---
language: vep
language_name: Veps
language_family: uralic_finnic
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-uralic_finnic
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: 4.518
  - name: best_isotropy
    type: isotropy
    value: 0.8646
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-11
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Veps** 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** | 3.784x | 3.79 | 0.1125% | 645,106 |
| **16k** | 4.095x | 4.10 | 0.1218% | 596,120 |
| **32k** | 4.332x | 4.33 | 0.1288% | 563,614 |
| **64k** | 4.518x 🏆 | 4.52 | 0.1344% | 540,326 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `27 (kaks'kümne seičeme) om lugu 26 da 28 keskes. Lugun ičendad Nece lugu om pala...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 2 7 ▁( kaks ' kümne ▁seičeme ) ▁om ... (+26 more)` | 36 |
| 16k | `▁ 2 7 ▁( kaks ' kümne ▁seičeme ) ▁om ... (+25 more)` | 35 |
| 32k | `▁ 2 7 ▁( kaks ' kümne ▁seičeme ) ▁om ... (+25 more)` | 35 |
| 64k | `▁ 2 7 ▁( kaks ' kümne ▁seičeme ) ▁om ... (+25 more)` | 35 |

**Sample 2:** `Kahesan nellikon identižuz om matematine teorem. Avaidud K. F. Degenal vodes. Ka...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kahes an ▁nellik on ▁ iden t ižuz ▁om ▁matemat ... (+37 more)` | 47 |
| 16k | `▁kahes an ▁nellik on ▁ ident ižuz ▁om ▁matematine ▁teor ... (+33 more)` | 43 |
| 32k | `▁kahesan ▁nellikon ▁ident ižuz ▁om ▁matematine ▁teorem . ▁avaid ud ... (+22 more)` | 32 |
| 64k | `▁kahesan ▁nellikon ▁identižuz ▁om ▁matematine ▁teorem . ▁avaid ud ▁k ... (+18 more)` | 28 |

**Sample 3:** `Lohj voib znamoita: Lohj vai Lohi i Atlantine lohi () — merikalan erik. Lohj (li...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lo hj ▁voib ▁znamoita : ▁lo hj ▁vai ▁l oh ... (+26 more)` | 36 |
| 16k | `▁lo hj ▁voib ▁znamoita : ▁lo hj ▁vai ▁loh i ... (+23 more)` | 33 |
| 32k | `▁lohj ▁voib ▁znamoita : ▁lohj ▁vai ▁lohi ▁i ▁atlantine ▁lohi ... (+17 more)` | 27 |
| 64k | `▁lohj ▁voib ▁znamoita : ▁lohj ▁vai ▁lohi ▁i ▁atlantine ▁lohi ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 64k achieves 4.518x compression
- **Lowest UNK Rate:** 8k with 0.1125% 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 | 9,305 | 13.18 | 32,176 | 17.0% | 43.1% |
| **2-gram** | Subword | 360 🏆 | 8.49 | 4,522 | 60.7% | 98.4% |
| **3-gram** | Word | 14,172 | 13.79 | 45,549 | 16.0% | 36.5% |
| **3-gram** | Subword | 2,938 | 11.52 | 34,072 | 22.2% | 66.3% |
| **4-gram** | Word | 24,360 | 14.57 | 72,845 | 13.6% | 30.1% |
| **4-gram** | Subword | 13,690 | 13.74 | 168,706 | 12.0% | 39.2% |
| **5-gram** | Word | 21,376 | 14.38 | 55,276 | 13.1% | 29.8% |
| **5-gram** | Subword | 38,297 | 15.22 | 397,934 | 7.9% | 28.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kirjamišton mödhe` | 6,425 |
| 2 | `se om` | 3,506 |
| 3 | `kaikiš suremb` | 3,269 |
| 4 | `homaičendad irdkosketused` | 3,121 |
| 5 | `eläjiden lugu` | 2,616 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `eläjiden lugu oli` | 2,528 |
| 2 | `lidnad kirjamišton mödhe` | 2,134 |
| 3 | `ü m t` | 2,049 |
| 4 | `geografijan andmused lidn` | 1,951 |
| 5 | `m ü m` | 1,882 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `m ü m t` | 1,882 |
| 2 | `geografijan andmused lidn sijadase` | 1,877 |
| 3 | `lidnan eläjiden lugu oli` | 1,629 |
| 4 | `m t keskmäižel korktusel` | 1,614 |
| 5 | `ü m t keskmäižel` | 1,612 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ü m t keskmäižel korktusel` | 1,612 |
| 2 | `m ü m t keskmäižel` | 1,511 |
| 3 | `mödhe lidnan eläjiden lugu oli` | 1,282 |
| 4 | `rahvahanlugemižen mödhe lidnan eläjiden lugu` | 1,273 |
| 5 | `kaikiš suremb lidnan ristitišt oli` | 1,071 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 297,019 |
| 2 | `a n` | 244,303 |
| 3 | `e n` | 184,024 |
| 4 | `_ k` | 155,498 |
| 5 | `d _` | 147,840 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n _` | 133,181 |
| 2 | `e n _` | 96,007 |
| 3 | `_ o m` | 58,636 |
| 4 | `a d _` | 55,725 |
| 5 | `i ž e` | 52,889 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l i d n` | 47,717 |
| 2 | `_ o m _` | 46,550 |
| 3 | `i d e n` | 42,797 |
| 4 | `d e n _` | 42,188 |
| 5 | `_ l i d` | 41,418 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l i d n` | 41,258 |
| 2 | `i d e n _` | 34,753 |
| 3 | `l i d n a` | 30,577 |
| 4 | `i ž e n _` | 20,063 |
| 5 | `i d n a n` | 17,767 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 360
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.7343 | 1.664 | 4.81 | 160,489 | 26.6% |
| **1** | Subword | 0.9597 | 1.945 | 6.73 | 2,266 | 4.0% |
| **2** | Word | 0.1972 | 1.146 | 1.48 | 770,285 | 80.3% |
| **2** | Subword | 0.8508 | 1.803 | 5.03 | 15,247 | 14.9% |
| **3** | Word | 0.0801 | 1.057 | 1.16 | 1,135,116 | 92.0% |
| **3** | Subword | 0.7921 | 1.732 | 3.95 | 76,651 | 20.8% |
| **4** | Word | 0.0421 🏆 | 1.030 | 1.08 | 1,309,508 | 95.8% |
| **4** | Subword | 0.6485 | 1.567 | 2.76 | 302,976 | 35.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `om 15 laiševo žilo sai lidnan eläjiden lugu oli kahesavoččen prihaižen kazvatuz seniden soladusen ai...`
2. `i saudud vll vspäi lugendlehtez lähtleb venäma eksportan 29 104 km kaikiš korktemb čokkoim om nügüd`
3. `vl kubink om kävutadud kirjutamha tailandan lebutahoihe homaičendad irdkosketused čeläbinskan agjan ...`

