README.md

---
language: ro
language_name: Romanian
language_family: romance_eastern
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_eastern
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: 4.390
  - name: best_isotropy
    type: isotropy
    value: 0.7633
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-17
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Romanian** 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** | 3.509x | 3.51 | 0.0794% | 2,993,510 |
| **16k** | 3.856x | 3.86 | 0.0872% | 2,724,242 |
| **32k** | 4.158x | 4.16 | 0.0941% | 2,526,285 |
| **64k** | 4.390x 🏆 | 4.39 | 0.0993% | 2,392,489 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Student la Iași este un film românesc din regizat de Iancu Moscu. Prezentare Not...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁stud ent ▁la ▁iași ▁este ▁un ▁film ▁românesc ▁din ▁regizat ... (+19 more)` | 29 |
| 16k | `▁student ▁la ▁iași ▁este ▁un ▁film ▁românesc ▁din ▁regizat ▁de ... (+17 more)` | 27 |
| 32k | `▁student ▁la ▁iași ▁este ▁un ▁film ▁românesc ▁din ▁regizat ▁de ... (+17 more)` | 27 |
| 64k | `▁student ▁la ▁iași ▁este ▁un ▁film ▁românesc ▁din ▁regizat ▁de ... (+16 more)` | 26 |

**Sample 2:** `Dellys (în ) este o comună din provincia Boumerdès, Algeria. Populația comunei e...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁del ly s ▁( în ▁) ▁este ▁o ▁comună ▁din ... (+32 more)` | 42 |
| 16k | `▁del ly s ▁( în ▁) ▁este ▁o ▁comună ▁din ... (+30 more)` | 40 |
| 32k | `▁del ly s ▁( în ▁) ▁este ▁o ▁comună ▁din ... (+28 more)` | 38 |
| 64k | `▁del lys ▁( în ▁) ▁este ▁o ▁comună ▁din ▁provincia ... (+27 more)` | 37 |

**Sample 3:** `Districtul Ghanzi este o unitate administrativă de gradul I a Botswanei. Reședin...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁districtul ▁gh an zi ▁este ▁o ▁unitate ▁administrativă ▁de ▁gradul ... (+20 more)` | 30 |
| 16k | `▁districtul ▁gh an zi ▁este ▁o ▁unitate ▁administrativă ▁de ▁gradul ... (+18 more)` | 28 |
| 32k | `▁districtul ▁gh an zi ▁este ▁o ▁unitate ▁administrativă ▁de ▁gradul ... (+16 more)` | 26 |
| 64k | `▁districtul ▁gh anzi ▁este ▁o ▁unitate ▁administrativă ▁de ▁gradul ▁i ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 4.390x compression
- **Lowest UNK Rate:** 8k with 0.0794% 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 | 205,060 | 17.65 | 2,532,825 | 7.4% | 20.1% |
| **2-gram** | Subword | 292 🏆 | 8.19 | 25,018 | 66.3% | 98.8% |
| **3-gram** | Word | 766,050 | 19.55 | 5,498,790 | 4.2% | 13.3% |
| **3-gram** | Subword | 2,777 | 11.44 | 204,577 | 23.4% | 68.1% |
| **4-gram** | Word | 1,571,159 | 20.58 | 9,773,331 | 4.5% | 12.6% |
| **4-gram** | Subword | 18,034 | 14.14 | 1,231,714 | 10.9% | 33.7% |
| **5-gram** | Word | 1,108,597 | 20.08 | 7,317,897 | 5.4% | 14.9% |
| **5-gram** | Subword | 81,535 | 16.32 | 4,440,105 | 5.8% | 19.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a fost` | 808,239 |
| 2 | `de la` | 359,725 |
| 3 | `și a` | 251,044 |
| 4 | `s a` | 242,444 |
| 5 | `este un` | 233,222 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `note vezi și` | 91,186 |
| 2 | `vezi și lista` | 71,949 |
| 3 | `este o comună` | 70,187 |
| 4 | `note legături externe` | 60,989 |
| 5 | `o populație de` | 60,015 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n a n a` | 56,941 |
| 2 | `a n a n` | 55,498 |
| 3 | `sit de importanță comunitară` | 47,608 |
| 4 | `este o comună în` | 46,035 |
| 5 | `note vezi și lista` | 40,899 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n a n a` | 55,482 |
| 2 | `n a n a n` | 55,475 |
| 3 | `vezi și lista comunelor din` | 35,488 |
| 4 | `în avea o populație de` | 35,072 |
| 5 | `o populație de de locuitori` | 31,758 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 28,265,039 |
| 2 | `a _` | 18,155,605 |
| 3 | `i _` | 15,711,698 |
| 4 | `_ d` | 15,332,304 |
| 5 | `_ a` | 15,214,376 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 8,942,495 |
| 2 | `d e _` | 7,054,943 |
| 3 | `_ î n` | 5,914,607 |
| 4 | `u l _` | 4,805,326 |
| 5 | `t e _` | 4,562,704 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 6,660,386 |
| 2 | `_ î n _` | 4,262,099 |
| 3 | `_ ș i _` | 3,485,100 |
| 4 | `_ d i n` | 2,798,373 |
| 5 | `d i n _` | 2,518,101 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i n _` | 2,482,885 |
| 2 | `e _ d e _` | 1,594,240 |
| 3 | `u l u i _` | 1,386,476 |
| 4 | `e s t e _` | 1,341,205 |
| 5 | `_ e s t e` | 1,226,918 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 292
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~19% 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 | 1.0073 | 2.010 | 13.21 | 2,248,490 | 0.0% |
| **1** | Subword | 1.1788 | 2.264 | 8.48 | 12,070 | 0.0% |
| **2** | Word | 0.3854 | 1.306 | 2.43 | 29,656,166 | 61.5% |
| **2** | Subword | 0.6779 | 1.600 | 4.67 | 102,322 | 32.2% |
| **3** | Word | 0.1722 | 1.127 | 1.41 | 71,943,902 | 82.8% |
| **3** | Subword | 0.7466 | 1.678 | 4.47 | 477,697 | 25.3% |
| **4** | Word | 0.0757 🏆 | 1.054 | 1.14 | 100,959,109 | 92.4% |
| **4** | Subword | 0.7131 | 1.639 | 3.72 | 2,133,043 | 28.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de mâl limosa lapponica gușă roșie fondat sau de științe of a fost cel mai putut`
2. `în este vizibil de de jos prezintă o anchetă jafurile venite fiind înlocuite cu fecalele umane`
3. `a populației localității tomașivka andriivka în la mână în armata roșie a a permite utilizatorilor c...`

