---
language: fi
language_name: Finnish
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: 5.221
  - name: best_isotropy
    type: isotropy
    value: 0.7459
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-12
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Finnish** 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** | 3.799x | 3.80 | 0.1369% | 3,461,300 |
| **16k** | 4.273x | 4.27 | 0.1539% | 3,077,483 |
| **32k** | 4.760x | 4.76 | 0.1714% | 2,763,001 |
| **64k** | 5.221x 🏆 | 5.22 | 0.1881% | 2,518,757 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Lähteet judokat olympiamitalistit syntyneet henkilöt`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lähteet ▁jud ok at ▁olympiamital istit ▁syntyneet ▁henkilöt` | 8 |
| 16k | `▁lähteet ▁jud ok at ▁olympiamital istit ▁syntyneet ▁henkilöt` | 8 |
| 32k | `▁lähteet ▁jud ok at ▁olympiamital istit ▁syntyneet ▁henkilöt` | 8 |
| 64k | `▁lähteet ▁jud okat ▁olympiamital istit ▁syntyneet ▁henkilöt` | 7 |

**Sample 2:** `Tapahtumia Anicetus vastaanotti paavin viran. Syntyneitä Chang Tao Ling, taolain...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁tapahtumia ▁an ic et us ▁vastaan otti ▁paa vin ▁viran ... (+16 more)` | 26 |
| 16k | `▁tapahtumia ▁an ic et us ▁vastaan otti ▁paavin ▁viran . ... (+14 more)` | 24 |
| 32k | `▁tapahtumia ▁an ic etus ▁vastaanotti ▁paavin ▁viran . ▁syntyneitä ▁chang ... (+11 more)` | 21 |
| 64k | `▁tapahtumia ▁an ic etus ▁vastaanotti ▁paavin ▁viran . ▁syntyneitä ▁chang ... (+9 more)` | 19 |

**Sample 3:** `Los Ríos on yksi Ecuadorin 24 maakunnasta. Sen pääkaupunki on Babahoyo, pinta-al...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁los ▁r í os ▁on ▁yksi ▁ec ua dor in ... (+43 more)` | 53 |
| 16k | `▁los ▁r í os ▁on ▁yksi ▁ec ua dorin ▁ ... (+41 more)` | 51 |
| 32k | `▁los ▁r í os ▁on ▁yksi ▁ecua dorin ▁ 2 ... (+38 more)` | 48 |
| 64k | `▁los ▁r í os ▁on ▁yksi ▁ecuadorin ▁ 2 4 ... (+37 more)` | 47 |


### Key Findings

- **Best Compression:** 64k achieves 5.221x compression
- **Lowest UNK Rate:** 8k with 0.1369% 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 | 468,139 | 18.84 | 3,042,410 | 6.0% | 13.9% |
| **2-gram** | Subword | 278 🏆 | 8.12 | 22,535 | 67.1% | 99.2% |
| **3-gram** | Word | 1,065,692 | 20.02 | 4,275,337 | 4.6% | 9.6% |
| **3-gram** | Subword | 2,642 | 11.37 | 185,096 | 22.8% | 69.4% |
| **4-gram** | Word | 2,274,790 | 21.12 | 6,954,562 | 3.3% | 7.6% |
| **4-gram** | Subword | 17,026 | 14.06 | 1,194,419 | 9.7% | 35.2% |
| **5-gram** | Word | 1,753,957 | 20.74 | 4,818,809 | 2.9% | 7.7% |
| **5-gram** | Subword | 77,677 | 16.25 | 4,549,709 | 5.0% | 20.0% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `aiheesta muualla` | 249,855 |
| 2 | `kitt peak` | 206,017 |
| 3 | `peak spacewatch` | 204,244 |
| 4 | `lähteet aiheesta` | 179,493 |
| 5 | `mount lemmon` | 164,266 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kitt peak spacewatch` | 204,244 |
| 2 | `lähteet aiheesta muualla` | 179,390 |
| 3 | `mt lemmon survey` | 67,208 |
| 4 | `lemmon mt lemmon` | 67,205 |
| 5 | `mount lemmon mt` | 67,205 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mount lemmon mt lemmon` | 67,205 |
| 2 | `lemmon mt lemmon survey` | 67,205 |
| 3 | `lemmon mount lemmon survey` | 48,518 |
| 4 | `mount lemmon mount lemmon` | 48,517 |
| 5 | `haleakala pan starrs 1` | 41,305 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mount lemmon mt lemmon survey` | 67,205 |
| 2 | `mount lemmon mount lemmon survey` | 48,517 |
| 3 | `lokakuuta mount lemmon mt lemmon` | 12,734 |
| 4 | `syyskuuta mount lemmon mt lemmon` | 9,683 |
| 5 | `0 0 0 0 0` | 9,576 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 35,431,794 |
| 2 | `a _` | 28,224,764 |
| 3 | `e n` | 20,320,601 |
| 4 | `i n` | 18,392,995 |
| 5 | `t a` | 18,015,565 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e n _` | 11,913,920 |
| 2 | `i n _` | 7,559,259 |
| 3 | `a n _` | 6,328,547 |
| 4 | `t a _` | 6,095,039 |
| 5 | `j a _` | 5,873,170 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ j a _` | 4,688,853 |
| 2 | `s s a _` | 3,594,453 |
| 3 | `n e n _` | 2,793,972 |
| 4 | `_ o n _` | 2,528,919 |
| 5 | `s t a _` | 2,335,812 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i n e n _` | 2,066,240 |
| 2 | `k u u t a` | 1,605,934 |
| 3 | `u u t a _` | 1,591,336 |
| 4 | `a _ j a _` | 1,344,019 |
| 5 | `_ o l i _` | 1,224,801 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 278
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~20% 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 | 0.9729 | 1.963 | 11.25 | 5,006,345 | 2.7% |
| **1** | Subword | 1.1405 | 2.205 | 8.17 | 12,030 | 0.0% |
| **2** | Word | 0.2871 | 1.220 | 1.85 | 56,234,784 | 71.3% |
| **2** | Subword | 0.6527 | 1.572 | 4.40 | 98,107 | 34.7% |
| **3** | Word | 0.0982 | 1.070 | 1.20 | 104,064,802 | 90.2% |
| **3** | Subword | 0.7699 | 1.705 | 4.59 | 431,251 | 23.0% |
| **4** | Word | 0.0383 🏆 | 1.027 | 1.07 | 124,192,112 | 96.2% |
| **4** | Subword | 0.7445 | 1.675 | 3.90 | 1,979,645 | 25.5% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ja qing dynastioiden 11 6 h f girolamo savonarolalta hellinckin poika golden age animaatioelokuvissa...`
2. `on yhdysvaltalainen rattikelkkailija william diller yhdysvaltalainen ooppera tampereen klassillisest...`
3. `oli sitten valmistui vuonna kuningas arthuriin venäjän tiedeakatemia isännöi toisen sijan koko heimo...`

