---
language: hu
language_name: Hungarian
language_family: uralic_ugric
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-uralic_ugric
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: 4.660
  - name: best_isotropy
    type: isotropy
    value: 0.7896
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-13
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Hungarian** 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** | 3.504x | 3.50 | 0.1728% | 3,324,472 |
| **16k** | 3.921x | 3.92 | 0.1933% | 2,971,202 |
| **32k** | 4.310x | 4.31 | 0.2125% | 2,702,863 |
| **64k** | 4.660x 🏆 | 4.66 | 0.2298% | 2,499,703 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `orvlövész, személy → lásd: mesterlövész Orvlövész amerikai akciófilm`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁orv l öv ész , ▁személy ▁ → ▁lásd : ... (+12 more)` | 22 |
| 16k | `▁orv löv ész , ▁személy ▁→ ▁lásd : ▁mester löv ... (+7 more)` | 17 |
| 32k | `▁orv löv ész , ▁személy ▁→ ▁lásd : ▁mester löv ... (+7 more)` | 17 |
| 64k | `▁orv lövész , ▁személy ▁→ ▁lásd : ▁mesterlövész ▁orv lövész ... (+2 more)` | 12 |

**Sample 2:** `Monterde, település Spanyolországban, Zaragoza tartományban Monterde de Albarrac...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mont er de , ▁település ▁spanyol országban , ▁zar ag ... (+19 more)` | 29 |
| 16k | `▁mont er de , ▁település ▁spanyol országban , ▁zar ag ... (+19 more)` | 29 |
| 32k | `▁mont er de , ▁település ▁spanyol országban , ▁zarag oza ... (+17 more)` | 27 |
| 64k | `▁monter de , ▁település ▁spanyol országban , ▁zaragoza ▁tartományban ▁monter ... (+14 more)` | 24 |

**Sample 3:** `A Nyoman szóra a következő lapok hivatkozhatnak: Nyoman, a Nyeman folyó belarusz...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁a ▁nyom an ▁szó ra ▁a ▁következő ▁lap ok ▁hivatkoz ... (+25 more)` | 35 |
| 16k | `▁a ▁nyom an ▁szó ra ▁a ▁következő ▁lapok ▁hivatkoz hatnak ... (+23 more)` | 33 |
| 32k | `▁a ▁nyom an ▁szó ra ▁a ▁következő ▁lapok ▁hivatkoz hatnak ... (+21 more)` | 31 |
| 64k | `▁a ▁nyom an ▁szóra ▁a ▁következő ▁lapok ▁hivatkoz hatnak : ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 64k achieves 4.660x compression
- **Lowest UNK Rate:** 8k with 0.1728% 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 | 534,583 | 19.03 | 4,267,292 | 5.3% | 13.6% |
| **2-gram** | Subword | 435 🏆 | 8.77 | 36,188 | 54.2% | 98.1% |
| **3-gram** | Word | 2,075,420 | 20.98 | 7,553,147 | 2.6% | 6.6% |
| **3-gram** | Subword | 4,599 | 12.17 | 265,628 | 17.2% | 55.9% |
| **4-gram** | Word | 4,222,921 | 22.01 | 12,285,779 | 2.7% | 6.1% |
| **4-gram** | Subword | 30,520 | 14.90 | 1,702,927 | 7.5% | 26.9% |
| **5-gram** | Word | 3,104,259 | 21.57 | 8,851,426 | 3.4% | 7.3% |
| **5-gram** | Subword | 140,455 | 17.10 | 6,669,073 | 3.8% | 16.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `és a` | 750,740 |
| 2 | `hogy a` | 246,908 |
| 3 | `további információk` | 239,762 |
| 4 | `és az` | 222,085 |
| 5 | `volt a` | 210,831 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jegyzetek további információk` | 116,226 |
| 2 | `népesség a település` | 75,437 |
| 3 | `személyek elhunyt személyek` | 70,441 |
| 4 | `született személyek elhunyt` | 69,726 |
| 5 | `további információk megye` | 43,373 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `született személyek elhunyt személyek` | 69,726 |
| 2 | `a település népességének változása` | 42,715 |
| 3 | `népesség a település népességének` | 42,581 |
| 4 | `jegyzetek további információk megye` | 41,857 |
| 5 | `megyében népesség a település` | 40,991 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `népesség a település népességének változása` | 42,500 |
| 2 | `jegyzetek további információk megye települései` | 39,789 |
| 3 | `további információk megye települései létrehozott` | 38,604 |
| 4 | `települései létrehozott francia település cikkek` | 33,554 |
| 5 | `megye települései létrehozott francia település` | 33,497 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a` | 28,615,318 |
| 2 | `a _` | 26,126,954 |
| 3 | `s z` | 20,526,948 |
| 4 | `t _` | 17,995,334 |
| 5 | `e l` | 17,138,516 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a _` | 14,744,854 |
| 2 | `_ s z` | 7,371,389 |
| 3 | `_ a z` | 5,409,490 |
| 4 | `é s _` | 5,376,301 |
| 5 | `s z e` | 5,046,767 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a z _` | 4,706,514 |
| 2 | `_ é s _` | 4,404,673 |
| 3 | `_ e g y` | 2,864,622 |
| 4 | `_ m e g` | 2,653,603 |
| 5 | `_ s z e` | 2,581,753 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ s z e r` | 1,290,178 |
| 2 | `_ a z _ e` | 1,248,859 |
| 3 | `_ é s _ a` | 1,122,375 |
| 4 | `_ e g y _` | 1,119,120 |
| 5 | `_ v o l t` | 1,080,101 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 435
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~16% 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 | 0.9149 | 1.885 | 11.86 | 5,253,585 | 8.5% |
| **1** | Subword | 1.3264 | 2.508 | 10.40 | 16,190 | 0.0% |
| **2** | Word | 0.3314 | 1.258 | 2.16 | 62,241,118 | 66.9% |
| **2** | Subword | 0.6166 | 1.533 | 4.07 | 168,239 | 38.3% |
| **3** | Word | 0.1296 | 1.094 | 1.28 | 134,211,461 | 87.0% |
| **3** | Subword | 0.6817 | 1.604 | 4.31 | 684,267 | 31.8% |
| **4** | Word | 0.0479 🏆 | 1.034 | 1.08 | 171,557,270 | 95.2% |
| **4** | Subword | 0.7163 | 1.643 | 3.92 | 2,950,554 | 28.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a legközelebbi piac volt az amerikai r hernádi judit lánya családjához tartozó veb kranbau hennigsdo...`
2. `az íreket a belül félprím kanonikus alakja a turistaút mellett támadhatók ám később v vlagyimir ilji...`
3. `és a krasznojarszki határterület melyből római korból ugyanis a kerlés beszterce naszód vármegyéhez ...`

