---
language: bm
language_name: Bambara
language_family: atlantic_other
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-atlantic_other
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: 4.018
  - name: best_isotropy
    type: isotropy
    value: 0.3203
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Bambara** 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** | 3.554x | 3.56 | 1.4079% | 103,986 |
| **16k** | 3.839x | 3.85 | 1.5205% | 96,281 |
| **32k** | 4.018x 🏆 | 4.03 | 1.5915% | 91,989 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `TusyɛninBailleul, Charles. Dictionnaire français-bambara. Bamako: Éditions Donni...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tu syɛn inbailleul , ▁charles . ▁dictionnaire ▁français - bambara ... (+8 more)` | 18 |
| 16k | `▁tusyɛn inbailleul , ▁charles . ▁dictionnaire ▁français - bambara . ... (+7 more)` | 17 |
| 32k | `▁tusyɛn inbailleul , ▁charles . ▁dictionnaire ▁français - bambara . ... (+7 more)` | 17 |

**Sample 2:** `Brains ye Faransi ka dugu ye. Dugumogo be taa jon yooro Sababou Kɔfɛ sira Brains...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁brains ▁ye ▁faransi ▁ka ▁dugu ▁ye . ▁dugumogo ▁be ▁taa ... (+10 more)` | 20 |
| 16k | `▁brains ▁ye ▁faransi ▁ka ▁dugu ▁ye . ▁dugumogo ▁be ▁taa ... (+10 more)` | 20 |
| 32k | `▁brains ▁ye ▁faransi ▁ka ▁dugu ▁ye . ▁dugumogo ▁be ▁taa ... (+10 more)` | 20 |

**Sample 3:** `KolanfuBailleul, Charles. Dictionnaire français-bambara. Bamako: Éditions Donniy...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kolan fu bailleul , ▁charles . ▁dictionnaire ▁français - bambara ... (+8 more)` | 18 |
| 16k | `▁kolan fubailleul , ▁charles . ▁dictionnaire ▁français - bambara . ... (+7 more)` | 17 |
| 32k | `▁kolanfubailleul , ▁charles . ▁dictionnaire ▁français - bambara . ▁bamako ... (+6 more)` | 16 |


### Key Findings

- **Best Compression:** 32k achieves 4.018x compression
- **Lowest UNK Rate:** 8k with 1.4079% 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 | 917 | 9.84 | 2,056 | 40.6% | 82.5% |
| **2-gram** | Subword | 271 🏆 | 8.08 | 1,816 | 67.8% | 98.7% |
| **3-gram** | Word | 757 | 9.56 | 2,167 | 44.4% | 79.2% |
| **3-gram** | Subword | 1,867 | 10.87 | 9,795 | 30.1% | 75.0% |
| **4-gram** | Word | 1,888 | 10.88 | 5,346 | 34.2% | 52.7% |
| **4-gram** | Subword | 7,991 | 12.96 | 35,277 | 14.7% | 47.2% |
| **5-gram** | Word | 1,411 | 10.46 | 4,196 | 36.6% | 54.4% |
| **5-gram** | Subword | 17,676 | 14.11 | 58,257 | 10.4% | 34.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ka dugu` | 524 |
| 2 | `éditions donniya` | 419 |
| 3 | `bambara bamako` | 419 |
| 4 | `charles dictionnaire` | 419 |
| 5 | `français bambara` | 419 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dictionnaire français bambara` | 419 |
| 2 | `charles dictionnaire français` | 419 |
| 3 | `français bambara bamako` | 419 |
| 4 | `bambara bamako éditions` | 419 |
| 5 | `éditions donniya isbn` | 419 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `bamako éditions donniya isbn` | 419 |
| 2 | `bambara bamako éditions donniya` | 419 |
| 3 | `français bambara bamako éditions` | 419 |
| 4 | `dictionnaire français bambara bamako` | 419 |
| 5 | `charles dictionnaire français bambara` | 419 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `bambara bamako éditions donniya isbn` | 419 |
| 2 | `charles dictionnaire français bambara bamako` | 419 |
| 3 | `dictionnaire français bambara bamako éditions` | 419 |
| 4 | `français bambara bamako éditions donniya` | 419 |
| 5 | `bamako éditions donniya isbn sababou` | 415 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 23,457 |
| 2 | `_ k` | 13,682 |
| 3 | `a n` | 13,488 |
| 4 | `n _` | 12,358 |
| 5 | `i _` | 9,793 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a` | 6,339 |
| 2 | `k a _` | 4,941 |
| 3 | `_ y e` | 4,556 |
| 4 | `a n _` | 3,990 |
| 5 | `n i _` | 3,929 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k a _` | 4,284 |
| 2 | `_ y e _` | 3,187 |
| 3 | `_ b ɛ _` | 1,824 |
| 4 | `_ n i _` | 1,804 |
| 5 | `_ m i n` | 1,782 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a m a n a` | 1,291 |
| 2 | `_ d u g u` | 1,271 |
| 3 | `_ m i n _` | 1,168 |
| 4 | `j a m a n` | 1,146 |
| 5 | `a _ k a _` | 1,065 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 271
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~34% 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 | 0.5962 | 1.512 | 3.33 | 17,463 | 40.4% |
| **1** | Subword | 1.1592 | 2.233 | 8.34 | 482 | 0.0% |
| **2** | Word | 0.2012 | 1.150 | 1.41 | 57,826 | 79.9% |
| **2** | Subword | 0.9871 | 1.982 | 5.02 | 4,012 | 1.3% |
| **3** | Word | 0.0638 | 1.045 | 1.10 | 81,186 | 93.6% |
| **3** | Subword | 0.7347 | 1.664 | 3.14 | 20,106 | 26.5% |
| **4** | Word | 0.0198 🏆 | 1.014 | 1.03 | 88,526 | 98.0% |
| **4** | Subword | 0.5000 | 1.414 | 2.08 | 63,024 | 50.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ka dugu ye ɲ ŋ ɔ ɲ ka k u la litwanie duchy belebele naninan ye`
2. `ye kan kaan kankan mali duo dɔnkilidalaw ye balikukalan ni faransi ka bɔ pretoria tɔgɔ ta`
3. `a ka kɛ mɔgɔ nɛrɛmaw ye nga u ko majigilenya majigin kɔrɔtalenba ala kelenpe ani san`