**Context Size 2:**

1. `aiheesta muualla albumit albumit crissin albumit`
2. `kitt peak spacewatch dy6 16 maaliskuuta socorro linear fs36 18 maaliskuuta oslossa miesten kalenteri...`
3. `peak spacewatch tl36 12 lokakuuta charles nunzio joka aloitti lähetyksensä 18 huhtikuuta kapkaupunki...`

**Context Size 3:**

1. `kitt peak spacewatch tym xa58 4 tammikuuta tincana m kusiak m żołnowsk aq12 5 lokakuuta kitt peak sp...`
2. `lähteet aiheesta muualla piirikunnat kartli pl chaszuri`
3. `mt lemmon survey yz11 17 tammikuuta haleakala pan starrs 1 17 lokakuuta mount lemmon mount lemmon su...`

**Context Size 4:**

1. `lemmon mt lemmon survey sv65 21 syyskuuta mount lemmon mount lemmon survey 22 toukokuuta wise wise k...`
2. `mount lemmon mt lemmon survey vv 8 marraskuuta mayhill mayhill vd8 8 marraskuuta catalina css 14 tou...`
3. `lemmon mount lemmon survey 8 tammikuuta mount lemmon mt lemmon survey fk38 28 maaliskuuta kitt peak ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_hätionewone_–_r`
2. `apuuikikakeniipo`
3. `in_sentalisaline`

