
    type: isotropy
    value: 0.8137
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ladin** 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** | 2.967x | 2.97 | 1.3342% | 390,873 |
| **16k** | 3.280x | 3.28 | 1.4750% | 353,549 |
| **32k** | 3.608x | 3.61 | 1.6228% | 321,368 |
| **64k** | 3.871x 🏆 | 3.87 | 1.7407% | 299,597 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `The G.G. Shinobi ie n videojuech svilupà da y publicà ai da . Storia Referënzes`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁the ▁g . g . ▁sh ino bi ▁ie ▁n ... (+10 more)` | 20 |
| 16k | `▁the ▁g . g . ▁sh ino bi ▁ie ▁n ... (+10 more)` | 20 |
| 32k | `▁the ▁g . g . ▁shinobi ▁ie ▁n ▁videojuech ▁svilupà ... (+8 more)` | 18 |
| 64k | `▁the ▁g . g . ▁shinobi ▁ie ▁n ▁videojuech ▁svilupà ... (+8 more)` | 18 |

**Sample 2:** `L Punta Cian ie n crëp te la Talia. L toca pra la ciadëina de crëps Elpes y à na...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁l ▁punta ▁cian ▁ie ▁n ▁crëp ▁te ▁la ▁talia . ... (+20 more)` | 30 |
| 16k | `▁l ▁punta ▁cian ▁ie ▁n ▁crëp ▁te ▁la ▁talia . ... (+20 more)` | 30 |
| 32k | `▁l ▁punta ▁cian ▁ie ▁n ▁crëp ▁te ▁la ▁talia . ... (+20 more)` | 30 |
| 64k | `▁l ▁punta ▁cian ▁ie ▁n ▁crëp ▁te ▁la ▁talia . ... (+20 more)` | 30 |

**Sample 3:** `L Urðafjall ie n crëp sun l'Ijules Feroe. L à na autëza de metri. Geografia Refe...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁l ▁ur ð a fjall ▁ie ▁n ▁crëp ▁sun ▁l ... (+18 more)` | 28 |
| 16k | `▁l ▁ur ð a fjall ▁ie ▁n ▁crëp ▁sun ▁l ... (+18 more)` | 28 |
| 32k | `▁l ▁ur ð a fjall ▁ie ▁n ▁crëp ▁sun ▁l ... (+18 more)` | 28 |
| 64k | `▁l ▁ur ð a fjall ▁ie ▁n ▁crëp ▁sun ▁l ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 3.871x compression
- **Lowest UNK Rate:** 8k with 1.3342% 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 | 532 | 9.06 | 33,996 | 67.5% | 87.2% |
| **2-gram** | Subword | 191 🏆 | 7.58 | 3,765 | 75.2% | 99.6% |
| **3-gram** | Word | 1,002 | 9.97 | 61,541 | 55.6% | 82.1% |
| **3-gram** | Subword | 894 | 9.80 | 29,033 | 45.0% | 87.8% |
| **4-gram** | Word | 1,883 | 10.88 | 126,323 | 47.4% | 74.6% |
| **4-gram** | Subword | 2,195 | 11.10 | 148,273 | 35.8% | 75.9% |
| **5-gram** | Word | 2,697 | 11.40 | 130,626 | 42.9% | 69.1% |
| **5-gram** | Subword | 3,726 | 11.86 | 363,496 | 30.6% | 71.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ie n` | 147,271 |
| 2 | `te la` | 136,121 |
| 3 | `populazion de` | 100,920 |
| 4 | `na populazion` | 100,855 |
| 5 | `de la` | 100,744 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `na populazion de` | 100,839 |
| 2 | `ovel na populazion` | 81,670 |
| 3 | `tl ovel na` | 76,090 |
| 4 | `na spersa de` | 64,015 |
| 5 | `sun na spersa` | 62,054 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ovel na populazion de` | 81,670 |
| 2 | `tl ovel na populazion` | 76,090 |
| 3 | `sun na spersa de` | 62,054 |
| 4 | `na spersa de km` | 54,437 |
| 5 | `na populazion de sun` | 49,272 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tl ovel na populazion de` | 76,090 |
| 2 | `sun na spersa de km` | 54,303 |
| 3 | `na populazion de sun na` | 49,272 |
| 4 | `populazion de sun na spersa` | 49,272 |
| 5 | `de sun na spersa de` | 49,272 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 1,383,241 |
| 2 | `e _` | 1,028,304 |
| 3 | `_ d` | 747,155 |
| 4 | `l _` | 646,000 |
| 5 | `d e` | 642,847 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 523,753 |
| 2 | `d e _` | 478,663 |
| 3 | `i a _` | 374,650 |
| 4 | `e _ l` | 361,999 |
| 5 | `l a _` | 322,949 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 475,477 |
| 2 | `_ l a _` | 270,169 |
| 3 | `_ t e _` | 242,721 |
| 4 | `e _ l a` | 240,131 |
| 5 | `_ t l _` | 235,810 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _ l a _` | 238,393 |
| 2 | `_ t e _ l` | 209,770 |
| 3 | `a _ d e _` | 199,173 |
| 4 | `_ i e _ n` | 179,284 |
| 5 | `i e _ n _` | 147,257 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 191
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~72% 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 | 0.4343 | 1.351 | 3.02 | 180,136 | 56.6% |
| **1** | Subword | 0.9572 | 1.942 | 8.64 | 947 | 4.3% |
| **2** | Word | 0.1793 | 1.132 | 1.44 | 541,125 | 82.1% |
| **2** | Subword | 0.9709 | 1.960 | 6.51 | 8,181 | 2.9% |
| **3** | Word | 0.0693 | 1.049 | 1.16 | 773,860 | 93.1% |
| **3** | Subword | 0.8601 | 1.815 | 4.51 | 53,238 | 14.0% |
| **4** | Word | 0.0320 🏆 | 1.022 | 1.09 | 891,955 | 96.8% |
| **4** | Subword | 0.6746 | 1.596 | 2.91 | 239,880 | 32.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de l poncione di ladins scrî balsan dl raion yadgir tl stat federel schleswig holstein tl`
2. `la contea monroe geografia referënzes dl vest l wank uchiri ie n luech te l india`
3. `te l domen ie n luech tl ecuador si pont plu aut ie n crëp te`

