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README.md

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+---
+language: kg
+language_name: Kongo
+language_family: bantu_central
+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-bantu_central
+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: 4.520
+  - name: best_isotropy
+    type: isotropy
+    value: 0.1871
+  - name: vocabulary_size
+    type: vocab
+    value: 0
+generated: 2026-01-10
+---
+
+# Kongo - Wikilangs Models
+## Comprehensive Research Report & Full Ablation Study
+
+This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kongo** 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** | 3.971x | 3.98 | 0.2014% | 98,310 |
+| **16k** | 4.333x | 4.34 | 0.2197% | 90,112 |
+| **32k** | 4.520x 🏆 | 4.53 | 0.2292% | 86,376 |
+
+### Tokenization Examples
+
+Below are sample sentences tokenized with each vocabulary size:
+
+**Sample 1:** `Tübingen kele kizunga ya Baden-Württemberg, Alemanyi.`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁t ü b ing en ▁kele ▁kizunga ▁ya ▁baden - ... (+4 more)` | 14 |
+| 16k | `▁t übingen ▁kele ▁kizunga ▁ya ▁baden - württemberg , ▁alemanyi ... (+1 more)` | 11 |
+| 32k | `▁tübingen ▁kele ▁kizunga ▁ya ▁baden - württemberg , ▁alemanyi .` | 10 |
+
+**Sample 2:** `Ubuntu kele mpila mosi ya Linux. Nkumbu ya Ubuntu (na kikongo: bumuntu to kimunt...`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁ubuntu ▁kele ▁mpila ▁mosi ▁ya ▁l inux . ▁nkumbu ▁ya ... (+27 more)` | 37 |
+| 16k | `▁ubuntu ▁kele ▁mpila ▁mosi ▁ya ▁linux . ▁nkumbu ▁ya ▁ubuntu ... (+24 more)` | 34 |
+| 32k | `▁ubuntu ▁kele ▁mpila ▁mosi ▁ya ▁linux . ▁nkumbu ▁ya ▁ubuntu ... (+24 more)` | 34 |
+
+**Sample 3:** `kele suka ya kondi ya Repubilika ya Kôngo. ya kondi`
+
+| Vocab | Tokens | Count |
+|-------|--------|-------|
+| 8k | `▁kele ▁suka ▁ya ▁kondi ▁ya ▁repubilika ▁ya ▁kôngo . ▁ya ... (+1 more)` | 11 |
+| 16k | `▁kele ▁suka ▁ya ▁kondi ▁ya ▁repubilika ▁ya ▁kôngo . ▁ya ... (+1 more)` | 11 |
+| 32k | `▁kele ▁suka ▁ya ▁kondi ▁ya ▁repubilika ▁ya ▁kôngo . ▁ya ... (+1 more)` | 11 |
+
+
+### Key Findings
+
+- **Best Compression:** 32k achieves 4.520x compression
+- **Lowest UNK Rate:** 8k with 0.2014% 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 | 1,534 | 10.58 | 3,731 | 31.2% | 75.1% |
+| **2-gram** | Subword | 168 🏆 | 7.39 | 1,390 | 77.7% | 99.7% |
+| **3-gram** | Word | 3,413 | 11.74 | 6,815 | 19.8% | 55.8% |
+| **3-gram** | Subword | 948 | 9.89 | 8,160 | 43.7% | 83.9% |
+| **4-gram** | Word | 6,222 | 12.60 | 11,303 | 15.0% | 42.1% |
+| **4-gram** | Subword | 3,320 | 11.70 | 28,230 | 28.1% | 63.0% |
+| **5-gram** | Word | 4,107 | 12.00 | 7,664 | 18.9% | 48.5% |
+| **5-gram** | Subword | 7,120 | 12.80 | 46,201 | 19.4% | 50.9% |
+
+### Top 5 N-grams by Size
+
+**2-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `sambu na` | 862 |
+| 2 | `ya kongo` | 704 |
+| 3 | `ya bantu` | 652 |
+| 4 | `kele na` | 649 |
+| 5 | `na yandi` | 613 |
+
+**3-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `ya kongo ya` | 375 |
+| 2 | `repubilika ya kongo` | 369 |
