README.md

---
language: nap
language_name: Neapolitan
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: 3.920
  - name: best_isotropy
    type: isotropy
    value: 0.8038
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Neapolitan** 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** | 3.334x | 3.34 | 0.0273% | 157,778 |
| **16k** | 3.567x | 3.57 | 0.0292% | 147,487 |
| **32k** | 3.772x | 3.78 | 0.0308% | 139,478 |
| **64k** | 3.920x 🏆 | 3.93 | 0.0320% | 134,201 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Roccagorga è nu comune 'e crestiane da pruvincia 'e Latina. da pruvincia 'e Lati...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁rocca gor ga ▁è ▁nu ▁comune ▁' e ▁crestiane ▁da ... (+18 more)` | 28 |
| 16k | `▁rocca gor ga ▁è ▁nu ▁comune ▁' e ▁crestiane ▁da ... (+18 more)` | 28 |
| 32k | `▁rocca gor ga ▁è ▁nu ▁comune ▁' e ▁crestiane ▁da ... (+18 more)` | 28 |
| 64k | `▁rocca gorga ▁è ▁nu ▁comune ▁' e ▁crestiane ▁da ▁pruvincia ... (+17 more)` | 27 |

**Sample 2:** `Osini è nu comune 'e 947 crestiane da pruvincia 'e Ogliastra. pruvincia 'e Oglia...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁o sini ▁è ▁nu ▁comune ▁' e ▁ 9 4 ... (+18 more)` | 28 |
| 16k | `▁o sini ▁è ▁nu ▁comune ▁' e ▁ 9 4 ... (+18 more)` | 28 |
| 32k | `▁o sini ▁è ▁nu ▁comune ▁' e ▁ 9 4 ... (+18 more)` | 28 |
| 64k | `▁o sini ▁è ▁nu ▁comune ▁' e ▁ 9 4 ... (+18 more)` | 28 |

**Sample 3:** `Cu 'a canzona Mare verde, Mario Trevi e Milva se piazzajeno 'o siconno posto ô G...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cu ▁' a ▁canzona ▁mare ▁verde , ▁mario ▁trevi ▁e ... (+16 more)` | 26 |
| 16k | `▁cu ▁' a ▁canzona ▁mare ▁verde , ▁mario ▁trevi ▁e ... (+16 more)` | 26 |
| 32k | `▁cu ▁' a ▁canzona ▁mare ▁verde , ▁mario ▁trevi ▁e ... (+15 more)` | 25 |
| 64k | `▁cu ▁' a ▁canzona ▁mare ▁verde , ▁mario ▁trevi ▁e ... (+13 more)` | 23 |


