README.md

---
language: koi
language_name: Komi-Permyak
language_family: uralic_permian
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_permian
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: 4.188
  - name: best_isotropy
    type: isotropy
    value: 0.5442
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Komi-Permyak - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Komi-Permyak** 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** | 3.334x | 3.34 | 0.0990% | 351,368 |
| **16k** | 3.681x | 3.68 | 0.1094% | 318,243 |
| **32k** | 3.938x | 3.94 | 0.1170% | 297,461 |
| **64k** | 4.188x 🏆 | 4.19 | 0.1244% | 279,684 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Лебедев Михаил Николаевич — коми гижись. Гижис зыряна моз. Олантуй Ыстісяннэз ги...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁л еб ед ев ▁михаил ▁николаевич ▁— ▁коми ▁гижись . ... (+7 more)` | 17 |
| 16k | `▁лебед ев ▁михаил ▁николаевич ▁— ▁коми ▁гижись . ▁гижис ▁зыряна ... (+5 more)` | 15 |
| 32k | `▁лебедев ▁михаил ▁николаевич ▁— ▁коми ▁гижись . ▁гижис ▁зыряна ▁моз ... (+4 more)` | 14 |
| 64k | `▁лебедев ▁михаил ▁николаевич ▁— ▁коми ▁гижись . ▁гижис ▁зыряна ▁моз ... (+4 more)` | 14 |

**Sample 2:** `Annona asplundiana () — быдмассэзлӧн аннона котырись аннона увтырын торья вид. А...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁annona ▁asp l und iana ▁() ▁— ▁быдмассэзлӧн ▁аннона ▁котырись ... (+9 more)` | 19 |
| 16k | `▁annona ▁aspl und iana ▁() ▁— ▁быдмассэзлӧн ▁аннона ▁котырись ▁аннона ... (+8 more)` | 18 |
| 32k | `▁annona ▁asplundiana ▁() ▁— ▁быдмассэзлӧн ▁аннона ▁котырись ▁аннона ▁увтырын ▁торья ... (+6 more)` | 16 |
| 64k | `▁annona ▁asplundiana ▁() ▁— ▁быдмассэзлӧн ▁аннона ▁котырись ▁аннона ▁увтырын ▁торья ... (+6 more)` | 16 |

**Sample 3:** `Зептамуканнез () - зепта пода Систематика Лунвыв зептамукань (Notoryctes typhlop...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁зепта му каннез ▁() ▁- ▁зепта ▁пода ▁систематика ▁лунвыв ▁зепта ... (+27 more)` | 37 |
| 16k | `▁зепта муканнез ▁() ▁- ▁зепта ▁пода ▁систематика ▁лунвыв ▁зепта му ... (+20 more)` | 30 |
| 32k | `▁зептамуканнез ▁() ▁- ▁зепта ▁пода ▁систематика ▁лунвыв ▁зептамукань ▁( notoryctes ... (+13 more)` | 23 |
| 64k | `▁зептамуканнез ▁() ▁- ▁зепта ▁пода ▁систематика ▁лунвыв ▁зептамукань ▁( notoryctes ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.188x compression
- **Lowest UNK Rate:** 8k with 0.0990% 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 | 2,251 | 11.14 | 6,246 | 30.0% | 65.4% |
| **2-gram** | Subword | 688 🏆 | 9.43 | 3,126 | 40.6% | 95.6% |
| **3-gram** | Word | 2,425 | 11.24 | 7,894 | 31.4% | 64.7% |
| **3-gram** | Subword | 5,502 | 12.43 | 26,121 | 14.0% | 50.2% |
| **4-gram** | Word | 3,845 | 11.91 | 14,635 | 29.5% | 57.3% |
| **4-gram** | Subword | 22,040 | 14.43 | 109,182 | 8.3% | 30.1% |
| **5-gram** | Word | 2,942 | 11.52 | 11,597 | 33.2% | 61.2% |
| **5-gram** | Subword | 45,190 | 15.46 | 199,483 | 6.7% | 24.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `туй ул` | 1,101 |
| 2 | `республики коми` | 907 |
| 3 | `ним йылісь` | 885 |
| 4 | `да быт` | 778 |
| 5 | `котырись быдмассэз` | 768 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `да быт культура` | 688 |
| 2 | `перем ладорись коми` | 648 |
| 3 | `ним йылісь география` | 642 |
| 4 | `ладорись коми кытшын` | 619 |
| 5 | `быт культура да` | 618 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `да быт культура да` | 618 |
| 2 | `перем ладорись коми кытшын` | 613 |
| 3 | `культура да ордча ландшафттэз` | 557 |
| 4 | `быт культура да ордча` | 543 |
| 5 | `пермяцкий национальный округ москва` | 497 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `быт культура да ордча ландшафттэз` | 543 |
| 2 | `да быт культура да ордча` | 543 |
| 3 | `коми пермяцкий национальный округ москва` | 497 |
| 4 | `пермяцкий национальный округ москва ленинград` | 497 |
| 5 | `история отир да быт культура` | 467 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. _` | 42,699 |
| 2 | `_ к` | 35,843 |
| 3 | `а _` | 26,811 |
| 4 | `, _` | 26,348 |
| 5 | `a _` | 25,171 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ к о` | 13,371 |
| 2 | `с ь _` | 9,563 |
| 3 | `i s _` | 8,088 |
| 4 | `i a _` | 7,916 |
| 5 | `к о м` | 7,738 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ к о м` | 7,266 |
| 2 | `к о м и` | 7,115 |
| 3 | `_ д а _` | 5,888 |
| 4 | `и с ь _` | 5,139 |
| 5 | `о м и _` | 4,261 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ к о м и` | 6,959 |
| 2 | `к о м и _` | 4,192 |
| 3 | `р а й о н` | 3,366 |
| 4 | `р и с ь _` | 3,221 |
| 5 | `_ р а й о` | 3,073 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 688
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.6021 | 1.518 | 3.33 | 64,076 | 39.8% |
| **1** | Subword | 1.2840 | 2.435 | 10.66 | 598 | 0.0% |
| **2** | Word | 0.1331 | 1.097 | 1.27 | 212,941 | 86.7% |
| **2** | Subword | 1.1237 | 2.179 | 7.04 | 6,371 | 0.0% |
| **3** | Word | 0.0468 | 1.033 | 1.09 | 268,517 | 95.3% |
| **3** | Subword | 0.8991 | 1.865 | 4.10 | 44,806 | 10.1% |
| **4** | Word | 0.0247 🏆 | 1.017 | 1.05 | 290,625 | 97.5% |
| **4** | Subword | 0.5751 | 1.490 | 2.34 | 183,679 | 42.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `коми кытшын юсьва муниципал район понда чоморыс нӧбӧтӧ ассис баитан кыввез вах ханты мансийского язы...`
2. `да ниппон sakhalin глен кӧз picea rubens anathallis jesupiorum anathallis abbreviata hopper a rich e...`
3. `и к жакова биармия в в америкаись sylvilagus graysoni кöч lepus увтырвыв indolagus хайнань кöч lepus`

