README.md

---
language: et
language_name: Estonian
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: 4.670
  - name: best_isotropy
    type: isotropy
    value: 0.8070
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-12
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Estonian** 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** | 3.499x | 3.50 | 0.1284% | 2,158,197 |
| **16k** | 3.902x | 3.90 | 0.1432% | 1,935,397 |
| **32k** | 4.294x | 4.30 | 0.1576% | 1,758,492 |
| **64k** | 4.670x 🏆 | 4.67 | 0.1714% | 1,617,034 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Kivikülä oli mitme Eesti küla nimi: Kivikülä (Kanepi vald) Kivikülä (Mooste vald...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kivik ü lä ▁oli ▁mitme ▁eesti ▁küla ▁nimi : ▁kivik ... (+38 more)` | 48 |
| 16k | `▁kivik ü lä ▁oli ▁mitme ▁eesti ▁küla ▁nimi : ▁kivik ... (+36 more)` | 46 |
| 32k | `▁kivik ü lä ▁oli ▁mitme ▁eesti ▁küla ▁nimi : ▁kivik ... (+36 more)` | 46 |
| 64k | `▁kivik ü lä ▁oli ▁mitme ▁eesti ▁küla ▁nimi : ▁kivik ... (+34 more)` | 44 |

**Sample 2:** `Ar on argooni keemiline sümbol arüülrühma tähis Vaata ka .ar a.r. AR Arar`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ar ▁on ▁ar g ooni ▁keemi line ▁sümb ol ▁ar ... (+16 more)` | 26 |
| 16k | `▁ar ▁on ▁ar g ooni ▁keemiline ▁sümbol ▁ar üül rühma ... (+12 more)` | 22 |
| 32k | `▁ar ▁on ▁arg ooni ▁keemiline ▁sümbol ▁ar üül rühma ▁tähis ... (+11 more)` | 21 |
| 64k | `▁ar ▁on ▁arg ooni ▁keemiline ▁sümbol ▁ar üülrühma ▁tähis ▁vaata ... (+10 more)` | 20 |

