---
language: pcd
language_name: Picard
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: 3.953
  - name: best_isotropy
    type: isotropy
    value: 0.8716
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Picard** 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** | 3.181x | 3.18 | 0.1032% | 391,604 |
| **16k** | 3.467x | 3.47 | 0.1124% | 359,330 |
| **32k** | 3.721x | 3.72 | 0.1207% | 334,772 |
| **64k** | 3.953x 🏆 | 3.96 | 0.1282% | 315,141 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Mòn·nhioe`d rozhioe , Moénieu des rosieus o Pleupleu, Diåle (Emberiza schoeniclu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁m òn · n h ioe ` d ▁ro z ... (+36 more)` | 46 |
| 16k | `▁m òn · nh ioe ` d ▁ro zh ioe ... (+31 more)` | 41 |
| 32k | `▁m òn · nhioe ` d ▁ro zh ioe ▁, ... (+25 more)` | 35 |
| 64k | `▁mòn · nhioe ` d ▁rozhioe ▁, ▁moénieu ▁des ▁ros ... (+18 more)` | 28 |

**Sample 2:** `Charles Perthane - ch'est un écrivin picard dé Tournai. Pourménade à kain Référi...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁charles ▁pert h ane ▁- ▁ch ' est ▁un ▁écrivin ... (+24 more)` | 34 |
| 16k | `▁charles ▁pert h ane ▁- ▁ch ' est ▁un ▁écrivin ... (+23 more)` | 33 |
| 32k | `▁charles ▁pert hane ▁- ▁ch ' est ▁un ▁écrivin ▁picard ... (+22 more)` | 32 |
| 64k | `▁charles ▁pert hane ▁- ▁ch ' est ▁un ▁écrivin ▁picard ... (+21 more)` | 31 |

**Sample 3:** `Is pinstte eq l’Église al est otchultèe per l’Église modernisse d’aprés Vatican ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁is ▁pins tte ▁eq ▁l ’ église ▁al ▁est ▁ot ... (+16 more)` | 26 |
| 16k | `▁is ▁pins tte ▁eq ▁l ’ église ▁al ▁est ▁ot ... (+15 more)` | 25 |
| 32k | `▁is ▁pinstte ▁eq ▁l ’ église ▁al ▁est ▁ot chult ... (+13 more)` | 23 |
| 64k | `▁is ▁pinstte ▁eq ▁l ’ église ▁al ▁est ▁ot chultèe ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 3.953x compression
- **Lowest UNK Rate:** 8k with 0.1032% 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 | 5,005 | 12.29 | 19,806 | 28.0% | 50.5% |
| **2-gram** | Subword | 313 🏆 | 8.29 | 3,246 | 62.8% | 98.9% |
| **3-gram** | Word | 6,300 | 12.62 | 26,054 | 29.5% | 46.9% |
| **3-gram** | Subword | 2,718 | 11.41 | 24,544 | 24.3% | 67.8% |
| **4-gram** | Word | 12,478 | 13.61 | 49,187 | 26.1% | 38.8% |
| **4-gram** | Subword | 15,376 | 13.91 | 120,683 | 11.7% | 37.2% |
| **5-gram** | Word | 8,364 | 13.03 | 36,813 | 30.5% | 43.5% |
| **5-gram** | Subword | 51,133 | 15.64 | 290,118 | 7.4% | 24.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ch est` | 7,744 |
| 2 | `et pi` | 4,190 |
| 3 | `pi référinches` | 3,217 |
| 4 | `notes pi` | 3,203 |
| 5 | `dins l` | 3,133 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `notes pi référinches` | 3,191 |
| 2 | `ch est un` | 2,136 |
| 3 | `pas d caleus` | 2,130 |
| 4 | `pi référinches loïens` | 1,891 |
| 5 | `référinches loïens intarnètes` | 1,886 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `notes pi référinches loïens` | 1,887 |
| 2 | `pi référinches loïens intarnètes` | 1,873 |
| 3 | `dech pas d caleus` | 1,722 |
| 4 | `pi dins l région` | 1,656 |
| 5 | `monumints pi lius d` | 938 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `notes pi référinches loïens intarnètes` | 1,869 |
| 2 | `chés monumints pi lius d` | 937 |
| 3 | `monumints pi lius d mémoére` | 937 |
| 4 | `d caleus pi dins l` | 864 |
| 5 | `pas d caleus pi dins` | 864 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 155,352 |
| 2 | `s _` | 129,694 |
| 3 | `i n` | 104,008 |
| 4 | `_ d` | 100,660 |
| 5 | `c h` | 91,456 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e s _` | 51,811 |
| 2 | `_ c h` | 40,114 |
| 3 | `_ d e` | 31,189 |
| 4 | `_ p i` | 28,519 |
| 5 | `i n _` | 27,112 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ p i _` | 16,853 |
| 2 | `_ c h '` | 15,871 |
| 3 | `e s t _` | 13,583 |
| 4 | `_ i n _` | 12,048 |
| 5 | `i n s _` | 10,867 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c h é s _` | 9,953 |
| 2 | `_ c h é s` | 8,355 |
| 3 | `d i n s _` | 8,136 |
| 4 | `_ d i n s` | 8,043 |
| 5 | `_ c h ' _` | 7,242 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 313
- **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 | 0.7856 | 1.724 | 4.61 | 96,583 | 21.4% |
| **1** | Subword | 0.7544 | 1.687 | 5.63 | 1,734 | 24.6% |
| **2** | Word | 0.2273 | 1.171 | 1.50 | 443,973 | 77.3% |
| **2** | Subword | 0.8257 | 1.772 | 5.15 | 9,754 | 17.4% |
| **3** | Word | 0.0801 | 1.057 | 1.13 | 663,556 | 92.0% |
| **3** | Subword | 0.8058 | 1.748 | 4.07 | 50,194 | 19.4% |
| **4** | Word | 0.0333 🏆 | 1.023 | 1.05 | 747,772 | 96.7% |
| **4** | Subword | 0.6621 | 1.582 | 2.81 | 204,083 | 33.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `d origine pilipin mariés de la contre neutre pi dins no cite intrèe à louis ch`
2. `l direkcion d mémoére l 15 éd teske ed l région picardie aménistrachon din echl éfant`
3. `ch dessinateu pi michel hamy emmanuelle poiret amiens mémoires de la rue du nord l aller`

