---
language: dsb
language_name: Lower 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: 4.367
  - name: best_isotropy
    type: isotropy
    value: 0.8231
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Lower 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** | 3.295x | 3.30 | 0.1090% | 314,655 |
| **16k** | 3.690x | 3.69 | 0.1221% | 280,957 |
| **32k** | 4.049x | 4.05 | 0.1339% | 256,086 |
| **64k** | 4.367x 🏆 | 4.37 | 0.1445% | 237,425 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Andrew Garfield (* 20. awgusta Los Angeles) jo amerikański grajaŕ. Eksterne wótk...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁andre w ▁gar fi el d ▁(* ▁ 2 0 ... (+12 more)` | 22 |
| 16k | `▁andre w ▁gar fi eld ▁(* ▁ 2 0 . ... (+11 more)` | 21 |
| 32k | `▁andrew ▁gar field ▁(* ▁ 2 0 . ▁awgusta ▁los ... (+9 more)` | 19 |
| 64k | `▁andrew ▁garfield ▁(* ▁ 2 0 . ▁awgusta ▁los ▁angeles ... (+8 more)` | 18 |

**Sample 2:** `Pabianice jo město w Pólskej, w łódźskem wójwodstwje, we wokrejsu Pabianice. W l...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pa bia nice ▁jo ▁město ▁w ▁pólskej , ▁w ▁łódźskem ... (+26 more)` | 36 |
| 16k | `▁pa bia nice ▁jo ▁město ▁w ▁pólskej , ▁w ▁łódźskem ... (+26 more)` | 36 |
| 32k | `▁pabianice ▁jo ▁město ▁w ▁pólskej , ▁w ▁łódźskem ▁wójwodstwje , ... (+22 more)` | 32 |
| 64k | `▁pabianice ▁jo ▁město ▁w ▁pólskej , ▁w ▁łódźskem ▁wójwodstwje , ... (+22 more)` | 32 |

**Sample 3:** `Żukowo (kaš. Żukòwò, nim. Zuckau) jo město w Pólskej, kótarež lažy w pomorskem w...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ż u kowo ▁( kaš . ▁ż uk ò w ... (+22 more)` | 32 |
| 16k | `▁ż u kowo ▁( kaš . ▁ż uk ò w ... (+22 more)` | 32 |
| 32k | `▁żukowo ▁( kaš . ▁ż ukòwò , ▁nim . ▁zu ... (+17 more)` | 27 |
| 64k | `▁żukowo ▁( kaš . ▁żukòwò , ▁nim . ▁zu ckau ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 64k achieves 4.367x compression
- **Lowest UNK Rate:** 8k with 0.1090% 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 | 4,470 | 12.13 | 8,572 | 17.8% | 48.2% |
| **2-gram** | Subword | 446 🏆 | 8.80 | 3,440 | 54.0% | 97.7% |
| **3-gram** | Word | 5,728 | 12.48 | 9,797 | 15.0% | 41.9% |
| **3-gram** | Subword | 4,110 | 12.01 | 24,943 | 18.0% | 57.3% |
| **4-gram** | Word | 10,398 | 13.34 | 16,574 | 10.9% | 31.5% |
| **4-gram** | Subword | 21,363 | 14.38 | 109,172 | 8.1% | 29.6% |
| **5-gram** | Word | 7,815 | 12.93 | 11,757 | 11.1% | 34.9% |
| **5-gram** | Subword | 57,069 | 15.80 | 221,040 | 5.0% | 20.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `až do` | 933 |
| 2 | `w lěśe` | 890 |
| 3 | `jo był` | 874 |
| 4 | `jo se` | 751 |
| 5 | `w pólskej` | 720 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jo město w` | 444 |
| 2 | `w lěśe jo` | 408 |
| 3 | `w pólskej w` | 301 |
| 4 | `jo how bydliło` | 290 |
| 5 | `město w pólskej` | 280 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jo město w pólskej` | 278 |
| 2 | `lěśe jo how bydliło` | 271 |
| 3 | `w lěśe jo how` | 271 |
| 4 | `město w pólskej w` | 265 |
| 5 | `luźi galerija w pólskej` | 195 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `w lěśe jo how bydliło` | 271 |
| 2 | `jo město w pólskej w` | 264 |
| 3 | `oslwokrejs górne błota łužyca bramborska` | 123 |
| 4 | `spohn was blüht denn da` | 92 |
| 5 | `bechtle spohn was blüht denn` | 92 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 64,101 |
| 2 | `e _` | 45,814 |
| 3 | `_ w` | 44,765 |
| 4 | `_ s` | 35,936 |
| 5 | `o _` | 35,677 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j o _` | 13,646 |
| 2 | `_ j o` | 12,615 |
| 3 | `_ a _` | 11,980 |
| 4 | `n a _` | 11,930 |
| 5 | `s k e` | 11,746 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ j o _` | 11,352 |
| 2 | `s k i _` | 7,449 |
| 3 | `s k e j` | 6,203 |
| 4 | `_ w ó t` | 6,170 |
| 5 | `s k a _` | 4,852 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ w ó t _` | 3,402 |
| 2 | `s e r b s` | 3,221 |
| 3 | `e r b s k` | 3,202 |
| 4 | `_ s e r b` | 2,762 |
| 5 | `a _ j o _` | 2,563 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 446
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~20% 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 | 0.6397 | 1.558 | 3.41 | 79,306 | 36.0% |
| **1** | Subword | 1.0660 | 2.094 | 8.70 | 993 | 0.0% |
| **2** | Word | 0.1672 | 1.123 | 1.33 | 269,674 | 83.3% |
| **2** | Subword | 0.9899 | 1.986 | 5.80 | 8,629 | 1.0% |
| **3** | Word | 0.0539 | 1.038 | 1.08 | 355,887 | 94.6% |
| **3** | Subword | 0.8277 | 1.775 | 3.86 | 50,014 | 17.2% |
| **4** | Word | 0.0234 🏆 | 1.016 | 1.03 | 383,185 | 97.7% |
| **4** | Subword | 0.6176 | 1.534 | 2.51 | 193,064 | 38.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a hiri słowo jo był historiski region region region iv december dartford engelska 6 kulojte až`
2. `w pomorskem wójewódstwje we chicago homepage lfn english creoles spoken in 3 349 300 źiśi ze`
3. `jo jano 13 v werner měškank serbski słownik za literaturu w pólskej w prien am nordrand`