+| 3 | `na kati ya` | 361 |
+| 4 | `kongo ya dimokalasi` | 332 |
+| 5 | `na nima ya` | 314 |
+
+**4-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `ya kongo ya dimokalasi` | 332 |
+| 2 | `repubilika ya kongo ya` | 283 |
+| 3 | `ya repubilika ya kongo` | 216 |
+| 4 | `mbanza ya kimfumu ya` | 181 |
+| 5 | `kimfumu ya kizunga ya` | 164 |
+
+**5-grams (Word):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `repubilika ya kongo ya dimokalasi` | 270 |
+| 2 | `ya repubilika ya kongo ya` | 172 |
+| 3 | `mbanza ya kimfumu ya kizunga` | 161 |
+| 4 | `ya kimfumu ya kizunga ya` | 160 |
+| 5 | `kele mbanza kimfumu ya yinsi` | 109 |
+
+**2-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a _` | 66,512 |
+| 2 | `_ y` | 30,798 |
+| 3 | `y a` | 27,604 |
+| 4 | `_ n` | 21,445 |
+| 5 | `_ k` | 21,155 |
+
+**3-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ y a` | 26,479 |
+| 2 | `y a _` | 23,101 |
+| 3 | `n a _` | 15,424 |
+| 4 | `_ n a` | 11,972 |
+| 5 | `a _ k` | 11,963 |
+
+**4-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `_ y a _` | 22,832 |
+| 2 | `_ n a _` | 11,648 |
+| 3 | `a _ y a` | 8,946 |
+| 4 | `u _ y a` | 6,395 |
+| 5 | `a k a _` | 5,692 |
+
+**5-grams (Subword):**
+
+| Rank | N-gram | Count |
+|------|--------|-------|
+| 1 | `a _ y a _` | 7,419 |
+| 2 | `u _ y a _` | 5,909 |
+| 3 | `_ y a _ k` | 5,126 |
+| 4 | `i _ y a _` | 4,012 |
+| 5 | `a _ n a _` | 3,703 |
+
+
+### Key Findings
+
+- **Best Perplexity:** 2-gram (subword) with 168
+- **Entropy Trend:** Decreases with larger n-grams (more predictable)
+- **Coverage:** Top-1000 patterns cover ~51% 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 | 0.6753 | 1.597 | 3.82 | 13,889 | 32.5% |
+| **1** | Subword | 1.1440 | 2.210 | 8.61 | 367 | 0.0% |
+| **2** | Word | 0.2863 | 1.219 | 1.74 | 52,840 | 71.4% |
+| **2** | Subword | 0.9575 | 1.942 | 5.20 | 3,158 | 4.3% |
+| **3** | Word | 0.1457 | 1.106 | 1.27 | 91,186 | 85.4% |
+| **3** | Subword | 0.7225 | 1.650 | 3.20 | 16,384 | 27.8% |
+| **4** | Word | 0.0715 🏆 | 1.051 | 1.11 | 115,336 | 92.9% |
+| **4** | Subword | 0.4661 | 1.381 | 2.03 | 52,366 | 53.4% |
+
+### Generated Text Samples (Word-based)
+
+Below are text samples generated from each word-based Markov chain model:
+
+**Context Size 1:**
+
+1. `ya 8 bantu ya kimpwanza mosi ya saint lucia saint marin serbie slovakia slovenia solomon islands`
+2. `na provense ya kutadila ntalu ya kutwadisa mpi bo na mayi na ouganda bantu ya dibulu`
+3. `kele mbanza goma mpi yo mutindu yina vandaka me tulaka yandi kele kaka na biro ya`
+
+**Context Size 2:**
+
+1. `sambu na kisalu mpi kutomisa bima ya nkaka ke sala nde bantu yina vandaka kumonisa nsoba ya`
+2. `ya kongo rdc category sénateur ya kasai na baluba ne mvuta ya bantu ya nkaka ya me`
+3. `ya bantu ya mubulu na mvu bo me binga sambu na kuzabisa luzayisu yayi kusalama na kutadila`
+
+**Context Size 3:**
+
+1. `ya kongo ya dimokalasi mbanza mfumu ya kizunga jiangsu ya sina ya sina`
+2. `na kati ya bazulunalu yina salaka mambu ya yimbi mpe kimbeni yina ke vuandaka na mukidi ya nzadi`