**Context Size 2:**

1. `charles dictionnaire français bambara bamako éditions donniya isbn sababou kɔkan sirilanw basshunter...`
2. `dictionnaire français bambara bamako éditions donniya isbn sababou kɔkan sirilanw michael jackson ka...`
3. `donniya isbn sababou kɔkan sirilanw ourebia ourebi nkolonin thryonomys swinderianus kɔɲinɛ nkansole ...`

**Context Size 3:**

1. `bambara bamako éditions donniya isbn sababou kɔkan sirilanw herpestes ichneumon`
2. `éditions donniya isbn sababou kɔkan sirilanw leptailurus serval`
3. `bamako éditions donniya isbn sababou dutafilm`

**Context Size 4:**

1. `bambara bamako éditions donniya isbn sababou kɔkan sirilanw tragelaphus spekii`
2. `dictionnaire français bambara bamako éditions donniya isbn sababou kɔkan sirilanw mungos mungo`
3. `français bambara bamako éditions donniya isbn sababou kɔkan sirilanw papio anubis`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_t_edo_ba_faainɛ`
2. `afoghmanọ_ne,_ji`
3. `nyerayedambòrɔnk`

**Context Size 2:**

1. `a_aniyala:_zara._`
2. `_kara_baridalatɔn`
3. `anginkun_walf-c._`

**Context Size 3:**

1. `_kan_fila-jɔnjɛ_ye`
2. `ka_san_na_ka_kɔrɔl`
3. `_ye_dugu._virgia,_`

**Context Size 4:**

1. `_ka_ɲa._shiya_gossy`
2. `_ye_danmasen_baara_`
3. `_bɛ_daɲε_minnu_bɛ_a`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (63,024 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 | 6,824 |
| Total Tokens | 94,926 |
| Mean Frequency | 13.91 |
| Median Frequency | 3 |
| Frequency Std Dev | 106.26 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ye | 4,371 |
| 2 | ka | 4,340 |
| 3 | a | 3,278 |
| 4 | la | 1,926 |
| 5 | ni | 1,899 |
| 6 | bɛ | 1,834 |
| 7 | na | 1,623 |
| 8 | min | 1,189 |
| 9 | o | 1,149 |
| 10 | ani | 1,076 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | abubakari | 2 |
| 2 | candaces | 2 |
| 3 | ameniras | 2 |
| 4 | kandasi | 2 |
| 5 | qore | 2 |
| 6 | candace | 2 |
| 7 | amɔn | 2 |
| 8 | bajiw | 2 |
| 9 | dunbagaw | 2 |
| 10 | mouvement | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0058 |
| R² (Goodness of Fit) | 0.984137 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 52.4% |
| Top 1,000 | 79.3% |
| Top 5,000 | 96.2% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9841 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 52.4% of corpus
- **Long Tail:** -3,176 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 | 0.3203 🏆 | 0.5260 | N/A | N/A |
| **mono_64d** | 64 | 0.0572 | 0.5107 | N/A | N/A |
| **mono_128d** | 128 | 0.0109 | 0.5108 | N/A | N/A |
| **aligned_32d** | 32 | 0.3203 | 0.5505 | 0.0040 | 0.0600 |
| **aligned_64d** | 64 | 0.0572 | 0.5015 | 0.0300 | 0.1740 |
| **aligned_128d** | 128 | 0.0109 | 0.5061 | 0.0400 | 0.1700 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.3203 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.5176. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 4.0% 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 | **0.589** | 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 |
|--------|----------|
| `-ma` | masurunyala, mansaya, magana |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | cɛnimusoya, fa, masurunyala |
| `-an` | jigilan, dilan, irisikan |
| `-en` | pen, tobilen, maliden |

