README.md

---
language: se
language_name: Northern Sami
language_family: uralic_saami
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_saami
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: 4.799
  - name: best_isotropy
    type: isotropy
    value: 0.6843
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Northern Sami - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Northern Sami** 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** | 3.790x | 3.80 | 0.2717% | 134,333 |
| **16k** | 4.161x | 4.17 | 0.2983% | 122,344 |
| **32k** | 4.506x | 4.52 | 0.3231% | 112,972 |
| **64k** | 4.799x 🏆 | 4.81 | 0.3440% | 106,091 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Gaskasudanalaš gielat lea sullii 60 giela joavku, mii adnojuvvo oassin nilosahar...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁gaska su da nalaš ▁gielat ▁lea ▁sullii ▁ 6 0 ... (+13 more)` | 23 |
| 16k | `▁gaska su da nalaš ▁gielat ▁lea ▁sullii ▁ 6 0 ... (+13 more)` | 23 |
| 32k | `▁gaskasudanalaš ▁gielat ▁lea ▁sullii ▁ 6 0 ▁giela ▁joavku , ... (+10 more)` | 20 |
| 64k | `▁gaskasudanalaš ▁gielat ▁lea ▁sullii ▁ 6 0 ▁giela ▁joavku , ... (+10 more)` | 20 |

**Sample 2:** `Herning lea gielda Gaska-Jyllándda regiuvnnas Dánmárkkus. regiuvnna gielddat`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁h ern ing ▁lea ▁gielda ▁gaska - jyllándda ▁regiuvnnas ▁dánmárkkus ... (+3 more)` | 13 |
| 16k | `▁h ern ing ▁lea ▁gielda ▁gaska - jyllándda ▁regiuvnnas ▁dánmárkkus ... (+3 more)` | 13 |
| 32k | `▁hern ing ▁lea ▁gielda ▁gaska - jyllándda ▁regiuvnnas ▁dánmárkkus . ... (+2 more)` | 12 |
| 64k | `▁herning ▁lea ▁gielda ▁gaska - jyllándda ▁regiuvnnas ▁dánmárkkus . ▁regiuvnna ... (+1 more)` | 11 |

**Sample 3:** `Meuse lea departemeanta Frankriikkas. departemeanttat`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁me use ▁lea ▁departemeanta ▁frankriikkas . ▁departemeanttat` | 7 |
| 16k | `▁me use ▁lea ▁departemeanta ▁frankriikkas . ▁departemeanttat` | 7 |
| 32k | `▁me use ▁lea ▁departemeanta ▁frankriikkas . ▁departemeanttat` | 7 |
| 64k | `▁me use ▁lea ▁departemeanta ▁frankriikkas . ▁departemeanttat` | 7 |


### Key Findings

- **Best Compression:** 64k achieves 4.799x compression
- **Lowest UNK Rate:** 8k with 0.2717% 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 | 2,031 | 10.99 | 5,208 | 29.3% | 63.1% |
| **2-gram** | Subword | 352 🏆 | 8.46 | 2,585 | 58.6% | 98.8% |
| **3-gram** | Word | 2,608 | 11.35 | 5,732 | 24.7% | 61.3% |
| **3-gram** | Subword | 3,132 | 11.61 | 19,959 | 20.3% | 64.1% |
| **4-gram** | Word | 4,513 | 12.14 | 9,877 | 19.0% | 51.5% |
| **4-gram** | Subword | 15,716 | 13.94 | 92,733 | 11.1% | 34.9% |
| **5-gram** | Word | 3,949 | 11.95 | 7,570 | 17.4% | 53.3% |
| **5-gram** | Subword | 40,919 | 15.32 | 192,050 | 8.1% | 25.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `no nn` | 4,642 |
| 2 | `lea gielda` | 1,023 |
| 3 | `geahča maid` | 882 |
| 4 | `olmmošlohku lea` | 685 |
| 5 | `viidodat lea` | 619 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dan olmmošlohku lea` | 487 |
| 2 | `gregoriánalaš kaleandara mielde` | 366 |
| 3 | `geahča maid kaleandar` | 366 |
| 4 | `kaleandara mielde jagi` | 365 |
| 5 | `lea gregoriánalaš kaleandara` | 365 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `gregoriánalaš kaleandara mielde jagi` | 365 |
| 2 | `lea gregoriánalaš kaleandara mielde` | 365 |
| 3 | `beaivi jagis leat vel` | 364 |
| 4 | `ávvudeamit geahča maid kaleandar` | 349 |
| 5 | `beaivi lea gregoriánalaš kaleandara` | 290 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `lea gregoriánalaš kaleandara mielde jagi` | 365 |
| 2 | `beaivi lea gregoriánalaš kaleandara mielde` | 290 |
| 3 | `jápmimat ávvudeamit geahča maid kaleandar` | 235 |
| 4 | `riegádeamit jápmimat ávvudeamit geahča maid` | 153 |
| 5 | `dáhpáhusat riegádeamit jápmimat ávvudeamit geahča` | 126 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 69,682 |
| 2 | `e a` | 47,932 |
| 3 | `t _` | 35,365 |
| 4 | `i _` | 34,686 |
| 5 | `_ l` | 33,406 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e` | 22,944 |
| 2 | `l e a` | 22,047 |
| 3 | `a t _` | 16,615 |
| 4 | `_ j a` | 14,438 |
| 5 | `e a _` | 13,614 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e a` | 19,712 |
| 2 | `l e a _` | 13,336 |
| 3 | `_ j a _` | 10,797 |
| 4 | `g i e l` | 10,236 |
| 5 | `i e l d` | 6,420 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ l e a _` | 13,325 |
| 2 | `_ g i e l` | 5,916 |
| 3 | `g i e l d` | 5,428 |
| 4 | `_ l e a t` | 4,734 |
| 5 | `, _ n n )` | 4,661 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 352
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.5666 | 1.481 | 3.04 | 79,826 | 43.3% |
| **1** | Subword | 0.9846 | 1.979 | 7.73 | 832 | 1.5% |
| **2** | Word | 0.1237 | 1.090 | 1.25 | 241,080 | 87.6% |
| **2** | Subword | 1.0067 | 2.009 | 5.88 | 6,431 | 0.0% |
| **3** | Word | 0.0353 | 1.025 | 1.06 | 297,643 | 96.5% |
| **3** | Subword | 0.8950 | 1.860 | 4.14 | 37,781 | 10.5% |
| **4** | Word | 0.0125 🏆 | 1.009 | 1.03 | 311,161 | 98.8% |
| **4** | Subword | 0.6478 | 1.567 | 2.58 | 156,127 | 35.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `lea ingeborg midttømme ášši bearehaga ja jordi sànchez ja finnmárkku fylkkas girku unjárgga gielddas...`
2. `ja laila dáhpáhusat honda vuođđuduvvui riegádeamit jápmimat guru henrik saijets tiina sanila aikio w...`
3. `no nn duoppalmohkki toppelbukt no nn boatka botkaeidet no nn čávžu sautso no nn loahccajávri bielvva...`

