---
language: eml
language_name: Unknown language [eml]
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: 3.369
  - name: best_isotropy
    type: isotropy
    value: 0.3584
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

# Unknown language [eml] - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Unknown language [eml]** 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** | 2.942x | 2.95 | 0.4433% | 289,426 |
| **16k** | 3.144x | 3.15 | 0.4738% | 270,763 |
| **32k** | 3.369x 🏆 | 3.37 | 0.5076% | 252,742 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `'l è 'l nòm 'd un domìni genèric. Al funsiòuna da 'l zógn dal ed domìni tachê a ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁' l ▁è ▁' l ▁nòm ▁' d ▁un ▁domìni ... (+17 more)` | 27 |
| 16k | `▁' l ▁è ▁' l ▁nòm ▁' d ▁un ▁domìni ... (+17 more)` | 27 |
| 32k | `▁' l ▁è ▁' l ▁nòm ▁' d ▁un ▁domìni ... (+17 more)` | 27 |

**Sample 2:** `'l è 'l nòm 'd un domìni genèric. Al funsiòuna da 'l setèmber dal ed domìni tach...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁' l ▁è ▁' l ▁nòm ▁' d ▁un ▁domìni ... (+17 more)` | 27 |
| 16k | `▁' l ▁è ▁' l ▁nòm ▁' d ▁un ▁domìni ... (+17 more)` | 27 |
| 32k | `▁' l ▁è ▁' l ▁nòm ▁' d ▁un ▁domìni ... (+17 more)` | 27 |

**Sample 3:** `Al 294 'l è 'n an edl III sécol dal Calendàri gregoriàn. Avenimèint Nê Mort III`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁al ▁ 2 9 4 ▁' l ▁è ▁' n ... (+12 more)` | 22 |
| 16k | `▁al ▁ 2 9 4 ▁' l ▁è ▁' n ... (+12 more)` | 22 |
| 32k | `▁al ▁ 2 9 4 ▁' l ▁è ▁' n ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 32k achieves 3.369x compression
- **Lowest UNK Rate:** 8k with 0.4433% 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 | 855 | 9.74 | 4,527 | 49.2% | 80.8% |
| **2-gram** | Subword | 342 🏆 | 8.42 | 2,464 | 62.9% | 97.8% |
| **3-gram** | Word | 936 | 9.87 | 6,071 | 49.5% | 79.8% |
| **3-gram** | Subword | 2,480 | 11.28 | 17,300 | 27.4% | 69.1% |
| **4-gram** | Word | 1,262 | 10.30 | 9,814 | 45.9% | 76.0% |
| **4-gram** | Subword | 9,840 | 13.26 | 65,901 | 17.3% | 46.3% |
| **5-gram** | Word | 1,050 | 10.04 | 7,194 | 45.5% | 79.7% |
| **5-gram** | Subword | 19,916 | 14.28 | 117,450 | 14.0% | 39.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l è` | 4,349 |
| 2 | `da l` | 2,854 |
| 3 | `d un` | 2,584 |
| 4 | `dal calendàri` | 1,948 |
| 5 | `è n` | 1,667 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l è n` | 1,665 |
| 2 | `dal calendàri gregoriàn` | 1,584 |
| 3 | `sécol dal calendàri` | 1,575 |
| 4 | `è n an` | 1,575 |
| 5 | `avenimèint nê mort` | 1,412 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l è n an` | 1,575 |
| 2 | `ed domìni tachê a` | 1,255 |
| 3 | `a funsionèr da l` | 1,255 |
| 4 | `domìni tachê a funsionèr` | 1,255 |
| 5 | `tachê a funsionèr da` | 1,255 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `domìni tachê a funsionèr da` | 1,255 |
| 2 | `ed domìni tachê a funsionèr` | 1,255 |
| 3 | `tachê a funsionèr da l` | 1,255 |
| 4 | `l è l nòm d` | 1,247 |
| 5 | `l nòm d un domìni` | 1,247 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 44,681 |
| 2 | `l _` | 36,354 |
| 3 | `_ d` | 31,152 |
| 4 | `_ a` | 28,707 |
| 5 | `n _` | 26,332 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a l _` | 19,233 |
| 2 | `_ d a` | 13,700 |
| 3 | `_ i n` | 10,014 |
| 4 | `l a _` | 9,054 |
| 5 | `d a l` | 8,840 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a l` | 8,766 |
| 2 | `d a l _` | 8,710 |
| 3 | `_ a l _` | 7,884 |
| 4 | `_ e d _` | 6,634 |
| 5 | `_ l a _` | 5,983 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a l _` | 8,679 |
| 2 | `_ d a _ '` | 2,988 |
| 3 | `' l _ è _` | 2,975 |
| 4 | `l _ è _ '` | 2,854 |
| 5 | `d a _ ' l` | 2,762 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 342
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~39% 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 | 0.6144 | 1.531 | 3.27 | 38,079 | 38.6% |
| **1** | Subword | 1.2142 | 2.320 | 11.72 | 398 | 0.0% |
| **2** | Word | 0.1859 | 1.138 | 1.39 | 123,729 | 81.4% |
| **2** | Subword | 1.1401 | 2.204 | 6.72 | 4,661 | 0.0% |
| **3** | Word | 0.0688 | 1.049 | 1.12 | 170,769 | 93.1% |
| **3** | Subword | 0.8376 | 1.787 | 3.69 | 31,279 | 16.2% |
| **4** | Word | 0.0286 🏆 | 1.020 | 1.05 | 189,112 | 97.1% |
| **4** | Subword | 0.5759 | 1.491 | 2.30 | 115,443 | 42.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `l é al progrâma pc 12 518 519 520 gonèl 22 ed domìni genèric al urèl`
2. `al funsiòuna da per 4 quèśi prim sfènic difetìv 322 in sensu laudator temporis acti prudentes`
3. `dal crìst 4 d oro una cumêdia d antonino inferito da l è l è l`