**Sample 3:** `Saaremetsa on küla Saare maakonnas Saaremaa vallas. Enne Eesti omavalitsuste hal...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁saare metsa ▁on ▁küla ▁saare ▁maakonnas ▁saaremaa ▁vallas . ▁enne ... (+14 more)` | 24 |
| 16k | `▁saare metsa ▁on ▁küla ▁saare ▁maakonnas ▁saaremaa ▁vallas . ▁enne ... (+14 more)` | 24 |
| 32k | `▁saare metsa ▁on ▁küla ▁saare ▁maakonnas ▁saaremaa ▁vallas . ▁enne ... (+13 more)` | 23 |
| 64k | `▁saare metsa ▁on ▁küla ▁saare ▁maakonnas ▁saaremaa ▁vallas . ▁enne ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.670x compression
- **Lowest UNK Rate:** 8k with 0.1284% 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 | 337,217 | 18.36 | 1,302,072 | 3.9% | 11.4% |
| **2-gram** | Subword | 305 🏆 | 8.25 | 17,718 | 66.3% | 98.6% |
| **3-gram** | Word | 703,095 | 19.42 | 1,646,892 | 1.8% | 6.7% |
| **3-gram** | Subword | 3,087 | 11.59 | 150,091 | 20.2% | 66.6% |
| **4-gram** | Word | 1,498,741 | 20.52 | 2,767,784 | 1.3% | 4.8% |
| **4-gram** | Subword | 21,422 | 14.39 | 895,848 | 8.0% | 30.4% |
| **5-gram** | Word | 1,153,730 | 20.14 | 1,968,292 | 1.5% | 5.2% |
| **5-gram** | Subword | 102,361 | 16.64 | 3,168,647 | 4.4% | 16.8% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `viited välislingid` | 58,582 |
| 2 | `vaata ka` | 44,369 |
| 3 | `mis on` | 36,684 |
| 4 | `ei ole` | 34,079 |
| 5 | `ta on` | 31,431 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `aastatel oli ta` | 7,225 |
| 2 | `aastad aastad aastad` | 4,677 |
| 3 | `ta lõpetas aastal` | 4,614 |
| 4 | `klassi teenetemärgi kavalerid` | 4,005 |
| 5 | `1 jaanuari seisuga` | 3,436 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `aastad aastad aastad aastad` | 4,154 |
| 2 | `1 jaanuari seisuga oli` | 2,589 |
| 3 | `veebiversioon vaadatud inglise keeles` | 2,420 |
| 4 | `on 2 järgu haldusüksus` | 2,367 |
| 5 | `jaanuari seisuga oli eestis` | 2,304 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `aastad aastad aastad aastad aastad` | 3,643 |
| 2 | `1 jaanuari seisuga oli eestis` | 2,301 |
| 3 | `enne eesti omavalitsuste haldusreformi aastal` | 2,161 |
| 4 | `eesti omavalitsuste haldusreformi aastal kuulus` | 2,082 |
| 5 | `omavalitsuste haldusreformi aastal kuulus küla` | 2,056 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 8,278,885 |
| 2 | `s t` | 6,917,693 |
| 3 | `e _` | 6,563,708 |
| 4 | `_ k` | 6,339,815 |
| 5 | `i s` | 6,018,773 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `j a _` | 2,098,392 |
| 2 | `a s t` | 1,970,831 |
| 3 | `_ j a` | 1,954,972 |
| 4 | `s t a` | 1,710,374 |
| 5 | `_ k a` | 1,562,032 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ j a _` | 1,609,350 |
| 2 | `_ o n _` | 1,151,253 |
| 3 | `a s t a` | 1,058,545 |
| 4 | `a a s t` | 907,854 |
| 5 | `_ a a s` | 846,069 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a a s t a` | 884,340 |
| 2 | `_ a a s t` | 837,803 |
| 3 | `_ e e s t` | 483,731 |
| 4 | `e e s t i` | 465,700 |
| 5 | `_ o l i _` | 419,244 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 305
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~17% 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 | 0.9682 | 1.956 | 10.20 | 2,501,318 | 3.2% |
| **1** | Subword | 1.1416 | 2.206 | 7.58 | 8,581 | 0.0% |
| **2** | Word | 0.2743 | 1.209 | 1.76 | 25,467,651 | 72.6% |
| **2** | Subword | 0.7354 | 1.665 | 5.04 | 64,997 | 26.5% |
| **3** | Word | 0.0845 | 1.060 | 1.15 | 44,752,862 | 91.5% |
| **3** | Subword | 0.7895 | 1.728 | 4.57 | 327,394 | 21.0% |
| **4** | Word | 0.0304 🏆 | 1.021 | 1.05 | 51,476,586 | 97.0% |
| **4** | Subword | 0.7345 | 1.664 | 3.70 | 1,496,614 | 26.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ja on endine hobupostijaama kohta on märkimisväärne summa kohta oli aga langenud lastest eraldada 10...`
2. `on india pandžab agra oli nõukogude liit mis halvab haigus pärslastel oli aastatel ogpu baasil sovho...`
3. `oli ta kuni 15 stefan hartmann solving a luha jooksja tollest keelestaadiumist pärineb 16 1 1`

**Context Size 2:**

1. `viited välislingid naise piibel kirik ja sellega seotud skandaalidega jättis jälje paleedejärgsele a...`
2. `vaata ka värska oja lammil kasvavaid käpalisi kaitseala pindala on 134 valgusaastat m75 tähesuurus o...`
3. `mis on kõige põhjapoolseima levikuga vaal ja mina ning helisev muusika tallinna linnahallis osales k...`

