---
language: ang
language_name: Old English
language_family: germanic_historical
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-germanic_historical
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: 4.012
  - name: best_isotropy
    type: isotropy
    value: 0.7896
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

# Old English - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Old English** 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** | 3.107x | 3.11 | 0.0859% | 252,634 |
| **16k** | 3.441x | 3.45 | 0.0951% | 228,129 |
| **32k** | 3.763x | 3.77 | 0.1040% | 208,636 |
| **64k** | 4.012x 🏆 | 4.02 | 0.1109% | 195,650 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Grēat Coldūn () is þorp in þæm East Þriding, se is Eoferƿicscire dǣl, on Englum....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁grēat ▁c old ūn ▁() ▁is ▁þorp ▁in ▁þæm ▁east ... (+15 more)` | 25 |
| 16k | `▁grēat ▁c old ūn ▁() ▁is ▁þorp ▁in ▁þæm ▁east ... (+15 more)` | 25 |
| 32k | `▁grēat ▁cold ūn ▁() ▁is ▁þorp ▁in ▁þæm ▁east ▁þriding ... (+14 more)` | 24 |
| 64k | `▁grēat ▁cold ūn ▁() ▁is ▁þorp ▁in ▁þæm ▁east ▁þriding ... (+14 more)` | 24 |

**Sample 2:** `Lingua Franca Nova is gehugod sprǣc. Utweardlice bendas elefen.org gereord`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁l ing ua ▁franc a ▁nov a ▁is ▁geh ug ... (+11 more)` | 21 |
| 16k | `▁l ing ua ▁franc a ▁nova ▁is ▁geh ug od ... (+10 more)` | 20 |
| 32k | `▁ling ua ▁franca ▁nova ▁is ▁gehugod ▁sprǣc . ▁utweardlice ▁bendas ... (+5 more)` | 15 |
| 64k | `▁lingua ▁franca ▁nova ▁is ▁gehugod ▁sprǣc . ▁utweardlice ▁bendas ▁ele ... (+4 more)` | 14 |

**Sample 3:** `Andreas Iǣxcūn ƿæs se seofoða Foresittend þāra Geānlǣhtra Rīca, fram þǣm gēare ō...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁andreas ▁i ǣ x c ūn ▁ƿæs ▁se ▁seof oða ... (+17 more)` | 27 |
| 16k | `▁andreas ▁iǣx c ūn ▁ƿæs ▁se ▁seofoða ▁foresittend ▁þāra ▁geānlǣhtra ... (+14 more)` | 24 |
| 32k | `▁andreas ▁iǣx c ūn ▁ƿæs ▁se ▁seofoða ▁foresittend ▁þāra ▁geānlǣhtra ... (+14 more)` | 24 |
| 64k | `▁andreas ▁iǣxcūn ▁ƿæs ▁se ▁seofoða ▁foresittend ▁þāra ▁geānlǣhtra ▁rīca , ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.012x compression
- **Lowest UNK Rate:** 8k with 0.0859% 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 | 3,551 | 11.79 | 7,095 | 21.2% | 53.1% |
| **2-gram** | Subword | 365 🏆 | 8.51 | 3,006 | 61.0% | 98.1% |
| **3-gram** | Word | 3,411 | 11.74 | 6,128 | 21.1% | 50.1% |
| **3-gram** | Subword | 3,332 | 11.70 | 23,711 | 22.3% | 62.8% |
| **4-gram** | Word | 6,747 | 12.72 | 11,452 | 16.3% | 36.7% |
| **4-gram** | Subword | 18,651 | 14.19 | 105,677 | 10.6% | 32.7% |
| **5-gram** | Word | 4,718 | 12.20 | 8,067 | 18.6% | 41.3% |
| **5-gram** | Subword | 56,790 | 15.79 | 217,768 | 6.4% | 20.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `on þǣm` | 784 |
| 2 | `in þǣm` | 762 |
| 3 | `in þæm` | 673 |
| 4 | `of the` | 645 |
| 5 | `se is` | 536 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `td valign top` | 529 |
| 2 | `þæs geānedan cynerīces` | 312 |
| 3 | `is þorp in` | 311 |
| 4 | `on eoferwicscīre þæs` | 248 |
| 5 | `eoferwicscīre þæs geānedan` | 248 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `on eoferwicscīre þæs geānedan` | 248 |
| 2 | `eoferwicscīre þæs geānedan cynerīces` | 248 |
| 3 | `is eoferƿicscire dǣl on` | 232 |
| 4 | `eoferƿicscire dǣl on englum` | 231 |
| 5 | `se is eoferƿicscire dǣl` | 229 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `on eoferwicscīre þæs geānedan cynerīces` | 248 |
| 2 | `is eoferƿicscire dǣl on englum` | 231 |
| 3 | `se is eoferƿicscire dǣl on` | 229 |
| 4 | `þriding se is eoferƿicscire dǣl` | 224 |
| 5 | `east þriding se is eoferƿicscire` | 170 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 68,542 |
| 2 | `a n` | 60,904 |
| 3 | `n _` | 55,318 |
| 4 | `s _` | 47,837 |
| 5 | `n d` | 40,759 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n d` | 24,396 |
| 2 | `n d _` | 20,668 |
| 3 | `a n _` | 16,952 |
| 4 | `_ a n` | 16,629 |
| 5 | `o n _` | 16,182 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n d _` | 16,673 |
| 2 | `_ a n d` | 14,847 |
| 3 | `_ o n _` | 10,364 |
| 4 | `_ i s _` | 10,180 |
| 5 | `_ i n _` | 9,895 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a n d _` | 14,216 |
| 2 | `_ t h e _` | 3,853 |
| 3 | `_ þ ǣ m _` | 3,654 |
| 4 | `_ þ æ s _` | 3,541 |
| 5 | `_ h i s _` | 3,480 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 365
- **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 | 0.6200 | 1.537 | 3.57 | 86,918 | 38.0% |
| **1** | Subword | 0.8434 | 1.794 | 6.43 | 1,235 | 15.7% |
| **2** | Word | 0.1550 | 1.113 | 1.30 | 307,624 | 84.5% |
| **2** | Subword | 0.9640 | 1.951 | 5.90 | 7,944 | 3.6% |
| **3** | Word | 0.0385 | 1.027 | 1.05 | 397,324 | 96.2% |
| **3** | Subword | 0.8649 | 1.821 | 4.02 | 46,823 | 13.5% |
| **4** | Word | 0.0127 🏆 | 1.009 | 1.02 | 415,064 | 98.7% |
| **4** | Subword | 0.6219 | 1.539 | 2.55 | 188,154 | 37.8% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `and bedældede hine in þǣm geānedum rīcum þā protest sang rocc and sīþe hrēðcyninges hām to`
2. `on francum in þæm miclum burgum and his ƿæter hit hê hê willgesweostor shes laid back`
3. `is unesco æfter déaðe drepe þrōƿade heorosƿeng heardn ond sēo hēafodmearc iesuitisces rǣses it was f...`