+3. `repubilika ya kongo ya dimokalasi sambu bo kezabaka nde nzo nkanda vandaka kufuta yves piron mpi sam...`
+
+**Context Size 4:**
+
+1. `repubilika ya kongo ya dimokalasi ya kati`
+2. `ya kongo ya dimokalasi category guvernere ya tshopo category lubutuku na zaire category avocat congo...`
+3. `ya repubilika ya kongo yandi vuandaka muene ya brazzaville ti kuna ná ntumua ya ntete ya repubilika ...`
+
+
+### Generated Text Samples (Subword-based)
+
+Below are text samples generated from each subword-based Markov chain model:
+
+**Context Size 1:**
+
+1. `_nakama_mbo_mba_`
+2. `alaba_a_yi_yikin`
+3. `n_yo_yasa_yingar`
+
+**Context Size 2:**
+
+1. `a_keles)_ta._ba_y`
+2. `_yan_john_luzwalb`
+3. `ya_ntu_ya_yandimo`
+
+**Context Size 3:**
+
+1. `_ya_kizunga_na_ket`
+2. `ya_kusalu_ya_los_k`
+3. `na_nkandakaataka_k`
+
+**Context Size 4:**
+
+1. `_ya_kuponaka_kimban`
+2. `_na_ntinu,_kinkundi`
+3. `a_ya_repubilika_ya_`
+
+
+### Key Findings
+
+- **Best Predictability:** Context-4 (word) with 92.9% predictability
+- **Branching Factor:** Decreases with context size (more deterministic)
+- **Memory Trade-off:** Larger contexts require more storage (52,366 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 | 6,048 |
+| Total Tokens | 147,208 |
+| Mean Frequency | 24.34 |
+| Median Frequency | 3 |
+| Frequency Std Dev | 343.74 |
+
+### Most Common Words
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | ya | 22,856 |
+| 2 | na | 11,712 |
+| 3 | kele | 3,421 |
+| 4 | yandi | 2,406 |
+| 5 | yina | 2,286 |
+| 6 | mpi | 2,116 |
+| 7 | ke | 1,925 |
+| 8 | bantu | 1,619 |
+| 9 | bo | 1,431 |
+| 10 | ti | 1,160 |
+
+### Least Common Words (from vocabulary)
+
+| Rank | Word | Frequency |
+|------|------|-----------|
+| 1 | lukwikulu | 2 |
+| 2 | kinama | 2 |
+| 3 | bangolo | 2 |
+| 4 | difuta | 2 |
+| 5 | mbatukulu | 2 |
+| 6 | kifumba | 2 |
+| 7 | weto | 2 |
+| 8 | metangama | 2 |
+| 9 | dieumerci | 2 |
+| 10 | xoon | 2 |
+
+### Zipf's Law Analysis
+
+| Metric | Value |
+|--------|-------|
+| Zipf Coefficient | 1.1604 |
+| R² (Goodness of Fit) | 0.989979 |
+| Adherence Quality | **excellent** |
+
+### Coverage Analysis
+
+| Top N Words | Coverage |
+|-------------|----------|
+| Top 100 | 59.2% |
+| Top 1,000 | 85.9% |
+| Top 5,000 | 98.6% |
+| Top 10,000 | 0.0% |
+
+### Key Findings
+
+- **Zipf Compliance:** R²=0.9900 indicates excellent adherence to Zipf's law
+- **High Frequency Dominance:** Top 100 words cover 59.2% of corpus
+- **Long Tail:** -3,952 words needed for remaining 100.0% 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 | 0.1871 🏆 | 0.4938 | N/A | N/A |
+| **mono_64d** | 64 | 0.0298 | 0.4879 | N/A | N/A |
+| **mono_128d** | 128 | 0.0037 | 0.5051 | N/A | N/A |
+| **aligned_32d** | 32 | 0.1871 | 0.5017 | 0.0140 | 0.0900 |
+| **aligned_64d** | 64 | 0.0298 | 0.4772 | 0.0120 | 0.1260 |
+| **aligned_128d** | 128 | 0.0037 | 0.4863 | 0.0100 | 0.1280 |
+
+### Key Findings
+
+- **Best Isotropy:** mono_32d with 0.1871 (more uniform distribution)
+- **Semantic Density:** Average pairwise similarity of 0.4920. Lower values indicate better semantic separation.