**Context Size 2:**

1. `kirjamišton mödhe agjan lidnad agjan lidnümbrikod administrativiž territorialižed vajehtused oliba v...`
2. `se om kaikiš varuližembišpäi mail mas om marganc hahktin cink vol fram raud nefrit i kalližarvoižed ...`
3. `kaikiš suremb lidnan ristitišt oli 22 006 ristitud vn 332 529 eläjad vl 39 490 eläjad vl`

**Context Size 3:**

1. `eläjiden lugu oli 43 888 ristitud lidnankundan 44 403 ristitud rajonan kaks koumandest kaik 47 608 r...`
2. `ü m t keskmäižel korktusel matkad alauz lidnhasai om 145 km pohjoižpäivnouzmha štatan administrativi...`
3. `geografijan andmused lidn sijadase valdkundan pohjoižes ümbrikon suvipäivlaskmas tel pälidnaspäi sen...`

**Context Size 4:**

1. `m ü m t keskmäižel korktusel matkad bakuhusai om 260 km päivnouzmha manrehkaidusiden magnitud voib s...`
2. `geografijan andmused lidn sijadase subjektan i rajonan suves slavänk jogen randoil nevan alangišton ...`
3. `lidnan eläjiden lugu oli 21 892 ristitud lidnümbrikon kaks koumandest vn lidnan ristitišt oli 40 658...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_kvranü._id_nd_t`
2. `asa_kedal,_pral.`
3. `ikan_m_lüz_ližet`

**Context Size 2:**

1. `n_hem_pörktradimi`
2. `anduren_avlaižket`
3. `enzime._(;_kollel`

**Context Size 3:**

1. `an_siba_nacii_—_km`
2. `en_südäine_eläjad_`
3. `_om_lidnad_(37_c°.`

**Context Size 4:**

1. `lidnankundha_konstr`
2. `_om_es-sanas_märiče`
3. `iden)._radosť_«todi`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (302,976 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 | 61,069 |
| Total Tokens | 1,553,490 |
| Mean Frequency | 25.44 |
| Median Frequency | 4 |
| Frequency Std Dev | 313.94 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | om | 47,295 |
| 2 | i | 27,147 |
| 3 | vl | 16,533 |
| 4 | da | 16,000 |
| 5 | oli | 13,414 |
| 6 | lidnan | 13,013 |
| 7 | mödhe | 12,936 |
| 8 | oma | 11,373 |
| 9 | km | 10,458 |
| 10 | vn | 10,170 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | jonne | 2 |
| 2 | järvelä | 2 |
| 3 | hunka | 2 |
| 4 | lunka | 2 |
| 5 | idja | 2 |
| 6 | sundin | 2 |
| 7 | jivarp | 2 |
| 8 | broiler | 2 |
| 9 | skydancer | 2 |
| 10 | projector | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0886 |
| R² (Goodness of Fit) | 0.994487 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 31.7% |
| Top 1,000 | 61.3% |
| Top 5,000 | 79.7% |
| Top 10,000 | 86.3% |