**Context Size 2:**

1. `туй ул центральная мир туй ул озерная уджалан туй ул северная ыджыт туй да совет туй ул`
2. `республики коми м дрофа isbn республика коми энциклопедия в 3 х томах сыктывкар коми кн изд во`
3. `ним йылісь ошыбын и радостев павел михайлович сьӧрті посад местаын вӧлісӧ ыджытся ыджыт ыббез кытӧн ...`

**Context Size 3:**

1. `да быт культура да ордча ландшафттэз коми пермяцкий автономный округ на рубеже веков кудымкар isbn к...`
2. `перем ладорись коми кытшын кӧчладор районісь кӧч посадмуын учӧтик грезд деревня одзжык татӧн вӧлі сэ...`
3. `ним йылісь география туйез история отир да быт культура да ордча ландшафттэз афанасьев а п топонимия...`

**Context Size 4:**

1. `да быт культура да ордча ландшафттэз афанасьев а п топонимия республики коми сыктывкар коми кн изд в...`
2. `перем ладорись коми кытшын иньваӧ усян исывлӧн шульга вож юыслӧн кузяыс км бассейныс км ыжда ваыс йы...`
3. `культура да ордча ландшафттэз коми пермяцкий национальный округ москва ленинград ыстісяннэз район`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_кӧсевомин,219_p`
2. `а.)_buna_лын._th`
3. `оёнт,_veranderia`