+- **Alignment Quality:** Aligned models achieve up to 1.4% 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 | **-0.048** | 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 |
+|--------|----------|
+| `-m` | mphotho, motángo, mapi |
+| `-k` | kimenga, kontina, kubutukaka |
+| `-ba` | balongoki, bavière, baministre |
+| `-b` | bzl, balongoki, bavière |
+| `-ku` | kubutukaka, kusadisa, kufua |
+| `-n` | nima, nzundu, ndalama |
+| `-ma` | mapi, maulalo, manimba |
+| `-ki` | kimenga, kimama, kinkita |
+
+#### Productive Suffixes
+| Suffix | Examples |
+|--------|----------|
+| `-a` | kimenga, tendula, nima |
+| `-e` | laurène, jenerale, bavière |
+| `-ka` | kubutukaka, twadisaka, vwandaka |
+| `-i` | tournoi, balongoki, mapi |
+| `-s` | chinois, awards, mois |
+| `-o` | mphotho, motángo, mpozo |
+| `-u` | nzundu, banduku, dibuku |
+| `-n` | installation, radiodiffusion, american |
+
+### 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 |
+|------|----------|------------------|----------|
+| `anga` | 1.59x | 42 contexts | sanga, tanga, nanga |
+| `angu` | 1.34x | 33 contexts | hangu, kangu, wangu |
+| `kand` | 1.75x | 12 contexts | kanda, kandy, nkandu |
+| `tion` | 1.77x | 11 contexts | option, action, motion |
+| `unga` | 1.38x | 23 contexts | zunga, lunga, tunga |
+| `ambu` | 1.31x | 26 contexts | sambu, mambu, wambu |
+| `ndak` | 1.61x | 12 contexts | vandaka, bandaka, fundaka |
+| `alak` | 1.60x | 12 contexts | palaki, talaka, salaka |
+| `laka` | 1.65x | 11 contexts | kulaka, talaka, bulaka |
+| `kisa` | 1.63x | 10 contexts | kisaka, vukisa, kisalu |
+| `anza` | 1.52x | 12 contexts | sanza, kanza, banza |
+| `bans` | 1.65x | 8 contexts | bansi, banswa, bansaka |
+
+### 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 |
+|--------|--------|-----------|----------|
+| `-k` | `-a` | 369 words | kimenga, kontina |
+| `-k` | `-ka` | 114 words | kubutukaka, kusalaka |
+| `-m` | `-a` | 102 words | mbânza, manimba |
+| `-ba` | `-a` | 90 words | bandînga, bafwana |
+| `-k` | `-la` | 55 words | kufokula, kubokila |
+| `-n` | `-a` | 48 words | nima, ndalama |
+| `-k` | `-i` | 48 words | kasi, kimosi |
+| `-ba` | `-i` | 46 words | balongoki, bankengi |
+| `-b` | `-a` | 46 words | bandînga, beba |
+| `-ba` | `-e` | 45 words | bavière, baministre |
+
+### 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 |
+|------|-----------------|------------|------|
+| kudibingaka | **`ku-di-bingaka`** | 7.5 | `bingaka` |
+| twadisama | **`twadis-a-ma`** | 7.5 | `a` |
+| kesalamaka | **`kesalam-a-ka`** | 7.5 | `a` |
+| tungamaka | **`tunga-ma-ka`** | 7.5 | `ma` |
+| kendimaka | **`kendim-a-ka`** | 7.5 | `a` |
+| commandant | **`command-a-nt`** | 7.5 | `a` |
+| nwaninaka | **`nwanin-a-ka`** | 7.5 | `a` |
+| kukutanaka | **`kukutan-a-ka`** | 7.5 | `a` |
+| entrepreneuriat | **`entrepreneuri-a-t`** | 7.5 | `a` |
+| azərbaycan | **`azərbayc-a-n`** | 7.5 | `a` |
+| nsambukila | **`nsambu-ki-la`** | 7.5 | `ki` |
+| kudibanza | **`ku-di-banza`** | 7.5 | `banza` |
+| twadisaka | **`twadis-a-ka`** | 7.5 | `a` |
+| acheulean | **`acheule-a-n`** | 7.5 | `a` |
+| championnat | **`championn-a-t`** | 7.5 | `a` |
+
+### 6.6 Linguistic Interpretation
+
+> **Automated Insight:**
+The language Kongo 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 | **32k BPE** | Best compression (4.52x) |
+| N-gram | **2-gram** | Lowest perplexity (168) |
+| Markov | **Context-4** | Highest predictability (92.9%) |
+| Embeddings | **100d** | Balanced semantic capture and isotropy |
+
+
+---
+## Appendix: Metrics Glossary & Interpretation Guide
+
+This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.