**Context Size 2:**

1. `on þǣm fylle þǣm þe nāhwæþer ne þā ġeānedan land sculon ne ǣniġ land sceal ætfōn oþþe`
2. `in þǣm indiscum lande uttar pradesh þæt land þæt ƿæs corēan independence activist politicians and jo...`
3. `in þæm east þriding se is eoferƿicscire dǣl on englum hit hæfþ 11 351 būendas on eoferwicscīre`

**Context Size 3:**

1. `td valign top ualentinianus ii td valign top td to 297 td valign top co emperor with honorius`
2. `is þorp in soria on castile and leóne in spēonlande and þorpas on sorie`
3. `eoferwicscīre þæs geānedan cynerīces and hēafodman þæs behealdenda hēapes siþðan mǣdmōnaþ he is gebē...`

**Context Size 4:**

1. `on eoferwicscīre þæs geānedan cynerīces`
2. `is eoferƿicscire dǣl on englalande on eoferwicscīre þæs geānedan cynerīces`
3. `eoferƿicscire dǣl on englum mid grēatum hǣþfelda ġesċieppaþ hie þone burgsċipe of hǣþfelda on eoferw...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_htofunes_anōre_`
2. `e_c_weaþǣfyn_sca`
3. `n_þeal_wun_berie`

**Context Size 2:**

1. `e_of_fi_94oðbe_tw`
2. `an_thoseadand_īeg`
3. `n_nīƿ_mesprytt,_þ`

**Context Size 3:**

1. `and_und_ofher_mā_s`
2. `nd_titutede_him._h`
3. `an_asscran_betwa_ǣ`

**Context Size 4:**

1. `and_belalan_(mother`
2. `_and_ġecosta_tƿiste`
3. `_on_þā_habbað_nofgo`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (188,154 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 | 31,186 |
| Total Tokens | 403,003 |
| Mean Frequency | 12.92 |
| Median Frequency | 3 |
| Frequency Std Dev | 156.70 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | and | 14,299 |
| 2 | on | 10,683 |
| 3 | is | 10,302 |
| 4 | in | 10,147 |
| 5 | of | 6,062 |
| 6 | se | 4,316 |
| 7 | the | 3,973 |
| 8 | þǣm | 3,669 |
| 9 | þæs | 3,610 |
| 10 | his | 3,501 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | minga | 2 |
| 2 | blæcfugolond | 2 |
| 3 | ƿīleacstede | 2 |
| 4 | cōcsċīre | 2 |
| 5 | winnebagsċīre | 2 |
| 6 | ælfrēdingtūn | 2 |
| 7 | irfung | 2 |
| 8 | larēodo | 2 |
| 9 | grœndā | 2 |
| 10 | dǣlungs | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9344 |
| R² (Goodness of Fit) | 0.998034 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 38.0% |
| Top 1,000 | 59.6% |
| Top 5,000 | 77.9% |
| Top 10,000 | 86.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9980 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 38.0% of corpus
- **Long Tail:** 21,186 words needed for remaining 13.8% 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 | 0.3585 | N/A | N/A |
| **mono_64d** | 64 | 0.4746 | 0.3175 | N/A | N/A |
| **mono_128d** | 128 | 0.1353 | 0.3004 | N/A | N/A |
| **aligned_32d** | 32 | 0.7896 🏆 | 0.3555 | 0.0300 | 0.2480 |
| **aligned_64d** | 64 | 0.4746 | 0.3090 | 0.0860 | 0.3400 |
| **aligned_128d** | 128 | 0.1353 | 0.3041 | 0.1280 | 0.4020 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7896 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3242. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 12.8% 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 | **1.044** | 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 |
