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README.md

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+---
+language: en
+language_name: English
+language_family: germanic_west_anglofrisian
+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_west_anglofrisian
+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: 4.699
+  - name: best_isotropy
+    type: isotropy
+    value: 0.7693
+  - name: vocabulary_size
+    type: vocab
+    value: 1867537
+generated: 2026-03-03
+---
+
+# English — Wikilangs Models
+
+Open-source tokenizers, n-gram & Markov language models, vocabulary stats, and word embeddings trained on **English** Wikipedia by [Wikilangs](https://wikilangs.org).
+
+🌐 [Language Page](https://wikilangs.org/languages/en/) · 🎮 [Playground](https://wikilangs.org/playground/?lang=en) · 📊 [Full Research Report](RESEARCH_REPORT.md)
+
+## Language Samples
+
+Example sentences drawn from the English Wikipedia corpus:
+
+> Alexander V may refer to: Alexander V of Macedon (died 294 BCE) Antipope Alexander V Alexander V of Imereti
+
+> Alfonso IV may refer to: Alfonso IV of León (924–931) Afonso IV of Portugal Alfonso IV of Aragon Alfonso IV of Ribagorza Alfonso IV d'Este Duke of Modena and Regg
+
+> Anastasius I or Anastasios I may refer to: Anastasius I Dicorus (–518), Roman emperor Anastasius I of Antioch (died 599), Patriarch of Antioch Pope Anastasius I (died 401), pope
+
+> Angula may refer to: Aṅgula, a measure equal to a finger's breadth Eel, a biological order of fish Nahas Angula, former Prime Minister of Namibia Helmut Angula See also Angul (disambiguation)
+
+> Two antipopes used the regnal name Victor IV: Antipope Victor IV Antipope Victor IV
+
+## Quick Start
+
+### Load the Tokenizer
+
+```python
+import sentencepiece as spm
+
+sp = spm.SentencePieceProcessor()
+sp.Load("en_tokenizer_32k.model")
+
+text = "Albrecht Achilles may refer to: Albrecht III Achilles, Elector of Brandenburg Al"
+tokens = sp.EncodeAsPieces(text)
+ids    = sp.EncodeAsIds(text)
+
+print(tokens)  # subword pieces
+print(ids)     # integer ids
+
+# Decode back
+print(sp.DecodeIds(ids))
+```
+
+<details>
+<summary><b>Tokenization examples (click to expand)</b></summary>
+
+**Sample 1:** `Albrecht Achilles may refer to: Albrecht III Achilles, Elector of Brandenburg Al…`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁alb recht ▁ach illes ▁may ▁refer ▁to : ▁alb recht … (+27 more)` | 37 |
+| 16k | `▁alb recht ▁ach illes ▁may ▁refer ▁to : ▁alb recht … (+26 more)` | 36 |
+| 32k | `▁albrecht ▁achilles ▁may ▁refer ▁to : ▁albrecht ▁iii ▁achilles , … (+17 more)` | 27 |
+| 64k | `▁albrecht ▁achilles ▁may ▁refer ▁to : ▁albrecht ▁iii ▁achilles , … (+16 more)` | 26 |
+
+**Sample 2:** `Alexander V may refer to: Alexander V of Macedon (died 294 BCE) Antipope Alexand…`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁maced … (+20 more)` | 30 |
+| 16k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon … (+18 more)` | 28 |
+| 32k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon … (+15 more)` | 25 |
+| 64k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon … (+15 more)` | 25 |
+
+**Sample 3:** `Two antipopes used the regnal name Victor IV: Antipope Victor IV Antipope Victor…`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁two ▁antip op es ▁used ▁the ▁reg nal ▁name ▁victor … (+8 more)` | 18 |
+| 16k | `▁two ▁antip opes ▁used ▁the ▁reg nal ▁name ▁victor ▁iv … (+7 more)` | 17 |
+| 32k | `▁two ▁antip opes ▁used ▁the ▁regnal ▁name ▁victor ▁iv : … (+6 more)` | 16 |
+| 64k | `▁two ▁antipopes ▁used ▁the ▁regnal ▁name ▁victor ▁iv : ▁antipope … (+5 more)` | 15 |
