---
language: am
language_name: Amharic
language_family: semitic_ethiopic
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-semitic_ethiopic
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: 3.293
  - name: best_isotropy
    type: isotropy
    value: 0.9137
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-03
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Amharic** 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** | 2.438x | 2.44 | 0.1566% | 682,453 |
| **16k** | 2.748x | 2.75 | 0.1765% | 605,553 |
| **32k** | 3.035x | 3.04 | 0.1950% | 548,316 |
| **64k** | 3.293x 🏆 | 3.29 | 0.2116% | 505,279 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `ናውሩ በሰላማዊ ውቅያኖስ የሚገኝ ደሴት አገር ነው። ዋና ከተማ የለውም፣ ትልቁ ከተማ ግን ያሬን ነው።`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ና ው ሩ ▁በሰ ላማዊ ▁ውቅያኖስ ▁የሚገኝ ▁ደሴት ▁አገር ▁ነው። ... (+10 more)` | 20 |
| 16k | `▁ና ውሩ ▁በሰላማዊ ▁ውቅያኖስ ▁የሚገኝ ▁ደሴት ▁አገር ▁ነው። ▁ዋና ▁ከተማ ... (+8 more)` | 18 |
| 32k | `▁ናውሩ ▁በሰላማዊ ▁ውቅያኖስ ▁የሚገኝ ▁ደሴት ▁አገር ▁ነው። ▁ዋና ▁ከተማ ▁የለውም፣ ... (+6 more)` | 16 |
| 64k | `▁ናውሩ ▁በሰላማዊ ▁ውቅያኖስ ▁የሚገኝ ▁ደሴት ▁አገር ▁ነው። ▁ዋና ▁ከተማ ▁የለውም፣ ... (+5 more)` | 15 |

**Sample 2:** `አሾካ ከ277 ስከ 240 ዓክልበ. ድረስ የሕንድ አገር ማውርያ መንግሥት ንጉሥ ነበር። በ271 ዓክልበ. ግድም የቡዲስም ተከታይ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁አ ሾ ካ ▁ከ 2 7 7 ▁ስ ከ ▁ ... (+42 more)` | 52 |
| 16k | `▁አ ሾ ካ ▁ከ 2 7 7 ▁ስ ከ ▁ ... (+39 more)` | 49 |
| 32k | `▁አሾ ካ ▁ከ 2 7 7 ▁ስ ከ ▁ 2 ... (+38 more)` | 48 |
| 64k | `▁አሾካ ▁ከ 2 7 7 ▁ስከ ▁ 2 4 0 ... (+34 more)` | 44 |

