README.md

---
language: rm
language_name: Romansh
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: 4.365
  - name: best_isotropy
    type: isotropy
    value: 0.8474
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Romansh** 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** | 3.691x | 3.69 | 0.0557% | 645,740 |
| **16k** | 3.994x | 4.00 | 0.0603% | 596,871 |
| **32k** | 4.211x | 4.21 | 0.0636% | 566,002 |
| **64k** | 4.365x 🏆 | 4.37 | 0.0659% | 546,149 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Neyruz-sur-Moudon è ina vischnanca svizra en il chantun Vad en il district Gros-...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁n ey ruz - sur - moudon ▁è ▁ina ▁vischnanca ... (+21 more)` | 31 |
| 16k | `▁neyruz - sur - moudon ▁è ▁ina ▁vischnanca ▁svizra ▁en ... (+19 more)` | 29 |
| 32k | `▁neyruz - sur - moudon ▁è ▁ina ▁vischnanca ▁svizra ▁en ... (+19 more)` | 29 |
| 64k | `▁neyruz - sur - moudon ▁è ▁ina ▁vischnanca ▁svizra ▁en ... (+19 more)` | 29 |

**Sample 2:** `Charmoille e ina fracziun da la vischnanca La Baroche dal chantun Giura en il di...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁char mo ille ▁e ▁ina ▁fracziun ▁da ▁la ▁vischnanca ▁la ... (+16 more)` | 26 |
| 16k | `▁char mo ille ▁e ▁ina ▁fracziun ▁da ▁la ▁vischnanca ▁la ... (+15 more)` | 25 |
| 32k | `▁charmoille ▁e ▁ina ▁fracziun ▁da ▁la ▁vischnanca ▁la ▁baroche ▁dal ... (+13 more)` | 23 |
| 64k | `▁charmoille ▁e ▁ina ▁fracziun ▁da ▁la ▁vischnanca ▁la ▁baroche ▁dal ... (+13 more)` | 23 |

**Sample 3:** `Hérémence è ina citad svizra en il chantun Vallais è ina district Hérens. en il ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁hér é men ce ▁è ▁ina ▁citad ▁svizra ▁en ▁il ... (+14 more)` | 24 |
| 16k | `▁hérémence ▁è ▁ina ▁citad ▁svizra ▁en ▁il ▁chantun ▁vallais ▁è ... (+11 more)` | 21 |
| 32k | `▁hérémence ▁è ▁ina ▁citad ▁svizra ▁en ▁il ▁chantun ▁vallais ▁è ... (+11 more)` | 21 |
| 64k | `▁hérémence ▁è ▁ina ▁citad ▁svizra ▁en ▁il ▁chantun ▁vallais ▁è ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.365x compression
- **Lowest UNK Rate:** 8k with 0.0557% unknown tokens
- **Trade-off:** Larger vocabularies improve compression but increase model size
- **Recommendation:** 32k vocabulary provides optimal balance for production use

---
## 2. N-gram Model Evaluation

![N-gram Perplexity](visualizations/ngram_perplexity.png)

![N-gram Unique](visualizations/ngram_unique.png)

![N-gram Coverage](visualizations/ngram_coverage.png)