**Context Size 2:**

1. `._—_тувтыв_вылі_ш`
2. `_колия_(fracencic`
3. `а_250_10,0_67.69,`

**Context Size 3:**

1. `_коми-пермь,_26:_5`
2. `сь_мушев_туялісӧ_к`
3. `is_angrandropedia_`

**Context Size 4:**

1. `_коми-пермяцкий_язы`
2. `коми_книжное_половь`
3. `_да_быт_кулач_ершов`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.5% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (183,679 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 | 22,928 |
| Total Tokens | 340,087 |
| Mean Frequency | 14.83 |
| Median Frequency | 3 |
| Frequency Std Dev | 91.92 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | коми | 6,643 |
| 2 | да | 5,961 |
| 3 | и | 2,497 |
| 4 | luer | 2,296 |
| 5 | туй | 2,096 |
| 6 | котырись | 2,060 |
| 7 | j | 1,805 |
| 8 | а | 1,758 |
| 9 | isbn | 1,579 |
| 10 | отир | 1,559 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | устар | 2 |
| 2 | видзӧттӧг | 2 |
| 3 | ассимилируйтісӧ | 2 |
| 4 | бессарабияись | 2 |
| 5 | молдаванец | 2 |
| 6 | русскӧйез | 2 |
| 7 | русинскӧй | 2 |
| 8 | этноязычнӧй | 2 |
| 9 | стойкостьыс | 2 |
| 10 | прутсянь | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0748 |
| R² (Goodness of Fit) | 0.991898 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 29.1% |
| Top 1,000 | 63.8% |
| Top 5,000 | 83.7% |
| Top 10,000 | 91.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9919 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 29.1% of corpus
- **Long Tail:** 12,928 words needed for remaining 8.8% 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 | 0.5442 🏆 | 0.3839 | N/A | N/A |
| **mono_64d** | 64 | 0.1977 | 0.3890 | N/A | N/A |
| **mono_128d** | 128 | 0.0304 | 0.3721 | N/A | N/A |
| **aligned_32d** | 32 | 0.5442 | 0.3825 | 0.0160 | 0.1340 |
| **aligned_64d** | 64 | 0.1977 | 0.3794 | 0.0320 | 0.1740 |
| **aligned_128d** | 128 | 0.0304 | 0.3783 | 0.0520 | 0.2440 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.5442 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3809. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.2% 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 | **1.522** | 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 |
|--------|----------|
| `-к` | карпом, кывтытын, кагыргын |
| `-с` | селезни, сфере, саридзӧн |
| `-п` | пырны, положеннёын, посаддэз |
| `-м` | майкоп, мортыс, митровчиыс |
| `-в` | вевттьӧсаӧсь, вит, вузалны |
| `-а` | афрамомум, азияыс, автомобиллез |
| `-ко` | косинса, колисӧ, косма |
| `-s` | spiculaea, schaueria, serapias |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | spiculaea, proctoria, pileata |
| `-н` | положеннёын, унаӧн, нятяинын |
| `-а` | окота, лымдорчача, подорова |
| `-s` | ursavus, cruciformis, cararensis |
| `-ь` | пантась, вевттьӧсаӧсь, боливияись |
| `-is` | cruciformis, cararensis, atabapensis |
| `-ын` | положеннёын, нятяинын, кывтытын |
| `-сь` | пантась, вевттьӧсаӧсь, боливияись |

### 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 |
|------|----------|------------------|----------|
| `anth` | 2.28x | 17 contexts | euanthe, anthrax, calanthe |
| `alli` | 2.17x | 19 contexts | dalli, ballii, allies |
| `адор` | 1.88x | 22 contexts | ладор, вадор, ладорӧ |
| `резд` | 1.97x | 15 contexts | грезд, грездӧ, грездас |
| `осад` | 1.99x | 14 contexts | посад, посадӧ, посадын |
| `ннэз` | 1.67x | 24 contexts | иннэз, воннэз, луннэз |
| `ensi` | 2.32x | 9 contexts | pensilis, loxensis, sinensis |
| `айон` | 1.86x | 16 contexts | район, района, районӧ |
| `вылы` | 1.84x | 15 contexts | вылын, вылыс, вылына |
| `поса` | 1.99x | 10 contexts | посад, эпоса, посадӧ |
| `ссэз` | 1.60x | 18 contexts | лиссэз, поссэз, мыссэз |
| `втыр` | 1.83x | 12 contexts | увтыр, увтырӧ, вывтыр |

### 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 |
|--------|--------|-----------|----------|
| `-s` | `-a` | 83 words | sertifera, sladeara |
| `-к` | `-н` | 73 words | кывтан, кореяын |
| `-к` | `-а` | 69 words | кулӧма, купрӧска |
| `-п` | `-н` | 57 words | политикаын, польшаын |
| `-с` | `-а` | 55 words | савкина, сёська |
| `-к` | `-ь` | 51 words | каддэзсянь, карись |
| `-в` | `-н` | 49 words | вевтӧсӧн, волейболӧн |
| `-п` | `-а` | 49 words | пирена, петӧма |
| `-s` | `-s` | 47 words | susanensis, sloths |
| `-м` | `-а` | 47 words | мылва, маркса |

### 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 |
|------|-----------------|------------|------|
| carruthersii | **`carruther-s-ii`** | 7.5 | `s` |
| институтас | **`институт-а-с`** | 7.5 | `а` |
| christieara | **`christie-a-ra`** | 7.5 | `a` |
| километрася | **`километра-с-я`** | 7.5 | `с` |
| вылынанас | **`вылына-на-с`** | 6.0 | `вылына` |
| америкаӧсь | **`америка-ӧ-сь`** | 6.0 | `америка` |
| янсӧтчӧны | **`янсӧтчӧ-ны`** | 4.5 | `янсӧтчӧ` |
| структураэз | **`структура-эз`** | 4.5 | `структура` |
| окружкомын | **`окружком-ын`** | 4.5 | `окружком` |
| кольччӧма | **`кольччӧм-а`** | 4.5 | `кольччӧм` |
| ӧтувтчӧмын | **`ӧтувтчӧм-ын`** | 4.5 | `ӧтувтчӧм` |
| pacificum | **`pacific-um`** | 4.5 | `pacific` |
| коммунаров | **`коммунар-ов`** | 4.5 | `коммунар` |
| anderssonii | **`andersson-ii`** | 4.5 | `andersson` |
| рытвывланьын | **`рытвывлань-ын`** | 4.5 | `рытвывлань` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Komi-Permyak 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 (4.19x) |
| N-gram | **2-gram** | Lowest perplexity (688) |
| Markov | **Context-4** | Highest predictability (97.5%) |
| 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 08:23:20*