---
language: ee
language_name: Ewe
language_family: atlantic_kwa
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_kwa
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: 4.309
  - name: best_isotropy
    type: isotropy
    value: 0.7155
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Ewe** 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** | 3.822x | 3.83 | 0.5658% | 181,329 |
| **16k** | 4.082x | 4.09 | 0.6044% | 169,762 |
| **32k** | 4.309x 🏆 | 4.31 | 0.6380% | 160,824 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ata Messan Ajavon Zeus nye Togo dunyahela, eye wònye Save Togo Collective ƒe zim...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ata ▁me ssan ▁aja von ▁ze us ▁nye ▁togo ▁dunyahela ... (+18 more)` | 28 |
| 16k | `▁ata ▁messan ▁ajavon ▁ze us ▁nye ▁togo ▁dunyahela , ▁eye ... (+15 more)` | 25 |
| 32k | `▁ata ▁messan ▁ajavon ▁zeus ▁nye ▁togo ▁dunyahela , ▁eye ▁wònye ... (+13 more)` | 23 |

**Sample 2:** `South Carolina nye dukɔ aɖe le United States. States`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁south ▁caro lina ▁nye ▁dukɔ ▁aɖe ▁le ▁united ▁states . ... (+1 more)` | 11 |
| 16k | `▁south ▁carolina ▁nye ▁dukɔ ▁aɖe ▁le ▁united ▁states . ▁states` | 10 |
| 32k | `▁south ▁carolina ▁nye ▁dukɔ ▁aɖe ▁le ▁united ▁states . ▁states` | 10 |

**Sample 3:** `GbɔeviAziaku, Vincent Erskine. A Linguistic Analysis of Ewe Animal Names among t...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gbɔe viaziaku , ▁vincent ▁erskine . ▁a ▁linguistic ▁analysis ▁of ... (+19 more)` | 29 |
| 16k | `▁gbɔe viaziaku , ▁vincent ▁erskine . ▁a ▁linguistic ▁analysis ▁of ... (+19 more)` | 29 |
| 32k | `▁gbɔeviaziaku , ▁vincent ▁erskine . ▁a ▁linguistic ▁analysis ▁of ▁ewe ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 32k achieves 4.309x compression
- **Lowest UNK Rate:** 8k with 0.5658% 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 | 3,050 | 11.57 | 7,157 | 23.6% | 56.9% |
| **2-gram** | Subword | 259 🏆 | 8.02 | 1,996 | 66.4% | 99.2% |
| **3-gram** | Word | 4,032 | 11.98 | 8,747 | 22.9% | 48.1% |
| **3-gram** | Subword | 1,781 | 10.80 | 12,826 | 32.5% | 74.7% |
| **4-gram** | Word | 6,737 | 12.72 | 13,766 | 19.8% | 37.5% |
| **4-gram** | Subword | 7,506 | 12.87 | 51,628 | 17.9% | 48.5% |
| **5-gram** | Word | 4,126 | 12.01 | 8,899 | 24.0% | 42.0% |
| **5-gram** | Subword | 18,211 | 14.15 | 94,077 | 11.1% | 34.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `le ƒe` | 2,279 |
| 2 | `ƒe me` | 1,784 |
| 3 | `me la` | 1,442 |
| 4 | `me le` | 1,115 |
| 5 | `si nye` | 1,012 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `le ƒe me` | 1,460 |
| 2 | `ƒe me la` | 652 |
| 3 | `va ɖo ƒe` | 327 |
| 4 | `ƒe va ɖo` | 319 |
| 5 | `tso ƒe va` | 311 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `le ƒe me la` | 540 |
| 2 | `ƒe va ɖo ƒe` | 316 |
| 3 | `tso ƒe va ɖo` | 302 |
| 4 | `vincent erskine a linguistic` | 256 |
| 5 | `erskine a linguistic analysis` | 256 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tso ƒe va ɖo ƒe` | 300 |
| 2 | `linguistic analysis of ewe animal` | 256 |
| 3 | `analysis of ewe animal names` | 256 |
| 4 | `of ewe animal names among` | 256 |
| 5 | `ewe animal names among the` | 256 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 93,022 |
| 2 | `a _` | 32,972 |
| 3 | `o _` | 26,746 |
| 4 | `w o` | 25,054 |
| 5 | `_ a` | 23,819 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ƒ e _` | 21,210 |
| 2 | `l e _` | 20,474 |
| 3 | `_ ƒ e` | 16,656 |
| 4 | `w o _` | 15,423 |
| 5 | `_ l e` | 14,771 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ƒ e _` | 16,518 |
| 2 | `_ l e _` | 14,241 |
| 3 | `n y e _` | 6,181 |
| 4 | `_ s i _` | 6,094 |
| 5 | `_ m e _` | 5,720 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k p l e _` | 4,986 |
| 2 | `_ k p l e` | 4,841 |
| 3 | `o _ ƒ e _` | 4,832 |
| 4 | `e _ ƒ e _` | 4,358 |
| 5 | `_ n y e _` | 3,640 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 259
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.7631 | 1.697 | 4.67 | 25,800 | 23.7% |
| **1** | Subword | 1.5369 | 2.902 | 11.32 | 389 | 0.0% |
| **2** | Word | 0.2897 | 1.222 | 1.68 | 120,194 | 71.0% |
| **2** | Subword | 1.0150 | 2.021 | 5.66 | 4,399 | 0.0% |
| **3** | Word | 0.1029 | 1.074 | 1.17 | 201,432 | 89.7% |
| **3** | Subword | 0.7954 | 1.736 | 3.60 | 24,892 | 20.5% |
| **4** | Word | 0.0390 🏆 | 1.027 | 1.06 | 235,375 | 96.1% |
| **4** | Subword | 0.5399 | 1.454 | 2.27 | 89,556 | 46.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ƒe sewɔtakpekpea me le berlin takpekpea me manya alesi wòhiã be yeƒe dukɔa ƒe dunyahehewo ƒe`
2. `le ho ʋlim le dukplɔla ƒe ɖoɖo aɖe ƒe bisiɔp gbãtɔ kple dzoɖagbe kple nubablawo gɔmee`
3. `me nuzazãwo kple la ŋkoe nye eƒe sukudede dzɔdzɔmeŋutinunya ƒe nuwɔna me be wòanye nutala afia`