**Context Size 2:**

1. `l è n an dal vii sécol dal calendàri gregoriàn avenimèint nê guélf vi mort xii`
2. `d un nùmer triangolèr moltìplica per 5 d un nùmer quèder moltìplica per 3 d un domìni`
3. `dal calendàri gregoriàn avenimèint nê mort x`

**Context Size 3:**

1. `l è n an edl iii sécol dal calendàri gregoriàn avenimèint nê mort i`
2. `dal calendàri gregoriàn avenimèint nê mort viii`
3. `è n an edl viii sécol dal calendàri gregoriàn avenimèint nê mort xvi`

**Context Size 4:**

1. `l è n an edl ix sécol dal calendàri gregoriàn avenimèint nê mort v`
2. `domìni tachê a funsionèr da l`
3. `ed domìni tachê a funsionèr da l`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pe_gotili_l'n_i`
2. `andogrin_menèiṣa`
3. `i_incōridl_stêst`

**Context Size 2:**

1. `a_cuns_e_tòra_fiō`
2. `l_séco,_ed_unèli_`
3. `_drê_avōl_è_'l_59`

**Context Size 3:**

1. `al_sît_la_cà_paolo`
2. `_da_63_in_difestìl`
3. `_in-dóvv_a_un_di_c`

**Context Size 4:**

1. `_dal_calendàri_greg`
2. `dal_viii_sèc._préma`
3. `_al_funsiòuna_da_'l`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (115,443 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 | 14,744 |
| Total Tokens | 272,012 |
| Mean Frequency | 18.45 |
| Median Frequency | 3 |
| Frequency Std Dev | 223.57 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | l | 12,992 |
| 2 | al | 10,267 |
| 3 | dal | 8,736 |
| 4 | a | 7,317 |
| 5 | ed | 6,740 |
| 6 | la | 6,622 |
| 7 | d | 5,491 |
| 8 | in | 5,032 |
| 9 | è | 4,792 |
| 10 | da | 4,480 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | espositìv | 2 |
| 2 | ecosistèma | 2 |
| 3 | trasformasiòun | 2 |
| 4 | galleria | 2 |
| 5 | space | 2 |
| 6 | velò | 2 |
| 7 | arriv | 2 |
| 8 | sèda | 2 |
| 9 | cumé | 2 |
| 10 | zûg | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0159 |
| R² (Goodness of Fit) | 0.990784 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 57.7% |
| Top 1,000 | 77.8% |
| Top 5,000 | 90.7% |
| Top 10,000 | 96.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9908 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 57.7% of corpus
- **Long Tail:** 4,744 words needed for remaining 3.5% 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 | 0.3584 | 0.4391 | N/A | N/A |
| **mono_64d** | 64 | 0.1134 | 0.4504 | N/A | N/A |
| **mono_128d** | 128 | 0.0166 | 0.4596 | N/A | N/A |
| **aligned_32d** | 32 | 0.3584 🏆 | 0.4411 | 0.0140 | 0.1660 |
| **aligned_64d** | 64 | 0.1134 | 0.4292 | 0.0460 | 0.2440 |
| **aligned_128d** | 128 | 0.0166 | 0.4457 | 0.0400 | 0.2640 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.3584 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4442. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.6% 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 | **1.037** | 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 |