**Context Size 2:**

1. `no nn áŋŋelvárri ongelvikfjellet no nn duopmásvággi tomasdalen no nn klubbočohkka storklubben no nn ...`
2. `lea gielda hordalándda fylkkas dan olmmošlohku lea 90 ceahki davát govdodagas ja lea gielda hovedsta...`
3. `geahča maid schwaben bayern distrivttat`

**Context Size 3:**

1. `dan olmmošlohku lea 20 184 ássi ja viidodat 9 409 km 0 80 is 4 norðurland vestra sauðárkrókur`
2. `geahča maid kaleandar guovvamánu 28 guovvamánu 29 njukčamánu 2 3 1 inkl 1 kāuakā māuakā ʻoluakā lāua...`
3. `gregoriánalaš kaleandara mielde jagi 69 beaivi gárgádusjagi 70 beaivi jagis leat vel 97 beaivvi namm...`

**Context Size 4:**

1. `lea gregoriánalaš kaleandara mielde jagi 237 gárgádusjagi 238 beaivi jagis leat vel 51 beaivve namma...`
2. `gregoriánalaš kaleandara mielde jagi 309 gárgádusjagi 310 beaivi jagis leat vel 176 beaivvi nammabea...`
3. `beaivi jagis leat vel 352 beaivve gárgádusjagis 353 nammabeaivvit sámi kaleandar nuvtte nuhtte dáža ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_o._2._ata_bi._a`
2. `aiesbacamo,_veai`
3. `i_sálean_s_nnggo`

