README.md

---
language: pms
language_name: Piedmontese
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: 4.075
  - name: best_isotropy
    type: isotropy
    value: 0.7640
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Piedmontese** 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** | 3.537x | 3.54 | 0.0838% | 171,777 |
| **16k** | 3.769x | 3.77 | 0.0893% | 161,202 |
| **32k** | 3.945x | 3.95 | 0.0935% | 153,994 |
| **64k** | 4.075x 🏆 | 4.08 | 0.0966% | 149,077 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Legnaro a l’é na comun-a ëd la provinsa ëd Pàdoa. Region aministrativa Véneto. S...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁le gn aro ▁a ▁l ’ é ▁na ▁comun - ... (+17 more)` | 27 |
| 16k | `▁le gn aro ▁a ▁l ’ é ▁na ▁comun - ... (+17 more)` | 27 |
| 32k | `▁legn aro ▁a ▁l ’ é ▁na ▁comun - a ... (+16 more)` | 26 |
| 64k | `▁legn aro ▁a ▁l ’ é ▁na ▁comun - a ... (+16 more)` | 26 |

**Sample 2:** `Nozay a l'é 'l nòm: d'un comun fransèis ant ël dipartiment d'Aube d'un comun fra...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁no za y ▁a ▁l ' é ▁' l ▁nòm ... (+23 more)` | 33 |
| 16k | `▁no zay ▁a ▁l ' é ▁' l ▁nòm : ... (+22 more)` | 32 |
| 32k | `▁no zay ▁a ▁l ' é ▁' l ▁nòm : ... (+22 more)` | 32 |
| 64k | `▁nozay ▁a ▁l ' é ▁' l ▁nòm : ▁d ... (+21 more)` | 31 |

**Sample 3:** `Bellefosse a l'é na comun-a fransèisa ant la region aministrativa dl'Alsassia, a...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁belle f osse ▁a ▁l ' é ▁na ▁comun - ... (+22 more)` | 32 |
| 16k | `▁belle f osse ▁a ▁l ' é ▁na ▁comun - ... (+22 more)` | 32 |
| 32k | `▁belle fosse ▁a ▁l ' é ▁na ▁comun - a ... (+21 more)` | 31 |
| 64k | `▁belle fosse ▁a ▁l ' é ▁na ▁comun - a ... (+21 more)` | 31 |


### Key Findings

- **Best Compression:** 64k achieves 4.075x compression
- **Lowest UNK Rate:** 8k with 0.0838% 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 | 3,141 | 11.62 | 77,121 | 41.9% | 64.4% |
| **2-gram** | Subword | 256 🏆 | 8.00 | 3,836 | 69.3% | 99.4% |
| **3-gram** | Word | 5,004 | 12.29 | 132,134 | 37.8% | 59.5% |
| **3-gram** | Subword | 1,638 | 10.68 | 31,027 | 34.2% | 77.5% |
| **4-gram** | Word | 8,275 | 13.01 | 214,916 | 32.4% | 54.5% |
| **4-gram** | Subword | 6,362 | 12.64 | 163,804 | 22.7% | 55.2% |
| **5-gram** | Word | 8,601 | 13.07 | 179,908 | 29.2% | 52.3% |
| **5-gram** | Subword | 16,383 | 14.00 | 457,622 | 17.6% | 45.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l` | 154,306 |
| 2 | `l é` | 116,837 |
| 3 | `ant ël` | 45,088 |
| 4 | `dipartiment ëd` | 43,742 |
| 5 | `é na` | 41,435 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l é` | 116,563 |
| 2 | `l é na` | 41,283 |
| 3 | `na comun a` | 36,182 |
| 4 | `é na comun` | 36,110 |
| 5 | `ant ël dipartiment` | 33,155 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l é na` | 41,263 |
| 2 | `é na comun a` | 36,110 |
| 3 | `l é na comun` | 36,108 |
| 4 | `con na densità ëd` | 32,499 |
| 5 | `na comun a fransèisa` | 30,354 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l é na comun a` | 36,108 |
| 2 | `a l é na comun` | 36,104 |
| 3 | `é na comun a fransèisa` | 30,343 |
| 4 | `abitant scond ël censiment dël` | 29,591 |
| 5 | `na comun a fransèisa ant` | 29,152 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 1,165,352 |
| 2 | `_ a` | 759,939 |
| 3 | `a n` | 521,874 |
| 4 | `_ d` | 517,379 |
| 5 | `_ l` | 463,625 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a _` | 302,714 |
| 2 | `n t _` | 258,541 |
| 3 | `_ ë d` | 251,242 |
| 4 | `ë d _` | 246,081 |
| 5 | `ë l _` | 238,083 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ë d _` | 245,889 |
| 2 | `_ a _ l` | 160,115 |
| 3 | `a _ l '` | 147,963 |
| 4 | `e n t _` | 137,969 |
| 5 | `m e n t` | 134,438 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a _ l '` | 139,497 |
| 2 | `m e n t _` | 128,287 |
| 3 | `_ d ë l _` | 126,779 |
| 4 | `i m e n t` | 119,300 |
| 5 | `a _ l ' é` | 108,685 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 256
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~45% 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 | 0.8327 | 1.781 | 5.52 | 169,530 | 16.7% |
| **1** | Subword | 0.8751 | 1.834 | 6.71 | 1,490 | 12.5% |
| **2** | Word | 0.3305 | 1.257 | 1.89 | 927,581 | 67.0% |
| **2** | Subword | 0.8947 | 1.859 | 6.10 | 9,975 | 10.5% |
| **3** | Word | 0.1336 | 1.097 | 1.29 | 1,740,248 | 86.6% |
| **3** | Subword | 0.7906 | 1.730 | 4.36 | 60,753 | 20.9% |
| **4** | Word | 0.0669 🏆 | 1.047 | 1.14 | 2,223,801 | 93.3% |
| **4** | Subword | 0.6809 | 1.603 | 3.09 | 264,501 | 31.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a së stend për na comun a l é parlà minca casela a l anglèis national`
2. `ëd le ròche o gbiri niragu o kaqchikel akatenango sud con na densità a fransèisa ant`
3. `l é vincenzo civitali vincenzo andrea guglielminetti lese ij cas assolù la region sardëgna d américa`