|--------|----------|
| `-ca` | cal, cavésin, caviân |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | scōla, algebra, câṣva |
| `-um` | coelum, adsum, 217śum |
| `-na` | vègna, teresina, ruvîna |

### 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 |
|------|----------|------------------|----------|
| `asiò` | 1.80x | 17 contexts | asiòṅ, asiòun, frasiòn |
| `siòu` | 1.79x | 17 contexts | asiòun, sesiòun, lesiòun |
| `purt` | 1.55x | 23 contexts | purtâ, purtê, purtä |
| `iòun` | 1.73x | 16 contexts | uniòun, asiòun, sesiòun |
| `nter` | 1.50x | 24 contexts | inter, nterra, dänter |
| `sèin` | 1.51x | 17 contexts | sèins, sèint, casèin |
| `tèin` | 1.48x | 16 contexts | latèin, estèin, putèin |
| `ital` | 1.53x | 14 contexts | italy, italo, vitali |
| `tôri` | 1.78x | 9 contexts | stôri, stôric, stôria |
| `rèin` | 1.46x | 14 contexts | rèina, trèin, terèin |
| `inte` | 1.59x | 11 contexts | inter, intern, interès |
| `mèin` | 1.79x | 8 contexts | mèint, camèin, mumèint |

### 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 |
|--------|--------|-----------|----------|
| `-ca` | `-a` | 53 words | cavacürta, canpâgna |
| `-ca` | `-na` | 16 words | canpâgna, catalógna |

### 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 |
|------|-----------------|------------|------|
| cascaggna | **`ca-scagg-na`** | 3.0 | `scagg` |
| califòrgna | **`ca-lifòrg-na`** | 3.0 | `lifòrg` |
| campàggna | **`ca-mpàgg-na`** | 3.0 | `mpàgg` |
| castlaran | **`ca-stlaran`** | 1.5 | `stlaran` |
| philosophum | **`philosoph-um`** | 1.5 | `philosoph` |
| privilegium | **`privilegi-um`** | 1.5 | `privilegi` |
| calandäri | **`ca-landäri`** | 1.5 | `landäri` |
| referendum | **`referend-um`** | 1.5 | `referend` |
| metropolitana | **`metropolita-na`** | 1.5 | `metropolita` |
| carabinieri | **`ca-rabinieri`** | 1.5 | `rabinieri` |
| parmigiana | **`parmigia-na`** | 1.5 | `parmigia` |
| funsiòuna | **`funsiòu-na`** | 1.5 | `funsiòu` |
| carpigiano | **`ca-rpigiano`** | 1.5 | `rpigiano` |
| caraterésstic | **`ca-raterésstic`** | 1.5 | `raterésstic` |
| indipendentîxum | **`indipendentîx-um`** | 1.5 | `indipendentîx` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Unknown language [eml] 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 | **32k BPE** | Best compression (3.37x) |
| N-gram | **2-gram** | Lowest perplexity (342) |
| Markov | **Context-4** | Highest predictability (97.1%) |
| 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: 2026-01-04 14:33:51*