**Context Size 2:**

1. `a_mimyhälä,_dása_`
2. `ea_bállačča_baded`
3. `t_.fišgus_beldea_`

**Context Size 3:**

1. `_leaba_ii_-_jagiel`
2. `leat_biohta,_ja_オ_`
3. `at_infilbmuijaorta`

**Context Size 4:**

1. `_lea_várri_jugosláv`
2. `lea_kántor:_ráfibál`
3. `_ja_tammimäenpää,_k`


### Key Findings

- **Best Predictability:** Context-4 (word) with 98.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (156,127 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 | 27,620 |
| Total Tokens | 319,888 |
| Mean Frequency | 11.58 |
| Median Frequency | 3 |
| Frequency Std Dev | 124.94 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | lea | 13,393 |
| 2 | ja | 10,814 |
| 3 | no | 4,757 |
| 4 | nn | 4,664 |
| 5 | leat | 3,861 |
| 6 | dan | 2,333 |
| 7 | gielda | 2,319 |
| 8 | gáldut | 2,032 |
| 9 | lei | 1,919 |
| 10 | go | 1,741 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | sztuka | 2 |
| 2 | kultura | 2 |
| 3 | muzea | 2 |
| 4 | britishpedia | 2 |
| 5 | encyklopedia | 2 |
| 6 | osobistości | 2 |
| 7 | rzeczypospolitej | 2 |
| 8 | polskiej | 2 |
| 9 | bph | 2 |
| 10 | publishing | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9432 |
| R² (Goodness of Fit) | 0.996992 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 32.6% |
| Top 1,000 | 58.5% |
| Top 5,000 | 77.6% |
| Top 10,000 | 86.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9970 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 32.6% of corpus
- **Long Tail:** 17,620 words needed for remaining 13.6% 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 | 0.6843 🏆 | 0.3758 | N/A | N/A |
| **mono_64d** | 64 | 0.2678 | 0.3587 | N/A | N/A |
| **mono_128d** | 128 | 0.0380 | 0.3695 | N/A | N/A |
| **aligned_32d** | 32 | 0.6843 | 0.3768 | 0.0200 | 0.1960 |
| **aligned_64d** | 64 | 0.2678 | 0.3475 | 0.0460 | 0.2380 |
| **aligned_128d** | 128 | 0.0380 | 0.3611 | 0.0500 | 0.2880 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.6843 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3649. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.0% 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 | **1.086** | 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 |
|--------|----------|
| `-s` | sáhte, stáda, suolovárri |
| `-b` | brannfjellet, birokratiija, brasil |
| `-m` | máŋggalágan, mearkkašumiid, máze |
| `-a` | almmáiolbmot, alluten, arvi |
| `-g` | gáivuotna, guimmiideaset, gislaved |
| `-l` | lr, logádin, loktii |
| `-k` | karvan, kvalnes, klæbu |
| `-r` | row, ribosomat, röntgengovas |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | ealgga, okinawa, gáivuotna |
| `-i` | loktii, suolovárri, viidánii |
| `-t` | almmáiolbmot, brannfjellet, guimmiideaset |
| `-n` | confrançon, karvan, duopmostuoluin |
| `-s` | kvalnes, invaders, zacatecas |
| `-at` | ribosomat, ivdnesáddagat, guorahallat |
| `-e` | førde, sáhte, máze |
| `-d` | gislaved, bálgáid, mearkkašumiid |

### 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 |
|------|----------|------------------|----------|
| `ikka` | 1.62x | 35 contexts | tikka, mikkal, riikka |
| `alaš` | 1.73x | 23 contexts | agalaš, dábalaš, fágalaš |
| `iell` | 1.75x | 15 contexts | jiella, miella, iellup |
| `llii` | 1.76x | 14 contexts | ollii, gillii, millii |
| `ovdd` | 1.48x | 23 contexts | ovddu, ovddal, ovddeš |
| `eaiv` | 1.74x | 13 contexts | beaivi, deaivá, beaivvi |
| `giel` | 1.53x | 16 contexts | giela, gield, gielat |
| `ield` | 1.53x | 16 contexts | mield, field, gield |
| `ldda` | 1.51x | 15 contexts | uldda, báldda, čuoldda |
| `iela` | 1.63x | 12 contexts | giela, miela, gielat |
| `vuođ` | 1.75x | 9 contexts | vuođu, vuođul, vuođus |
| `ávpo` | 1.87x | 7 contexts | gávpot, gávpoga, gávpogas |

### 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` | 130 words | sandvika, strömma |
| `-k` | `-a` | 110 words | kristina, kavantola |
| `-s` | `-t` | 85 words | suopmanat, svartfjellet |
| `-g` | `-t` | 85 words | geahčadit, guovlogielddat |
| `-g` | `-a` | 84 words | gállojohka, geahpesdávda |
| `-m` | `-a` | 84 words | merula, musihka |
| `-s` | `-n` | 81 words | sinun, sathon |
| `-r` | `-a` | 78 words | runeberga, rinjárga |
| `-s` | `-s` | 76 words | solís, sálliris |
| `-s` | `-i` | 74 words | stuoravárri, suonenjoki |

### 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 |
|------|-----------------|------------|------|
| aegithalidae | **`aegithalid-a-e`** | 7.5 | `a` |
| miljovnnaid | **`miljovnn-a-id`** | 7.5 | `a` |
| stávvaliid | **`stávval-i-id`** | 7.5 | `i` |
| kapillearaid | **`kapillear-a-id`** | 7.5 | `a` |
| čuovvumušaid | **`čuovvumuš-a-id`** | 7.5 | `a` |
| vuoittahalai | **`vuoittahal-a-i`** | 7.5 | `a` |
| skandinávia | **`skandináv-i-a`** | 7.5 | `i` |
| maŋŋálaga | **`maŋŋá-la-ga`** | 7.5 | `la` |
| universitehtain | **`universiteht-a-in`** | 7.5 | `a` |
| čoahkkimis | **`čoahkki-mi-s`** | 7.5 | `mi` |
| veardádala | **`veardád-a-la`** | 7.5 | `a` |
| gonagasaid | **`gonagas-a-id`** | 7.5 | `a` |
| botswanai | **`botswan-a-i`** | 7.5 | `a` |
| antibiohtaid | **`antibioht-a-id`** | 7.5 | `a` |
| ludvigsen | **`ludvig-s-en`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Northern Sami 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 (4.80x) |
| N-gram | **2-gram** | Lowest perplexity (352) |
| Markov | **Context-4** | Highest predictability (98.8%) |
| 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: 2026-01-10 19:51:09*