+
+### Tokenizer Metrics
+
+**Compression Ratio**
+> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
+>
+> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
+>
+> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.
+
+**Average Token Length (Fertility)**
+> *Definition:* Mean number of characters per token produced by the tokenizer.
+>
+> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
+>
+> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.
+
+**Unknown Token Rate (OOV Rate)**
+> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
+>
+> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
+>
+> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.
+
+### N-gram Model Metrics
+
+**Perplexity**
+> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
+>
+> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
+>
+> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.
+
+**Entropy**
+> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
+>
+> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
+>
+> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.
+
+**Coverage (Top-K)**
+> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
+>
+> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
+>
+> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.
+
+### Markov Chain Metrics
+
+**Average Entropy**
+> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
+>
+> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
+>
+> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.
+
+**Branching Factor**
+> *Definition:* Average number of unique next tokens observed for each context.
+>
+> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
+>
+> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.
+
+**Predictability**
+> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
+>
+> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
+>
+> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.
+
+### Vocabulary & Zipf's Law Metrics
+
+**Zipf's Coefficient**
+> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
+>
+> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
+>
+> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.
+
+**R² (Coefficient of Determination)**
+> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
+>
+> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
+>
+> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.
+
+**Vocabulary Coverage**
+> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
+>
+> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
+>
+> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.
+
+### Word Embedding Metrics
+
+**Isotropy**
+> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
+>
+> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
+>
+> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.
+
+**Average Norm**
+> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
+>
+> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
+>
+> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).
+
+**Cosine Similarity**
+> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
+>
+> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
+>
+> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.
+
+**t-SNE Visualization**
+> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
+>
+> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
+>
+> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.
+
+### General Interpretation Guidelines
+
+1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
+2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
+3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
+4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
+5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.
+
+
+### Visualizations Index
+
+| Visualization | Description |
+|---------------|-------------|
+| Tokenizer Compression | Compression ratios by vocabulary size |
+| Tokenizer Fertility | Average token length by vocabulary |
+| Tokenizer OOV | Unknown token rates |
+| Tokenizer Total Tokens | Total tokens by vocabulary |
+| N-gram Perplexity | Perplexity by n-gram size |
+| N-gram Entropy | Entropy by n-gram size |
+| N-gram Coverage | Top pattern coverage |
+| N-gram Unique | Unique n-gram counts |
+| Markov Entropy | Entropy by context size |
+| Markov Branching | Branching factor by context |
+| Markov Contexts | Unique context counts |
+| Zipf's Law | Frequency-rank distribution with fit |
+| Vocab Frequency | Word frequency distribution |
+| Top 20 Words | Most frequent words |
+| Vocab Coverage | Cumulative coverage curve |
+| Embedding Isotropy | Vector space uniformity |
+| Embedding Norms | Vector magnitude distribution |
+| Embedding Similarity | Word similarity heatmap |
+| Nearest Neighbors | Similar words for key terms |
+| t-SNE Words | 2D word embedding visualization |
+| t-SNE Sentences | 2D sentence embedding visualization |
+| Position Encoding | Encoding method comparison |
+| Model Sizes | Storage requirements |
+| Performance Dashboard | Comprehensive performance overview |
+
+---
+## About This Project
+
+### Data Source
+
+Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.
+
+### Project
+
+A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.
+
+### Maintainer
+
+[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)
+
+### Citation
+
+If you use these models in your research, please cite:
+
+```bibtex
+@misc{wikilangs2025,
+  author = {Kamali, Omar},
+  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
+  year = {2025},
+  doi = {10.5281/zenodo.18073153},
+  publisher = {Zenodo},
+  url = {https://huggingface.co/wikilangs}
+  institution = {Omneity Labs}
+}
+```
+
+### License
+
+MIT License - Free for academic and commercial use.
+
+### Links
+
+- 🌐 Website: [wikilangs.org](https://wikilangs.org)
+- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
+- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
+- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
+- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
+---
+*Generated by Wikilangs Models Pipeline*
+
+*Report Date: 2026-01-10 07:31:40*

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