---
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*