README.md

---
language: oc
language_name: Occitan
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: 4.442
  - name: best_isotropy
    type: isotropy
    value: 0.7759
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Occitan** 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** | 3.591x | 3.59 | 0.0580% | 1,039,006 |
| **16k** | 3.939x | 3.94 | 0.0637% | 947,222 |
| **32k** | 4.234x | 4.24 | 0.0684% | 881,100 |
| **64k** | 4.442x 🏆 | 4.44 | 0.0718% | 839,942 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Lucas Reiner (n. es un actor e productor de cinèma american. american a Los Ange...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lu cas ▁rein er ▁( n . ▁es ▁un ▁actor ... (+11 more)` | 21 |
| 16k | `▁lu cas ▁rein er ▁( n . ▁es ▁un ▁actor ... (+11 more)` | 21 |
| 32k | `▁lucas ▁rein er ▁( n . ▁es ▁un ▁actor ▁e ... (+10 more)` | 20 |
| 64k | `▁lucas ▁reiner ▁( n . ▁es ▁un ▁actor ▁e ▁productor ... (+9 more)` | 19 |

**Sample 2:** `Altwis es un vilatjòt, e comuna soïssa, situat dins lo districte d'Hochdorf, e l...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁alt w is ▁es ▁un ▁vilat j òt , ▁e ... (+29 more)` | 39 |
| 16k | `▁alt wis ▁es ▁un ▁vilat j òt , ▁e ▁comuna ... (+26 more)` | 36 |
| 32k | `▁alt wis ▁es ▁un ▁vilatjòt , ▁e ▁comuna ▁soïssa , ... (+24 more)` | 34 |
| 64k | `▁alt wis ▁es ▁un ▁vilatjòt , ▁e ▁comuna ▁soïssa , ... (+22 more)` | 32 |

**Sample 3:** `Puebla de la Calzada es un municipi de la província espanhòla de Badajoz e de la...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pu eb la ▁de ▁la ▁cal z ada ▁es ▁un ... (+19 more)` | 29 |
| 16k | `▁pu eb la ▁de ▁la ▁cal zada ▁es ▁un ▁municipi ... (+15 more)` | 25 |
| 32k | `▁puebla ▁de ▁la ▁cal zada ▁es ▁un ▁municipi ▁de ▁la ... (+13 more)` | 23 |
| 64k | `▁puebla ▁de ▁la ▁calzada ▁es ▁un ▁municipi ▁de ▁la ▁província ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.442x compression
- **Lowest UNK Rate:** 8k with 0.0580% 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 | 40,858 | 15.32 | 382,833 | 16.0% | 32.3% |
| **2-gram** | Subword | 256 🏆 | 8.00 | 9,724 | 69.1% | 99.1% |
| **3-gram** | Word | 99,251 | 16.60 | 691,705 | 13.3% | 25.5% |
| **3-gram** | Subword | 2,095 | 11.03 | 74,490 | 29.1% | 73.4% |
| **4-gram** | Word | 144,878 | 17.14 | 1,152,073 | 14.3% | 26.4% |
| **4-gram** | Subword | 11,826 | 13.53 | 411,965 | 14.7% | 42.1% |
| **5-gram** | Word | 78,202 | 16.25 | 807,722 | 17.0% | 32.1% |
| **5-gram** | Subword | 46,870 | 15.52 | 1,292,254 | 8.9% | 27.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la` | 213,501 |
| 2 | `de l` | 104,259 |
| 3 | `es una` | 53,804 |
| 4 | `e la` | 52,175 |
| 5 | `dins lo` | 51,918 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `es una comuna` | 35,541 |
| 2 | `e monuments personalitats` | 35,308 |
| 3 | `monuments personalitats ligadas` | 31,330 |
| 4 | `e la region` | 31,001 |
| 5 | `ligams extèrnes nòtas` | 30,871 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e monuments personalitats ligadas` | 31,329 |
| 2 | `luòcs e monuments personalitats` | 29,121 |
| 3 | `ligadas amb la comuna` | 28,401 |
| 4 | `personalitats ligadas amb la` | 28,400 |
| 5 | `monuments personalitats ligadas amb` | 27,977 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `personalitats ligadas amb la comuna` | 28,398 |
| 2 | `e monuments personalitats ligadas amb` | 27,976 |
| 3 | `monuments personalitats ligadas amb la` | 27,973 |
| 4 | `luòcs e monuments personalitats ligadas` | 27,614 |
| 5 | `demografia luòcs e monuments personalitats` | 27,263 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 3,234,853 |
| 2 | `e _` | 3,172,126 |
| 3 | `s _` | 3,063,418 |
| 4 | `_ d` | 3,054,602 |
| 5 | `_ l` | 2,264,276 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 2,037,812 |
| 2 | `d e _` | 1,436,433 |
| 3 | `_ l a` | 884,600 |
| 4 | `l a _` | 867,260 |
| 5 | `a s _` | 793,636 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 1,401,348 |
| 2 | `_ l a _` | 689,470 |
| 3 | `d e _ l` | 434,454 |
| 4 | `i o n _` | 370,419 |
| 5 | `a _ d e` | 370,367 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _ l` | 432,360 |
| 2 | `e _ l a _` | 285,044 |
| 3 | `d e _ l a` | 266,977 |
| 4 | `s _ d e _` | 254,104 |
| 5 | `a _ d e _` | 253,709 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 256
- **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 | 0.9719 | 1.961 | 8.13 | 622,832 | 2.8% |
| **1** | Subword | 0.8487 | 1.801 | 5.90 | 5,768 | 15.1% |
| **2** | Word | 0.3692 | 1.292 | 2.14 | 5,057,510 | 63.1% |
| **2** | Subword | 0.7604 | 1.694 | 4.98 | 33,998 | 24.0% |
| **3** | Word | 0.1556 | 1.114 | 1.32 | 10,822,711 | 84.4% |
| **3** | Subword | 0.7496 | 1.681 | 4.18 | 169,232 | 25.0% |
| **4** | Word | 0.0609 🏆 | 1.043 | 1.10 | 14,277,493 | 93.9% |
| **4** | Subword | 0.6863 | 1.609 | 3.33 | 707,794 | 31.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de comunas vesinas e solidaritat s auçant quitament d una comuna veire tanben ligams extèrnes nòtas`
2. `la corona mas es l intoxicacion son concentradas de govèrn francés livre premier estudi meninosa d`
3. `e posicion relativa istòria l entorn istòria revòlta del grand glise est attestée semble que depend`

