---
language: ksh
language_name: Colognian
language_family: germanic_west_continental
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_continental
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: 4.350
  - name: best_isotropy
    type: isotropy
    value: 0.6361
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Colognian** 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** | 3.395x | 3.40 | 0.0711% | 323,305 |
| **16k** | 3.728x | 3.73 | 0.0781% | 294,475 |
| **32k** | 4.048x | 4.05 | 0.0848% | 271,163 |
| **64k** | 4.350x 🏆 | 4.36 | 0.0911% | 252,338 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Wat frööer woo Dr Zweide Weltkresch jäng ä Europa em Joohr z Äng.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wat ▁frööer ▁woo ▁dr ▁zweide ▁weltkresch ▁jäng ▁ä ▁europa ▁em ... (+4 more)` | 14 |
| 16k | `▁wat ▁frööer ▁woo ▁dr ▁zweide ▁weltkresch ▁jäng ▁ä ▁europa ▁em ... (+4 more)` | 14 |
| 32k | `▁wat ▁frööer ▁woo ▁dr ▁zweide ▁weltkresch ▁jäng ▁ä ▁europa ▁em ... (+4 more)` | 14 |
| 64k | `▁wat ▁frööer ▁woo ▁dr ▁zweide ▁weltkresch ▁jäng ▁ä ▁europa ▁em ... (+4 more)` | 14 |

**Sample 2:** `Zu Lülsdorp jehührt da Verein Jungjeselle "Einstracht" Lülsdorp.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁zu ▁lü l sd orp ▁jeh ührt ▁da ▁verein ▁jung ... (+14 more)` | 24 |
| 16k | `▁zu ▁lü l sd orp ▁jeh ührt ▁da ▁verein ▁jung ... (+12 more)` | 22 |
| 32k | `▁zu ▁lülsdorp ▁jehührt ▁da ▁verein ▁jung jeselle ▁" ein stracht ... (+3 more)` | 13 |
| 64k | `▁zu ▁lülsdorp ▁jehührt ▁da ▁verein ▁jungjeselle ▁" ein stracht " ... (+2 more)` | 12 |

**Sample 3:** `Wat_paßßeed_ėß Kattaßtrofe Pollitikk Weßßeschaff Täshnigk Weetschaff D Port More...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁wat _ paßßeed _ ėß ▁kattaßtrofe ▁pollitikk ▁weßßeschaff ▁täshnigk ▁weetschaff ... (+22 more)` | 32 |
| 16k | `▁wat _ paßßeed _ ėß ▁kattaßtrofe ▁pollitikk ▁weßßeschaff ▁täshnigk ▁weetschaff ... (+19 more)` | 29 |
| 32k | `▁wat _ paßßeed _ ėß ▁kattaßtrofe ▁pollitikk ▁weßßeschaff ▁täshnigk ▁weetschaff ... (+17 more)` | 27 |
| 64k | `▁wat _ paßßeed _ ėß ▁kattaßtrofe ▁pollitikk ▁weßßeschaff ▁täshnigk ▁weetschaff ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 64k achieves 4.350x compression
- **Lowest UNK Rate:** 8k with 0.0711% 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 | 4,620 | 12.17 | 9,188 | 18.6% | 46.7% |
| **2-gram** | Subword | 306 🏆 | 8.26 | 2,112 | 63.6% | 99.2% |
| **3-gram** | Word | 5,003 | 12.29 | 7,288 | 13.5% | 38.5% |
| **3-gram** | Subword | 2,664 | 11.38 | 18,120 | 24.5% | 67.3% |
| **4-gram** | Word | 6,956 | 12.76 | 8,920 | 9.3% | 30.7% |
| **4-gram** | Subword | 15,309 | 13.90 | 84,897 | 11.4% | 34.7% |
| **5-gram** | Word | 4,149 | 12.02 | 4,961 | 11.0% | 39.4% |
| **5-gram** | Subword | 51,982 | 15.67 | 191,501 | 6.0% | 20.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `van d` | 1,533 |
| 2 | `em joohr` | 1,416 |
| 3 | `en d` | 1,240 |
| 4 | `d r` | 843 |
| 5 | `hollywood blvd` | 803 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jätt z lääse` | 625 |
| 2 | `wood em joohr` | 383 |
| 3 | `em joohr jeboore` | 327 |
| 4 | `z lääse övver` | 206 |
| 5 | `stervd em joohr` | 174 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `wood em joohr jeboore` | 296 |
| 2 | `jätt z lääse övver` | 205 |
| 3 | `jätt z lääse d` | 58 |
| 4 | `z lääse övver dr` | 53 |
| 5 | `z lääse övver d` | 49 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `jätt z lääse övver dr` | 53 |
| 2 | `jätt z lääse övver d` | 49 |
| 3 | `jätt z lääse d siij` | 45 |
| 4 | `em rhingland en nordrhein westfalen` | 38 |
| 5 | `z lääse un z kikke` | 32 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 71,697 |
| 2 | `_ d` | 64,400 |
| 3 | `c h` | 55,009 |
| 4 | `n _` | 48,143 |
| 5 | `e r` | 47,342 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s c h` | 26,961 |
| 2 | `e r _` | 21,326 |
| 3 | `c h _` | 20,142 |
| 4 | `d e _` | 16,739 |
| 5 | `u n _` | 13,928 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ u n _` | 10,471 |
| 2 | `_ d e _` | 7,995 |
| 3 | `_ e n _` | 7,657 |
| 4 | `s c h e` | 7,420 |
| 5 | `_ d a t` | 7,229 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d a t _` | 6,862 |
| 2 | `s c h e _` | 4,753 |
| 3 | `_ v a n _` | 3,604 |
| 4 | `_ w o o d` | 3,470 |
| 5 | `v v e r _` | 3,429 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 306
- **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 | 0.6606 | 1.581 | 4.16 | 71,078 | 33.9% |
| **1** | Subword | 0.8544 | 1.808 | 7.02 | 708 | 14.6% |
| **2** | Word | 0.1990 | 1.148 | 1.42 | 294,468 | 80.1% |
| **2** | Subword | 1.0513 | 2.072 | 6.64 | 4,967 | 0.0% |
| **3** | Word | 0.0498 | 1.035 | 1.07 | 417,475 | 95.0% |
| **3** | Subword | 0.9520 | 1.935 | 4.38 | 32,959 | 4.8% |
| **4** | Word | 0.0123 🏆 | 1.009 | 1.02 | 444,432 | 98.8% |
| **4** | Subword | 0.6772 | 1.599 | 2.73 | 144,143 | 32.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `un bochhändler ä filme un die eijenart dat litt öt kluster zo dat en singer achseneijung`
2. `d partisane kämpfe usserdäm entstäng önö spanische statthalderin in t b schünnheet en land en norrem`
3. `de loire jelejene deeler nieuwvliet esu ene ëijrfode d profis van drommer de ëijn vun de`