**Context Size 2:**

1. `ch est le romant de la statistique et des environs de béthune sud du soudan dousqu au`
2. `et pi al o té bérzillée pindint l batale d adville jean luc vigneux présinte el langue`
3. `notes pi référinches loïens intarnètes catiau l gare pérnes camblin anchiène brasserie malterie dite...`

**Context Size 3:**

1. `notes pi référinches loïens intarnètes hédeuville dseur ch site éd l institut géographique national ...`
2. `ch est un anchien ju d cartes notes l dimainch j allos au cabaret p pou jwer au`
3. `pi référinches loïens intarnètes anmérikin`

**Context Size 4:**

1. `notes pi référinches loïens intarnètes rouvroé édseur l site à l institut des textes et manuscrits m...`
2. `pi référinches loïens intarnètes dech pas d caleus pi dins l région picardie aménistrachon démografi...`
3. `pi dins l région nord pas d caleus aménistrachon nombe ed gins héraldique parti au premier de gueule...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ss_14_e-lité-do`
2. `e_s_so_lotêtoét_`
3. `ileshutotr_ccoom`

**Context Size 2:**

1. `e_:_l'be_=_thés_l`
2. `s_aux_800_0000_mu`
3. `ins_à_cou,_et_une`

**Context Size 3:**

1. `es_l'in_depuis_var`
2. `_ch'_eune_rome_cho`
3. `_del_solisainsch_j`

**Context Size 4:**

1. `_pi_mérachon_diteus`
2. `_ch'_berg,_imprimin`
3. `est_eune_parsonnage`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (204,083 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 | 42,676 |
| Total Tokens | 874,727 |
| Mean Frequency | 20.50 |
| Median Frequency | 3 |
| Frequency Std Dev | 309.45 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | d | 30,264 |
| 2 | l | 24,902 |
| 3 | ch | 19,929 |
| 4 | pi | 16,980 |
| 5 | à | 15,562 |
| 6 | in | 14,862 |
| 7 | est | 13,362 |
| 8 | de | 11,091 |
| 9 | chés | 9,886 |
| 10 | et | 9,764 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | bondes | 2 |
| 2 | benezit | 2 |
| 3 | kukës | 2 |
| 4 | tortuses | 2 |
| 5 | tchière | 2 |
| 6 | commindeu | 2 |
| 7 | sènes | 2 |
| 8 | armonista | 2 |
| 9 | sellerio | 2 |
| 10 | palerme | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0173 |
| R² (Goodness of Fit) | 0.999106 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 44.2% |
| Top 1,000 | 65.9% |
| Top 5,000 | 81.3% |
| Top 10,000 | 87.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9991 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 44.2% of corpus
- **Long Tail:** 32,676 words needed for remaining 12.3% 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 | 0.8716 | 0.3203 | N/A | N/A |
| **mono_64d** | 64 | 0.6802 | 0.2753 | N/A | N/A |
| **mono_128d** | 128 | 0.2264 | 0.2645 | N/A | N/A |
| **aligned_32d** | 32 | 0.8716 🏆 | 0.3221 | 0.0520 | 0.2580 |
| **aligned_64d** | 64 | 0.6802 | 0.2726 | 0.0720 | 0.3580 |
| **aligned_128d** | 128 | 0.2264 | 0.2727 | 0.1360 | 0.4200 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8716 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2879. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 13.6% 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 | **0.802** | High formulaic/idiomatic 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 |
