---
language: hsb
language_name: Upper Sorbian
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: 4.478
  - name: best_isotropy
    type: isotropy
    value: 0.8367
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Upper Sorbian - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Upper Sorbian** 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** | 3.442x | 3.44 | 0.2404% | 413,488 |
| **16k** | 3.823x | 3.83 | 0.2670% | 372,334 |
| **32k** | 4.173x | 4.18 | 0.2914% | 341,064 |
| **64k** | 4.478x 🏆 | 4.48 | 0.3127% | 317,901 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Das Karpatenblatt su němskorěčne nowiny za němsku mjeńšinu (něhdźe 5.500 ludźi) ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁das ▁kar pat en bla tt ▁su ▁němskorěč ne ▁nowiny ... (+20 more)` | 30 |
| 16k | `▁das ▁karpat en blatt ▁su ▁němskorěč ne ▁nowiny ▁za ▁němsku ... (+15 more)` | 25 |
| 32k | `▁das ▁karpat en blatt ▁su ▁němskorěčne ▁nowiny ▁za ▁němsku ▁mjeńšinu ... (+13 more)` | 23 |
| 64k | `▁das ▁karpat en blatt ▁su ▁němskorěčne ▁nowiny ▁za ▁němsku ▁mjeńšinu ... (+13 more)` | 23 |

**Sample 2:** `Gotho je asteroid, kotryž ma přeměr 58 km a kotryž wotkry Karl Wilhelm Reinmuth ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁got ho ▁je ▁asteroid , ▁kotryž ▁ma ▁přeměr ▁ 5 ... (+15 more)` | 25 |
| 16k | `▁got ho ▁je ▁asteroid , ▁kotryž ▁ma ▁přeměr ▁ 5 ... (+13 more)` | 23 |
| 32k | `▁got ho ▁je ▁asteroid , ▁kotryž ▁ma ▁přeměr ▁ 5 ... (+13 more)` | 23 |
| 64k | `▁got ho ▁je ▁asteroid , ▁kotryž ▁ma ▁přeměr ▁ 5 ... (+13 more)` | 23 |

**Sample 3:** `Tha abo sa (arab. ثاء‎‎) je štwórty pismik arabskeho alfabeta a woznamjenja zwuk...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tha ▁abo ▁sa ▁( arab . ▁ ث ا ء ... (+31 more)` | 41 |
| 16k | `▁tha ▁abo ▁sa ▁( arab . ▁ ث ا ء ... (+24 more)` | 34 |
| 32k | `▁tha ▁abo ▁sa ▁( arab . ▁ ث ا ء ... (+24 more)` | 34 |
| 64k | `▁tha ▁abo ▁sa ▁( arab . ▁ ث ا ء ... (+24 more)` | 34 |


### Key Findings

- **Best Compression:** 64k achieves 4.478x compression
- **Lowest UNK Rate:** 8k with 0.2404% 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 | 7,472 | 12.87 | 36,994 | 24.4% | 49.2% |
| **2-gram** | Subword | 432 🏆 | 8.75 | 5,177 | 55.1% | 97.8% |
| **3-gram** | Word | 7,937 | 12.95 | 54,451 | 29.3% | 49.8% |
| **3-gram** | Subword | 3,653 | 11.83 | 38,557 | 19.7% | 60.6% |
| **4-gram** | Word | 10,360 | 13.34 | 90,527 | 31.2% | 48.3% |
| **4-gram** | Subword | 17,324 | 14.08 | 184,751 | 9.7% | 35.1% |
| **5-gram** | Word | 6,543 | 12.68 | 69,594 | 36.6% | 53.8% |
| **5-gram** | Subword | 48,335 | 15.56 | 450,452 | 6.5% | 26.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `w lěće` | 6,496 |
| 2 | `hač do` | 4,857 |
| 3 | `ze swójby` | 3,718 |
| 4 | `wot lěta` | 3,612 |
| 5 | `so w` | 3,439 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `słownik hornjołužiskeje rěče` | 2,945 |
| 2 | `serbski wšowědny słownik` | 2,828 |
| 3 | `němsko serbski wšowědny` | 2,828 |
| 4 | `wšowědny słownik hornjołužiskeje` | 2,827 |
| 5 | `hornjołužiskeje rěče donnerhak` | 2,815 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `němsko serbski wšowědny słownik` | 2,828 |
| 2 | `wšowědny słownik hornjołužiskeje rěče` | 2,827 |
| 3 | `serbski wšowědny słownik hornjołužiskeje` | 2,827 |
| 4 | `słownik hornjołužiskeje rěče donnerhak` | 2,815 |
| 5 | `filip němsko serbski wšowědny` | 2,814 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `němsko serbski wšowědny słownik hornjołužiskeje` | 2,827 |
| 2 | `serbski wšowědny słownik hornjołužiskeje rěče` | 2,827 |
| 3 | `wšowědny słownik hornjołužiskeje rěče donnerhak` | 2,815 |
| 4 | `filip němsko serbski wšowědny słownik` | 2,814 |
| 5 | `słownik hornjołužiskeje rěče donnerhak budyšin` | 2,811 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 280,688 |
| 2 | `e _` | 244,497 |
| 3 | `j e` | 227,943 |
| 4 | `_ w` | 207,965 |
| 5 | `_ s` | 178,194 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j e _` | 95,450 |
| 2 | `_ w o` | 74,945 |
| 3 | `s k e` | 65,512 |
| 4 | `s k i` | 54,698 |
| 5 | `n a _` | 54,030 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s k i _` | 31,701 |
| 2 | `_ w o t` | 30,128 |
| 3 | `s k e j` | 29,139 |
| 4 | `n j e _` | 28,786 |
| 5 | `_ j e _` | 27,490 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s e r b s` | 24,332 |
| 2 | `e r b s k` | 23,519 |
| 3 | `_ s e r b` | 19,511 |
| 4 | `_ r o s t` | 18,011 |
| 5 | `s t l i n` | 17,455 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 432
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.7366 | 1.666 | 4.48 | 174,223 | 26.3% |
| **1** | Subword | 1.1524 | 2.223 | 9.47 | 1,407 | 0.0% |
| **2** | Word | 0.2172 | 1.163 | 1.50 | 778,883 | 78.3% |
| **2** | Subword | 0.9361 | 1.913 | 5.84 | 13,316 | 6.4% |
| **3** | Word | 0.0830 | 1.059 | 1.15 | 1,160,767 | 91.7% |
| **3** | Subword | 0.7921 | 1.732 | 4.05 | 77,743 | 20.8% |
| **4** | Word | 0.0410 🏆 | 1.029 | 1.07 | 1,326,579 | 95.9% |
| **4** | Subword | 0.6449 | 1.564 | 2.82 | 315,129 | 35.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a wopytowaše wot lěta podawki narodniny 15 septembra w lěće jako tajki z konjom karl wilhelm`
2. `w hornjołužiskim budyskim wokrjesu w europskim dźělu oceana na cd rom rěčny centrum witaj wudaće za`
3. `je rostlina je wjesna gmejna słuša w oktobrje samsneho lěta za 239 30 nowembra železniska čara`