**Context Size 2:**

1. `le ƒe me eye wòtso bole le savanna nutome wodzi mahama le november 28 dzi le guadeloupe`
2. `ƒe me emegbe exɔ ɖɔkta ƒe dzeside adre kple afã tso dukɔ yome me le south africa`
3. `me la gold coast le tedoxe 26 dzi kple agbalẽtamɔ̃ gãwo siaa me wotsɔ nya ɖe ame`

**Context Size 3:**

1. `le ƒe me eye archdeacon le ƒe enye sinima gbãtɔ si woɖe le ƒe me eye wòka atam`
2. `ƒe me la eɖe eme be mefia be wò agbe mele vevie o 11 koe gblɔ be ameyibɔwo`
3. `va ɖo ƒe dome defontaine ku le hénin sur cojeul ƒe dumegã le ƒe va ɖo ƒe le`

**Context Size 4:**

1. `le ƒe me la enye europa dukɔwo ƒe habɔbɔ me eƒe zimenɔla si woti le ƒe me lae nye`
2. `ƒe va ɖo ƒe tso ƒe va ɖo ƒe dɔmedzoedonamea xɔ ƒe eve agbalẽa me tɔ vevitɔe nye dɔwɔhawo`
3. `tso ƒe va ɖo ƒe enɔ pyrénées atlantiques dɔwɔƒea teƒe grenet nye radical party me tɔ enye orléans ƒe`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_aƒe_aɖena_(_na_`
2. `e_dzu_alaxa_etsi`
3. `ameɖonye_si_d_ye`

**Context Size 2:**

1. `e_la_nyations_me_`
2. `a_culymmakple_du_`
3. `o_frafia_ƒe_a._me`

**Context Size 3:**

1. `ƒe_3,_dzɔ_dome_ŋgɔ`
2. `le_ta_12._don_le_a`
3. `_ƒe_nu_dze_la,_wod`

**Context Size 4:**

1. `_ƒe_me_da_asitsi_et`
2. `_le_du_be_la,_eye_w`
3. `nye_to_february_raw`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (89,556 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 | 11,578 |
| Total Tokens | 260,556 |
| Mean Frequency | 22.50 |
| Median Frequency | 3 |
| Frequency Std Dev | 257.37 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ƒe | 16,951 |
| 2 | le | 14,512 |
| 3 | me | 8,468 |
| 4 | si | 6,279 |
| 5 | la | 4,866 |
| 6 | kple | 4,852 |
| 7 | be | 3,745 |
| 8 | nye | 3,709 |
| 9 | ɖe | 3,263 |
| 10 | siwo | 2,545 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | woɖunɛ | 2 |
| 2 | couscous | 2 |
| 3 | fufú | 2 |
| 4 | loi | 2 |
| 5 | klottey | 2 |
| 6 | korle | 2 |
| 7 | domelovo | 2 |
| 8 | agorbaya | 2 |
| 9 | uttar | 2 |
| 10 | pradesh | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1638 |
| R² (Goodness of Fit) | 0.992157 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 49.7% |
| Top 1,000 | 78.5% |
| Top 5,000 | 93.7% |
| Top 10,000 | 98.8% |