**Context Size 3:**

1. `aastatel oli ta tallinna linna vene gümnaasiumi aastatel õppis tartu ülikoolis aastatel töötas laasi...`
2. `aastad aastad aastad sündmused maailmas sündmused eestis liivimaa kindralsuperintendendiks sai pieti...`
3. `ta lõpetas aastal stanfordi ülikooli omakoostatud õppekava järgi organisatsioonilise käitumise alal ...`

**Context Size 4:**

1. `aastad aastad aastad aastad aastad aastad aastad aastad aastad aastad sündmused maailmas sündmused e...`
2. `1 jaanuari seisuga oli eestis eesnimi villem 407 mehel 1 jaanuari seisuga mehel ja naisel perekonnan...`
3. `on 2 järgu haldusüksus munitsipaalrajoon venemaal kurski oblasti kaguosas rajooni keskus on zmijovka...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_le_a_akeetaa_si`
2. `ast_biome_sestad`
3. `iisemateisvusana`

**Context Size 2:**

1. `a_abietustutal_vä`
2. `stakteel_rogutses`
3. `e_sosi»_otsitleva`

**Context Size 3:**

1. `ja_vikusti_šotis_h`
2. `astate,_umbertaani`
3. `_ja_ene_teaduse_li`

**Context Size 4:**

1. `_ja_et_univeti"._se`
2. `_on_olul_olences_ol`
3. `astatistikute,_kui_`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,496,614 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 | 1,127,453 |
| Total Tokens | 57,757,838 |
| Mean Frequency | 51.23 |
| Median Frequency | 4 |
| Frequency Std Dev | 2262.40 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ja | 1,615,015 |
| 2 | on | 1,161,574 |
| 3 | oli | 421,670 |
| 4 | ta | 389,552 |
| 5 | eesti | 378,379 |
| 6 | aastal | 378,162 |
| 7 | ka | 324,963 |
| 8 | ning | 279,896 |
| 9 | et | 232,528 |
| 10 | mis | 231,904 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 𝐵 | 2 |
| 2 | mõõduruum | 2 |
| 3 | saie | 2 |
| 4 | chichibus | 2 |
| 5 | vooruspäraselt | 2 |
| 6 | eudaimoniast | 2 |
| 7 | pyrrho | 2 |
| 8 | ligipääsetud | 2 |
| 9 | viiruskampaaniad | 2 |
| 10 | sisuvormid | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9401 |
| R² (Goodness of Fit) | 0.996663 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 21.3% |
| Top 1,000 | 42.1% |
| Top 5,000 | 59.2% |
| Top 10,000 | 66.7% |

### Key Findings

- **Zipf Compliance:** R²=0.9967 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 21.3% of corpus
- **Long Tail:** 1,117,453 words needed for remaining 33.3% 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 | 0.8070 | 0.3589 | N/A | N/A |
| **mono_64d** | 64 | 0.7822 | 0.2915 | N/A | N/A |
| **mono_128d** | 128 | 0.6876 | 0.2237 | N/A | N/A |
| **aligned_32d** | 32 | 0.8070 🏆 | 0.3616 | 0.3020 | 0.7040 |
| **aligned_64d** | 64 | 0.7822 | 0.2794 | 0.4740 | 0.8320 |
| **aligned_128d** | 128 | 0.6876 | 0.2187 | 0.5880 | 0.8600 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8070 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2890. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 58.8% 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 | **-0.693** | 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` | saatelehti, stsintsillisma, süfiliitikute |
| `-a` | anjan, augustikriisist, arengueesmärkide |
| `-k` | kiirgusresistentsuse, käibekasvataja, kauniduse |
| `-ma` | masile, mattson, manussüsteemide |
| `-m` | musicology, masile, mosaiiksuse |
| `-p` | pilgutas, peatreenerjõhvi, pikkadeks |
| `-t` | töölepanemine, tapmislüliti, tsurphu |
| `-ka` | kauniduse, kausitäis, kalmistutega |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | kiirgusresistentsuse, arengueesmärkide, vangivalvurite |
| `-s` | pilgutas, pikkadeks, gamblers |
| `-a` | venemaanatalja, vītola, käibekasvataja |
| `-t` | augustikriisist, oliviinbasalt, põlvkondadest |
| `-i` | naftareostusi, weißensteini, repjekalnsi |
| `-d` | immatrikulerad, generalistid, kehtivaid |
| `-st` | augustikriisist, põlvkondadest, kosmast |
| `-ga` | kerstiniga, nicolasega, weissmaniga |

