---
language: jbo
language_name: Lojban
language_family: constructed_other
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-constructed_other
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: 2.964
  - name: best_isotropy
    type: isotropy
    value: 0.2678
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lojban** 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** | 2.856x | 2.86 | 0.0265% | 740,723 |
| **16k** | 2.911x | 2.91 | 0.0270% | 726,775 |
| **32k** | 2.964x 🏆 | 2.97 | 0.0275% | 713,753 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `le si'o dekna'a cu gradu lo veldetri lo niltei i lo dekna'a cu nanca li 10`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁le ▁si ' o ▁dekna ' a ▁cu ▁gradu ▁lo ... (+14 more)` | 24 |
| 16k | `▁le ▁si ' o ▁dekna ' a ▁cu ▁gradu ▁lo ... (+14 more)` | 24 |
| 32k | `▁le ▁si ' o ▁dekna ' a ▁cu ▁gradu ▁lo ... (+14 more)` | 24 |

**Sample 2:** `lo zdotu'a goi zy. cu barda tumla .i zy cu pamoi le'i tumla leka barda .i zy. cu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lo ▁zdotu ' a ▁goi ▁zy . ▁cu ▁barda ▁tumla ... (+31 more)` | 41 |
| 16k | `▁lo ▁zdotu ' a ▁goi ▁zy . ▁cu ▁barda ▁tumla ... (+31 more)` | 41 |
| 32k | `▁lo ▁zdotu ' a ▁goi ▁zy . ▁cu ▁barda ▁tumla ... (+31 more)` | 41 |

**Sample 3:** `da poi ce'u du ka'o goi ko'a zo'u li ka'o te'a re du li ni'u pa .i je ko'a cu re...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁da ▁poi ▁ce ' u ▁du ▁ka ' o ▁goi ... (+30 more)` | 40 |
| 16k | `▁da ▁poi ▁ce ' u ▁du ▁ka ' o ▁goi ... (+30 more)` | 40 |
| 32k | `▁da ▁poi ▁ce ' u ▁du ▁ka ' o ▁goi ... (+30 more)` | 40 |


### Key Findings

- **Best Compression:** 32k achieves 2.964x compression
- **Lowest UNK Rate:** 8k with 0.0265% 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 | 263 | 8.04 | 5,763 | 71.1% | 90.0% |
| **2-gram** | Subword | 150 🏆 | 7.23 | 1,249 | 81.8% | 99.9% |
| **3-gram** | Word | 426 | 8.73 | 11,175 | 65.5% | 84.7% |
| **3-gram** | Subword | 631 | 9.30 | 9,433 | 58.0% | 87.9% |
| **4-gram** | Word | 1,152 | 10.17 | 31,022 | 54.5% | 73.7% |
| **4-gram** | Subword | 1,589 | 10.63 | 41,211 | 49.2% | 73.9% |
| **5-gram** | Word | 1,669 | 10.70 | 33,007 | 49.2% | 68.6% |
| **5-gram** | Subword | 2,683 | 11.39 | 80,410 | 44.9% | 68.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de i` | 19,178 |
| 2 | `la o` | 17,721 |
| 3 | `a cu` | 17,142 |
| 4 | `ke a` | 16,638 |
| 5 | `noi ke` | 16,409 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `noi ke a` | 16,408 |
| 2 | `ke a cu` | 16,375 |
| 3 | `i de i` | 16,359 |
| 4 | `la o zoi` | 16,326 |
| 5 | `zoi noi ke` | 15,958 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `noi ke a cu` | 16,335 |
| 2 | `zoi noi ke a` | 15,958 |
| 3 | `cu jbena i de` | 10,133 |
| 4 | `jbena i de i` | 10,133 |
| 5 | `ke a cu merko` | 8,277 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `zoi noi ke a cu` | 15,957 |
| 2 | `cu jbena i de i` | 10,133 |
| 3 | `noi ke a cu merko` | 8,276 |
| 4 | `ke a cu merko ke` | 7,065 |
| 5 | `i de i lo la` | 6,474 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _` | 97,095 |
| 2 | `o _` | 78,639 |
| 3 | `u _` | 72,524 |
| 4 | `a _` | 66,871 |
| 5 | `_ l` | 65,646 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c u _` | 39,185 |
| 2 | `_ c u` | 39,177 |
| 3 | `_ l a` | 35,334 |
| 4 | `_ z o` | 33,172 |
| 5 | `z o i` | 32,926 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ c u _` | 38,551 |
| 2 | `_ z o i` | 32,836 |
| 3 | `o i . _` | 32,436 |
| 4 | `z o i .` | 32,435 |
| 5 | `_ . i _` | 20,318 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `z o i . _` | 32,435 |
| 2 | `_ z o i .` | 32,422 |
| 3 | `d e ' i _` | 19,209 |
| 4 | `_ d e ' i` | 19,179 |
| 5 | `a _ c u _` | 17,854 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 150
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~68% 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 | 0.4807 | 1.395 | 3.36 | 24,999 | 51.9% |
| **1** | Subword | 0.8928 | 1.857 | 5.71 | 606 | 10.7% |
| **2** | Word | 0.2439 | 1.184 | 1.71 | 83,598 | 75.6% |
| **2** | Subword | 0.8298 | 1.777 | 5.00 | 3,459 | 17.0% |
| **3** | Word | 0.1180 | 1.085 | 1.28 | 142,297 | 88.2% |
| **3** | Subword | 0.8915 | 1.855 | 3.94 | 17,283 | 10.8% |
| **4** | Word | 0.0638 🏆 | 1.045 | 1.18 | 181,290 | 93.6% |
| **4** | Subword | 0.5626 | 1.477 | 2.30 | 67,967 | 43.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `i de i de i ckaji lo mutce farvi co turni cu jbena i 7 la`
2. `cu brito ke a cu brito ke xeldraci gasnu cu mrobi o zoi noi ke xeldraci`
3. `la xamast la gaimast la gaimast la somast la o zoi noi ke a cu sfe`