**Context Size 2:**

1. `w lěće je zmóžnjene wopisanje twarske a stawizniske drobnostki kulturneho pomnika lisćina kulturnych...`
2. `hač do nektara docpěć za čas ndr bě nimo toho je wón pohibowansku załožbu awstriska bewegungsstiftun...`
3. `ze swójby rupikowych rostlinow saxifragaceae dalše serbske mjeno pochadźa z lěta ditmarus miles de z...`

**Context Size 3:**

1. `słownik hornjołužiskeje rěče donnerhak budyšin eksterne wotkazy kategorija drapalcowe rostliny`
2. `serbski wšowědny słownik hornjołužiskeje rěče donnerhak budyšin kategorija wijawkowe rostliny`
3. `němsko serbski wšowědny słownik hornjołužiskeje rěče donnerhak budyšin eksterne wotkazy rostliny płó...`

**Context Size 4:**

1. `němsko serbski wšowědny słownik hornjołužiskeje rěče donnerhak budyšin rostliny rostliny`
2. `serbski wšowědny słownik hornjołužiskeje rěče donnerhak budyšin eksterne wotkazy rostliny rostliny f...`
3. `wšowědny słownik hornjołužiskeje rěče donnerhak budyšin kategorija křižnokwětne rostliny kategorija ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_rspodntranar_k_`
2. `anspitowet_zaron`
3. `e_homolět_c_stko`

**Context Size 2:**

1. `a_-_mjesej_juho_k`
2. `e_pryskotryčarij:`
3. `je_17_a_dle_hronj`

**Context Size 3:**

1. `je_mje._wotesać._c`
2. `_wot_lěta_frankačk`
3. `skej_skupuje_flerj`

**Context Size 4:**

1. `ski_gymna_rozšěrjen`
2. `_wot_a_př._chětrow_`
3. `nje_k_boliwišerstwj`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (315,129 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 | 74,135 |
| Total Tokens | 1,812,376 |
| Mean Frequency | 24.45 |
| Median Frequency | 4 |
| Frequency Std Dev | 358.06 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 51,679 |
| 2 | w | 47,800 |
| 3 | je | 27,682 |
| 4 | na | 21,213 |
| 5 | wot | 17,579 |
| 6 | so | 17,137 |
| 7 | z | 16,585 |
| 8 | do | 13,766 |
| 9 | za | 8,969 |
| 10 | po | 8,787 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kaschcżik | 2 |
| 2 | rukowom | 2 |
| 3 | bydlišćemi | 2 |
| 4 | direktorojo | 2 |
| 5 | łuchowom | 2 |
| 6 | groźišćom | 2 |
| 7 | perfektna | 2 |
| 8 | herzbergskeho | 2 |
| 9 | herzbergom | 2 |
| 10 | jg | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0600 |
| R² (Goodness of Fit) | 0.996792 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.2% |
| Top 1,000 | 61.3% |
| Top 5,000 | 77.8% |
| Top 10,000 | 84.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9968 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.2% of corpus
- **Long Tail:** 64,135 words needed for remaining 15.7% coverage