**Context Size 2:**

1. `de la municipalitat qu es connectat e diferents ph es segon la definicion d un rai de`
2. `de l arnm pòrta l anèl latin digitus annularis det de l industria unica de l union`
3. `es una proprietat sus la luna esquèrra vinheta moïses trencant las taules de la nauta marna e`

**Context Size 3:**

1. `es una comuna francesa del departament de tarn e garona ligams extèrnes nòtas de gironda de la regio...`
2. `e monuments personalitats ligadas amb la comuna véser tanben ligams extèrnes nòtas e referéncias de ...`
3. `monuments personalitats ligadas amb la comuna véser tanben ligams extèrnes nòtas de la nauta garona ...`

**Context Size 4:**

1. `e monuments personalitats ligadas amb la comuna véser tanben ligams extèrnes nòtas dels vòges`
2. `luòcs e monuments personalitats ligadas amb la comuna véser tanben ligams extèrnes nòtas de normandi...`
3. `ligadas amb la comuna véser tanben ligams extèrnes nòtas de normandia de la marga`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_daurenèrd'anaio`
2. `art_deabesime,_p`
3. `e_uzarive_se_ge_`

**Context Size 2:**

1. `a_doppsi_morlà_10`
2. `e_menregièrnasist`
3. `s_panar_mil_de_pl`

**Context Size 3:**

1. `_desfistòria_cap_a`
2. `de_jacque_dismeniv`
3. `_la_(∗)_régions_en`

**Context Size 4:**

1. `_de_la_grat_de_la_c`
2. `_la_fibrairie_e_avi`
3. `de_lieux_forcèt_l'a`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (707,794 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 | 298,767 |
| Total Tokens | 19,561,503 |
| Mean Frequency | 65.47 |
| Median Frequency | 4 |
| Frequency Std Dev | 3567.99 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 1,412,762 |
| 2 | la | 704,581 |
| 3 | e | 516,061 |
| 4 | d | 382,843 |
| 5 | en | 367,851 |
| 6 | lo | 364,128 |
| 7 | l | 357,372 |
| 8 | a | 301,072 |
| 9 | es | 226,360 |
| 10 | un | 196,170 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | shonkinita | 2 |
| 2 | piròp | 2 |
| 3 | lherzolita | 2 |
| 4 | miéj | 2 |
| 5 | mangiato | 2 |
| 6 | ignaure | 2 |
| 7 | langfors | 2 |
| 8 | accouplés | 2 |
| 9 | theodiscus | 2 |
| 10 | nyamuragira | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0382 |
| R² (Goodness of Fit) | 0.998226 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 45.3% |
| Top 1,000 | 64.4% |
| Top 5,000 | 78.5% |
| Top 10,000 | 84.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9982 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 45.3% of corpus
- **Long Tail:** 288,767 words needed for remaining 16.0% 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 | 0.7759 | 0.3605 | N/A | N/A |
| **mono_64d** | 64 | 0.7311 | 0.2808 | N/A | N/A |
| **mono_128d** | 128 | 0.7021 | 0.2184 | N/A | N/A |
| **aligned_32d** | 32 | 0.7759 🏆 | 0.3741 | 0.2480 | 0.6180 |
| **aligned_64d** | 64 | 0.7311 | 0.2733 | 0.3600 | 0.7300 |
| **aligned_128d** | 128 | 0.7021 | 0.2172 | 0.5080 | 0.8180 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7759 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2874. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 50.8% 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 | **0.170** | 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 |