**Context Size 2:**

1. `de i 31 la pamast la o zoi dirk bogarde zoi noi ke a cu merko skina`
2. `la o zoi buddy bolden zoi noi ke a cu merko ke xeldraci gasnu cu jbena i`
3. `a cu brito ke xeldraci gasnu cu jbena i de i 24 la vomast cu 15moi djedi`

**Context Size 3:**

1. `noi ke a cu merko ke xeldraci gasnu cu jbena i de i 14 la cimast i de`
2. `ke a cu dotco ke xeldraci gasnu cu jbena i de i 13 la cimast la o zoi`
3. `i de i 4 la remast cu 21moi djedi fi o masti lo rebjukma i i de i`

**Context Size 4:**

1. `noi ke a cu merko ke xeldraci gasnu cu jbena i de i 27 la gaimast la o zoi`
2. `zoi noi ke a cu brito ke xeldraci gasnu cu jbena i de i 25 la zemast la o`
3. `cu jbena i de i lo la o zoi jason statham zoi noi ke a cu cimoi masti i`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_lagast._li_t_e_`
2. `i_xe'au_ja_zoike`
3. `ast._._keloifino`

**Context Size 2:**

1. `i_51_la'o_ke'i_be`
2. `o_smu_cu_la_barga`
3. `u_ke'a_cu_cu_jics`

**Context Size 3:**

1. `cu_cu_je_na_.i_kie`
2. `_cu_mrobi'o_dju_sr`
3. `_la_zei_.i_darxi_k`

**Context Size 4:**

1. `_cu_mrobi'o_to_mrob`
2. `_zoi._noi_ke'a_cu_m`
3. `oi._ai_se_casnu_cu_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (67,967 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 | 10,828 |
| Total Tokens | 529,379 |
| Mean Frequency | 48.89 |
| Median Frequency | 3 |
| Frequency Std Dev | 936.81 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | i | 43,370 |
| 2 | cu | 38,594 |
| 3 | la | 34,021 |
| 4 | zoi | 32,918 |
| 5 | o | 29,624 |
| 6 | ke | 29,615 |
| 7 | a | 21,084 |
| 8 | de | 19,406 |
| 9 | lo | 19,206 |
| 10 | noi | 17,016 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | correspondente | 2 |
| 2 | sitio | 2 |
| 3 | oficial | 2 |
| 4 | sperma | 2 |
| 5 | sexual | 2 |
| 6 | health | 2 |
| 7 | linguistics | 2 |
| 8 | olympiad | 2 |
| 9 | iol | 2 |
| 10 | pragmatika | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1384 |
| R² (Goodness of Fit) | 0.986369 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 80.8% |
| Top 1,000 | 92.3% |
| Top 5,000 | 97.6% |
| Top 10,000 | 99.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9864 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 80.8% of corpus
- **Long Tail:** 828 words needed for remaining 0.3% coverage

