---
language: sc
language_name: Sardinian
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: 4.260
  - name: best_isotropy
    type: isotropy
    value: 0.8587
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Sardinian** 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** | 3.473x | 3.47 | 0.0446% | 549,623 |
| **16k** | 3.769x | 3.77 | 0.0484% | 506,460 |
| **32k** | 4.039x | 4.04 | 0.0518% | 472,647 |
| **64k** | 4.260x 🏆 | 4.26 | 0.0547% | 448,103 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Thomas Duane "Tom" Lister, Jr. (Compton, California, 24 làmpadas, – Marina del R...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁thomas ▁du ane ▁" t om " ▁l ister , ... (+36 more)` | 46 |
| 16k | `▁thomas ▁du ane ▁" t om " ▁l ister , ... (+34 more)` | 44 |
| 32k | `▁thomas ▁du ane ▁" tom " ▁l ister , ▁jr ... (+32 more)` | 42 |
| 64k | `▁thomas ▁du ane ▁" tom " ▁l ister , ▁jr ... (+31 more)` | 41 |

**Sample 2:** `Harly est unu comunu frantzesu de 1.803 abitantes posti in su dipartimentu de s'...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁h arl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 ... (+30 more)` | 40 |
| 16k | `▁h arl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 ... (+27 more)` | 37 |
| 32k | `▁h arl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 ... (+25 more)` | 35 |
| 64k | `▁harl y ▁est ▁unu ▁comunu ▁frantzesu ▁de ▁ 1 . ... (+24 more)` | 34 |

**Sample 3:** `Wikipedia in danesu est sa versione in limba danesa de Wikipedia. Ligàmenes este...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁dan esa ... (+7 more)` | 17 |
| 16k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁danesa ▁de ... (+5 more)` | 15 |
| 32k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁danesa ▁de ... (+5 more)` | 15 |
| 64k | `▁wikipedia ▁in ▁danesu ▁est ▁sa ▁versione ▁in ▁limba ▁danesa ▁de ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.260x compression
- **Lowest UNK Rate:** 8k with 0.0446% 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 | 10,116 | 13.30 | 48,306 | 21.8% | 41.6% |
| **2-gram** | Subword | 212 🏆 | 7.73 | 4,052 | 75.4% | 99.3% |
| **3-gram** | Word | 34,903 | 15.09 | 73,271 | 6.8% | 22.4% |
| **3-gram** | Subword | 1,622 | 10.66 | 28,188 | 33.1% | 78.3% |
| **4-gram** | Word | 67,185 | 16.04 | 105,292 | 4.7% | 13.9% |
| **4-gram** | Subword | 8,775 | 13.10 | 131,212 | 17.0% | 45.8% |
| **5-gram** | Word | 45,338 | 15.47 | 61,362 | 4.7% | 14.0% |
| **5-gram** | Subword | 32,250 | 14.98 | 327,721 | 10.4% | 28.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de su` | 26,241 |
| 2 | `de sa` | 19,958 |
| 3 | `in su` | 16,843 |
| 4 | `de s` | 13,070 |
| 5 | `a su` | 7,083 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a pustis de` | 2,120 |
| 2 | `sa provìntzia de` | 1,125 |
| 3 | `de sa provìntzia` | 923 |
| 4 | `e in su` | 665 |
| 5 | `de su de` | 661 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de sa provìntzia de` | 812 |
| 2 | `a pustis de sa` | 566 |
| 3 | `est una bidda de` | 362 |
| 4 | `àteros progetos de s` | 351 |
| 5 | `in su mese de` | 325 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nùmeros romanos est un annu` | 223 |
| 2 | `in nùmeros romanos est un` | 223 |
| 3 | `romanos est un annu incomintzadu` | 213 |
| 4 | `àteros progetos de s ispagna` | 191 |
| 5 | `progetos de s ispagna de` | 187 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 405,145 |
| 2 | `_ s` | 350,527 |
| 3 | `a _` | 339,728 |
| 4 | `u _` | 299,991 |
| 5 | `s _` | 254,458 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `d e _` | 190,941 |
| 2 | `_ d e` | 187,576 |
| 3 | `e _ s` | 119,077 |
| 4 | `_ s u` | 115,536 |
| 5 | `s u _` | 104,724 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 170,944 |
| 2 | `_ s u _` | 92,319 |
| 3 | `d e _ s` | 79,656 |
| 4 | `_ i n _` | 69,238 |
| 5 | `_ s a _` | 67,044 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _ s` | 77,101 |
| 2 | `u _ d e _` | 40,816 |
| 3 | `a _ d e _` | 38,441 |
| 4 | `e _ s u _` | 37,005 |
| 5 | `s _ d e _` | 34,532 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 212
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~29% 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 | 0.8701 | 1.828 | 5.46 | 151,383 | 13.0% |
| **1** | Subword | 1.0011 | 2.002 | 7.08 | 1,758 | 0.0% |
| **2** | Word | 0.3078 | 1.238 | 1.81 | 823,593 | 69.2% |
| **2** | Subword | 0.8639 | 1.820 | 4.95 | 12,441 | 13.6% |
| **3** | Word | 0.1271 | 1.092 | 1.24 | 1,483,665 | 87.3% |
| **3** | Subword | 0.7559 | 1.689 | 3.77 | 61,608 | 24.4% |
| **4** | Word | 0.0475 🏆 | 1.033 | 1.07 | 1,828,163 | 95.3% |
| **4** | Subword | 0.6290 | 1.547 | 2.78 | 232,073 | 37.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de su nùmeru de custu casu est cunsiderau su laboratòriu suu fiat però cherian prenare sos`
2. `su mesi de monk dizzy miss italia nelle collezioni civiche del film pro sa contea de`
3. `in diversas sa metade de deghe annos chimbanta detzidende cale aiad appidu puru si repitit comenti`