**Context Size 2:**

1. `ie n crëp te la nghiltiera tl riam unì geografia referënzes dl vest te l india tl`
2. `te la spania geografia referënzes de la contea lynn geografia storia notes de l usa jersey de`
3. `populazion de sun na spersa de km prescott fej pert de la contea de skåne te la`

**Context Size 3:**

1. `na populazion de sun na spersa de km cullison fej pert de la contea dane geografia storia notes`
2. `ovel na populazion de persones sun na spersa de km raleigh fej pert de la contea pierce geografia`
3. `tl ovel na populazion de storia geografia referënzes dl vest te l india tl stat federel karnataka l`

**Context Size 4:**

1. `ovel na populazion de sun na spersa de km woodacre fej pert de la contea ashtabula geografia storia ...`
2. `tl ovel na populazion de geografia storia notes de la franzia d azur dipartimënt`
3. `sun na spersa de km kaunakakai fej pert de la contea clark geografia storia notes de l usa de`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pmlas_deschator`
2. `evelicrc_ier_la_`
3. `alin_ke_pa_hian_`

**Context Size 2:**

1. `a_y_à_de_ngaostor`
2. `e_n_ciaphireferëp`
3. `_danity_fereguita`

**Context Size 3:**

1. `_de_persa_de_l'ind`
2. `de_la_polor_na_aut`
3. `ia_geografia_te_l'`

**Context Size 4:**

1. `_de_13,09_km²._stor`
2. `_la_contea_rio_fran`
3. `_te_l'austria_germa`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (239,880 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 | 63,469 |
| Total Tokens | 5,731,726 |
| Mean Frequency | 90.31 |
| Median Frequency | 3 |
| Frequency Std Dev | 3411.00 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 478,030 |
| 2 | la | 273,769 |
| 3 | te | 242,805 |
| 4 | tl | 235,975 |
| 5 | na | 230,710 |
| 6 | ie | 225,753 |
| 7 | l | 225,270 |
| 8 | n | 153,000 |
| 9 | geografia | 143,463 |
| 10 | referënzes | 123,520 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | zeigt | 2 |
| 2 | einfache | 2 |
| 3 | kalotermes | 2 |
| 4 | flavicollis | 2 |
| 5 | wilhalm | 2 |
| 6 | artenvielfalt | 2 |
| 7 | nipot | 2 |
| 8 | diplomingenieur | 2 |
| 9 | eletrizità | 2 |
| 10 | orecchini | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2167 |
| R² (Goodness of Fit) | 0.994267 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 80.6% |
| Top 1,000 | 90.4% |
| Top 5,000 | 95.1% |
| Top 10,000 | 96.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9943 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 80.6% of corpus
- **Long Tail:** 53,469 words needed for remaining 3.3% 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 | 0.8137 🏆 | 0.3614 | N/A | N/A |
| **mono_64d** | 64 | 0.7009 | 0.3154 | N/A | N/A |
| **mono_128d** | 128 | 0.4008 | 0.2966 | N/A | N/A |
| **aligned_32d** | 32 | 0.8137 | 0.3635 | 0.0480 | 0.3080 |
| **aligned_64d** | 64 | 0.7009 | 0.3247 | 0.0900 | 0.3660 |
| **aligned_128d** | 128 | 0.4008 | 0.2981 | 0.1740 | 0.5120 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8137 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3266. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 17.4% 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 | **-0.037** | 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 |