---
## 5. Word Embeddings Evaluation

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

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

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

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


### 5.1 Cross-Lingual Alignment

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

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


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.2678 | 0.4864 | N/A | N/A |
| **mono_64d** | 64 | 0.0649 | 0.4754 | N/A | N/A |
| **mono_128d** | 128 | 0.0083 | 0.4760 | N/A | N/A |
| **aligned_32d** | 32 | 0.2678 🏆 | 0.4767 | 0.0100 | 0.0780 |
| **aligned_64d** | 64 | 0.0649 | 0.4612 | 0.0080 | 0.0760 |
| **aligned_128d** | 128 | 0.0083 | 0.4657 | 0.0120 | 0.0860 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.2678 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4736. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 1.2% 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 | **0.004** | 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 |
|--------|----------|
| `-s` | seljalge, sunyaev, selpoi |
| `-c` | cangan, carlos, crepu |
| `-m` | major, mesurier, mccardie |
| `-b` | blackmore, bedelia, burmeister |
| `-k` | kitaro, klaus, ki |
| `-t` | trefi, téa, tunka |
| `-p` | pristmen, patchen, pairnu |
| `-r` | ritli, rossi, riemer |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | nintendos, eros, carlos |
| `-n` | pristmen, whitman, cangan |
| `-e` | blackmore, seljalge, émilie |
| `-i` | farvi, selpoi, ritli |
| `-a` | bedelia, fipma, guttera |
| `-u` | crepu, camgu, dotybau |
| `-r` | major, burmeister, dar |
| `-o` | kitaro, xrabo, sembello |

### 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 |
|------|----------|------------------|----------|
| `jinm` | 1.87x | 15 contexts | jinme, jinmrne, jinmrni |
| `selc` | 1.69x | 12 contexts | selci, selce, selcu |
| `selp` | 1.75x | 10 contexts | selpe, selpa, selpo |
| `skeg` | 1.88x | 6 contexts | skegau, eskegau, xumskegau |
| `ygau` | 1.40x | 12 contexts | sagygau, popygau, micygau |
| `anti` | 1.47x | 9 contexts | manti, ranti, canti |
| `rgau` | 1.31x | 11 contexts | orgau, irgau, argau |
| `arna` | 1.34x | 5 contexts | rarna, barna, garna |
| `atni` | 1.53x | 3 contexts | ratni, catni, datni |
| `cmac` | 1.36x | 3 contexts | cmaci, ocmaci, cmacypre |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-i` | 68 words | sanji, skoselti |
| `-s` | `-a` | 50 words | simkansa, selka |
| `-m` | `-n` | 49 words | marian, milton |
| `-m` | `-s` | 48 words | manatus, maksimianus |
| `-s` | `-s` | 47 words | sabines, sulaues |
| `-c` | `-e` | 47 words | cemtruje, catnrkonsule |
| `-s` | `-n` | 44 words | sn, shepperton |
| `-c` | `-n` | 42 words | chan, copenhagen |
| `-t` | `-i` | 41 words | terkagni, truci |
| `-b` | `-n` | 38 words | brannan, beauchemin |

### 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 |
|------|-----------------|------------|------|
| erlandson | **`erland-s-on`** | 7.5 | `s` |
| naknolraitru | **`na-k-nolraitru`** | 7.5 | `nolraitru` |
| danielson | **`daniel-s-on`** | 7.5 | `s` |
| humphries | **`humphr-i-es`** | 7.5 | `i` |
| andersson | **`anders-s-on`** | 7.5 | `s` |
| gustafson | **`gustaf-s-on`** | 7.5 | `s` |
| spaskegau | **`s-pa-skegau`** | 6.0 | `skegau` |
| françoise | **`françois-e`** | 4.5 | `françois` |
| dominikan | **`dominik-an`** | 4.5 | `dominik` |
| tedyskegau | **`te-d-yskegau`** | 4.5 | `yskegau` |
| colasanto | **`co-la-santo`** | 4.5 | `santo` |
| antioxeias | **`antioxei-as`** | 4.5 | `antioxei` |
| jefferson | **`jeffers-on`** | 4.5 | `jeffers` |
| esperantos | **`esperanto-s`** | 4.5 | `esperanto` |
| dimitrios | **`dimitri-os`** | 4.5 | `dimitri` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lojban 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 | **32k BPE** | Best compression (2.96x) |
| N-gram | **2-gram** | Lowest perplexity (150) |
| Markov | **Context-4** | Highest predictability (93.6%) |
| 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 05:55:02*