**Context Size 2:**

1. `až do drjowku w lěśe jo how bydliło 2 467 luźi galerija w pólskej w kujawsko pomorskem`
2. `w lěśe wóna jo była hanka krawcec cłonkojstwo domowinje pśisłušaju slědujuce towaristwa župy budyšyn...`
3. `jo był dolnołužyska wjas pla chóśebuza wót lěta pśecej na pjerwjejšnych systemach by mógło se snaź d...`

**Context Size 3:**

1. `jo město w pólskej w podkarpatskem wójwodstwje we wokrejsu chełmno w lěśe jo how bydliło 57 458 luźi`
2. `w lěśe jo w sankt petersburgu jo był jaden z nejwuznamnjejšych zastupnikow tak pomjenjonego bergaŕsk...`
3. `w pólskej w kujawsko pomorskem wójwodstwje we wokrejsu leżajsk w lěśe jo how bydliło 127 602 luźi ek...`

**Context Size 4:**

1. `jo město w pólskej w lublińskem wójwodstwje we wokrejsu hrubieszów w lěśe jo how bydliło 13 766 luźi...`
2. `lěśe jo how bydliło 65 149 luźi historiski centrum jo na lisćinje unesco mě w drugich rěcach vilnius...`
3. `w lěśe jo how bydliło 3 223 luźi galerija eksterne wótkaze biała rawska pól biała rawska pól w pólsk...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_zojejost_łnja_s`
2. `aropynderoveiin.`
3. `epruroni_dpekaru`

**Context Size 2:**

1. `a_kótka_źiw_mil_w`
2. `e_da_kuchórbski_t`
3. `_w_sertika_wu_re_`

**Context Size 3:**

1. `jo_spis_krěpojcne_`
2. `_jo_septemata_kral`
3. `_a_wótšy_pśeder_wi`

**Context Size 4:**

1. `_jo_kupki_spisowaśe`
2. `ski_casom_stiftung_`
3. `_wótwezeł._pěś_žołt`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (193,064 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 | 31,116 |
| Total Tokens | 390,195 |
| Mean Frequency | 12.54 |
| Median Frequency | 3 |
| Frequency Std Dev | 136.48 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 12,373 |
| 2 | w | 12,119 |
| 3 | jo | 11,480 |
| 4 | na | 4,655 |
| 5 | z | 4,220 |
| 6 | se | 3,637 |
| 7 | wót | 3,522 |
| 8 | su | 2,923 |
| 9 | do | 2,438 |
| 10 | za | 1,989 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | wikowje | 2 |
| 2 | kšace | 2 |
| 3 | gotował | 2 |
| 4 | moderěrował | 2 |
| 5 | procowarjow | 2 |
| 6 | zachdniego | 2 |
| 7 | gdanskiego | 2 |
| 8 | podzially | 2 |
| 9 | ujazd | 2 |
| 10 | mojš | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9483 |
| R² (Goodness of Fit) | 0.996724 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 30.7% |
| Top 1,000 | 56.8% |
| Top 5,000 | 76.7% |
| Top 10,000 | 85.6% |

