---
language: mg
language_name: Malagasy
language_family: austronesian_malagasy
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-austronesian_malagasy
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: 4.455
  - name: best_isotropy
    type: isotropy
    value: 0.8042
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Malagasy** 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** | 3.717x | 3.72 | 1.0106% | 763,492 |
| **16k** | 4.029x | 4.03 | 1.0955% | 704,362 |
| **32k** | 4.266x | 4.27 | 1.1597% | 665,323 |
| **64k** | 4.455x 🏆 | 4.46 | 1.2113% | 637,017 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `I Taquaritinga dia kaominina ao , ao amin'i . Jeografia . Ny isam-ponina dia 56....`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁i ▁ta qu arit inga ▁dia ▁kaominina ▁ao ▁, ▁ao ... (+34 more)` | 44 |
| 16k | `▁i ▁ta qu arit inga ▁dia ▁kaominina ▁ao ▁, ▁ao ... (+34 more)` | 44 |
| 32k | `▁i ▁ta qu arit inga ▁dia ▁kaominina ▁ao ▁, ▁ao ... (+34 more)` | 44 |
| 64k | `▁i ▁taqu aritinga ▁dia ▁kaominina ▁ao ▁, ▁ao ▁amin ' ... (+32 more)` | 42 |

**Sample 2:** `Zoltán Stieber dia mpilalao baolina kitra teraka ny 16 Oktobra tao Hongaria Jere...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁z ol t án ▁st i eb er ▁dia ▁mpilalao ... (+16 more)` | 26 |
| 16k | `▁z olt án ▁st i eber ▁dia ▁mpilalao ▁baolina ▁kitra ... (+13 more)` | 23 |
| 32k | `▁zoltán ▁st i eber ▁dia ▁mpilalao ▁baolina ▁kitra ▁teraka ▁ny ... (+11 more)` | 21 |
| 64k | `▁zoltán ▁sti eber ▁dia ▁mpilalao ▁baolina ▁kitra ▁teraka ▁ny ▁ ... (+10 more)` | 20 |

**Sample 3:** `Rutger Backe dia mpilalao baolina kitra mizaka ny zom-pirenen'i Soeda teraka ny ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁r ut ger ▁ba cke ▁dia ▁mpilalao ▁baolina ▁kitra ▁mizaka ... (+18 more)` | 28 |
| 16k | `▁rut ger ▁ba cke ▁dia ▁mpilalao ▁baolina ▁kitra ▁mizaka ▁ny ... (+17 more)` | 27 |
| 32k | `▁rut ger ▁ba cke ▁dia ▁mpilalao ▁baolina ▁kitra ▁mizaka ▁ny ... (+17 more)` | 27 |
| 64k | `▁rut ger ▁ba cke ▁dia ▁mpilalao ▁baolina ▁kitra ▁mizaka ▁ny ... (+17 more)` | 27 |