---
## 5. Word Embeddings Evaluation

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

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

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

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


### 5.1 Cross-Lingual Alignment

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

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


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.8367 🏆 | 0.3521 | N/A | N/A |
| **mono_64d** | 64 | 0.7985 | 0.2796 | N/A | N/A |
| **mono_128d** | 128 | 0.5471 | 0.2451 | N/A | N/A |
| **aligned_32d** | 32 | 0.8367 | 0.3504 | 0.0560 | 0.2700 |
| **aligned_64d** | 64 | 0.7985 | 0.2762 | 0.0740 | 0.3240 |
| **aligned_128d** | 128 | 0.5471 | 0.2552 | 0.1060 | 0.4020 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8367 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2931. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.6% 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 | **1.068** | 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 |
|--------|----------|
| `-s` | skalický, sora, schweiz |
| `-p` | polygaleae, pokazowaše, phil |
| `-k` | konfesiji, kawkaski, kóždy |
| `-b` | beethoven, biotit, botaniskeje |
| `-m` | morjo, měnjenjach, małoróstna |
| `-w` | wysokosću, wječorki, wustawowa |
| `-d` | dresdner, döbeln, dołach |
| `-a` | asclepias, apple, arndt |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | radomia, rjemjeslnistwa, wustawowa |
| `-e` | polygaleae, noémie, pokazowaše |
| `-je` | južnoafriskeje, himalaje, botaniskeje |
| `-ch` | měnjenjach, kašecach, hustich |
| `-i` | wječorki, konfesiji, kawkaski |
| `-y` | goramśicy, ćahawy, kóždy |
| `-m` | triumfowym, scabrum, tuchwilnym |
| `-h` | měnjenjach, kašecach, hustich |

### 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 |
|------|----------|------------------|----------|
| `skic` | 2.28x | 33 contexts | skica, skicy, skicow |
| `jenj` | 1.76x | 85 contexts | jenje, rjenje, mjenja |
| `skej` | 1.69x | 79 contexts | muskej, ošskej, ruskej |
| `tlin` | 2.28x | 24 contexts | catlin, rostlin, watling |
| `mjen` | 1.47x | 87 contexts | kmjen, mjena, mjenu |
| `owan` | 1.39x | 77 contexts | głowan, wowanus, głowana |
| `iske` | 1.43x | 68 contexts | niske, aziske, bliske |
| `słow` | 1.79x | 28 contexts | słowo, słowa, słowu |
| `keje` | 2.10x | 15 contexts | muskeje, małkeje, tajkeje |
| `stli` | 2.39x | 10 contexts | rostlin, östlich, rostlinu |
| `erbs` | 1.75x | 22 contexts | verbs, zerbst, herbst |
| `rbsk` | 1.79x | 20 contexts | srbská, serbske, serbska |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-e` | 144 words | přeněmčenje, priwatnje |
| `-p` | `-a` | 140 words | paederija, pućowanska |
| `-w` | `-e` | 123 words | wozrodźenje, watowe |
| `-s` | `-a` | 120 words | svitava, stachowa |
| `-s` | `-e` | 107 words | spódnje, shane |
| `-k` | `-a` | 103 words | kuala, kajkostnika |
| `-w` | `-a` | 98 words | widźa, wersija |
| `-m` | `-a` | 78 words | majska, mina |
| `-b` | `-a` | 76 words | bira, bzeža |
| `-k` | `-e` | 74 words | kotmarje, knježerstwje |

### 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 |
|------|-----------------|------------|------|
| serbskeju | **`serbsk-e-ju`** | 7.5 | `e` |
| thomaschk | **`thomas-ch-k`** | 7.5 | `ch` |
| maćičneje | **`maćičn-e-je`** | 7.5 | `e` |
| přesadźichu | **`přesadźi-ch-u`** | 7.5 | `ch` |
| bibliotekach | **`bibliotek-a-ch`** | 7.5 | `a` |
| wjedźechu | **`wjedźe-ch-u`** | 7.5 | `ch` |
| systematischen | **`systematis-ch-en`** | 7.5 | `ch` |
| mróčelach | **`mróčel-a-ch`** | 7.5 | `a` |
| zběhnychu | **`zběhny-ch-u`** | 7.5 | `ch` |
| handbücher | **`handbü-ch-er`** | 7.5 | `ch` |
| ćišćaneho | **`ćišćan-e-ho`** | 7.5 | `e` |
| demokratische | **`demokratis-ch-e`** | 7.5 | `ch` |
| biographical | **`biographic-a-l`** | 7.5 | `a` |
| utahensis | **`utahen-s-is`** | 7.5 | `s` |
| rubježneho | **`rubježn-e-ho`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Upper Sorbian 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 | **64k BPE** | Best compression (4.48x) |
| N-gram | **2-gram** | Lowest perplexity (432) |
| Markov | **Context-4** | Highest predictability (95.9%) |
| 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 02:59:16*