### Results

| N-gram | Variant | Perplexity | Entropy | Unique N-grams | Top-100 Coverage | Top-1000 Coverage |
|--------|---------|------------|---------|----------------|------------------|-------------------|
| **2-gram** | Word | 17,916 | 14.13 | 74,933 | 14.7% | 35.1% |
| **2-gram** | Subword | 230 🏆 | 7.85 | 3,376 | 70.8% | 99.4% |
| **3-gram** | Word | 53,185 | 15.70 | 119,039 | 6.2% | 19.2% |
| **3-gram** | Subword | 1,797 | 10.81 | 27,903 | 30.0% | 75.9% |
| **4-gram** | Word | 94,120 | 16.52 | 161,618 | 4.4% | 13.1% |
| **4-gram** | Subword | 9,576 | 13.23 | 144,146 | 14.9% | 43.5% |
| **5-gram** | Word | 54,308 | 15.73 | 84,789 | 5.6% | 15.5% |
| **5-gram** | Subword | 34,278 | 15.07 | 382,834 | 8.4% | 26.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `da la` | 32,817 |
| 2 | `da l` | 19,781 |
| 3 | `en il` | 16,052 |
| 4 | `en la` | 9,522 |
| 5 | `da las` | 8,260 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `en il chantun` | 2,817 |
| 2 | `ultra da quai` | 1,397 |
| 3 | `svizra en il` | 1,207 |
| 4 | `è ina vischnanca` | 1,203 |
| 5 | `en l europa` | 1,148 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `svizra en il chantun` | 1,050 |
| 2 | `en il chantun vad` | 779 |
| 3 | `è ina vischnanca svizra` | 586 |
| 4 | `vischnanca svizra en il` | 585 |
| 5 | `è ina vischnanca politica` | 584 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ina vischnanca svizra en il` | 583 |
| 2 | `è ina vischnanca svizra en` | 582 |
| 3 | `vischnanca svizra en il chantun` | 565 |
| 4 | `è ina vischnanca politica svizra` | 508 |
| 5 | `vischnanca politica svizra en il` | 484 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 758,306 |
| 2 | `s _` | 412,089 |
| 3 | `_ d` | 368,200 |
| 4 | `n _` | 345,394 |
| 5 | `d a` | 340,317 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a` | 247,757 |
| 2 | `d a _` | 210,483 |
| 3 | `_ l a` | 159,443 |
| 4 | `l a _` | 151,625 |
| 5 | `a s _` | 133,920 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a _` | 165,902 |
| 2 | `_ l a _` | 117,111 |
| 3 | `_ i l _` | 76,863 |
| 4 | `d a _ l` | 68,179 |
| 5 | `_ e n _` | 64,184 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a _ l` | 65,677 |
| 2 | `a _ l a _` | 48,613 |
| 3 | `d a _ l a` | 43,880 |
| 4 | `a _ d a _` | 41,853 |
| 5 | `_ d a l _` | 40,324 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 230
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~27% 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 | 1.0978 | 2.140 | 8.07 | 124,534 | 0.0% |
| **1** | Subword | 1.2098 | 2.313 | 10.41 | 715 | 0.0% |
| **2** | Word | 0.3787 | 1.300 | 2.03 | 1,003,829 | 62.1% |
| **2** | Subword | 1.0702 | 2.100 | 6.71 | 7,436 | 0.0% |
| **3** | Word | 0.1550 | 1.113 | 1.30 | 2,037,689 | 84.5% |
| **3** | Subword | 0.9144 | 1.885 | 4.63 | 49,875 | 8.6% |
| **4** | Word | 0.0598 🏆 | 1.042 | 1.09 | 2,637,985 | 94.0% |
| **4** | Subword | 0.7105 | 1.636 | 3.08 | 231,080 | 29.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `da chasa nova relaziun tranter ils liuns ma a moda optimala dal 18avel tschientaner èn vastas`
2. `la frantscha da meters pudaiva l osce è pront per l emprova da stgaudament global wealth`
3. `il palatinat sco terz nivel da la fom vegnivan pretendidas da l enviern utschels aves urden`

**Context Size 2:**

1. `da la pagina center small panorama da hamburg èn ins puspè reavert ina lingia da la musica`
2. `da l akademie der wissenschaften minca p 270 christine lienemann perrin wolfgang lienemann ed politi...`
3. `en il vest latin da la federaziun da medis ed ospitals privats il tractament dal retg pippin`

**Context Size 3:**

1. `en il chantun vallais dal chantun vallais en il chantun tessin vischnancas svizras maggia`
2. `ultra da quai il concept da la strategia u da la tora la quala furma l emprim epos`
3. `svizra en il chantun friburg en il district jura nord vaudois en il chantun vad en il district`

**Context Size 4:**

1. `svizra en il chantun vad en il district nyon en il chantun vad dal chantun vad`
2. `en il chantun vad dal chantun vad`
3. `è ina vischnanca svizra en il chantun tessin che appartegna al circul verzasca dal district locarno ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_c_castaun:_s_ch`
2. `a_iolasil_ialèn_`
3. `ig_ilema_sgn_rim`