### Key Findings

- **Best Compression:** 64k achieves 4.455x compression
- **Lowest UNK Rate:** 8k with 1.0106% 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 | 3,283 | 11.68 | 138,920 | 38.8% | 67.4% |
| **2-gram** | Subword | 188 🏆 | 7.55 | 7,308 | 76.8% | 99.3% |
| **3-gram** | Word | 6,811 | 12.73 | 327,650 | 31.9% | 62.3% |
| **3-gram** | Subword | 1,135 | 10.15 | 56,079 | 43.5% | 83.4% |
| **4-gram** | Word | 13,815 | 13.75 | 695,396 | 27.5% | 57.0% |
| **4-gram** | Subword | 4,270 | 12.06 | 297,339 | 28.3% | 63.5% |
| **5-gram** | Word | 15,415 | 13.91 | 666,811 | 25.9% | 55.7% |
| **5-gram** | Subword | 10,797 | 13.40 | 801,473 | 21.0% | 52.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `amin ny` | 363,322 |
| 2 | `andro taona` | 205,790 |
| 3 | `ao amin` | 204,188 |
| 4 | `au au` | 199,079 |
| 5 | `au andro` | 199,066 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `au andro taona` | 199,066 |
| 2 | `au au andro` | 199,066 |
| 3 | `ao amin ny` | 165,787 |
| 4 | `tamin ny taona` | 75,724 |
| 5 | `taona au au` | 52,606 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `au au andro taona` | 199,066 |
| 2 | `au andro taona au` | 52,606 |
| 3 | `andro taona au au` | 52,606 |
| 4 | `taona au au andro` | 52,598 |
| 5 | `amin ny faritr i` | 42,015 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `au andro taona au au` | 52,606 |
| 2 | `au au andro taona au` | 52,606 |
| 3 | `andro taona au au andro` | 52,598 |
| 4 | `taona au au andro taona` | 52,598 |
| 5 | `ao amin ny faritr i` | 41,743 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `y _` | 2,972,630 |
| 2 | `a _` | 2,871,965 |
| 3 | `a n` | 2,624,146 |
| 4 | `_ a` | 2,225,943 |
| 5 | `n y` | 2,058,703 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n y _` | 1,991,132 |
| 2 | `n a _` | 984,036 |
| 3 | `_ n y` | 972,813 |
| 4 | `m i n` | 698,997 |
| 5 | `a n a` | 687,522 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n y _` | 971,989 |
| 2 | `a m i n` | 574,682 |
| 3 | `m i n '` | 543,499 |
| 4 | `' n y _` | 517,014 |
| 5 | `n ' n y` | 516,967 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a m i n '` | 543,348 |
| 2 | `n ' n y _` | 516,918 |
| 3 | `_ d i a _` | 465,119 |
| 4 | `_ a m i n` | 438,819 |
| 5 | `a u ) _ a` | 398,149 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 188
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~52% 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 | 0.6521 | 1.571 | 4.93 | 355,569 | 34.8% |
| **1** | Subword | 0.6364 | 1.554 | 5.02 | 4,923 | 36.4% |
| **2** | Word | 0.2834 | 1.217 | 1.88 | 1,748,434 | 71.7% |
| **2** | Subword | 0.7914 | 1.731 | 4.56 | 24,686 | 20.9% |
| **3** | Word | 0.1358 | 1.099 | 1.33 | 3,283,841 | 86.4% |
| **3** | Subword | 0.8149 | 1.759 | 4.15 | 112,579 | 18.5% |
| **4** | Word | 0.0673 🏆 | 1.048 | 1.15 | 4,348,637 | 93.3% |
| **4** | Subword | 0.6559 | 1.576 | 3.01 | 467,417 | 34.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ny masoandro mitatao ho an drenirano sy tsy hita eo amin ny fivavahana iraniana manodidina amin`
2. `dia ary maty tamin ny toerana avo indrindra dia tanàna ao amin ny fehiben ny insee`
3. `amin ny insee dia degre jereo koa hainkintana zavatra ara daharanjarahasin ilay kaominina ao amin ny`

**Context Size 2:**

1. `amin ny boribory lavoraryizay antsoina koa hoe excentricité amin ny soratra desimaly ny faritr i nou...`
2. `andro taona au au andro taona karenfletch au au andro taona bomans rg au au andro taona`
3. `ao amin ny 0 2 0 3 ary manana hafanana eo amin ny fivondronan i guéret ao`

**Context Size 3:**

1. `au andro taona jb13 au au andro taona ja59 au au andro taona xn45 au au andro taona`
2. `au au andro taona tk27 au au andro taona qj2 au au andro taona au au andro taona`
3. `ao amin ny vondronosy maley ho aty madagasikara notarihin i roger le goff no ben ny tanàna mandritry`

**Context Size 4:**

1. `au au andro taona oe4 au au andro taona sq3 au au andro taona au au andro taona om23`
2. `au andro taona au au andro taona au au andro taona wp3 au au andro taona xy4 au au`
3. `andro taona au au andro taona au au andro taona sg92 au au andro taona au au andro taona`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `asogrewwrau)_any`
2. `_aom4)_a_eliantr`
3. `navony_bamiieser`

**Context Size 2:**

1. `y_mats.com-ponial`
2. `a_dia_sy_hity_sy_`
3. `andray_fy_ny_ambo`

**Context Size 3:**

1. `ny_ary_olomer_sns.`
2. `na_rohy_i_juantsah`
3. `_ny_ham-panodikoro`

**Context Size 4:**

1. `_ny_14_dia_mpilala_`
2. `amin'_i_bernambaràn`
3. `min'_ny_faritimes,_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (467,417 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 | 186,416 |
| Total Tokens | 12,311,117 |
| Mean Frequency | 66.04 |
| Median Frequency | 3 |
| Frequency Std Dev | 4301.01 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ny | 1,518,386 |
| 2 | dia | 465,913 |
| 3 | amin | 435,633 |
| 4 | au | 412,623 |
| 5 | i | 399,465 |
| 6 | taona | 314,686 |
| 7 | ao | 283,721 |
| 8 | andro | 214,534 |
| 9 | ary | 149,725 |
| 10 | tamin | 113,939 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | clavaud | 2 |
| 2 | holaboay | 2 |
| 3 | olaboay | 2 |
| 4 | marggie | 2 |
| 5 | xiomara | 2 |
| 6 | tapias | 2 |
| 7 | firmo | 2 |
| 8 | gentofte | 2 |
| 9 | amalienborg | 2 |
| 10 | vyborg | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2392 |
| R² (Goodness of Fit) | 0.998231 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 60.0% |
| Top 1,000 | 81.4% |
| Top 5,000 | 89.6% |
| Top 10,000 | 92.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9982 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 60.0% of corpus
- **Long Tail:** 176,416 words needed for remaining 7.7% 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 | 0.8042 | 0.3503 | N/A | N/A |
| **mono_64d** | 64 | 0.7680 | 0.2980 | N/A | N/A |
| **mono_128d** | 128 | 0.7205 | 0.2509 | N/A | N/A |
| **aligned_32d** | 32 | 0.8042 🏆 | 0.3596 | 0.0820 | 0.3280 |
| **aligned_64d** | 64 | 0.7680 | 0.2994 | 0.1540 | 0.4960 |
| **aligned_128d** | 128 | 0.7205 | 0.2597 | 0.2000 | 0.5660 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8042 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3030. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 20.0% 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 | **0.070** | Low formulaic content | - |