### Key Findings

- **Zipf Compliance:** R²=0.9945 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 31.7% of corpus
- **Long Tail:** 51,069 words needed for remaining 13.7% 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 | 0.8646 | 0.3534 | N/A | N/A |
| **mono_64d** | 64 | 0.8357 | 0.2592 | N/A | N/A |
| **mono_128d** | 128 | 0.6335 | 0.2276 | N/A | N/A |
| **aligned_32d** | 32 | 0.8646 🏆 | 0.3528 | 0.0300 | 0.2140 |
| **aligned_64d** | 64 | 0.8357 | 0.2584 | 0.0760 | 0.3180 |
| **aligned_128d** | 128 | 0.6335 | 0.2219 | 0.1360 | 0.4020 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8646 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2789. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 13.6% 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 | **0.059** | 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` | sekcii, solmuiktusenke, semnen |
| `-k` | kukazjärvespäi, komin, kaksin |
| `-a` | avaros, arestantad, asha |
| `-p` | pasport, pohjoižkorejas, pirdoiden |
| `-m` | meždurečenskan, manita, mifižen |
| `-ka` | kaksin, kazan, kacui |
| `-t` | talon, tehnižel, tehmaha |
| `-ma` | manita, mas, maidho |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | ruslan, instrumentan, meždurečenskan |
| `-an` | ruslan, instrumentan, meždurečenskan |
| `-en` | erineden, pirdoiden, semnen |
| `-d` | ecijad, hindid, hätkeližed |
| `-e` | buržuazijale, solmuiktusenke, korenke |
| `-i` | kukazjärvespäi, sekcii, vanajavezi |
| `-s` | fateras, barrios, rahanpörundas |
| `-ad` | ecijad, arestantad, deputatad |

### 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 |
|------|----------|------------------|----------|
| `oide` | 2.21x | 104 contexts | oiden, goiden, toiden |
| `ižed` | 2.43x | 54 contexts | hižed, vižed, pižed |
| `ijan` | 1.93x | 76 contexts | dijan, mijan, kijan |
| `ndan` | 1.79x | 64 contexts | indan, andan, löndan |
| `ižen` | 1.63x | 86 contexts | ližen, tižen, pižen |
| `enda` | 1.52x | 98 contexts | lenda, kendan, vendal |
| `aiže` | 1.79x | 45 contexts | aižen, jaižed, jaižen |
| `tuse` | 1.57x | 53 contexts | tusen, ištuse, katusen |
| `išto` | 1.59x | 42 contexts | višton, puištol, erišton |
| `unda` | 1.34x | 77 contexts | munda, kunda, sunday |
| `ndad` | 1.72x | 24 contexts | andad, möndad, pindad |
| `isti` | 1.58x | 32 contexts | kristi, ristit, kristin |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-k` | `-n` | 192 words | kingston, kolumbusan |
| `-s` | `-n` | 155 words | sirdanuziden, samižsarakon |
| `-m` | `-n` | 135 words | muziksädusen, menpätajan |
| `-p` | `-n` | 133 words | purendan, permižiden |
| `-k` | `-d` | 109 words | krizisad, kopijad |
| `-k` | `-e` | 104 words | kundoidenke, kirjamele |
| `-t` | `-n` | 96 words | tukiden, tehnikumpavlovon |
| `-p` | `-d` | 94 words | päühtnijad, päjärgvaličendad |
| `-a` | `-n` | 92 words | arvlahjoiden, adjektivoiden |
| `-m` | `-d` | 91 words | märad, maksimumad |

### 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 |
|------|-----------------|------------|------|
| babuškinan | **`babuški-n-an`** | 7.5 | `n` |
| udessündund | **`udessündu-n-d`** | 7.5 | `n` |
| amerikadme | **`amerikad-m-e`** | 7.5 | `m` |
| franklinan | **`frankli-n-an`** | 7.5 | `n` |
| läžundkodinno | **`läžundkodi-n-no`** | 7.5 | `n` |
| philippines | **`philippi-n-es`** | 7.5 | `n` |
| zaozörnii | **`zaozör-n-ii`** | 7.5 | `n` |
| argentinas | **`argenti-n-as`** | 7.5 | `n` |
| basseinha | **`bassei-n-ha`** | 7.5 | `n` |
| jüridenke | **`jüride-n-ke`** | 7.5 | `n` |
| jonohosai | **`jonoho-s-ai`** | 7.5 | `s` |
| ceremonii | **`ceremo-n-ii`** | 7.5 | `n` |
| mandarinad | **`mandari-n-ad`** | 7.5 | `n` |
| pautkinno | **`pautki-n-no`** | 7.5 | `n` |
| basseinan | **`bassei-n-an`** | 7.5 | `n` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Veps 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 (4.52x) |
| N-gram | **2-gram** | Lowest perplexity (360) |
| Markov | **Context-4** | Highest predictability (95.8%) |
| 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: 2026-01-11 02:50:54*