+
+</details>
+
+### Load Word Embeddings
+
+```python
+from gensim.models import KeyedVectors
+
+# Aligned embeddings (cross-lingual, mapped to English vector space)
+wv = KeyedVectors.load("en_embeddings_128d_aligned.kv")
+
+similar = wv.most_similar("word", topn=5)
+for word, score in similar:
+    print(f"  {word}: {score:.3f}")
+```
+
+### Load N-gram Model
+
+```python
+import pyarrow.parquet as pq
+
+df = pq.read_table("en_3gram_word.parquet").to_pandas()
+print(df.head())
+```
+
+## Models Overview
+
+![Performance Dashboard](visualizations/performance_dashboard.png)
+
+| Category | Assets |
+|----------|--------|
+| Tokenizers | BPE at 8k, 16k, 32k, 64k vocab sizes |
+| N-gram models | 2 / 3 / 4 / 5-gram (word & subword) |
+| Markov chains | Context 1–5 (word & subword) |
+| Embeddings | 32d, 64d, 128d — mono & aligned |
+| Vocabulary | Full frequency list + Zipf analysis |
+| Statistics | Corpus & model statistics JSON |
+
+## Metrics Summary
+
+| Component | Model | Key Metric | Value |
+|-----------|-------|------------|-------|
+| Tokenizer | 8k BPE | Compression | 3.84x |
+| Tokenizer | 16k BPE | Compression | 4.22x |
+| Tokenizer | 32k BPE | Compression | 4.51x |
+| Tokenizer | 64k BPE | Compression | 4.70x 🏆 |
+| N-gram | 2-gram (subword) | Perplexity | 257 🏆 |
+| N-gram | 2-gram (word) | Perplexity | 386,225 |
+| N-gram | 3-gram (subword) | Perplexity | 2,180 |
+| N-gram | 3-gram (word) | Perplexity | 4,093,782 |
+| N-gram | 4-gram (subword) | Perplexity | 12,758 |
+| N-gram | 4-gram (word) | Perplexity | 14,465,722 |
+| N-gram | 5-gram (subword) | Perplexity | 55,700 |
+| N-gram | 5-gram (word) | Perplexity | 12,820,936 |
+| Markov | ctx-1 (subword) | Predictability | 0.0% |
+| Markov | ctx-1 (word) | Predictability | 6.2% |
+| Markov | ctx-2 (subword) | Predictability | 46.4% |
+| Markov | ctx-2 (word) | Predictability | 48.3% |
+| Markov | ctx-3 (subword) | Predictability | 45.8% |
+| Markov | ctx-3 (word) | Predictability | 75.9% |
+| Markov | ctx-4 (subword) | Predictability | 36.8% |
+| Markov | ctx-4 (word) | Predictability | 89.2% 🏆 |
+| Vocabulary | full | Size | 1,867,537 |
+| Vocabulary | full | Zipf R² | 0.9862 |
+| Embeddings | mono_32d | Isotropy | 0.7693 🏆 |
+| Embeddings | mono_64d | Isotropy | 0.7388 |
+| Embeddings | mono_128d | Isotropy | 0.6687 |
+
+📊 **[Full ablation study, per-model breakdowns, and interpretation guide →](RESEARCH_REPORT.md)**
+
+---
+
+## About
+
+Trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) — monthly snapshots of 300+ Wikipedia languages.
+
+A project by **[Wikilangs](https://wikilangs.org)** · Maintainer: [Omar Kamali](https://omarkamali.com) · [Omneity Labs](https://omneitylabs.com)
+
+### Citation
+
+```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}
+}
+```
+
+### Links
+
+- 🌐 [wikilangs.org](https://wikilangs.org)
+- 🌍 [Language page](https://wikilangs.org/languages/en/)
+- 🎮 [Playground](https://wikilangs.org/playground/?lang=en)
+- 🤗 [HuggingFace models](https://huggingface.co/wikilangs)
+- 📊 [wikipedia-monthly dataset](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
+- 👤 [Omar Kamali](https://huggingface.co/omarkamali)
+- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
+
+**License:** MIT — free for academic and commercial use.
+
+---
+*Generated by Wikilangs Pipeline · 2026-03-03 22:59:51*

RESEARCH_REPORT.md

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+# English — Full Ablation Study & Research Report
+
+Detailed evaluation of all model variants trained on **English** Wikipedia data by [Wikilangs](https://wikilangs.org).