### Key Findings

- **Zipf Compliance:** R²=0.9967 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 30.7% of corpus
- **Long Tail:** 21,116 words needed for remaining 14.4% 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 | 0.8231 🏆 | 0.3397 | N/A | N/A |
| **mono_64d** | 64 | 0.5887 | 0.3131 | N/A | N/A |
| **mono_128d** | 128 | 0.1790 | 0.3018 | N/A | N/A |
| **aligned_32d** | 32 | 0.8231 | 0.3455 | 0.0460 | 0.2420 |
| **aligned_64d** | 64 | 0.5887 | 0.3066 | 0.0660 | 0.3060 |
| **aligned_128d** | 128 | 0.1790 | 0.3019 | 0.0860 | 0.3460 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.8231 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3181. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.6% 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 | **0.741** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | trilogija, rinetta, kenija |
| `-e` | gališćinje, evidence, hercegowinje |
| `-je` | gališćinje, hercegowinje, wótstoje |
| `-ch` | reichenbach, proch, žurnalistiskich |
| `-ka` | hypotetiska, francoska, wěrika |
| `-ki` | monotypiski, wólšynki, keltiski |
| `-ow` | dokusow, wunjow, basnikow |
| `-nje` | gališćinje, hercegowinje, wótchylenje |

### 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 |
|------|----------|------------------|----------|
| `šćin` | 1.95x | 41 contexts | češćinu, češćina, češćiny |
| `jenj` | 1.71x | 62 contexts | jenje, mjenju, mjenja |
| `ótar` | 2.17x | 19 contexts | kótara, kótaru, kótare |
| `skej` | 1.53x | 56 contexts | českej, wuskej, irskej |
| `měst` | 1.87x | 25 contexts | městy, města, město |
| `rbsk` | 1.95x | 17 contexts | srbská, serbsku, serbsko |
| `owan` | 1.70x | 26 contexts | głowan, cowanje, źěkowano |
| `kóta` | 2.17x | 12 contexts | kótara, kótaru, kótare |
| `iski` | 1.63x | 25 contexts | niski, bliski, leniski |
| `iske` | 1.46x | 36 contexts | niske, aziske, bliske |
| `erbs` | 1.90x | 14 contexts | herbst, serbsku, serbsko |
| `imsk` | 1.72x | 16 contexts | nimska, nimsko, nimske |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| wóznamjenjenje | **`wóznam-je-nje-nje`** | 7.5 | `wóznam` |
| biologowka | **`biolog-ow-ka`** | 6.0 | `biolog` |
| pósćonych | **`pósćony-ch`** | 4.5 | `pósćony` |
| wótstojecych | **`wótstojecy-ch`** | 4.5 | `wótstojecy` |
| pomorskeje | **`pomorske-je`** | 4.5 | `pomorske` |
| halšterje | **`halšter-je`** | 4.5 | `halšter` |
| nejlěpšych | **`nejlěpšy-ch`** | 4.5 | `nejlěpšy` |
| kamjentnych | **`kamjentny-ch`** | 4.5 | `kamjentny` |
| pódpołnocnje | **`pódpołnoc-nje`** | 4.5 | `pódpołnoc` |
| spominanje | **`spomina-nje`** | 4.5 | `spomina` |
| pódwjacorneje | **`pódwjacorne-je`** | 4.5 | `pódwjacorne` |
| organiskeje | **`organiske-je`** | 4.5 | `organiske` |
| wótpósłańcka | **`wótpósłańc-ka`** | 4.5 | `wótpósłańc` |
| chinskeje | **`chinske-je`** | 4.5 | `chinske` |
| twarjenjach | **`twarjenja-ch`** | 4.5 | `twarjenja` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Lower 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 (4.37x) |
| N-gram | **2-gram** | Lowest perplexity (446) |
| Markov | **Context-4** | Highest predictability (97.7%) |
| 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 02:35:27*