**Context Size 2:**

1. `és a vérlemezke szám vizsgálatok az eklampsiasok vérének calciumion concentratiójáról bodó richárdda...`
2. `hogy a tábornagy unokája teschen harmadik hercegének és aragóniai nyelven nyelvjárásban íxar bárója ...`
3. `további információk görög irodalom története athenaeum november 4 a aguja km 279 36 32 53 2 45`

**Context Size 3:**

1. `jegyzetek további információk színészek született személyek személyek színésznők humoristák york iak...`
2. `népesség a település népessége az elmúlt években az alábbi módon változott jegyzetek további informá...`
3. `született személyek elhunyt személyek becsületrend lovagjai tárcaírók származású magyarok emigránsok...`

**Context Size 4:**

1. `született személyek elhunyt személyek nők eurovíziós dalfesztivál pontbejelentői`
2. `a település népességének változása jegyzetek további információk települései létrehozott spanyol tel...`
3. `népesség a település népességének változása jegyzetek további információk megye települései létrehoz...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_bódáműválla_ém_`
2. `etotéspa_mégóncs`
3. `apcigyla_em_k)_h`

**Context Size 2:**

1. `_avallés_ma_akasz`
2. `a_+_céletőbbeild.`
3. `szettáraminterico`

**Context Size 3:**

1. `_a_tor_anni_volsen`
2. `_szólósításai_form`
3. `_az_amika_végzeti_`

**Context Size 4:**

1. `_az_le_a_muzsikus_b`
2. `_és_4-i_egyet_érkez`
3. `_egy_kir._idős_diss`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,950,554 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 | 2,314,804 |
| Total Tokens | 210,700,540 |
| Mean Frequency | 91.02 |
| Median Frequency | 4 |
| Frequency Std Dev | 11249.15 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 15,266,391 |
| 2 | az | 4,841,770 |
| 3 | és | 4,422,301 |
| 4 | is | 1,350,461 |
| 5 | egy | 1,181,563 |
| 6 | hogy | 978,556 |
| 7 | volt | 963,293 |
| 8 | 1 | 909,318 |
| 9 | nem | 804,148 |
| 10 | 2 | 677,083 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | vichyvel | 2 |
| 2 | ftpf | 2 |
| 3 | hakeimi | 2 |
| 4 | ixkun | 2 |
| 5 | demannt | 2 |
| 6 | summercamp | 2 |
| 7 | madguy | 2 |
| 8 | meisterleistung | 2 |
| 9 | copín | 2 |
| 10 | transparentete | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9342 |
| R² (Goodness of Fit) | 0.996484 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.6% |
| Top 1,000 | 45.5% |
| Top 5,000 | 61.8% |
| Top 10,000 | 69.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9965 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.6% of corpus
- **Long Tail:** 2,304,804 words needed for remaining 31.0% 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 | 0.7896 | 0.3549 | N/A | N/A |
| **mono_64d** | 64 | 0.7843 | 0.2900 | N/A | N/A |
| **mono_128d** | 128 | 0.7205 | 0.2280 | N/A | N/A |
| **aligned_32d** | 32 | 0.7896 🏆 | 0.3731 | 0.3780 | 0.7580 |
| **aligned_64d** | 64 | 0.7843 | 0.2877 | 0.5600 | 0.8860 |
| **aligned_128d** | 128 | 0.7205 | 0.2242 | 0.7160 | 0.9400 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7896 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2930. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 71.6% 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 | **-0.542** | 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` | szedhessék, sejttípusban, szemszínű |