+
+👈 [Back to README](README.md)
+
+## 📋 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** | 3.837x | 3.84 | 0.1338% | 6,415,993 |
+| **16k** | 4.221x | 4.22 | 0.1472% | 5,832,191 |
+| **32k** | 4.511x | 4.51 | 0.1573% | 5,458,111 |
+| **64k** | 4.699x 🏆 | 4.70 | 0.1638% | 5,239,573 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Albrecht Achilles may refer to: Albrecht III Achilles, Elector of Brandenburg Al...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁alb recht ▁ach illes ▁may ▁refer ▁to : ▁alb recht ... (+27 more)` | 37 |
+| 16k | `▁alb recht ▁ach illes ▁may ▁refer ▁to : ▁alb recht ... (+26 more)` | 36 |
+| 32k | `▁albrecht ▁achilles ▁may ▁refer ▁to : ▁albrecht ▁iii ▁achilles , ... (+17 more)` | 27 |
+| 64k | `▁albrecht ▁achilles ▁may ▁refer ▁to : ▁albrecht ▁iii ▁achilles , ... (+16 more)` | 26 |
+
+**Sample 2:** `Alexander V may refer to: Alexander V of Macedon (died 294 BCE) Antipope Alexand...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁maced ... (+20 more)` | 30 |
+| 16k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon ... (+18 more)` | 28 |
+| 32k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon ... (+15 more)` | 25 |
+| 64k | `▁alexander ▁v ▁may ▁refer ▁to : ▁alexander ▁v ▁of ▁macedon ... (+15 more)` | 25 |
+
+**Sample 3:** `Two antipopes used the regnal name Victor IV: Antipope Victor IV Antipope Victor...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁two ▁antip op es ▁used ▁the ▁reg nal ▁name ▁victor ... (+8 more)` | 18 |
+| 16k | `▁two ▁antip opes ▁used ▁the ▁reg nal ▁name ▁victor ▁iv ... (+7 more)` | 17 |
+| 32k | `▁two ▁antip opes ▁used ▁the ▁regnal ▁name ▁victor ▁iv : ... (+6 more)` | 16 |
+| 64k | `▁two ▁antipopes ▁used ▁the ▁regnal ▁name ▁victor ▁iv : ▁antipope ... (+5 more)` | 15 |
+
+
+### Key Findings
+
+- **Best Compression:** 64k achieves 4.699x compression
+- **Lowest UNK Rate:** 8k with 0.1338% 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 | 386,225 | 18.56 | 9,782,066 | 8.6% | 17.8% |
+| **2-gram** | Subword | 257 🏆 | 8.01 | 64,688 | 68.7% | 99.4% |
+| **3-gram** | Word | 4,093,782 | 21.97 | 29,170,233 | 2.0% | 6.5% |
+| **3-gram** | Subword | 2,180 | 11.09 | 375,974 | 27.2% | 71.8% |
+| **4-gram** | Word | 14,465,722 | 23.79 | 54,673,289 | 1.7% | 4.4% |
+| **4-gram** | Subword | 12,758 | 13.64 | 2,193,365 | 14.2% | 38.3% |
+| **5-gram** | Word | 12,820,936 | 23.61 | 37,691,280 | 2.5% | 5.0% |
+| **5-gram** | Subword | 55,700 | 15.77 | 8,078,460 | 8.7% | 23.9% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `of the` | 7,591,708 |
+| 2 | `in the` | 5,221,237 |
+| 3 | `to the` | 2,361,743 |
+| 4 | `and the` | 1,799,614 |
+| 5 | `on the` | 1,518,298 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `the united states` | 408,936 |
+| 2 | `one of the` | 329,510 |
+| 3 | `as well as` | 264,322 |
+| 4 | `part of the` | 247,900 |
+| 5 | `references external links` | 203,098 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `in the united states` | 156,847 |
+| 2 | `under the age of` | 101,794 |
+| 3 | `the age of 18` | 97,188 |
+| 4 | `the end of the` | 88,360 |
+| 5 | `of age or older` | 86,112 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `under the age of 18` | 95,573 |
+| 2 | `years of age or older` | 85,203 |
+| 3 | `65 years of age or` | 84,639 |
+| 4 | `of age or older the` | 81,589 |
+| 5 | `the median income for a` | 59,537 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `e _` | 117,498,416 |
+| 2 | `_ t` | 97,071,904 |
+| 3 | `t h` | 84,506,441 |
+| 4 | `_ a` | 84,102,037 |
+| 5 | `s _` | 80,981,888 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ t h` | 65,028,534 |
+| 2 | `t h e` | 60,632,216 |
+| 3 | `h e _` | 53,951,238 |
+| 4 | `e d _` | 29,954,463 |
+| 5 | `_ i n` | 29,022,901 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ t h e` | 55,274,199 |
+| 2 | `t h e _` | 50,142,942 |
+| 3 | `_ o f _` | 26,136,576 |
+| 4 | `a n d _` | 22,544,155 |
+| 5 | `_ a n d` | 20,891,023 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ t h e _` | 49,351,863 |
+| 2 | `_ a n d _` | 20,550,921 |
+| 3 | `_ o f _ t` | 8,921,160 |
+| 4 | `n _ t h e` | 8,394,629 |
+| 5 | `o f _ t h` | 8,311,158 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 257