|--------|----------|
| `-ge` | geondrīcisce, gebold, gemyndgung |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | ārwurðnysse, cǣġe, farende |
| `-s` | celebrations, villages, annivs |
| `-es` | villages, ides, missiles |
| `-an` | þēodacynewīsan, hāligan, europiscan |
| `-um` | dorsætum, maniȝum, elpendum |
| `-de` | farende, ungeƿilde, bestandende |
| `-en` | ƿriten, eċġen, hyrneġen |
| `-on` | edmonton, huffington, aragon |

### 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 |
|------|----------|------------------|----------|
| `enne` | 2.04x | 48 contexts | fenne, etenne, cenneþ |
| `mani` | 2.03x | 43 contexts | amani, maniȝ, maniġ |
| `wear` | 1.91x | 43 contexts | wearð, wearg, weard |
| `ster` | 1.67x | 59 contexts | sister, ēaster, faster |
| `unge` | 1.77x | 46 contexts | tunge, tunges, jungen |
| `tion` | 2.19x | 19 contexts | motion, nation, action |
| `inga` | 1.72x | 34 contexts | þinga, minga, ðinga |
| `ning` | 1.64x | 35 contexts | mining, cining, cyning |
| `aste` | 1.69x | 27 contexts | taste, easte, ēaste |
| `ynin` | 2.21x | 11 contexts | cynin, cyning, cyninȝ |
| `afod` | 1.82x | 18 contexts | hēafod, heafod, ƿafode |
| `nisc` | 1.49x | 27 contexts | rūnisc, denisc, dēnisc |

### 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 |
|--------|--------|-----------|----------|
| `-ge` | `-e` | 79 words | geƿorhte, geƿǣre |
| `-ge` | `-en` | 35 words | getimbroden, geferræden |
| `-ge` | `-de` | 35 words | geanede, gehiersomode |
| `-ge` | `-s` | 29 words | genus, geardas |
| `-ge` | `-an` | 20 words | gegildan, gemæccan |
| `-ge` | `-um` | 20 words | gerādum, germanicum |
| `-ge` | `-es` | 17 words | geofones, geānlǣhtes |
| `-ge` | `-on` | 9 words | gestaðoledon, gestrēon |

### 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 |
|------|-----------------|------------|------|
| gehƿilcum | **`ge-hƿilc-um`** | 6.0 | `hƿilc` |
| gefeahten | **`ge-feaht-en`** | 6.0 | `feaht` |
| underbyrigum | **`underbyrig-um`** | 4.5 | `underbyrig` |
| geþoftscipe | **`ge-þoftscipe`** | 4.5 | `þoftscipe` |
| sanghordes | **`sanghord-es`** | 4.5 | `sanghord` |
| gesweoster | **`ge-sweoster`** | 4.5 | `sweoster` |
| russlandes | **`russland-es`** | 4.5 | `russland` |
| þēodisclandes | **`þēodiscland-es`** | 4.5 | `þēodiscland` |
| gestrēonum | **`ge-strē-on-um`** | 4.5 | `strē` |
| drȳġelandes | **`drȳġeland-es`** | 4.5 | `drȳġeland` |
| drēamhordes | **`drēamhord-es`** | 4.5 | `drēamhord` |
| andweardum | **`andweard-um`** | 4.5 | `andweard` |
| engliscan | **`englisc-an`** | 4.5 | `englisc` |
| stǣrlican | **`stǣrlic-an`** | 4.5 | `stǣrlic` |
| bedæleden | **`bedæled-en`** | 4.5 | `bedæled` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Old English 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 (4.01x) |
| N-gram | **2-gram** | Lowest perplexity (365) |
| Markov | **Context-4** | Highest predictability (98.7%) |
| 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: 2026-01-03 16:22:13*