**Context Size 2:**

1. `de su deretu chi su protzessore esistent vàrios algoritmos de pianificatzione chi òrdinat in su nche...`
2. `de sa scrivania e is musulmanos in sa rivolutzione de làmpadas tatjana rojc limba islovenu joan isaa...`
3. `in su sud de sa fae su casteddu de crabas s agatat in bèrziu in uccle a`

**Context Size 3:**

1. `a pustis de sa gherra at progetadu su computadore ace e at fatu sos primos istùdios in nùgoro`
2. `sa provìntzia de nùgoro su sartu a segunda si podet narrer de gastone chi est istada a fatu`
3. `de sa provìntzia de cùllieri e in su suzuki umpare a ei ichi negishi e akira suzuki aian`

**Context Size 4:**

1. `de sa provìntzia de aristanis de 945 abitantes de sa provìntzia de aristanis de sa provìntzia de su ...`
2. `a pustis de sa ruta de su regìmene comunista ghiadu dae su conducator faeddu rumenu chi currespondet...`
3. `est una bidda de sa provìntzia de aristanis s agatat a 165 metros in pitzu de su mare e`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ba,_ta_pe_cu_in`
2. `addet._fiabamesu`
3. `e_dun_pomulmamic`

**Context Size 2:**

1. `e_casariettis_ber`
2. `_sa_coreges._“abb`
3. `a_is_s'it_e_un_un`

**Context Size 3:**

1. `de_sud_altarrùbica`
2. `_de_sa_madde_sa_de`
3. `e_s'impostoresu,_c`

**Context Size 4:**

1. `_de_orrosa,_candiga`
2. `_su_lìgure)._in_s'a`
3. `de_sos_aiat_pinness`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (232,073 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 | 69,823 |
| Total Tokens | 2,025,890 |
| Mean Frequency | 29.01 |
| Median Frequency | 4 |
| Frequency Std Dev | 942.93 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 171,535 |
| 2 | su | 94,182 |
| 3 | in | 71,523 |
| 4 | sa | 68,420 |
| 5 | a | 60,170 |
| 6 | e | 54,061 |
| 7 | s | 51,018 |
| 8 | est | 30,045 |
| 9 | chi | 26,027 |
| 10 | sos | 20,994 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | activitystreams | 2 |
| 2 | hubzilla | 2 |
| 3 | pleroma | 2 |
| 4 | əm | 2 |
| 5 | bonòmine | 2 |
| 6 | henley | 2 |
| 7 | cuntribuidore | 2 |
| 8 | fowey | 2 |
| 9 | acres | 2 |
| 10 | holywell | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9676 |
| R² (Goodness of Fit) | 0.998085 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 48.9% |
| Top 1,000 | 66.1% |
| Top 5,000 | 80.2% |
| Top 10,000 | 86.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9981 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 48.9% of corpus
- **Long Tail:** 59,823 words needed for remaining 13.7% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.8587 🏆 | 0.3155 | N/A | N/A |
| **mono_64d** | 64 | 0.8247 | 0.2399 | N/A | N/A |
| **mono_128d** | 128 | 0.5602 | 0.1987 | N/A | N/A |
| **aligned_32d** | 32 | 0.8587 | 0.3275 | 0.0680 | 0.2960 |
| **aligned_64d** | 64 | 0.8247 | 0.2427 | 0.1140 | 0.4040 |
| **aligned_128d** | 128 | 0.5602 | 0.1921 | 0.1720 | 0.4840 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8587 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2527. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 17.2% 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 | **-0.511** | 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` | aparcadores, aràbbia, alter |