**Context Size 2:**

1. `a l é na comun a fransèisa ant la literatura a l é un comun dla lombardìa`
2. `l é gemelà con anliure esterne sit istitussional dla provincia ëd turin a l é parlà la`
3. `ant ël dipartiment ëd vaucluse as dëstend an sna surfassa ëd 85 ab km dël dipartiment dla`

**Context Size 3:**

1. `a l é na comun a fransèisa ant la region aministrativa dl àuta normandìa ant ël dipartiment ëd`
2. `l é na comun a fransèisa ant la region aministrativa dla picardìa ant ël dipartiment ëd creuse a`
3. `na comun a fransèisa ant la region aministrativa dla bassa normandìa ant ël dipartiment ëd la nièvre...`

**Context Size 4:**

1. `a l é na comun a fransèisa ant la region aministrativa dla picardìa ant ël dipartiment ëd cantal a`
2. `é na comun a fransèisa ant la region aministrativa ëd champagne ardënne ant ël dipartiment d allier ...`
3. `l é na comun a fransèisa ant la region aministrativa ëd champagne ardënne ant ël dipartiment d hérau...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pondan-ntré_d_t`
2. `a_sst_latrsio_so`
3. `n_chentet_pel'al`

**Context Size 2:**

1. `a_ëd_a_la_cottera`
2. `_agna_la_rep_decì`
3. `an_gruzeyrus_a_tu`

**Context Size 3:**

1. `_a_concorphan._com`
2. `nt_ëd_va_a_l'é_d'u`
3. `_ëd_km²,_cons_(tal`

**Context Size 4:**

1. `_ëd_tarda_ant_ij_27`
2. `_a_l'arnota_l'é_par`
3. `a_l'é_na_dense_regi`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (264,501 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 | 80,217 |
| Total Tokens | 5,297,235 |
| Mean Frequency | 66.04 |
| Median Frequency | 5 |
| Frequency Std Dev | 2213.41 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 388,771 |
| 2 | ëd | 246,106 |
| 3 | l | 200,451 |
| 4 | dël | 126,964 |
| 5 | é | 118,244 |
| 6 | na | 116,817 |
| 7 | ël | 109,927 |
| 8 | la | 108,231 |
| 9 | ant | 97,115 |
| 10 | e | 91,172 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | andividuassion | 2 |
| 2 | sètim | 2 |
| 3 | guacamole | 2 |
| 4 | anviromentaj | 2 |
| 5 | tonelé | 2 |
| 6 | spurgh | 2 |
| 7 | solidëssa | 2 |
| 8 | ruscha | 2 |
| 9 | houten | 2 |
| 10 | maudagna | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1911 |
| R² (Goodness of Fit) | 0.999309 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 61.6% |
| Top 1,000 | 80.4% |
| Top 5,000 | 89.7% |
| Top 10,000 | 92.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9993 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 61.6% of corpus
- **Long Tail:** 70,217 words needed for remaining 7.1% 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 | 0.7640 🏆 | 0.3601 | N/A | N/A |
| **mono_64d** | 64 | 0.7270 | 0.2907 | N/A | N/A |
| **mono_128d** | 128 | 0.6128 | 0.2654 | N/A | N/A |
| **aligned_32d** | 32 | 0.7640 | 0.3674 | 0.0740 | 0.3760 |
| **aligned_64d** | 64 | 0.7270 | 0.2772 | 0.1400 | 0.5080 |
| **aligned_128d** | 128 | 0.6128 | 0.2519 | 0.1600 | 0.5340 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7640 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3021. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 16.0% 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 | **0.156** | 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` | anvità, anetù, awun |