### Key Findings

- **Zipf Compliance:** R²=0.9922 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 49.7% of corpus
- **Long Tail:** 1,578 words needed for remaining 1.2% 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 | 0.7155 🏆 | 0.3892 | N/A | N/A |
| **mono_64d** | 64 | 0.2811 | 0.3672 | N/A | N/A |
| **mono_128d** | 128 | 0.0660 | 0.3770 | N/A | N/A |
| **aligned_32d** | 32 | 0.7155 | 0.4123 | 0.0180 | 0.1660 |
| **aligned_64d** | 64 | 0.2811 | 0.3853 | 0.0500 | 0.2600 |
| **aligned_128d** | 128 | 0.0660 | 0.3736 | 0.0840 | 0.2920 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7155 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3841. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.4% 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 | **0.210** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | okeke, dzoe, exɔe |
| `-wo` | yeyeawo, kadodowo, eɖewo |
| `-awo` | yeyeawo, franseawo, kɔwlɔawo |

### 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 |
|------|----------|------------------|----------|
| `gbal` | 1.65x | 17 contexts | gbalɛ, gbale, gbalé |
| `lawo` | 1.59x | 14 contexts | xɔlawo, dolawo, nɔlawo |
| `pekp` | 1.82x | 9 contexts | kpekpe, kpekpea, kpekpeme |
| `dɔwɔ` | 1.66x | 11 contexts | dɔwɔm, dɔwɔla, dɔwɔƒe |
| `balẽ` | 1.72x | 9 contexts | agbalẽ, gbalẽa, lãgbalẽ |
| `omet` | 1.44x | 14 contexts | wometa, tometi, ƒometɔ |
| `dziɖ` | 1.82x | 7 contexts | dziɖum, dziɖuɖu, dziɖula |
| `ziɖu` | 1.89x | 6 contexts | dziɖum, dziɖuɖu, dziɖula |
| `takp` | 1.74x | 7 contexts | takpɔha, takpɔƒe, takpɔƒea |
| `nyat` | 1.68x | 7 contexts | nyati, nyatia, nyatiwo |
| `iɖuɖ` | 1.91x | 5 contexts | dziɖuɖu, dziɖuɖua, dziɖuɖuha |
| `iawo` | 1.64x | 7 contexts | siawo, fiawo, viawo |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| gbegbɔgblɔwo | **`gbegbɔgblɔ-wo`** | 4.5 | `gbegbɔgblɔ` |
| aƒemelãwo | **`aƒemelã-wo`** | 4.5 | `aƒemelã` |
| gbebiamewo | **`gbebiame-wo`** | 4.5 | `gbebiame` |
| srɔ̃tɔawo | **`srɔ̃tɔ-awo`** | 4.5 | `srɔ̃tɔ` |
| lebanontɔwo | **`lebanontɔ-wo`** | 4.5 | `lebanontɔ` |
| wuietɔ̃awo | **`wuietɔ̃-awo`** | 4.5 | `wuietɔ̃` |
| domenyiŋkɔwo | **`domenyiŋkɔ-wo`** | 4.5 | `domenyiŋkɔ` |
| ŋkuɖodzikpewo | **`ŋkuɖodzikpe-wo`** | 4.5 | `ŋkuɖodzikpe` |
| nukpɔsusuwo | **`nukpɔsusu-wo`** | 4.5 | `nukpɔsusu` |
| swedentɔwo | **`swedentɔ-wo`** | 4.5 | `swedentɔ` |
| asanteawo | **`asante-awo`** | 4.5 | `asante` |
| sɔlemexɔwo | **`sɔlemexɔ-wo`** | 4.5 | `sɔlemexɔ` |
| akpɔkplɔwo | **`akpɔkplɔ-wo`** | 4.5 | `akpɔkplɔ` |
| amegãxiwo | **`amegãxi-wo`** | 4.5 | `amegãxi` |
| ukrainetɔwo | **`ukrainetɔ-wo`** | 4.5 | `ukrainetɔ` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Ewe 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 (4.31x) |
| N-gram | **2-gram** | Lowest perplexity (259) |
| Markov | **Context-4** | Highest predictability (96.1%) |
| 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: 2026-01-04 03:05:37*