| `-s` | stromboli, struth, spargi |
| `-c` | clannad, contant, cosmològicu |
| `-p` | prumonite, printzipiada, pelle |
| `-b` | bagazos, berb, bahn |
| `-m` | male, metrologia, meridiana |
| `-t` | temperadura, tinto, tzicatritzes |
| `-ma` | male, mascia, maidan |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | bagazos, aparcadores, ingendradas |
| `-a` | jonia, metrologia, temperadura |
| `-e` | male, àbside, ɔampanile |
| `-u` | individuu, cosmològicu, circùitu |
| `-os` | bagazos, interventos, rènnios |
| `-as` | ingendradas, liliàceas, calicunas |
| `-i` | stromboli, spargi, cardinali |
| `-es` | aparcadores, tzicatritzes, immazines |

### 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 |
|------|----------|------------------|----------|
| `atzi` | 2.19x | 81 contexts | fatzi, latziu, capatzi |
| `adas` | 2.35x | 59 contexts | ladas, adasl, badas |
| `ados` | 2.31x | 53 contexts | dados, lados, nados |
| `zion` | 2.07x | 65 contexts | azioni, azione, rezione |
| `tzio` | 1.88x | 92 contexts | tzios, sòtzio, sotzio |
| `ores` | 2.00x | 69 contexts | cores, mores, oreste |
| `ntzi` | 1.88x | 63 contexts | àntzis, antzis, dòntzi |
| `tadu` | 1.89x | 58 contexts | itadu, stadu, istadu |
| `idad` | 1.80x | 55 contexts | fidada, midade, fidadu |
| `cont` | 1.66x | 76 contexts | contu, contr, conta |
| `sard` | 2.26x | 23 contexts | sarde, sardi, sardu |
| `ntza` | 1.88x | 43 contexts | untza, mantza, lantza |

### 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` | 218 words | cuns, cuntatos |
| `-a` | `-s` | 169 words | amministrados, antzianos |
| `-c` | `-a` | 164 words | càndia, cunfinada |
| `-a` | `-u` | 155 words | altipianu, au |
| `-p` | `-s` | 146 words | principalis, predis |
| `-c` | `-e` | 136 words | cambiende, controllare |
| `-c` | `-u` | 135 words | contu, chidàriu |
| `-a` | `-a` | 132 words | afetada, anastàtica |
| `-p` | `-u` | 121 words | provau, potàssiu |
| `-p` | `-a` | 121 words | parodia, professionista |

### 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 |
|------|-----------------|------------|------|
| bielorùssia | **`bielorùs-s-ia`** | 7.5 | `s` |
| apostrofadu | **`apostrof-a-du`** | 7.5 | `a` |
| controidu | **`contro-i-du`** | 7.5 | `i` |
| cuntzedit | **`cuntze-di-t`** | 7.5 | `di` |
| anteriores | **`anterio-re-s`** | 7.5 | `re` |
| henderson | **`hender-s-on`** | 7.5 | `s` |
| apartment | **`apartm-e-nt`** | 7.5 | `e` |
| atzellerada | **`atzeller-a-da`** | 7.5 | `a` |
| venetzuela | **`venetzu-e-la`** | 7.5 | `e` |
| parlophone | **`parloph-o-ne`** | 7.5 | `o` |
| lentiscus | **`lentis-cu-s`** | 7.5 | `cu` |
| averguadu | **`avergu-a-du`** | 7.5 | `a` |
| française | **`françai-s-e`** | 7.5 | `s` |
| intervìsta | **`intervì-s-ta`** | 7.5 | `s` |
| percursos | **`percur-s-os`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Sardinian 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 (4.26x) |
| N-gram | **2-gram** | Lowest perplexity (212) |
| Markov | **Context-4** | Highest predictability (95.3%) |
| 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 19:44:03*