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.9382 | 1.916 | 19.86 | 4,365,871 | 6.2% |
+| **1** | Subword | 1.2026 | 2.302 | 11.62 | 32,517 | 0.0% |
+| **2** | Word | 0.5167 | 1.431 | 3.51 | 86,666,437 | 48.3% |
+| **2** | Subword | 0.5363 | 1.450 | 3.31 | 377,790 | 46.4% |
+| **3** | Word | 0.2409 | 1.182 | 1.68 | 303,940,373 | 75.9% |
+| **3** | Subword | 0.5420 | 1.456 | 3.45 | 1,251,354 | 45.8% |
+| **4** | Word | 0.1077 🏆 | 1.078 | 1.22 | 509,562,649 | 89.2% |
+| **4** | Subword | 0.6319 | 1.550 | 3.50 | 4,322,061 | 36.8% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `the move in july 2 respectively the murders in e bachs art deco building society was`
+2. `of the death in the buachaille etive ship to the signaling involves neuronal signals as the`
+3. `and left by his hysterical night and chieftain of measure in allowed for a number 3`
+
+**Context Size 2:**
+
+1. `of the big story is off limits to permanent employment in most notably in the shoot dying`
+2. `in the city of lübeck later sold to supermarkets hotels cinemas and four mpvs on the other`
+3. `to the limestone florida department of veteran hard rock version in featuring another lengthy playof...`
+
+**Context Size 3:**
+
+1. `the united states was raised significantly due to the interplay of light color etc hearing protectio...`
+2. `one of the few performed to significant recognition notable achievements include first indian batsma...`
+3. `as well as finishing sixth in the ferrari 312b and stirling mosss lotus in which he took to`
+
+**Context Size 4:**
+
+1. `in the united states helped revive the french economy with the marshall plan until the nys w shut do...`
+2. `under the age of 18 living with them 57 1 were married couples living together 9 4 had a`
+3. `the age of 18 living with them 44 6 were married couples living together 13 9 had a female`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_an_ainalltyarmo`
+2. `ere_isorandaltii`
+3. `agean._he_trhed,`
+
+**Context Size 2:**
+
+1. `e_co-con_ithe_sto`
+2. `_the_gh_todent's_`
+3. `th_arantime'_toft`
+
+**Context Size 3:**
+
+1. `_the_abird_native_`
+2. `the_10_olynoldavit`
+3. `he_der_–_to_the_fi`
+
+**Context Size 4:**
+
+1. `_the_treased:_"indo`
+2. `the_unit_by_made_fi`
+3. `_of_indies_in_the_s`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 89.2% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (4,322,061 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 | 1,867,537 |
+| Total Tokens | 739,735,080 |
+| Mean Frequency | 396.10 |
+| Median Frequency | 4 |
+| Frequency Std Dev | 51092.36 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | the | 50,118,217 |
+| 2 | of | 26,210,950 |
+| 3 | and | 20,755,074 |
+| 4 | in | 19,609,387 |
+| 5 | a | 14,271,839 |
+| 6 | to | 14,219,669 |
+| 7 | was | 7,449,828 |
+| 8 | for | 5,821,739 |
+| 9 | as | 5,815,121 |
+| 10 | is | 5,683,775 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | brevetting | 2 |
+| 2 | karuppukatti | 2 |
+| 3 | cirrhatum | 2 |
+| 4 | paða | 2 |
+| 5 | вим | 2 |
+| 6 | correya | 2 |
+| 7 | bulamaq | 2 |
+| 8 | boorik | 2 |
+| 9 | spanishe | 2 |
+| 10 | gitarrenmusik | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.0573 |
+| R² (Goodness of Fit) | 0.986242 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 38.8% |
+| Top 1,000 | 61.6% |
+| Top 5,000 | 80.1% |
+| Top 10,000 | 86.4% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9862 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 38.8% of corpus
+- **Long Tail:** 1,857,537 words needed for remaining 13.6% 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
+
+> *Note: Multilingual alignment visualization not available for this language.*
+
+
+### 5.2 Model Comparison
+
+| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
+|-------|-----------|----------|------------------|---------------|----------------|
+| **mono_32d** | 32 | 0.7693 🏆 | 0.4027 | N/A | N/A |
+| **mono_64d** | 64 | 0.7388 | 0.3350 | N/A | N/A |
+| **mono_128d** | 128 | 0.6687 | 0.2629 | N/A | N/A |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.7693 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.3335. Lower values indicate better semantic separation.