**Context Size 2:**

1. `van d ischde joohre noch net schläät vöör dütschland send slut walks och ä lostije stöcker un`
2. `em joohr jeboore isaac newton stervd em joohr jeboore jeshtorrve alexius ii 23 februar ä wien woch`
3. `en d usa beschlosse beede siije bes an öt emerson college em fach konst vong hä a`

**Context Size 3:**

1. `jätt z lääse fanny brice lääve ä knappe wööd da vinci leonardo da vinci jeboore woode es anchiano`
2. `wood em joohr jeboore anzelika ahmetšina wood em joohr jeboore yanina gonzález wood em joohr jeboore...`
3. `em joohr jeboore marco weiss wood em joohr jeboore henri matisse wood em joohr jeboore marco weiss w...`

**Context Size 4:**

1. `wood em joohr jeboore jean jenniches stervd em joohr`
2. `jätt z lääse övver riedewald`
3. `jätt z lääse d siij van d helaba`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ööt_gitee_uscas`
2. `e_6._wiplee_schl`
3. `n_warchöt_fe'r_a`

**Context Size 2:**

1. `e_anumposse_op_dö`
2. `_dände_woch_pards`
3. `chextorjedörchd_e`

**Context Size 3:**

1. `sche_se_decomt._fr`
2. `er_em_192_hät_deut`
3. `ch_lääse_col_krand`

**Context Size 4:**

1. `_un_solld_emmeles._`
2. `_de_wöhre,_di_mo_da`
3. `_en_priiß_et_jetz_e`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (144,143 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 | 25,333 |
| Total Tokens | 425,434 |
| Mean Frequency | 16.79 |
| Median Frequency | 3 |
| Frequency Std Dev | 168.02 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | un | 10,390 |
| 2 | d | 10,342 |
| 3 | de | 8,156 |
| 4 | en | 7,567 |
| 5 | dat | 7,131 |
| 6 | dä | 5,422 |
| 7 | em | 4,972 |
| 8 | öt | 4,919 |
| 9 | dr | 4,608 |
| 10 | di | 3,737 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | vallabhbhai | 2 |
| 2 | nunavik | 2 |
| 3 | ureinwohner | 2 |
| 4 | stadacona | 2 |
| 5 | bauwerke | 2 |
| 6 | zerstörung | 2 |
| 7 | kööritiba | 2 |
| 8 | sushi | 2 |
| 9 | suurrees | 2 |
| 10 | meerestiere | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0272 |
| R² (Goodness of Fit) | 0.997669 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 42.1% |
| Top 1,000 | 67.4% |
| Top 5,000 | 84.0% |
| Top 10,000 | 91.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9977 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 42.1% of corpus
- **Long Tail:** 15,333 words needed for remaining 9.0% 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 | 0.6361 | 0.3999 | N/A | N/A |
| **mono_64d** | 64 | 0.2385 | 0.3565 | N/A | N/A |
| **mono_128d** | 128 | 0.0474 | 0.3953 | N/A | N/A |
| **aligned_32d** | 32 | 0.6361 🏆 | 0.3935 | 0.0260 | 0.1380 |
| **aligned_64d** | 64 | 0.2385 | 0.3635 | 0.0340 | 0.2100 |
| **aligned_128d** | 128 | 0.0474 | 0.3865 | 0.0280 | 0.2060 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.6361 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3825. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 3.4% 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 | **0.964** | High formulaic/idiomatic content | - |