**Sample 3:** `ኔትፍሊክስ (እንግሊዝኛ: Netflix) በመስመር ላይ ፊልሞችን እና የቴሌቪዥን ፕሮግራሞችን ለመመልከት የሚያስችል የዥረት አገል...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ኔ ት ፍ ሊ ክስ ▁( እንግሊዝኛ : ▁n et ... (+36 more)` | 46 |
| 16k | `▁ኔ ትፍ ሊ ክስ ▁( እንግሊዝኛ : ▁n et fl ... (+29 more)` | 39 |
| 32k | `▁ኔ ትፍ ሊክስ ▁( እንግሊዝኛ : ▁net fl ix ) ... (+23 more)` | 33 |
| 64k | `▁ኔ ትፍ ሊክስ ▁( እንግሊዝኛ : ▁net flix ) ▁በመስመር ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 64k achieves 3.293x compression
- **Lowest UNK Rate:** 8k with 0.1566% 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 | 9,101 | 13.15 | 28,185 | 19.6% | 39.5% |
| **2-gram** | Subword | 2,069 🏆 | 11.01 | 23,787 | 34.1% | 69.3% |
| **3-gram** | Word | 9,934 | 13.28 | 35,745 | 22.2% | 40.6% |
| **3-gram** | Subword | 19,035 | 14.22 | 153,217 | 11.9% | 35.6% |
| **4-gram** | Word | 36,871 | 15.17 | 91,072 | 13.9% | 25.7% |
| **4-gram** | Subword | 94,475 | 16.53 | 551,504 | 6.6% | 19.5% |
| **5-gram** | Word | 32,696 | 15.00 | 78,497 | 14.6% | 26.2% |
| **5-gram** | Subword | 213,435 | 17.70 | 879,311 | 5.0% | 14.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ዓ ም` | 8,266 |
| 2 | `ምሳሌ ነው` | 5,623 |
| 3 | `የአማርኛ ምሳሌ` | 5,562 |
| 4 | `እ ኤ` | 4,014 |
| 5 | `ኤ አ` | 3,948 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `የአማርኛ ምሳሌ ነው` | 5,562 |
| 2 | `እ ኤ አ` | 3,896 |
| 3 | `ምሳሌ ነው ትርጉሙ` | 3,454 |
| 4 | `መደብ ተረትና ምሳሌ` | 3,051 |
| 5 | `ነው ትርጉሙ መደብ` | 2,530 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `የአማርኛ ምሳሌ ነው ትርጉሙ` | 3,452 |
| 2 | `ምሳሌ ነው ትርጉሙ መደብ` | 2,530 |
| 3 | `ትርጉሙ መደብ ያልተተረጎመ ምሳሌ` | 2,115 |
| 4 | `ነው ትርጉሙ መደብ ያልተተረጎመ` | 2,111 |
| 5 | `ምሳሌ መደብ ተረትና ምሳሌ` | 1,854 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `የአማርኛ ምሳሌ ነው ትርጉሙ መደብ` | 2,529 |
| 2 | `ምሳሌ ነው ትርጉሙ መደብ ያልተተረጎመ` | 2,111 |
| 3 | `ነው ትርጉሙ መደብ ያልተተረጎመ ምሳሌ` | 2,111 |
| 4 | `መደብ ያልተተረጎመ ምሳሌ መደብ ተረትና` | 1,812 |
| 5 | `ያልተተረጎመ ምሳሌ መደብ ተረትና ምሳሌ` | 1,811 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ የ` | 172,656 |
| 2 | `ት _` | 146,889 |
| 3 | `_ በ` | 142,558 |
| 4 | `ን _` | 134,273 |
| 5 | `_ አ` | 115,168 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ እ ን` | 32,943 |
| 2 | `_ ነ ው` | 26,886 |
| 3 | `_ እ ና` | 24,633 |
| 4 | `ው ። _` | 24,427 |
| 5 | `እ ና _` | 23,097 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ እ ና _` | 22,966 |
| 2 | `_ ነ ው ።` | 19,603 |
| 3 | `ነ ው ። _` | 19,130 |
| 4 | `_ እ ን ደ` | 14,167 |
| 5 | `_ ላ ይ _` | 13,064 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ ነ ው ። _` | 19,000 |
| 2 | `_ ው ስ ጥ _` | 9,650 |
| 3 | `ኢ ት ዮ ጵ ያ` | 7,988 |
| 4 | `_ ም ሳ ሌ _` | 7,852 |
| 5 | `_ እ ን ደ _` | 6,562 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 2,069
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~14% 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 | 0.7520 | 1.684 | 4.82 | 237,556 | 24.8% |
| **1** | Subword | 1.2212 | 2.331 | 17.49 | 2,857 | 0.0% |
| **2** | Word | 0.1473 | 1.108 | 1.28 | 1,142,374 | 85.3% |
| **2** | Subword | 1.0395 | 2.055 | 6.98 | 49,956 | 0.0% |
| **3** | Word | 0.0354 | 1.025 | 1.06 | 1,462,526 | 96.5% |
| **3** | Subword | 0.6359 | 1.554 | 3.37 | 348,652 | 36.4% |
| **4** | Word | 0.0157 🏆 | 1.011 | 1.02 | 1,537,232 | 98.4% |
| **4** | Subword | 0.4526 | 1.368 | 2.15 | 1,173,222 | 54.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ነው ያኽዱን ሊም ዓክልበ የነገሠ የሊፒት እሽታርን እርዳታ የማግኘት መብቱ የተጠበቀ ስለሆነ ፈጽሞ ይበላል ፍሬው ሳይበስል`
2. `እና ኢኮኖሚያዊ እና አመለካከቶችን ለመግለጽ ይወዳል የወዳጅሽ የመሠወሪያው ማዕበልም ያማታዋል ዳግመኛም የከበረውን የመልክተኛዎን የቃል ትርጉም ሊያዳብር`
3. `ላይ አፈፃፀምን በራስ መተማመን አይችሉም ከሚለው ቃል በሲቪል ደግሞ ለየተለያዩ በአፍሪካ ውስጥ የተረጋገጠ ይመስላል ከዚያም የሶቪየት`