**Context Size 2:**

1. `a fost numit asistent la disciplina giuridica delle onorificenze cavalleresche nota a comentând mai ...`
2. `de la modestul preț de către uniunea sovietică comandanți supremi după încheierea primului război mo...`
3. `și a celei de a șaptea printre care nows the time of the world spider catalog platnick`

**Context Size 3:**

1. `note vezi și lista comunelor din charente din charente`
2. `vezi și lista comunelor din provincia caltanissetta din provincia caltanissetta din provincia caltan...`
3. `este o comună din landul renania palatinat germania din renania palatinat germania din renania de no...`

**Context Size 4:**

1. `n a n a n a n a n a n a n a n a n a n`
2. `a n a n a n a n a n a n a n a n a n a`
3. `sit de importanță comunitară în pentru a proteja 1 specie de animale situl a fost protejat și ca ari...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_wintocie,_îm_tr`
2. `eniul_ଭାଦ୍ରବର୍ଷା_fg._a`
3. `iafă_diidiulanng`

**Context Size 2:**

1. `e_clațărie_dineto`
2. `a_întustele_dovtá`
3. `i_dențăralkune_op`

**Context Size 3:**

1. `_de_timporțelea_pe`
2. `de_joc_o_scu_20._v`
3. `_în_trum._i._trang`

**Context Size 4:**

1. `_de_iluzional_terne`
2. `_în_prevăzute_în_ar`
3. `_și_svensiunea_și_d`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,133,043 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 | 1,063,320 |
| Total Tokens | 148,931,070 |
| Mean Frequency | 140.06 |
| Median Frequency | 4 |
| Frequency Std Dev | 10923.94 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 6,793,212 |
| 2 | în | 4,430,805 |
| 3 | a | 4,231,898 |
| 4 | și | 3,652,227 |
| 5 | din | 2,514,433 |
| 6 | la | 2,115,037 |
| 7 | o | 1,474,530 |
| 8 | cu | 1,397,534 |
| 9 | este | 1,225,578 |
| 10 | pe | 1,161,786 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | dyschronia | 2 |
| 2 | 藍より群青 | 2 |
| 3 | sklshōter | 2 |
| 4 | mawaru | 2 |
| 5 | penguindrum | 2 |
| 6 | gyukaku | 2 |
| 7 | yūshō | 2 |
| 8 | nittere | 2 |
| 9 | もうどうなってもいいや | 2 |
| 10 | moonlightspeed | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9601 |
| R² (Goodness of Fit) | 0.997513 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 35.0% |
| Top 1,000 | 55.0% |
| Top 5,000 | 71.4% |
| Top 10,000 | 78.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9975 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 35.0% of corpus
- **Long Tail:** 1,053,320 words needed for remaining 21.5% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.7633 🏆 | 0.3701 | N/A | N/A |
| **mono_64d** | 64 | 0.7375 | 0.2901 | N/A | N/A |
| **mono_128d** | 128 | 0.6913 | 0.2301 | N/A | N/A |
| **aligned_32d** | 32 | 0.7633 | 0.3630 | 0.4660 | 0.8300 |
| **aligned_64d** | 64 | 0.7375 | 0.2868 | 0.6720 | 0.9220 |
| **aligned_128d** | 128 | 0.6913 | 0.2408 | 0.8020 | 0.9680 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7633 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2968. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 80.2% 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 | **-0.235** | 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` | sogodianus, sénaillac, seymours |