### 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 |
|------|----------|------------------|----------|
| `atel` | 2.50x | 141 contexts | ratel, katel, natel |
| `jand` | 2.13x | 203 contexts | janda, ajand, ojand |
| `ised` | 2.31x | 119 contexts | lised, öised, meised |
| `isek` | 2.05x | 100 contexts | cisek, pisek, iseka |
| `ndus` | 1.55x | 349 contexts | indus, andus, aindus |
| `umis` | 1.50x | 406 contexts | jumis, umist, dumis |
| `alit` | 1.57x | 206 contexts | alito, alita, balit |
| `utat` | 1.51x | 254 contexts | mutat, jutat, ceutat |
| `imis` | 1.35x | 416 contexts | imiss, mimis, nimis |
| `stri` | 1.33x | 324 contexts | strid, strip, strik |
| `eadu` | 2.08x | 37 contexts | seadu, eadui, teadud |
| `ikoo` | 1.71x | 82 contexts | ikoon, tikoo, ikooni |

### 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` | `-e` | 169 words | kurje, kõrbeisade |
| `-k` | `-s` | 144 words | kodukaitseks, kinabaluensis |
| `-s` | `-e` | 137 words | sopranplokkflöödile, südamenõrkuse |
| `-p` | `-e` | 136 words | perfektsete, petukirjade |
| `-k` | `-t` | 131 words | kiirpaat, koolijuhtidelt |
| `-t` | `-e` | 120 words | tuulemeelne, tipptaseme |
| `-k` | `-a` | 120 words | kaubasaaja, kaalukama |
| `-k` | `-i` | 110 words | kambri, keskaadli |
| `-a` | `-e` | 105 words | ametisseasumise, argidae |
| `-p` | `-s` | 104 words | pardies, polyus |

### 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 |
|------|-----------------|------------|------|
| meediakanalitest | **`meediakanali-te-st`** | 7.5 | `te` |
| villakiud | **`villak-i-ud`** | 7.5 | `i` |
| tähemärkidest | **`tähemärkid-e-st`** | 7.5 | `e` |
| sõjajärgsetes | **`sõjajärgse-te-s`** | 7.5 | `te` |
| totalitarianism | **`totalitariani-s-m`** | 7.5 | `s` |
| intrusioonidena | **`intrusioonid-e-na`** | 7.5 | `e` |
| peapoolses | **`peapool-se-s`** | 7.5 | `se` |
| crispolti | **`crispol-t-i`** | 7.5 | `t` |
| orgaaniliseks | **`orgaanili-se-ks`** | 7.5 | `se` |
| fibroblastideks | **`fibroblastid-e-ks`** | 7.5 | `e` |
| mõttemuiged | **`mõttemuig-e-d`** | 7.5 | `e` |
| saksimaasse | **`saksimaa-s-se`** | 7.5 | `s` |
| neopositivism | **`neopositivi-s-m`** | 7.5 | `s` |
| esmaalusteni | **`esmaalus-te-ni`** | 7.5 | `te` |
| väljundkeeles | **`väljundkee-le-s`** | 7.5 | `le` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Estonian 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 (4.67x) |
| N-gram | **2-gram** | Lowest perplexity (305) |
| Markov | **Context-4** | Highest predictability (97.0%) |
| 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: 2026-01-12 11:23:31*