+- **Alignment Quality:** No aligned models evaluated in this run.
+- **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 | **-0.793** | Low formulaic content | - |
+
+### 6.2 Affix Inventory (Productive Units)
+
+These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.
+
+#### Productive Prefixes
+| Prefix | Examples |
+|--------|----------|
+| `-s` | skulltrail, scroggins, salatin |
+| `-a` | alpana, ayopaya, aekyung |
+| `-k` | kairos, kunigundes, kumwartok |
+| `-m` | mapae, muktafi, meirás |
+| `-c` | cutpurses, ceste, centurynear |
+| `-p` | pustynsky, phet, propertys |
+| `-w` | wnbd, wrestlerdecember, walska |
+| `-t` | technor, tvmaze, twistor |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-s` | scroggins, donoughues, kairos |
+| `-e` | forebode, mapae, tvmaze |
+| `-n` | salatin, gedruckten, fursten |
+| `-a` | alpana, ayopaya, flavicauda |
+| `-r` | wrestlerdecember, haalandmanchester, shoulder |
+| `-i` | rosai, badaczewski, muktafi |
+| `-es` | donoughues, kunigundes, cutpurses |
+| `-t` | stillmaticchart, phet, quenstedt |
+
+### 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 |
+|------|----------|------------------|----------|
+| `tter` | 1.46x | 1019 contexts | atter, otter, itter |
+| `ubli` | 1.63x | 215 contexts | tubli, ublic, dubli |
+| `ttle` | 1.45x | 375 contexts | attle, ittle, ottle |
+| `ount` | 1.52x | 208 contexts | count, yount, fount |
+| `ontr` | 1.54x | 183 contexts | ontra, kontr, contr |
+| `icia` | 1.44x | 202 contexts | licia, ticia, nicia |
+| `itie` | 1.57x | 129 contexts | mitie, nitie, itier |
+| `esid` | 1.55x | 123 contexts | yesid, cesid, resid |
+| `itio` | 1.46x | 142 contexts | aitio, ition, vitio |
+| `rsit` | 1.96x | 37 contexts | ḥarsit, parsit, fersit |
+| `ucti` | 1.73x | 60 contexts | aucti, fructi, ductis |
+| `oduc` | 1.85x | 44 contexts | produc, koduck, roduco |
+
+### 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 |
+|--------|--------|-----------|----------|
+| `-s` | `-s` | 117 words | superhumps, squiggs |
+| `-c` | `-s` | 102 words | cheirogaleus, cuddys |
+| `-b` | `-s` | 88 words | betlemitas, bracelins |
+| `-p` | `-s` | 88 words | paros, paars |
+| `-a` | `-s` | 85 words | abdülhamids, aguasbonenses |
+| `-s` | `-e` | 82 words | sulene, solene |
+| `-m` | `-s` | 80 words | mascas, mollis |
+| `-t` | `-s` | 78 words | tracklines, tirthankaras |
+| `-m` | `-e` | 70 words | magnetoreceptive, matratze |
+| `-c` | `-e` | 68 words | coudreville, clanvowe |
+
+### 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 |
+|------|-----------------|------------|------|
+| parintintin | **`parintin-t-in`** | 7.5 | `t` |
+| haakonssen | **`haakons-s-en`** | 7.5 | `s` |
+| writernet | **`writern-e-t`** | 7.5 | `e` |
+| kyŏngsang | **`kyŏngs-a-ng`** | 7.5 | `a` |
+| neoformalism | **`neoformali-s-m`** | 7.5 | `s` |
+| counterfeit | **`counterfe-i-t`** | 7.5 | `i` |
+| glossarist | **`glossari-s-t`** | 7.5 | `s` |
+| guitarless | **`guitar-le-ss`** | 7.5 | `le` |
+| kyoryusho | **`kyoryus-h-o`** | 7.5 | `h` |
+| harrisonharrison | **`harrisonharri-s-on`** | 7.5 | `s` |
+| frankowsk | **`frankow-s-k`** | 7.5 | `s` |
+| pxseattle | **`pxseat-t-le`** | 7.5 | `t` |
+| maribulan | **`maribu-l-an`** | 7.5 | `l` |
+| slighhouses | **`slighhou-s-es`** | 7.5 | `s` |
+| limaysaurus | **`limaysau-r-us`** | 7.5 | `r` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language English 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 (4.70x) |
+| N-gram | **2-gram** | Lowest perplexity (257) |
+| Markov | **Context-4** | Highest predictability (89.2%) |
+| Embeddings | **100d** | Balanced semantic capture and isotropy |
+
+
+---
+## Appendix: Metrics Glossary & Interpretation Guide
+
+This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.
