---
language: cs
language_name: Czech
language_family: slavic_west
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-slavic_west
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: 4.591
  - name: best_isotropy
    type: isotropy
    value: 0.7988
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-08
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Czech** 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** | 3.417x | 3.42 | 0.0769% | 2,893,388 |
| **16k** | 3.845x | 3.85 | 0.0865% | 2,570,989 |
| **32k** | 4.245x | 4.25 | 0.0955% | 2,328,840 |
| **64k** | 4.591x 🏆 | 4.59 | 0.1033% | 2,153,192 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `<tr> Související články Seznam kulturních památek v okrese Znojmo Externí odkazy...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁< tr > ▁související ▁články ▁seznam ▁kultur ních ▁pam átek ... (+17 more)` | 27 |
| 16k | `▁< tr > ▁související ▁články ▁seznam ▁kulturních ▁památek ▁v ▁okrese ... (+13 more)` | 23 |
| 32k | `▁< tr > ▁související ▁články ▁seznam ▁kulturních ▁památek ▁v ▁okrese ... (+11 more)` | 21 |
| 64k | `▁< tr > ▁související ▁články ▁seznam ▁kulturních ▁památek ▁v ▁okrese ... (+11 more)` | 21 |

**Sample 2:** `Mirovice <tr> Sochovice <tr> Související články Seznam kulturních památek v okre...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mi rovice ▁< tr > ▁so ch ovice ▁< tr ... (+17 more)` | 27 |
| 16k | `▁mi rovice ▁< tr > ▁so chovice ▁< tr > ... (+14 more)` | 24 |
| 32k | `▁mi rovice ▁< tr > ▁so chovice ▁< tr > ... (+14 more)` | 24 |
| 64k | `▁mi rovice ▁< tr > ▁so chovice ▁< tr > ... (+14 more)` | 24 |

**Sample 3:** `Sabra může být: sabra – hebrejské slovo Sabra (tank) Sabra – sídlo v Libanonu, d...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sa bra ▁může ▁být : ▁sa bra ▁– ▁hebrej ské ... (+22 more)` | 32 |
| 16k | `▁sa bra ▁může ▁být : ▁sa bra ▁– ▁hebrej ské ... (+21 more)` | 31 |
| 32k | `▁sa bra ▁může ▁být : ▁sa bra ▁– ▁hebrejské ▁slovo ... (+17 more)` | 27 |
| 64k | `▁sa bra ▁může ▁být : ▁sa bra ▁– ▁hebrejské ▁slovo ... (+15 more)` | 25 |