|--------|----------|
| `-s` | scür, spiritual, stauning |
| `-a` | arabi, assessëur, arnoldsville |
| `-b` | blockton, backpacker, bestimmte |
| `-m` | murdock, minot, markleysburg |
| `-c` | courtney, cashiers, caltanissetta |
| `-ma` | markleysburg, magura, mahish |
| `-p` | paoli, perugia, patkhor |
| `-t` | tuscola, topawa, tavella |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | flamma, dhanyahana, perugia |
| `-e` | giraffe, kalbe, verdigre |
| `-n` | blockton, heiden, irwin |
| `-s` | cashiers, gillis, freaks |
| `-r` | scür, patkhor, assessëur |
| `-le` | arnoldsville, giornale, bicycle |
| `-i` | paoli, arabi, nephi |
| `-es` | lerges, montagnes, stokes |

### 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 |
|------|----------|------------------|----------|
| `alia` | 2.24x | 49 contexts | galia, balia, malia |
| `azio` | 2.30x | 32 contexts | dazio, lazio, azion |
| `tali` | 2.08x | 41 contexts | talia, talit, satali |
| `iera` | 2.33x | 21 contexts | riera, miera, ciera |
| `ranz` | 2.12x | 22 contexts | franz, franzl, franzos |
| `fran` | 2.16x | 19 contexts | frana, franz, frank |
| `ogra` | 1.97x | 22 contexts | mogra, geograf, program |
| `onte` | 1.63x | 41 contexts | monte, ponte, fonte |
| `ubli` | 1.96x | 19 contexts | public, dublië, lublin |
| `efer` | 2.27x | 8 contexts | refer, kiefer, referì |
| `rafi` | 2.04x | 7 contexts | grafia, grafich, trafich |
| `metr` | 1.85x | 8 contexts | metro, metri, metris |

### 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 |
|--------|--------|-----------|----------|
| `-c` | `-a` | 101 words | conta, calpella |
| `-c` | `-s` | 88 words | caloniainuemes, compilations |
| `-c` | `-e` | 78 words | copahue, champagne |
| `-s` | `-a` | 75 words | scola, solgohalia |
| `-s` | `-n` | 72 words | saverton, stratton |
| `-b` | `-a` | 70 words | ballena, balsa |
| `-m` | `-e` | 70 words | merville, mëteste |
| `-c` | `-n` | 70 words | cigun, chameleon |
| `-p` | `-a` | 66 words | psicologia, pelicia |
| `-b` | `-e` | 66 words | bidre, buncombe |

### 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 |
|------|-----------------|------------|------|
| bridgford | **`bridgfo-r-d`** | 7.5 | `r` |
| tramaneda | **`traman-e-da`** | 7.5 | `e` |
| sylvarena | **`sylva-re-na`** | 7.5 | `re` |
| vivafanes | **`vivafa-n-es`** | 7.5 | `n` |
| jacksonport | **`jacksonpo-r-t`** | 7.5 | `r` |
| armoniëusa | **`armoniëu-s-a`** | 7.5 | `s` |
| cristiagn | **`cristia-g-n`** | 7.5 | `g` |
| chemagari | **`ch-e-magari`** | 7.5 | `magari` |
| scheinberg | **`scheinb-e-rg`** | 7.5 | `e` |
| cottonport | **`cottonpo-r-t`** | 7.5 | `r` |
| creatüras | **`creatür-a-s`** | 7.5 | `a` |
| salzgitter | **`salzgit-t-er`** | 7.5 | `t` |
| falconidae | **`falconi-da-e`** | 7.5 | `da` |
| bandieres | **`bandi-er-es`** | 6.0 | `bandi` |
| manganeses | **`mangan-es-es`** | 6.0 | `mangan` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ladin 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 (3.87x) |
| N-gram | **2-gram** | Lowest perplexity (191) |
| Markov | **Context-4** | Highest predictability (96.8%) |
| 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 11:11:26*