+
+### Tokenizer Metrics
+
+**Compression Ratio**
+> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
+>
+> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
+>
+> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.
+
+**Average Token Length (Fertility)**
+> *Definition:* Mean number of characters per token produced by the tokenizer.
+>
+> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
+>
+> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.
+
+**Unknown Token Rate (OOV Rate)**
+> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
+>
+> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
+>
+> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.
+
+### N-gram Model Metrics
+
+**Perplexity**
+> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
+>
+> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
+>
+> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.
+
+**Entropy**
+> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
+>
+> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
+>
+> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.
+
+**Coverage (Top-K)**
+> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
+>
+> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
+>
+> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.
+
+### Markov Chain Metrics
+
+**Average Entropy**
+> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
+>
+> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
+>
+> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.
+
+**Branching Factor**
+> *Definition:* Average number of unique next tokens observed for each context.
+>
+> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
+>
+> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.
+
+**Predictability**
+> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
+>
+> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
+>
+> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.
+
+### Vocabulary & Zipf's Law Metrics
+
+**Zipf's Coefficient**
+> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
+>
+> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
+>
+> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.
+
+**R² (Coefficient of Determination)**
+> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
+>
+> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
+>
+> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.
+
+**Vocabulary Coverage**
+> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
+>
+> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
+>
+> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.
+
+### Word Embedding Metrics
+
+**Isotropy**
+> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
+>
+> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
+>
+> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.
+
+**Average Norm**
+> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
+>
+> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
+>
+> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).
+
+**Cosine Similarity**
+> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
+>
+> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
+>
+> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.
+
+**t-SNE Visualization**
+> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
+>
+> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
+>
+> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.
+
+### General Interpretation Guidelines
+
+1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
+2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
+3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
+4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
+5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.
+
+
+### Visualizations Index
+
+| Visualization | Description |
+|---------------|-------------|
+| Tokenizer Compression | Compression ratios by vocabulary size |
+| Tokenizer Fertility | Average token length by vocabulary |
+| Tokenizer OOV | Unknown token rates |
+| Tokenizer Total Tokens | Total tokens by vocabulary |
+| N-gram Perplexity | Perplexity by n-gram size |
+| N-gram Entropy | Entropy by n-gram size |
+| N-gram Coverage | Top pattern coverage |
+| N-gram Unique | Unique n-gram counts |
+| Markov Entropy | Entropy by context size |
+| Markov Branching | Branching factor by context |
+| Markov Contexts | Unique context counts |
+| Zipf's Law | Frequency-rank distribution with fit |
+| Vocab Frequency | Word frequency distribution |
+| Top 20 Words | Most frequent words |
+| Vocab Coverage | Cumulative coverage curve |
+| Embedding Isotropy | Vector space uniformity |
+| Embedding Norms | Vector magnitude distribution |
+| Embedding Similarity | Word similarity heatmap |
+| Nearest Neighbors | Similar words for key terms |
+| t-SNE Words | 2D word embedding visualization |
+| t-SNE Sentences | 2D sentence embedding visualization |
+| Position Encoding | Encoding method comparison |
+| Model Sizes | Storage requirements |
+| Performance Dashboard | Comprehensive performance overview |
+
+---
+👈 [Back to README](README.md)
+
+*Generated by Wikilangs Pipeline · 2026-03-04 03:44:40*

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