### 6.2 Affix Inventory (Productive Units)

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

#### Productive Prefixes
| Prefix | Examples |
|--------|----------|
| `-s` | stenopetalum, stenay, sumiyoshi |
| `-a` | andriamarobasy, anggun, aboville |
| `-r` | reignat, rm97, raty |
| `-t` | tm67, td34, tp34 |
| `-c` | christensen, ce6, celentano |
| `-b` | bakkoury, bev, bakr |
| `-f` | famantaranavaratra, frisano, fanandraman |
| `-g` | gp6, gq54, gc61 |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | donnera, kwaśniewska, famantaranavaratra |
| `-na` | fanasokajiana, andaminana, hampijoroana |
| `-n` | nosoniavin, anggun, christensen |
| `-s` | pégairolles, aups, tauxières |
| `-e` | aboville, bartole, louze |
| `-y` | andriamarobasy, namitany, stenay |
| `-o` | frisano, celentano, shapiro |
| `-i` | oerstedii, sumiyoshi, salviani |

### 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 |
|------|----------|------------------|----------|
| `inin` | 2.33x | 55 contexts | minin, vining, jining |
| `indr` | 1.81x | 124 contexts | indre, indri, indry |
| `andr` | 1.49x | 336 contexts | andry, andro, andra |
| `ndra` | 1.67x | 176 contexts | ondra, andra, indra |
| `itra` | 1.69x | 141 contexts | mitra, ritra, kitra |
| `iana` | 1.64x | 164 contexts | kiana, riana, niana |
| `ndri` | 1.63x | 161 contexts | endri, indri, andri |
| `ants` | 1.70x | 116 contexts | sants, antsa, wants |
| `ahar` | 1.66x | 111 contexts | nahar, bahar, ahary |
| `ndro` | 1.58x | 111 contexts | andro, indro, androy |
| `inta` | 1.74x | 60 contexts | vinta, linta, kinta |
| `ntan` | 1.49x | 111 contexts | entan, entana, antany |

### 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 |
|--------|--------|-----------|----------|
| `-a` | `-a` | 134 words | ansikilika, aminata |
| `-f` | `-a` | 128 words | fanononana, fanaparitahana |
| `-f` | `-na` | 105 words | fanononana, fanaparitahana |
| `-h` | `-a` | 103 words | hetaheta, hamitika |
| `-t` | `-a` | 77 words | theodosia, tuberifera |
| `-s` | `-a` | 64 words | serrania, sirasida |
| `-f` | `-n` | 62 words | furlan, flaxman |
| `-c` | `-s` | 61 words | citées, cisterciensis |
| `-a` | `-na` | 56 words | alamàna, andriankotonavalona |
| `-b` | `-a` | 52 words | bizantioma, botovasoa |

### 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 |
|------|-----------------|------------|------|
| miratoerana | **`mi-ra-toerana`** | 7.5 | `toerana` |
| namoronany | **`namoro-na-ny`** | 7.5 | `na` |
| fanakanana | **`fanaka-na-na`** | 7.5 | `na` |
| newfoundland | **`newfoundl-an-d`** | 7.5 | `an` |
| fampitany | **`fampit-a-ny`** | 7.5 | `a` |
| firenenena | **`firenen-e-na`** | 7.5 | `e` |
| holazainao | **`holazai-na-o`** | 7.5 | `na` |
| boetticher | **`boetti-ch-er`** | 7.5 | `ch` |
| cucurbiteae | **`cucurbite-a-e`** | 7.5 | `a` |
| cobergher | **`coberg-h-er`** | 7.5 | `h` |
| fankanesana | **`fankanes-a-na`** | 7.5 | `a` |
| fahatoranana | **`fahatora-na-na`** | 7.5 | `na` |
| nanohanany | **`nanoha-na-ny`** | 7.5 | `na` |
| anamafana | **`anamaf-a-na`** | 7.5 | `a` |
| fampirantiana | **`fampiranti-a-na`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Malagasy shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.46x) |
| N-gram | **2-gram** | Lowest perplexity (188) |
| Markov | **Context-4** | Highest predictability (93.3%) |
| 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 12:09:55*