| `-s` | sie, sorcière, surrender |
| `-c` | conession, cyrano, celtica |
| `-b` | bassin, be, braunfels |
| `-ma` | magnolia, martinsicuro, marchisio |
| `-m` | mecatrònich, magnolia, miria |
| `-p` | pratica, prèivi, passo |
| `-t` | teatino, thomasset, tip |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | ghilarza, hepatica, magnolia |
| `-e` | sie, urbe, sorcière |
| `-n` | bassin, conession, ecitassion |
| `-s` | facilitates, braunfels, heidekreis |
| `-o` | teatino, cyrano, martinsicuro |
| `-i` | flavi, canzoni, gritti |
| `-on` | conession, ecitassion, incursion |
| `-t` | nuriment, riconossiment, thomasset |

### 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 |
|------|----------|------------------|----------|
| `assa` | 1.63x | 143 contexts | lassa, nassa, fassa |
| `ssio` | 1.80x | 86 contexts | possio, fassio, lassio |
| `ensi` | 1.52x | 80 contexts | sensi, kensiu, mensis |
| `imen` | 1.81x | 39 contexts | imeni, ciment, crimen |
| `cond` | 1.63x | 59 contexts | condé, conde, scond |
| `sten` | 1.54x | 51 contexts | stend, osten, stent |
| `leng` | 1.83x | 26 contexts | eleng, lengo, lenga |
| `nist` | 1.72x | 31 contexts | sniste, snistr, snista |
| `inis` | 1.55x | 43 contexts | finiss, cinism, inisse |
| `istr` | 1.43x | 53 contexts | istro, bistr, istria |
| `itan` | 1.36x | 59 contexts | titan, ritan, gitan |
| `engh` | 1.77x | 20 contexts | fengh, vengh, lenghe |

### 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` | `-a` | 149 words | cussìtica, castagnòla |
| `-p` | `-a` | 136 words | predecessora, praetoria |
| `-a` | `-a` | 126 words | agta, arcostruìa |
| `-s` | `-a` | 105 words | sewa, sarvaja |
| `-c` | `-o` | 94 words | capitignano, caivano |
| `-c` | `-e` | 84 words | cane, castroreale |
| `-c` | `-s` | 72 words | candicans, cruzières |
| `-a` | `-e` | 68 words | avvenire, abele |
| `-b` | `-a` | 63 words | bauma, brunetta |
| `-s` | `-e` | 62 words | suceduje, strutture |

### 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 |
|------|-----------------|------------|------|
| williamson | **`william-s-on`** | 7.5 | `s` |
| lombardore | **`lombard-o-re`** | 7.5 | `o` |
| spantiasse | **`spantia-s-se`** | 7.5 | `s` |
| yutanduchi | **`yutandu-ch-i`** | 7.5 | `ch` |
| castiadas | **`castiad-a-s`** | 7.5 | `a` |
| costituent | **`costitu-e-nt`** | 7.5 | `e` |
| rochester | **`ro-ch-ester`** | 7.5 | `ester` |
| condorcet | **`condorc-e-t`** | 7.5 | `e` |
| camposano | **`campo-sa-no`** | 7.5 | `sa` |
| lalacelle | **`la-la-celle`** | 7.5 | `celle` |
| franchetii | **`franchet-i-i`** | 7.5 | `i` |
| napolioni | **`napoli-on-i`** | 6.0 | `napoli` |
| alcantara | **`al-cantar-a`** | 6.0 | `cantar` |
| paternità | **`pa-terni-tà`** | 6.0 | `terni` |
| franchista | **`franch-is-ta`** | 6.0 | `franch` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Piedmontese 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 (4.08x) |
| N-gram | **2-gram** | Lowest perplexity (256) |
| Markov | **Context-4** | Highest predictability (93.3%) |
| 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 18:09:59*