### Key Findings

- **Best Compression:** 64k achieves 3.920x compression
- **Lowest UNK Rate:** 8k with 0.0273% 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 | 1,553 | 10.60 | 14,483 | 42.3% | 65.9% |
| **2-gram** | Subword | 233 🏆 | 7.86 | 2,804 | 70.9% | 99.1% |
| **3-gram** | Word | 1,319 | 10.37 | 17,108 | 45.9% | 70.7% |
| **3-gram** | Subword | 1,644 | 10.68 | 21,244 | 34.8% | 77.4% |
| **4-gram** | Word | 1,944 | 10.93 | 26,074 | 40.9% | 70.8% |
| **4-gram** | Subword | 7,694 | 12.91 | 97,053 | 23.1% | 48.2% |
| **5-gram** | Word | 2,009 | 10.97 | 18,790 | 35.5% | 73.0% |
| **5-gram** | Subword | 22,083 | 14.43 | 219,213 | 19.9% | 35.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `categoria comune` | 17,776 |
| 2 | `pruvincia e` | 16,185 |
| 3 | `da pruvincia` | 14,509 |
| 4 | `comune e` | 13,766 |
| 5 | `comune da` | 11,499 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `da pruvincia e` | 14,465 |
| 2 | `categoria comune da` | 11,374 |
| 3 | `è nu comune` | 7,948 |
| 4 | `nu comune e` | 7,776 |
| 5 | `e l italia` | 6,831 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `è nu comune e` | 7,772 |
| 2 | `comune da pruvincia e` | 5,907 |
| 3 | `categoria comune e l` | 5,901 |
| 4 | `comune e l italia` | 5,901 |
| 5 | `categoria comune da pruvincia` | 5,899 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `categoria comune e l italia` | 5,901 |
| 2 | `categoria comune da pruvincia e` | 5,899 |
| 3 | `e abitante da pruvincia e` | 3,717 |
| 4 | `è nu comune e e` | 2,507 |
| 5 | `nu comune e e abitante` | 2,506 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 256,791 |
| 2 | `a _` | 167,602 |
| 3 | `o _` | 102,609 |
| 4 | `_ c` | 99,915 |
| 5 | `_ '` | 94,748 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `' e _` | 63,827 |
| 2 | `_ ' e` | 63,192 |
| 3 | `n e _` | 60,363 |
| 4 | `_ c a` | 40,897 |
| 5 | `e _ d` | 34,274 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ' e _` | 63,082 |
| 2 | `u n e _` | 28,433 |
| 3 | `m u n e` | 27,493 |
| 4 | `c o m u` | 26,319 |
| 5 | `o m u n` | 26,310 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `m u n e _` | 27,267 |
| 2 | `c o m u n` | 26,309 |
| 3 | `o m u n e` | 26,017 |
| 4 | `e _ ' e _` | 25,239 |
| 5 | `a _ ' e _` | 21,668 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 233
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.7129 | 1.639 | 4.16 | 90,826 | 28.7% |
| **1** | Subword | 0.9473 | 1.928 | 7.06 | 1,028 | 5.3% |
| **2** | Word | 0.2155 | 1.161 | 1.48 | 376,611 | 78.5% |
| **2** | Subword | 0.9373 | 1.915 | 5.69 | 7,253 | 6.3% |
| **3** | Word | 0.0686 | 1.049 | 1.11 | 555,576 | 93.1% |
| **3** | Subword | 0.8624 | 1.818 | 4.10 | 41,221 | 13.8% |
| **4** | Word | 0.0236 🏆 | 1.016 | 1.04 | 613,933 | 97.6% |
| **4** | Subword | 0.6629 | 1.583 | 2.73 | 168,878 | 33.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `e pallone taliano d o salvador grenada o primmo decennio d italia marocco 16 ac 57`
2. `a suoja se mpara l m giugrafia categoria comune e la štrada rëggiunal 509 e francesco`
3. `comune da pruvincia e l italia teen angels fall first lady starlight e silenzio cantatore museca`

**Context Size 2:**

1. `categoria comune e crestiane da pruvincia e messina categoria comune da pruvincia e padova categoria...`
2. `pruvincia e messina categoria comune e 191 e abitante da pruvincia e arrezzo categoria comune da reg...`
3. `da pruvincia e ancona categoria comune da reggione veneto categoria comune e crestiane da pruvincia ...`

**Context Size 3:**

1. `da pruvincia e teramo è na pruvincia da reggione autonoma da zardegna categoria comune e l italia o`
2. `categoria comune da pruvincia e rovigo categoria comune da reggione veneto categoria comune e l ital...`
3. `è nu comune e e abitante da pruvincia e brescia categoria comune da reggione pùglia categoria comune...`

**Context Size 4:**

1. `è nu comune e e abitante da pruvincia e torino categoria comune da pruvincia e brescia categoria com...`
2. `comune da pruvincia e cuneo categoria comune da pruvincia e pavia categoria comune da pruvincia e ta...`
3. `categoria comune e l italia nutarelle`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_d_cionettegggop`
2. `e_'estulliù_25_d`
3. `a_catrtetru_cali`