### Key Findings

- **Best Compression:** 64k achieves 4.591x compression
- **Lowest UNK Rate:** 8k with 0.0769% 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 | 644,039 | 19.30 | 4,952,358 | 4.8% | 11.9% |
| **2-gram** | Subword | 449 🏆 | 8.81 | 30,223 | 53.9% | 98.0% |
| **3-gram** | Word | 2,339,059 | 21.16 | 8,925,525 | 2.6% | 6.4% |
| **3-gram** | Subword | 4,755 | 12.22 | 255,109 | 16.7% | 54.3% |
| **4-gram** | Word | 5,475,376 | 22.38 | 14,408,434 | 1.3% | 3.9% |
| **4-gram** | Subword | 32,796 | 15.00 | 1,646,964 | 6.8% | 24.8% |
| **5-gram** | Word | 4,645,198 | 22.15 | 10,221,820 | 1.0% | 3.6% |
| **5-gram** | Subword | 160,592 | 17.29 | 6,437,902 | 3.7% | 13.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `v roce` | 1,319,715 |
| 2 | `externí odkazy` | 445,741 |
| 3 | `odkazy reference` | 238,320 |
| 4 | `reference externí` | 226,335 |
| 5 | `v letech` | 212,278 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `reference externí odkazy` | 226,294 |
| 2 | `odkazy reference externí` | 124,877 |
| 3 | `v roce v` | 123,855 |
| 4 | `v roce se` | 91,582 |
| 5 | `v roce byl` | 64,824 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `odkazy reference externí odkazy` | 124,850 |
| 2 | `odkazy reference související články` | 42,127 |
| 3 | `v roce v roce` | 34,075 |
| 4 | `reference externí odkazy v` | 29,798 |
| 5 | `externí odkazy oficiální stránky` | 20,103 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `odkazy reference externí odkazy v` | 16,236 |
| 2 | `odkazy reference literatura externí odkazy` | 12,685 |
| 3 | `reference externí odkazy oficiální stránky` | 11,834 |
| 4 | `historie první písemná zmínka o` | 11,754 |
| 5 | `reference externí odkazy v okrese` | 11,425 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 24,781,439 |
| 2 | `_ p` | 22,589,509 |
| 3 | `e _` | 22,268,109 |
| 4 | `_ s` | 22,095,879 |
| 5 | `_ v` | 19,926,387 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n í _` | 7,673,842 |
| 2 | `_ p o` | 7,582,650 |
| 3 | `_ v _` | 7,272,309 |
| 4 | `n a _` | 6,690,107 |
| 5 | `_ a _` | 6,501,417 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n a _` | 3,511,209 |
| 2 | `_ s e _` | 3,364,693 |
| 3 | `_ p r o` | 3,186,267 |
| 4 | `_ b y l` | 2,542,448 |
| 5 | `ý c h _` | 2,252,305 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k t e r` | 1,412,346 |
| 2 | `_ r o c e` | 1,383,042 |
| 3 | `_ v _ r o` | 1,382,611 |
| 4 | `r o c e _` | 1,354,432 |
| 5 | `v _ r o c` | 1,321,210 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 449
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~14% 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 | 1.0698 | 2.099 | 16.20 | 3,817,910 | 0.0% |
| **1** | Subword | 1.2123 | 2.317 | 8.62 | 14,369 | 0.0% |
| **2** | Word | 0.3832 | 1.304 | 2.35 | 61,779,051 | 61.7% |
| **2** | Subword | 0.6716 | 1.593 | 4.71 | 123,767 | 32.8% |
| **3** | Word | 0.1433 | 1.104 | 1.31 | 144,949,424 | 85.7% |
| **3** | Subword | 0.7660 | 1.701 | 4.77 | 583,275 | 23.4% |
| **4** | Word | 0.0564 🏆 | 1.040 | 1.10 | 189,649,924 | 94.4% |
| **4** | Subword | 0.7409 | 1.671 | 4.00 | 2,782,368 | 25.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `v podobě vystavěn byl opětovně pohřbena ve dveřích některých případech může vytvořit jediné dopravní...`
2. `a příslušník staré město zbiroh živa je americký teoretický kvantový stav potrvá v létě odešel na`
3. `na fakt že neměl v červenci i z původních 113 120 metrů vysokém tlaku na východě`

**Context Size 2:**

1. `v roce lidé 6 prosince praha byl michal kraus čssd čssd 48 rychnov nad kněžnou kaple stojí`
2. `externí odkazy jihovýchodní evropy jihozápadní asie kavkazu číny sibiře východní asie hustě chlupatá...`
3. `odkazy reference externí odkazy sdružení na praze 4 rozhovor vznikl v roce kde bojoval proti ostrogó...`

**Context Size 3:**

1. `reference externí odkazy v ternopilské oblasti na řece strypa v historickém regionu horní lužice mim...`
2. `odkazy reference externí odkazy speleologická společnost vševěd romantismu hudební skladatelé klavír...`
3. `v roce v angličtině se pro celou skupinu alfred crompton catherine musinsky jose bonaparte bhart anj...`

**Context Size 4:**

1. `odkazy reference externí odkazy strategie série`
2. `odkazy reference související články fotografie v norsku externí odkazy na seznamu světového dědictví...`
3. `v roce v roce v praze pilotní školu druhá světová válka po roce vojenské služby v polské armádě prot...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_hraloponodovo._`
2. `os_zu_va_vu_dulo`
3. `ekodici_micl_v_s`