**Context Size 2:**

1. `ዓ ም በኋላ ለሆኑት ዓመታት ግን በሌላ ቀን ላይ መሆኑን ይገንዘቡ ለእነዚያ ዓመቶች ይህ የቀን መለወጫ መሣርያ`
2. `ምሳሌ ነው ትርጉሙ መደብ ያልተተረጎመ ምሳሌ መደብ ተረትና ምሳሌ መደብ ተረትና ምሳሌ መደብ ተረትና ምሳሌ ምናልባትም ከቤ`
3. `የአማርኛ ምሳሌ ነው ትርጉሙ ሚስጥር አይደበቅ ይመስላል ትርጉሙ መደብ ተረትና ምሳሌ መደብ ተረትና ምሳሌ መደብ ተረትና ምሳሌ`

**Context Size 3:**

1. `የአማርኛ ምሳሌ ነው ትርጉሙ መደብ ያልተተረጎመ ምሳሌ መደብ ተረትና ምሳሌ ምግባር ሳይኖር ስም እንደማለት ነዉ`
2. `እ ኤ አ የእንግሊዝ ካላንደር ማሻሻያ ተከትሎ የንግሥቲቱን ሞት መመዝገብ የተለመደ ቢሆንም እንግሊዝ መጋቢት 25 ቀን ማለት ነው`
3. `ምሳሌ ነው ትርጉሙ የተያያዙ ነገሮችን ለመለየት የሚያገለግል ፈሊጥ መደብ ተረትና ምሳሌ ምሳሌ`

**Context Size 4:**

1. `የአማርኛ ምሳሌ ነው ትርጉሙ መደብ ተረትና ምሳሌ በሬ ካራጁ ይዉላል`
2. `ምሳሌ ነው ትርጉሙ መደብ ያልተተረጎመ ምሳሌ መደብ ተረትና ምሳሌ መደብ ያልተተረጎመ ምሳሌ`
3. `ነው ትርጉሙ መደብ ያልተተረጎመ ምሳሌ መደብ ተረትና ምሳሌ ሴት ሁሉን ቻይ ናት`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_በይምነዉ፡ቢቢትር_የተፅሀ`
2. `ን_እንዋጮችት_crcue_አ`
3. `ት_ው_ፈርዕስክሎ_አስ_po`