**Context Size 2:**

1. `a_che_betg_un_las`
2. `s_p._ofarling_prü`
3. `_da_l’il_co_er,_d`

**Context Size 3:**

1. `_da_nadella_gronis`
2. `da_la_dal_probalk:`
3. `_la_da_diffenser_l`

**Context Size 4:**

1. `_da_s._p._38s._part`
2. `_la_mauren_ha_il_cu`
3. `_il_territoric_è_la`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (231,080 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 | 63,266 |
| Total Tokens | 3,028,553 |
| Mean Frequency | 47.87 |
| Median Frequency | 4 |
| Frequency Std Dev | 1094.76 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | da | 166,290 |
| 2 | la | 118,196 |
| 3 | il | 79,956 |
| 4 | l | 69,320 |
| 5 | en | 67,320 |
| 6 | e | 53,149 |
| 7 | dal | 40,449 |
| 8 | a | 39,768 |
| 9 | è | 33,261 |
| 10 | ils | 31,735 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | planisadra | 2 |
| 2 | hzr | 2 |
| 3 | khizr | 2 |
| 4 | pereslawl | 2 |
| 5 | zalesskij | 2 |
| 6 | tawjihi | 2 |
| 7 | gate | 2 |
| 8 | palestinians | 2 |
| 9 | tregua | 2 |
| 10 | cumpusiziun | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0749 |
| R² (Goodness of Fit) | 0.994918 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 45.9% |
| Top 1,000 | 68.3% |
| Top 5,000 | 84.5% |
| Top 10,000 | 90.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9949 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 45.9% of corpus
- **Long Tail:** 53,266 words needed for remaining 9.7% 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 | 0.8474 | 0.3419 | N/A | N/A |
| **mono_64d** | 64 | 0.8324 | 0.2577 | N/A | N/A |
| **mono_128d** | 128 | 0.8002 | 0.1915 | N/A | N/A |
| **aligned_32d** | 32 | 0.8474 🏆 | 0.3398 | 0.1380 | 0.4520 |
| **aligned_64d** | 64 | 0.8324 | 0.2625 | 0.2280 | 0.5880 |
| **aligned_128d** | 128 | 0.8002 | 0.1883 | 0.2940 | 0.6020 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8474 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2636. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 29.4% 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 | **-0.421** | 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` | sylvain, socialdemocratica, strobl |
| `-a` | ams, aristocrazia, average |
| `-p` | promoturs, passione, pandemias |
| `-b` | breton, bloccadas, brünisried |
| `-c` | communal, champester, consecrar |
| `-m` | magistrat, moëns, metallurgia |
| `-d` | demokratisches, dero, deditgà |
| `-g` | gruscha, gründliche, grammaticalas |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | ams, moëns, helveticarchives |
| `-a` | socialdemocratica, aristocrazia, metallurgia |
| `-n` | sylvain, breton, tessin |
| `-as` | explitgadas, aviartas, organellas |
| `-r` | champester, consecrar, terrur |
| `-e` | älteste, average, homme |
| `-t` | magistrat, rendaquint, industriegesellschaft |
| `-er` | champester, schindler, hausberger |

### 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 |
|------|----------|------------------|----------|
| `itad` | 2.01x | 54 contexts | mitad, citad, citads |
| `ment` | 1.73x | 88 contexts | mument, dement, mentis |
| `usch` | 1.62x | 86 contexts | kusch, uschè, cusch |
| `tica` | 1.71x | 62 contexts | etica, antica, betica |
| `aziu` | 1.71x | 53 contexts | naziun, raziun, grazius |
| `urma` | 1.84x | 37 contexts | furma, burma, surmar |
| `ntan` | 1.71x | 42 contexts | entant, sentan, muntan |
| `egni` | 1.68x | 42 contexts | regni, vegni, tegnia |
| `iuns` | 2.11x | 18 contexts | liuns, aviuns, uniuns |
| `ents` | 1.74x | 33 contexts | dents, vents, cents |
| `furm` | 1.57x | 47 contexts | furma, furmo, furmà |
| `nter` | 1.40x | 65 contexts | unter, enter, inter |

### 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` | `-s` | 216 words | civitates, carstgauns |
| `-s` | `-s` | 202 words | sillogissems, soluziuns |
| `-p` | `-s` | 163 words | polineices, playmates |
| `-s` | `-a` | 161 words | spendra, spezialisada |
| `-c` | `-a` | 148 words | cortina, charenta |
| `-p` | `-a` | 138 words | primministra, preferescha |
| `-a` | `-s` | 131 words | atletas, abstractas |
| `-s` | `-n` | 111 words | seen, selen |
| `-m` | `-s` | 107 words | mémoires, misteris |
| `-d` | `-s` | 97 words | diabetes, digerids |

### 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 |
|------|-----------------|------------|------|
| modernism | **`moderni-s-m`** | 7.5 | `s` |
| promontori | **`promonto-r-i`** | 7.5 | `r` |
| democratisà | **`democrati-s-à`** | 7.5 | `s` |
| chamutsch | **`chamut-s-ch`** | 7.5 | `s` |
| mediatisà | **`mediati-s-à`** | 7.5 | `s` |
| hollandse | **`holland-s-e`** | 7.5 | `s` |
| novreligiusas | **`novreligiu-s-as`** | 7.5 | `s` |
| cinquesensi | **`cinquesen-s-i`** | 7.5 | `s` |
| victoriusas | **`victoriu-s-as`** | 7.5 | `s` |
| pretensiusas | **`pretensiu-s-as`** | 7.5 | `s` |
| extravagant | **`extravag-a-nt`** | 7.5 | `a` |
| naziunelas | **`naziun-el-as`** | 6.0 | `naziun` |
| mesiradas | **`mesira-da-s`** | 6.0 | `mesira` |
| daventond | **`davent-on-d`** | 6.0 | `davent` |
| traversavan | **`traversa-va-n`** | 6.0 | `traversa` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Romansh 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 (4.36x) |
| N-gram | **2-gram** | Lowest perplexity (230) |
| Markov | **Context-4** | Highest predictability (94.0%) |
| 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 18:48:27*