**Context Size 2:**

1. `e_l_3:21_'ato_'o_`
2. `a_canno_23_1_cune`
3. `o_(quistegordìa_c`

**Context Size 3:**

1. `'e_cano._cano,_and`
2. `_'e_cchiuvasco_fuj`
3. `ne_da_pruvincia_da`

**Context Size 4:**

1. `_'e_se_caglie_nòrd_`
2. `une_rre_casalermo_c`
3. `mune_'e_veneto_club`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (168,878 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 | 36,283 |
| Total Tokens | 817,123 |
| Mean Frequency | 22.52 |
| Median Frequency | 3 |
| Frequency Std Dev | 557.45 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | e | 82,690 |
| 2 | a | 29,343 |
| 3 | comune | 26,008 |
| 4 | da | 25,087 |
| 5 | o | 21,371 |
| 6 | categoria | 20,079 |
| 7 | pruvincia | 16,344 |
| 8 | è | 16,054 |
| 9 | nu | 12,737 |
| 10 | l | 10,986 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | boo | 2 |
| 2 | horror | 2 |
| 3 | nestate | 2 |
| 4 | accumula | 2 |
| 5 | livelli | 2 |
| 6 | pallòne | 2 |
| 7 | fàtte | 2 |
| 8 | orobica | 2 |
| 9 | dacchessì | 2 |
| 10 | totàle | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0191 |
| R² (Goodness of Fit) | 0.998411 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 51.9% |
| Top 1,000 | 71.4% |
| Top 5,000 | 84.8% |
| Top 10,000 | 90.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9984 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 51.9% of corpus
- **Long Tail:** 26,283 words needed for remaining 9.5% 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 | 0.8038 🏆 | 0.3434 | N/A | N/A |
| **mono_64d** | 64 | 0.5268 | 0.3001 | N/A | N/A |
| **mono_128d** | 128 | 0.1336 | 0.3015 | N/A | N/A |
| **aligned_32d** | 32 | 0.8038 | 0.3363 | 0.0320 | 0.2220 |
| **aligned_64d** | 64 | 0.5268 | 0.3106 | 0.0660 | 0.2860 |
| **aligned_128d** | 128 | 0.1336 | 0.2965 | 0.1240 | 0.3880 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8038 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3147. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 12.4% 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 | **1.085** | 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 |
|--------|----------|
| `-s` | suspira, séa, signure |
| `-c` | cholesterolo, capeto, cë |
| `-a` | avetrana, accummenzanno, avvène |
| `-p` | parla, pajise, porcellana |
| `-m` | mporta, mètte, musolino |
| `-ca` | capeto, cacciá, cartiere |
| `-n` | nucliare, nudo, nsediamiente |
| `-r` | roncalli, racconti, races |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | nucliare, avvène, edifice |
| `-o` | accummenzanno, nudo, cholesterolo |
| `-a` | parla, avetrana, porcellana |
| `-te` | derette, accerette, nsediamiente |
| `-ne` | avvène, guaglione, tròvene |
| `-to` | capeto, conquistato, muderato |
| `-no` | accummenzanno, vomano, musolino |
| `-i` | aeterni, roncalli, shinji |

### 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` | 1.70x | 114 contexts | mette, iette, rette |
| `tali` | 2.05x | 39 contexts | talia, talian, ëtalia |
| `zion` | 1.92x | 45 contexts | azione, frazion, azziona |
| `ione` | 1.92x | 29 contexts | rione, gione, lione |
| `ggio` | 1.65x | 40 contexts | aggio, ggion, maggio |
| `gion` | 1.78x | 27 contexts | gione, ggion, légion |
| `uvin` | 2.19x | 12 contexts | ruvine, pruvinc, pruvinge |
| `inci` | 1.58x | 26 contexts | incis, vinci, mincio |
| `eggi` | 1.34x | 46 contexts | leggi, reggie, leggia |
| `itan` | 1.40x | 37 contexts | titan, titano, aitanic |
| `ital` | 1.53x | 25 contexts | italy, italo, vitale |
| `stia` | 1.70x | 17 contexts | ostia, bastia, bestia |

### 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` | 290 words | cunzèrve, cruate |
| `-c` | `-o` | 229 words | completo, cattoleco |
| `-p` | `-e` | 224 words | perdette, puaése |
| `-a` | `-e` | 218 words | arretiraje, agge |
| `-s` | `-e` | 212 words | setteciénde, specialmente |
| `-c` | `-a` | 177 words | concetta, conca |
| `-a` | `-o` | 170 words | aspettando, arvero |
| `-s` | `-o` | 158 words | socio, severino |
| `-p` | `-o` | 147 words | piccerillo, paleuliteco |
| `-a` | `-a` | 142 words | ammerecana, agordina |

### 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 |
|------|-----------------|------------|------|
| schiavona | **`schiav-o-na`** | 7.5 | `o` |
| montescheno | **`montesch-e-no`** | 7.5 | `e` |
| piccolomini | **`piccolom-i-ni`** | 7.5 | `i` |
| cuntinuato | **`cuntinu-a-to`** | 7.5 | `a` |
| questione | **`questi-o-ne`** | 7.5 | `o` |
| davisvideo | **`davisvid-e-o`** | 7.5 | `e` |
| tenéssene | **`tenés-se-ne`** | 7.5 | `se` |
| aristofane | **`aristof-a-ne`** | 7.5 | `a` |
| macchiaiole | **`macchiai-o-le`** | 7.5 | `o` |
| possebbeletà | **`possebbel-e-tà`** | 7.5 | `e` |
| ucchiarone | **`ucchiar-o-ne`** | 7.5 | `o` |
| recensione | **`recensi-o-ne`** | 7.5 | `o` |
| accuminciaie | **`accumincia-i-e`** | 7.5 | `i` |
| ascensore | **`ascens-o-re`** | 7.5 | `o` |
| prubbecato | **`prubbec-a-to`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Neapolitan 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 (3.92x) |
| N-gram | **2-gram** | Lowest perplexity (233) |
| Markov | **Context-4** | Highest predictability (97.6%) |
| 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 14:48:02*