|--------|----------|
| `-a` | arcs, atestè, abistoké |
| `-c` | cro, camanéter, català |
| `-s` | symbolisses, sorrus, shahmukhi |
| `-b` | bonduelle, brochant, bourgache |
| `-p` | partitchulier, poteries, pintatonikes |
| `-d` | devenir, description, délibérer |
| `-m` | moyin, monastique, mêle |
| `-co` | coin, commintateu, coup |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | monastique, linotte, bonduelle |
| `-s` | poteries, pintatonikes, symbolisses |
| `-es` | poteries, pintatonikes, symbolisses |
| `-t` | ressortit, brochant, walincourt |
| `-n` | moyin, description, heineken |
| `-r` | devenir, partitchulier, délibérer |
| `-on` | description, ptilostemon, manillon |
| `-le` | bonduelle, trémoille, mêle |

### 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 |
|------|----------|------------------|----------|
| `ette` | 1.79x | 114 contexts | bette, vette, mette |
| `ques` | 1.90x | 74 contexts | aques, quest, vaques |
| `ranc` | 2.08x | 42 contexts | rance, ranch, franc |
| `ique` | 1.79x | 75 contexts | mique, pique, niquet |
| `nche` | 1.71x | 81 contexts | anche, lanche, panche |
| `anch` | 1.58x | 85 contexts | ranch, anche, lanche |
| `cion` | 1.97x | 31 contexts | nacion, akcion, accion |
| `tion` | 1.84x | 29 contexts | action, option, nation |
| `icar` | 2.13x | 16 contexts | wicar, ricard, picard |
| `ogra` | 1.67x | 26 contexts | beograd, biografe, ortograf |
| `rinc` | 1.59x | 28 contexts | prince, frinco, frincs |
| `cart` | 1.60x | 27 contexts | écart, carta, carte |

### 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` | `-e` | 205 words | comminde, crozète |
| `-c` | `-s` | 177 words | camps, cros |
| `-p` | `-e` | 153 words | pake, prostituèe |
| `-a` | `-e` | 147 words | academie, amiabe |
| `-p` | `-s` | 116 words | picus, porions |
| `-m` | `-e` | 115 words | médiatèke, malade |
| `-d` | `-e` | 105 words | delgorgue, delepine |
| `-s` | `-e` | 97 words | sangiovese, solèye |
| `-m` | `-s` | 95 words | matématikes, mardis |
| `-a` | `-s` | 93 words | ardennes, anthiusses |

### 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 |
|------|-----------------|------------|------|
| essayisse | **`essayis-s-e`** | 7.5 | `s` |
| alexandrins | **`alexandr-in-s`** | 7.5 | `in` |
| carcahutes | **`carcahu-t-es`** | 7.5 | `t` |
| bilderbogen | **`bilderbog-e-n`** | 7.5 | `e` |
| comminchent | **`comminch-e-nt`** | 7.5 | `e` |
| conmunnes | **`conmun-n-es`** | 7.5 | `n` |
| anciennement | **`anciennem-e-nt`** | 7.5 | `e` |
| kilomètres | **`kilomèt-re-s`** | 7.5 | `re` |
| lituanien | **`lituani-e-n`** | 7.5 | `e` |
| albertville | **`albertvi-l-le`** | 7.5 | `l` |
| stevenson | **`steven-s-on`** | 7.5 | `s` |
| vanwelkenhuyzen | **`vanwelkenhuyz-e-n`** | 7.5 | `e` |
| management | **`managem-e-nt`** | 7.5 | `e` |
| pikardien | **`pikardi-e-n`** | 7.5 | `e` |
| richesses | **`riches-s-es`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Picard shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (3.95x) |
| N-gram | **2-gram** | Lowest perplexity (313) |
| Markov | **Context-4** | Highest predictability (96.7%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 17:37:03*