**Context Size 2:**

1. `_የኢትዮጵያ_ዘን_ሳይንስ_ተ`
2. `ት_ነው።_እንግሥታት_ናይትድ`
3. `_በወራ_ህብረ_የሳምን_ወይ_`

**Context Size 3:**

1. `_እንዲህ፡መልክ_ፈላሁ_ዐንሁ_`
2. `_ነው።_እንዲህም፡ዅሉ፡_ደግሞ`
3. `_እና_ከተያዙ_እንዲሸከሙአቸው`

**Context Size 4:**

1. `_እና_ቁሳዊ_ነገሥታት_መሽኛ_ት`
2. `_ነው።_ከግብጽ_ዘውድ_ጭነው_ነ`
3. `ነው።_ሁሉም_የተነሳ_በኋላም_ያ`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,173,222 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 | 100,186 |
| Total Tokens | 1,652,256 |
| Mean Frequency | 16.49 |
| Median Frequency | 3 |
| Frequency Std Dev | 176.36 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ነው | 26,831 |
| 2 | እና | 23,089 |
| 3 | ላይ | 13,382 |
| 4 | ምሳሌ | 11,608 |
| 5 | ውስጥ | 9,891 |
| 6 | ነበር | 9,130 |
| 7 | ዓ | 8,627 |
| 8 | ወደ | 8,565 |
| 9 | ም | 8,525 |
| 10 | እንደ | 6,906 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ጂኒካ | 2 |
| 2 | ዲኒካላ | 2 |
| 3 | ወስደሽ | 2 |
| 4 | አንኳኳ | 2 |
| 5 | መዳልወ | 2 |
| 6 | ረድእ | 2 |
| 7 | አንደኛይቱ | 2 |
| 8 | ወደሰልፍ | 2 |
| 9 | የኒኮፖሊስ | 2 |
| 10 | ጂምናዚየም | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9364 |
| R² (Goodness of Fit) | 0.995158 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 22.7% |
| Top 1,000 | 45.8% |
| Top 5,000 | 66.2% |
| Top 10,000 | 74.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9952 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 22.7% of corpus
- **Long Tail:** 90,186 words needed for remaining 25.1% 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 | 0.9098 | 0.3240 | N/A | N/A |
| **mono_64d** | 64 | 0.9137 🏆 | 0.2319 | N/A | N/A |
| **mono_128d** | 128 | 0.8452 | 0.1755 | N/A | N/A |
| **aligned_32d** | 32 | 0.9098 | 0.3259 | 0.0200 | 0.1420 |
| **aligned_64d** | 64 | 0.9137 | 0.2299 | 0.0480 | 0.1860 |
| **aligned_128d** | 128 | 0.8452 | 0.1764 | 0.0840 | 0.2800 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.9137 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2439. 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 | **0.840** | 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.

*No productive affixes detected.*


### 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 |
|------|----------|------------------|----------|
| `እንደሚ` | 2.30x | 158 contexts | እንደሚሹ, እንደሚሻ, እንደሚል |
| `ርስቲያ` | 2.39x | 61 contexts | ክርስቲያ, ከርስቲያን, ክርስቲያን |
| `ትዮጵያ` | 2.17x | 57 contexts | ኢትዮጵያ, እትዮጵያ, ኢትዮጵያን |
| `መንግስ` | 2.10x | 49 contexts | መንግስቱ, መንግስተ, መንግስት |
| `ግዚአብ` | 2.58x | 23 contexts | እግዚአብሐር, እግዚአብሔር, እግዚአብሄር |
| `ኢትዮጵ` | 2.08x | 46 contexts | ኢትዮጵያ, ኢትዮጵያን, ኢትዮጵያና |
| `እንግሊ` | 2.00x | 52 contexts | እንግሊዝ, እንግሊዙ, እንግሊኛ |
| `ፈረንሳ` | 2.23x | 34 contexts | ፈረንሳዊ, ፈረንሳይ, ከፈረንሳዩ |
| `መንግሥ` | 2.04x | 46 contexts | መንግሥቱ, መንግሥት, መንግሥተ |
| `tion` | 2.71x | 17 contexts | action, nation, section |
| `አስተዳ` | 2.21x | 33 contexts | አስተዳደጉ, አስተዳደሪ, አስተዳደጓ |
| `ግሊዝኛ` | 2.54x | 19 contexts | እንግሊዝኛ, በእንግሊዝኛ, ኢንግሊዝኛው |

### 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`).

*Insufficient data for recursive segmentation.*


### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Amharic 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 | **64k BPE** | Best compression (3.29x) |
| N-gram | **2-gram** | Lowest perplexity (2,069) |
| Markov | **Context-4** | Highest predictability (98.4%) |
| 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 16:28:42*