| `-a` | adile, aethionema, adjudecător |
| `-m` | meryamun, midnattens, maletici |
| `-ma` | maletici, malinivka, mayura |
| `-b` | bosak, barwice, buildinguri |
| `-p` | preacinstitul, posljednji, preservarea |
| `-c` | cluentius, catalige, collesano |
| `-k` | kerestur, klosterwald, korzeniewski |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | demontare, disunitae, adile |
| `-i` | posljednji, urșii, parahnevîci |
| `-a` | preservarea, naadokila, aethionema |
| `-s` | sogodianus, seymours, cluentius |
| `-n` | meryamun, pinson, seddon |
| `-r` | tecar, patelar, adjudecător |
| `-l` | preacinstitul, perforatorul, piroluzitul |
| `-le` | adile, cătanele, générale |

### 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 |
|------|----------|------------------|----------|
| `itat` | 1.81x | 410 contexts | uitat, mitat, itata |
| `omân` | 2.37x | 83 contexts | român, români, românt |
| `nter` | 1.60x | 441 contexts | anter, inter, enter |
| `orul` | 1.74x | 188 contexts | forul, porul, horul |
| `reșt` | 1.76x | 132 contexts | creșt, rești, crești |
| `stru` | 1.39x | 360 contexts | strum, struś, astru |
| `embr` | 1.67x | 128 contexts | membr, embry, embru |
| `ătur` | 1.57x | 169 contexts | mătur, bătură, pătura |
| `înce` | 1.96x | 56 contexts | încet, încep, începă |
| `ific` | 1.38x | 305 contexts | tific, ificle, tifici |
| `ații` | 1.63x | 125 contexts | jații, tații, nații |
| `ităț` | 1.86x | 59 contexts | unități, zeități, legități |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-e` | 106 words | politechnique, podlešje |
| `-s` | `-e` | 101 words | superspațiile, shadowmachine |
| `-s` | `-i` | 84 words | sanguigni, senaatintori |
| `-a` | `-a` | 83 words | adâncimea, alivepasărea |
| `-s` | `-a` | 83 words | saitta, sidusa |
| `-c` | `-e` | 82 words | capoise, concetrate |
| `-c` | `-i` | 76 words | climaxului, calmuri |
| `-a` | `-e` | 75 words | antiastmatice, ardiège |
| `-c` | `-a` | 75 words | ciobănia, ctla |
| `-p` | `-a` | 73 words | pannonica, pampana |

### 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 |
|------|-----------------|------------|------|
| cooperage | **`coopera-g-e`** | 7.5 | `g` |
| trebuinta | **`trebui-n-ta`** | 7.5 | `n` |
| montesson | **`montes-s-on`** | 7.5 | `s` |
| dobropillea | **`dobropil-le-a`** | 7.5 | `le` |
| încercari | **`încerc-a-ri`** | 7.5 | `a` |
| trangensis | **`trangen-s-is`** | 7.5 | `s` |
| eliminatorieplay | **`eliminatoriepl-a-y`** | 7.5 | `a` |
| eishöhlen | **`eishöh-le-n`** | 7.5 | `le` |
| professor | **`profes-s-or`** | 7.5 | `s` |
| caterinei | **`caterin-e-i`** | 7.5 | `e` |
| bivittata | **`bivit-ta-ta`** | 7.5 | `ta` |
| enterotoxină | **`enterotoxi-n-ă`** | 7.5 | `n` |
| villexavier | **`villexav-i-er`** | 7.5 | `i` |
| arixeniidae | **`arixeniid-a-e`** | 7.5 | `a` |
| molligodai | **`molligod-a-i`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Romanian 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 (4.39x) |
| N-gram | **2-gram** | Lowest perplexity (292) |
| Markov | **Context-4** | Highest predictability (92.4%) |
| 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: 2026-01-17 02:43:30*