**Context Size 2:**

1. `n_outehiaan_taan,`
2. `a_1_kuusopirthred`
3. `en_pilöys._kerumi`

**Context Size 3:**

1. `en_eze._brit_dimik`
2. `in_sureisi_lan_”tj`
3. `an_koin_(s._29._ta`

**Context Size 4:**

1. `_ja_myös_aren_regio`
2. `ssa_101,56_metriä_l`
3. `nen_tuottana._vuott`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.2% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,979,645 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 | 2,250,455 |
| Total Tokens | 145,574,709 |
| Mean Frequency | 64.69 |
| Median Frequency | 4 |
| Frequency Std Dev | 4199.88 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ja | 4,696,959 |
| 2 | on | 2,545,540 |
| 3 | oli | 1,230,343 |
| 4 | hän | 1,028,773 |
| 5 | vuonna | 905,604 |
| 6 | 1 | 689,784 |
| 7 | myös | 653,305 |
| 8 | s | 616,597 |
| 9 | 2 | 541,496 |
| 10 | lähteet | 519,252 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | navkatin | 2 |
| 2 | xovosista | 2 |
| 3 | sauvagetin | 2 |
| 4 | bundžikatin | 2 |
| 5 | keltaeväkuukala | 2 |
| 6 | glädjekällan | 2 |
| 7 | wydlerin | 2 |
| 8 | joshualla | 2 |
| 9 | charmatzn | 2 |
| 10 | kidugala | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9214 |
| R² (Goodness of Fit) | 0.998159 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.8% |
| Top 1,000 | 41.3% |
| Top 5,000 | 57.6% |
| Top 10,000 | 64.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9982 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.8% of corpus
- **Long Tail:** 2,240,455 words needed for remaining 35.1% 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 | 0.7459 | 0.3486 | N/A | N/A |
| **mono_64d** | 64 | 0.7204 | 0.2821 | N/A | N/A |
| **mono_128d** | 128 | 0.6228 | 0.2311 | N/A | N/A |
| **aligned_32d** | 32 | 0.7459 🏆 | 0.3499 | 0.3560 | 0.7800 |
| **aligned_64d** | 64 | 0.7204 | 0.2899 | 0.5740 | 0.8760 |
| **aligned_128d** | 128 | 0.6228 | 0.2356 | 0.7020 | 0.9140 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7459 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2895. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 70.2% 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 | **-0.615** | 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` | sorapohjille, suus, suolamminpuro |
| `-a` | asiakkuuksien, anregungen, anglosaksissa |
| `-k` | kanadansuomalaiset, kotitaloustyöntekijöiden, kampanjoimalla |
| `-t` | taskilassa, tehostuu, tujh |
| `-p` | puhalluksen, pantaisiin, poismeno |
| `-m` | mq, männistönpolun, miehittäjävaltioiden |
| `-e` | eddarunoutta, everst, edsevö |
| `-b` | boeingillä, bratslavista, bundille |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | puhalluksen, asiakkuuksien, anregungen |
| `-a` | anglosaksissa, taskilassa, unimatka |
| `-en` | puhalluksen, asiakkuuksien, anregungen |
| `-in` | näyttelyihin, pantaisiin, tulviviin |
| `-ta` | bratslavista, todetuista, karstulasta |
| `-i` | darski, suolaiseksi, kuvernööreiksi |
| `-sa` | anglosaksissa, taskilassa, nerjassa |
| `-an` | ulosteitaan, vallankumoustaan, apsaran |

### 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 |
|------|----------|------------------|----------|
| `ivat` | 1.84x | 221 contexts | nivat, ivata, livat |
| `ttii` | 1.81x | 221 contexts | ottii, uttiin, fättii |
| `ises` | 1.76x | 230 contexts | sises, isesi, rises |
| `tett` | 1.36x | 562 contexts | tette, tetto, tettu |
| `staa` | 1.45x | 361 contexts | staav, staar, staab |
| `ukse` | 1.35x | 445 contexts | uksen, ukset, suksea |
| `sess` | 1.58x | 144 contexts | sessa, sessi, sesso |
| `uome` | 1.73x | 78 contexts | suome, luomen, luomea |
| `isuu` | 1.65x | 85 contexts | fisuu, fisuun, paisuu |
| `äytt` | 1.56x | 109 contexts | käyttä, käytto, näyttä |
| `tuks` | 1.32x | 244 contexts | tuksu, tuksa, tuksi |
| `htee` | 1.43x | 137 contexts | ahtee, yhteet, ähteet |

### 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` | 338 words | kaksoisruokolehdykkäsoittimien, kyanzitthan |
| `-k` | `-a` | 304 words | käyttäytymisongelmia, karjalohja |
| `-s` | `-n` | 259 words | sisustusarkkitehtuurin, sallyyn |
| `-p` | `-a` | 236 words | paviaanista, polyamorisia |
| `-s` | `-a` | 228 words | sairausjaksoista, sponsoroinnista |
| `-m` | `-n` | 195 words | mamemon, mustionselän |
| `-p` | `-n` | 194 words | poweraden, puolueettomuuspolitiikkaan |
| `-t` | `-n` | 189 words | täyttämiin, tieoikeuteen |
| `-t` | `-a` | 180 words | tutkalaitteella, tappioissa |
| `-m` | `-a` | 160 words | maeba, minisarjassa |

### 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 |
|------|-----------------|------------|------|
| päätoimessaan | **`päätoimes-sa-an`** | 7.5 | `sa` |
| nicolasia | **`nicola-si-a`** | 7.5 | `si` |
| seksiaiheisia | **`seksiaihei-si-a`** | 7.5 | `si` |
| elämänlangat | **`elämänlang-a-t`** | 7.5 | `a` |
| vauvanruokaa | **`vauvanruok-a-a`** | 7.5 | `a` |
| puuttunutkaan | **`puuttunutk-a-an`** | 7.5 | `a` |
| antenniverkkonsa | **`antenniverkko-n-sa`** | 7.5 | `n` |
| kirjoittamistaan | **`kirjoittamis-ta-an`** | 7.5 | `ta` |
| biogeenisiin | **`biogeeni-si-in`** | 7.5 | `si` |
| torppasivat | **`torppasiv-a-t`** | 7.5 | `a` |
| mediatoimijat | **`mediatoimij-a-t`** | 7.5 | `a` |
| artemísio | **`artemí-si-o`** | 7.5 | `si` |
| havaintoasemaa | **`havaintoasem-a-a`** | 7.5 | `a` |
| christóforos | **`christófor-o-s`** | 7.5 | `o` |
| porontiman | **`porontim-a-n`** | 7.5 | `a` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Finnish 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 (5.22x) |
| N-gram | **2-gram** | Lowest perplexity (278) |
| Markov | **Context-4** | Highest predictability (96.2%) |
| 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: 2026-01-13 06:45:42*