**Context Size 2:**

1. `a_stříjna_se_rozh`
2. `_příčku_uraven_pe`
3. `e_na_vítlická_hov`

**Context Size 3:**

1. `ní_nejčastoru_o_sp`
2. `_polik_v_com_trans`
3. `_v_195_zúčasná_náz`

**Context Size 4:**

1. `_na_v_nicméně_chlaz`
2. `_se_proje_asistenci`
3. `_pro_pozdně,_lze_sa`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,782,368 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 | 1,830,714 |
| Total Tokens | 237,612,209 |
| Mean Frequency | 129.79 |
| Median Frequency | 5 |
| Frequency Std Dev | 9362.17 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | v | 7,396,110 |
| 2 | a | 6,633,731 |
| 3 | na | 3,536,561 |
| 4 | se | 3,396,490 |
| 5 | je | 2,110,163 |
| 6 | s | 1,781,636 |
| 7 | z | 1,747,028 |
| 8 | do | 1,440,810 |
| 9 | roce | 1,383,007 |
| 10 | ve | 1,284,897 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mihty | 2 |
| 2 | socionaut | 2 |
| 3 | mafjar | 2 |
| 4 | vlta | 2 |
| 5 | havlátková | 2 |
| 6 | makbúsu | 2 |
| 7 | propfanů | 2 |
| 8 | propfanu | 2 |
| 9 | ochmeloff | 2 |
| 10 | luncași | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9138 |
| R² (Goodness of Fit) | 0.997539 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 27.1% |
| Top 1,000 | 45.7% |
| Top 5,000 | 63.0% |
| Top 10,000 | 70.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9975 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 27.1% of corpus
- **Long Tail:** 1,820,714 words needed for remaining 29.4% 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 | 0.7988 | 0.3622 | N/A | N/A |
| **mono_64d** | 64 | 0.7835 | 0.2893 | N/A | N/A |
| **mono_128d** | 128 | 0.7363 | 0.2299 | N/A | N/A |
| **aligned_32d** | 32 | 0.7988 🏆 | 0.3646 | 0.3500 | 0.7360 |
| **aligned_64d** | 64 | 0.7835 | 0.2898 | 0.5900 | 0.8980 |
| **aligned_128d** | 128 | 0.7363 | 0.2271 | 0.7320 | 0.9520 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7988 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2938. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 73.2% 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 | **-0.741** | 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 |
|--------|----------|
| `-ne` | nezamítl, neomorf, nenapájeným |
| `-po` | poštulky, ponoršťování, powerkiting |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-em` | charmsem, treitschkem, holtem |
| `-ch` | orbitalech, lekebusch, sklízených |
| `-ho` | vladivostockého, sertoliho, cenokarpního |
| `-ou` | hobgarskou, výfukovou, robotou |

### 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 |
|------|----------|------------------|----------|
| `ovýc` | 2.16x | 487 contexts | ových, xových, nových |
| `skéh` | 2.15x | 392 contexts | ského, lského, urského |
| `skýc` | 1.97x | 237 contexts | ských, skýcov, tských |
| `ický` | 1.57x | 496 contexts | tický, bický, úpický |
| `nské` | 1.53x | 491 contexts | anské, inské, ínské |
| `ován` | 1.44x | 594 contexts | ování, kován, zování |
| `ické` | 1.46x | 499 contexts | tické, lické, mické |
| `ledn` | 1.59x | 250 contexts | lednu, ledna, ledný |
| `itel` | 1.36x | 634 contexts | nitel, litel, pitel |
| `cház` | 1.52x | 287 contexts | chází, schází, ochází |
| `dkaz` | 2.66x | 23 contexts | odkaz, odkaze, odkazy |
| `xter` | 1.81x | 76 contexts | exter, xterm, extern |

### 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 |
|--------|--------|-----------|----------|
| `-ne` | `-ch` | 14 words | nepropouštějících, netermínovaných |
| `-ne` | `-ho` | 10 words | nejpokročilejšího, nezpochybnitelného |
| `-ne` | `-ou` | 9 words | nestejnou, nerozšiřitelnou |
| `-po` | `-ho` | 9 words | podmínkového, polštářovitého |
| `-po` | `-ch` | 7 words | pohodlnějších, polohovkách |
| `-po` | `-ou` | 6 words | ponitranskou, pomátnou |
| `-po` | `-em` | 3 words | pollackem, povříslem |

### 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 |
|------|-----------------|------------|------|
| nedoloženou | **`ne-doložen-ou`** | 6.0 | `doložen` |
| nepochybovala | **`ne-po-chybovala`** | 6.0 | `chybovala` |
| nepostaral | **`ne-po-staral`** | 6.0 | `staral` |
| nacionálem | **`nacionál-em`** | 4.5 | `nacionál` |
| chimentiho | **`chimenti-ho`** | 4.5 | `chimenti` |
| prostonárodního | **`prostonárodní-ho`** | 4.5 | `prostonárodní` |
| klokotských | **`klokotský-ch`** | 4.5 | `klokotský` |
| bibliografického | **`bibliografické-ho`** | 4.5 | `bibliografické` |
| nesvědčily | **`ne-svědčily`** | 4.5 | `svědčily` |
| nenavázali | **`ne-navázali`** | 4.5 | `navázali` |
| ibragimovem | **`ibragimov-em`** | 4.5 | `ibragimov` |
| zeměplošských | **`zeměplošský-ch`** | 4.5 | `zeměplošský` |
| hliníkových | **`hliníkový-ch`** | 4.5 | `hliníkový` |
| etylenglykolem | **`etylenglykol-em`** | 4.5 | `etylenglykol` |
| mnohosamicového | **`mnohosamicové-ho`** | 4.5 | `mnohosamicové` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Czech 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 (4.59x) |
| N-gram | **2-gram** | Lowest perplexity (449) |
| Markov | **Context-4** | Highest predictability (94.4%) |
| 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: 2026-01-08 17:02:58*