### 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 |
|------|----------|------------------|----------|
| `alan` | 1.63x | 24 contexts | balan, kalan, jalan |
| `aman` | 1.32x | 25 contexts | daman, baman, saman |
| `riya` | 1.72x | 11 contexts | miriya, sariya, suriya |
| `aara` | 1.66x | 12 contexts | naara, yaara, taara |
| `alen` | 1.36x | 20 contexts | salen, nalen, dalen |
| `ɔgɔn` | 1.72x | 10 contexts | ɲɔgɔn, nɔgɔn, dɔgɔn |
| `anka` | 1.52x | 13 contexts | yankan, kankan, dankan |
| `elen` | 1.56x | 12 contexts | selen, kelen, yelen |
| `amin` | 1.42x | 15 contexts | lamini, damina, daminè |
| `ɛbɛn` | 1.74x | 8 contexts | sɛbɛn, sɛbɛnw, sɛbɛnni |
| `nkan` | 1.37x | 14 contexts | yankan, kankan, benkan |
| `ilan` | 1.33x | 13 contexts | tilan, dilan, filan |

### 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 |
|--------|--------|-----------|----------|
| `-ma` | `-a` | 20 words | mansamara, masa |
| `-ma` | `-an` | 8 words | manyan, man |
| `-ma` | `-en` | 5 words | maralen, madonnen |

### 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 |
|------|-----------------|------------|------|
| datugunen | **`datugun-en`** | 4.5 | `datugun` |
| masurunya | **`ma-surunya`** | 4.5 | `surunya` |
| maninkakan | **`ma-ninkak-an`** | 3.0 | `ninkak` |
| masafugulan | **`ma-safugul-an`** | 3.0 | `safugul` |
| mandenkan | **`ma-ndenk-an`** | 3.0 | `ndenk` |
| wolonwulanan | **`wolonwul-an-an`** | 3.0 | `wolonwul` |
| maramafen | **`ma-ramaf-en`** | 3.0 | `ramaf` |
| kɔrɔnyanfan | **`kɔrɔnyanf-an`** | 1.5 | `kɔrɔnyanf` |
| tamashiyen | **`tamashiy-en`** | 1.5 | `tamashiy` |
| quotidien | **`quotidi-en`** | 1.5 | `quotidi` |
| bolofaran | **`bolofar-an`** | 1.5 | `bolofar` |
| marcusenius | **`ma-rcusenius`** | 1.5 | `rcusenius` |
| manuskrip | **`ma-nuskrip`** | 1.5 | `nuskrip` |
| sεbεnnisen | **`sεbεnnis-en`** | 1.5 | `sεbεnnis` |
| kɔnɔntɔnnan | **`kɔnɔntɔnn-an`** | 1.5 | `kɔnɔntɔnn` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Bambara 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 | **32k BPE** | Best compression (4.02x) |
| N-gram | **2-gram** | Lowest perplexity (271) |
| Markov | **Context-4** | Highest predictability (98.0%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


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

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

### Tokenizer Metrics

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

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

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

### N-gram Model Metrics

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

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

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

### Markov Chain Metrics

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

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

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

### Vocabulary & Zipf's Law Metrics

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

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

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

### Word Embedding Metrics

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

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

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

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

### General Interpretation Guidelines

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


### Visualizations Index

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

---
## About This Project

### Data Source

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

### Project

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

### Maintainer

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

### Citation

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

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

### License

MIT License - Free for academic and commercial use.

### Links

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

*Report Date: 2026-01-03 19:12:39*