|--------|----------|
| `-a` | arrecebèva, auroish, apròhe |
| `-s` | sfrf, suris, saëns |
| `-ma` | manqueront, mahlkirch, maçacans |
| `-c` | colomberiis, chaohusaurus, campanhard |
| `-b` | bièle, brixey, bartl |
| `-m` | mcgowan, manqueront, mahlkirch |
| `-p` | pennante, pousser, pisuerga |
| `-ca` | campanhard, casalabriva, castelpers |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | suris, kohs, colomberiis |
| `-a` | goja, fonologica, arrecebèva |
| `-e` | pennante, bièle, podiosalicone |
| `-t` | manqueront, projèct, convertissent |
| `-n` | mcgowan, esteron, réligion |
| `-as` | termonuclearas, taças, refractàrias |
| `-es` | ecoulettes, vongnes, neuffontaines |
| `-on` | esteron, réligion, diferencièron |

### 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` | 2.00x | 167 contexts | pitat, gitat, itata |
| `acio` | 2.06x | 128 contexts | acion, bacio, racion |
| `ogra` | 1.83x | 133 contexts | dogra, logran, lograr |
| `raci` | 1.80x | 136 contexts | racim, oraci, braci |
| `tats` | 2.06x | 67 contexts | stats, états, etats |
| `ntre` | 1.86x | 105 contexts | antre, entre, intre |
| `énci` | 2.13x | 49 contexts | éncia, réncia, siéncia |
| `icio` | 1.84x | 83 contexts | licio, vicios, bricio |
| `stra` | 1.35x | 282 contexts | stray, strat, strad |
| `lita` | 1.67x | 94 contexts | litas, elita, clita |
| `anbe` | 2.53x | 19 contexts | anben, tanbe, tanben |
| `tanb` | 2.49x | 19 contexts | tanbn, tanbe, tanban |

### 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` | 210 words | conreats, cippus |
| `-a` | `-s` | 171 words | annexis, annuentes |
| `-p` | `-s` | 168 words | palays, prébois |
| `-s` | `-s` | 126 words | senˈtises, sevas |
| `-c` | `-a` | 119 words | casalta, conoguda |
| `-a` | `-a` | 101 words | abjura, abominabla |
| `-b` | `-s` | 94 words | brindas, barangays |
| `-c` | `-e` | 94 words | colloverge, coroe |
| `-p` | `-a` | 91 words | partidària, plantada |
| `-m` | `-s` | 80 words | meus, majusculas |

### 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 |
|------|-----------------|------------|------|
| velhiment | **`velhi-me-nt`** | 7.5 | `me` |
| hermaphroditism | **`hermaphroditi-s-m`** | 7.5 | `s` |
| tuscaloosa | **`tuscaloo-s-a`** | 7.5 | `s` |
| drepanocitòsi | **`drepanocitò-s-i`** | 7.5 | `s` |
| sarrasiet | **`sarrasi-e-t`** | 7.5 | `e` |
| acomplisca | **`acompli-s-ca`** | 7.5 | `s` |
| daissarem | **`daissar-e-m`** | 7.5 | `e` |
| condusent | **`condus-e-nt`** | 7.5 | `e` |
| étroussat | **`étrous-s-at`** | 7.5 | `s` |
| garrwanas | **`garrw-an-as`** | 7.5 | `an` |
| prehistoria | **`p-re-historia`** | 7.5 | `historia` |
| cerevisiae | **`cerevisi-a-e`** | 7.5 | `a` |
| billinghurst | **`billinghur-s-t`** | 7.5 | `s` |
| europeans | **`europe-an-s`** | 7.5 | `an` |
| cherquesses | **`cherques-s-es`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Occitan 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 (4.44x) |
| N-gram | **2-gram** | Lowest perplexity (256) |
| Markov | **Context-4** | Highest predictability (93.9%) |
| 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 18:02:02*