### 6.2 Affix Inventory (Productive Units)

These are the most productive prefixes and suffixes identified by sampling the vocabulary for global substitutability patterns. A unit is considered an affix if stripping it leaves a valid stem that appears in other contexts.

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-s` | spure, steenzitt, suppermaat |
| `-b` | bänsberch, bergische, belljie |
| `-je` | jefährte, jereeschßbeschloß, jewääh |
| `-j` | jugoslawe, jefährte, jereeschßbeschloß |
| `-k` | krippsche, ken, klan |
| `-d` | deit, dränge, deep |
| `-a` | allgemeine, aiköl, antarktische |
| `-m` | musikschull, meddelmoss, marianne |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | spure, nėėderdeutsche, reiche |
| `-ch` | bänsberch, nomannesch, bräuch |
| `-r` | fenster, ocher, kluster |
| `-h` | bänsberch, nomannesch, jewääh |
| `-er` | fenster, ocher, kluster |
| `-t` | steenzitt, präsidentschaft, zokonft |
| `-n` | ken, klan, stuben |
| `-he` | nėėderdeutsche, reiche, republikanische |

### 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 |
|------|----------|------------------|----------|
| `schl` | 1.69x | 50 contexts | schlof, schloß, schlau |
| `chte` | 1.60x | 46 contexts | ochte, ächte, echte |
| `nder` | 1.45x | 68 contexts | onder, under, ander |
| `eech` | 1.51x | 47 contexts | weech, beech, deech |
| `scha` | 1.54x | 42 contexts | schah, schau, schal |
| `annd` | 1.55x | 40 contexts | annde, nannd, rannd |
| `tsch` | 1.37x | 63 contexts | atsch, ketsch, dütsch |
| `nger` | 1.36x | 63 contexts | ónger, onger, enger |
| `icht` | 1.54x | 32 contexts | nicht, licht, vicht |
| `scht` | 1.38x | 46 contexts | ischt, ischte, lischt |
| `jebo` | 1.52x | 28 contexts | jebout, jebore, jeboud |
| `schw` | 1.46x | 31 contexts | schwa, schwär, schwer |

### 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` | `-e` | 194 words | sprachgeschichte, shtökke |
| `-b` | `-e` | 125 words | belldsche, bleeve |
| `-je` | `-e` | 119 words | jebouwde, jedenke |
| `-a` | `-e` | 99 words | autoindustrie, ame |
| `-k` | `-e` | 90 words | kölsche, karlsruhe |
| `-s` | `-r` | 76 words | stüür, seiner |
| `-m` | `-e` | 72 words | moore, macintyre |
| `-je` | `-t` | 66 words | jeweiht, jebraaht |
| `-j` | `-e` | 65 words | josefine, jolde |
| `-s` | `-er` | 61 words | seiner, schreber |

### 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 |
|------|-----------------|------------|------|
| jöräätichkeed | **`jöräätichke-e-d`** | 7.5 | `e` |
| faasteleer | **`faastel-e-er`** | 7.5 | `e` |
| periodesüßteem | **`periodesüßte-e-m`** | 7.5 | `e` |
| usszeechnet | **`usszeechn-e-t`** | 7.5 | `e` |
| produzeere | **`produze-er-e`** | 7.5 | `er` |
| säujedeere | **`säujede-er-e`** | 7.5 | `er` |
| raderberg | **`raderb-er-g`** | 7.5 | `er` |
| stadtdeel | **`stadt-de-el`** | 7.5 | `de` |
| konzentriert | **`konzentri-er-t`** | 7.5 | `er` |
| beischpell | **`beischp-e-ll`** | 7.5 | `e` |
| württemberch | **`württemb-er-ch`** | 7.5 | `er` |
| schleverbrett | **`schleverbr-e-tt`** | 7.5 | `e` |
| existiert | **`existi-er-t`** | 7.5 | `er` |
| fohiirohd | **`fohiiro-h-d`** | 7.5 | `h` |
| jözeechnet | **`jözeechn-e-t`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Colognian 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 (4.35x) |
| N-gram | **2-gram** | Lowest perplexity (306) |
| Markov | **Context-4** | Highest predictability (98.8%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 08:38:07*