| `-k` | kóborlónak, kőalappal, küldetéseikben |
| `-m` | meklēt, morarano, megbüntethették |
| `-a` | ammaniti, aurignacian, aranybaglyok |
| `-t` | tagként, távhőtermelő, terepviszony |
| `-b` | bolondozott, buga, birkózással |
| `-ma` | manbij, macham, magánszínházakban |
| `-e` | elaborate, elitegyetemek, eugène |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-t` | cseréphéjazat, tagként, irritációkat |
| `-k` | kóborlónak, érbetegségek, szedhessék |
| `-n` | vardaman, pihenőhelyükön, sejttípusban |
| `-a` | hera, buga, philosophya |
| `-l` | hurból, lavel, vranishtnál |
| `-s` | francoizmus, nativizálás, öndiagnózis |
| `-i` | ammaniti, lendvai, diófalvi |
| `-e` | elaborate, piauiense, eugène |

### 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 |
|------|----------|------------------|----------|
| `mber` | 1.61x | 605 contexts | ember, umber, ámber |
| `epül` | 1.89x | 164 contexts | repül, repüle, repülő |
| `erül` | 1.60x | 344 contexts | terül, kerül, merül |
| `örté` | 2.09x | 79 contexts | törté, körtés, sörtéi |
| `ület` | 1.50x | 362 contexts | fület, szület, ízület |
| `atás` | 1.41x | 443 contexts | katás, fatás, hatás |
| `rtén` | 2.05x | 57 contexts | artén, értény, történ |
| `ítot` | 1.62x | 161 contexts | ított, sított, vított |
| `ítás` | 1.38x | 376 contexts | sítás, újítás, ámítás |
| `ormá` | 1.46x | 267 contexts | ormán, ormát, dormán |
| `alál` | 1.43x | 226 contexts | talál, halál, valál |
| `lepü` | 2.81x | 14 contexts | telepü, telepük, települ |

### 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 |
|--------|--------|-----------|----------|
| `-k` | `-k` | 118 words | kinyissanak, konowalik |
| `-s` | `-t` | 87 words | szvetlánát, szkádit |
| `-k` | `-t` | 84 words | konceptalbumokat, kevesebbért |
| `-k` | `-l` | 84 words | kártyacsomagokkal, karmáról |
| `-s` | `-l` | 84 words | szénül, szőnyeggyárból |
| `-s` | `-k` | 81 words | sóraktárnak, számolhatnánk |
| `-s` | `-n` | 80 words | sarrewerden, sumbawán |
| `-s` | `-a` | 77 words | sserunkuma, sztalina |
| `-k` | `-a` | 77 words | kruczynska, kivételszámba |
| `-m` | `-k` | 75 words | manhunterek, megbetegedéseik |

### 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 |
|------|-----------------|------------|------|
| családira | **`család-i-ra`** | 7.5 | `i` |
| xantofilek | **`xantofi-l-ek`** | 7.5 | `l` |
| marinaviale | **`marinavi-al-e`** | 7.5 | `al` |
| castillának | **`castillá-n-ak`** | 7.5 | `n` |
| karakterjének | **`karakterjé-n-ek`** | 7.5 | `n` |
| kampánystábjának | **`kampánystábjá-n-ak`** | 7.5 | `n` |
| nyelveire | **`nyelve-i-re`** | 7.5 | `i` |
| távharcban | **`távharc-ba-n`** | 7.5 | `ba` |
| guadalcanalt | **`guadalcan-al-t`** | 7.5 | `al` |
| palesztínai | **`palesztín-a-i`** | 7.5 | `a` |
| idénymunkákon | **`idénymunká-k-on`** | 7.5 | `k` |
| képzőművészeknek | **`képzőművészek-n-ek`** | 7.5 | `n` |
| paakkanen | **`paakka-n-en`** | 7.5 | `n` |
| körlapnak | **`körlap-n-ak`** | 7.5 | `n` |
| férfimunkások | **`férfimunká-s-ok`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Hungarian 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 (4.66x) |
| N-gram | **2-gram** | Lowest perplexity (435) |
| Markov | **Context-4** | Highest predictability (95.2%) |
| 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: 2026-01-13 20:45:23*