---
language: kl
language_name: Kalaallisut
language_family: eskimoaleut
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-eskimoaleut
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: 6.102
  - name: best_isotropy
    type: isotropy
    value: 0.1725
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Kalaallisut** 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** | 4.780x | 4.79 | 0.1746% | 61,845 |
| **16k** | 5.606x | 5.61 | 0.2048% | 52,738 |
| **32k** | 6.102x 🏆 | 6.11 | 0.2229% | 48,447 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Qaammat tassaavoq nunarsuup pinngortitami satellittaa (terra). ilisimatusarneq`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁qaammat ▁tassaavoq ▁nunarsuup ▁pinngortitami ▁satell ittaa ▁( ter ra ). ... (+1 more)` | 11 |
| 16k | `▁qaammat ▁tassaavoq ▁nunarsuup ▁pinngortitami ▁satellittaa ▁( ter ra ). ▁ilisimatusarneq` | 10 |
| 32k | `▁qaammat ▁tassaavoq ▁nunarsuup ▁pinngortitami ▁satellittaa ▁( terra ). ▁ilisimatusarneq` | 9 |

**Sample 2:** `Sarfannguaq nunaqarfiuvoq 100 sinnilaarlugit inulik Sisimiut kommunerigaluani it...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sarfannguaq ▁nunaqarfiuvoq ▁ 1 0 0 ▁sinnilaarlugit ▁inulik ▁sisimiut ▁kommunerig ... (+9 more)` | 19 |
| 16k | `▁sarfannguaq ▁nunaqarfiuvoq ▁ 1 0 0 ▁sinnilaarlugit ▁inulik ▁sisimiut ▁kommunerig ... (+9 more)` | 19 |
| 32k | `▁sarfannguaq ▁nunaqarfiuvoq ▁ 1 0 0 ▁sinnilaarlugit ▁inulik ▁sisimiut ▁kommunerig ... (+9 more)` | 19 |

**Sample 3:** `Kalaallit Arsaattartut Kattuffiat (KAK) kattuffiuvoq nunatsinni isikkammik arsaa...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁kalaallit ▁arsaattartut ▁kattuffiat ▁( k ak ) ▁kattuffi uvoq ▁nunatsinni ... (+14 more)` | 24 |
| 16k | `▁kalaallit ▁arsaattartut ▁kattuffiat ▁( k ak ) ▁kattuffiuvoq ▁nunatsinni ▁isikkammik ... (+11 more)` | 21 |
| 32k | `▁kalaallit ▁arsaattartut ▁kattuffiat ▁( kak ) ▁kattuffiuvoq ▁nunatsinni ▁isikkammik ▁arsaannermik ... (+9 more)` | 19 |


### Key Findings

- **Best Compression:** 32k achieves 6.102x compression
- **Lowest UNK Rate:** 8k with 0.1746% 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 | 93 🏆 | 6.54 | 112 | 94.2% | 100.0% |
| **2-gram** | Subword | 171 | 7.42 | 845 | 81.8% | 100.0% |
| **3-gram** | Word | 109 | 6.77 | 124 | 87.1% | 100.0% |
| **3-gram** | Subword | 1,043 | 10.03 | 4,548 | 34.8% | 87.9% |
| **4-gram** | Word | 211 | 7.72 | 238 | 55.6% | 100.0% |
| **4-gram** | Subword | 4,126 | 12.01 | 14,779 | 16.3% | 57.9% |
| **5-gram** | Word | 136 | 7.09 | 155 | 73.1% | 100.0% |
| **5-gram** | Subword | 9,582 | 13.23 | 24,277 | 9.5% | 37.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kalaallit nunaanni` | 63 |
| 2 | `nunat avannarliit` | 36 |
| 3 | `kalaallit nunaat` | 33 |
| 4 | `kalaallit nunaata` | 23 |
| 5 | `aamma takuuk` | 22 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nunat avannarliit siunnersuisoqatigiit` | 21 |
| 2 | `kommunerigaluani ilaasoq ullumikkut` | 14 |
| 3 | `animalia siuleriit chordata` | 12 |
| 4 | `250px kunngeqarfik animalia` | 12 |
| 5 | `chordata inuiaqatigiinni inissisimanerit` | 12 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `siuleriit chordata inuiaqatigiinni inissisimanerit` | 12 |
| 2 | `animalia siuleriit chordata inuiaqatigiinni` | 12 |
| 3 | `kunngeqarfik animalia siuleriit chordata` | 12 |
| 4 | `250px kunngeqarfik animalia siuleriit` | 12 |
| 5 | `chordata inuiaqatigiinni inissisimanerit mammalia` | 9 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `250px kunngeqarfik animalia siuleriit chordata` | 12 |
| 2 | `animalia siuleriit chordata inuiaqatigiinni inissisimanerit` | 12 |
| 3 | `kunngeqarfik animalia siuleriit chordata inuiaqatigiinni` | 12 |
| 4 | `siuleriit chordata inuiaqatigiinni inissisimanerit mammalia` | 9 |
| 5 | `chordata inuiaqatigiinni inissisimanerit mammalia tullerit` | 8 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a a` | 7,840 |
| 2 | `a r` | 7,296 |
| 3 | `t _` | 5,447 |
| 4 | `e r` | 5,172 |
| 5 | `i n` | 5,166 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u t _` | 2,403 |
| 2 | `q a r` | 2,155 |
| 3 | `n e r` | 2,064 |
| 4 | `i n n` | 1,849 |
| 5 | `i k _` | 1,811 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e q a r` | 1,246 |
| 2 | `n e q a` | 977 |
| 3 | `n u n a` | 811 |
| 4 | `_ n u n` | 797 |
| 5 | `n i k _` | 724 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n e q a r` | 834 |
| 2 | `_ n u n a` | 785 |
| 3 | `a a m m a` | 519 |
| 4 | `q a r f i` | 467 |
| 5 | `_ a a m m` | 454 |


### Key Findings

- **Best Perplexity:** 2-gram (word) with 93
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~38% 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 | 0.3534 | 1.278 | 1.74 | 13,585 | 64.7% |
| **1** | Subword | 1.7216 | 3.298 | 13.15 | 117 | 0.0% |
| **2** | Word | 0.0454 | 1.032 | 1.06 | 23,361 | 95.5% |
| **2** | Subword | 1.2971 | 2.457 | 5.98 | 1,535 | 0.0% |
| **3** | Word | 0.0111 | 1.008 | 1.01 | 24,552 | 98.9% |
| **3** | Subword | 0.8333 | 1.782 | 3.16 | 9,164 | 16.7% |
| **4** | Word | 0.0041 🏆 | 1.003 | 1.00 | 24,604 | 99.6% |
| **4** | Subword | 0.4968 | 1.411 | 2.00 | 28,935 | 50.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `aamma ilisimasanik suliaqarneq ilaqutariit myrmecophagidae uniaaluttuumasut vermilingua 250px kunnge...`
2. `kalaallit nunaanni namminersorlutik oqartussanit pigineqartut kni a big feeling aamma krati aqutsine...`
3. `1 kinaluunniit peqatigiiffimmi sumiluunniit ilaasotaanissamut pinngitsaalineqarsinnaanngilaq immikko...`

**Context Size 2:**

1. `kalaallit nunaanni kalaallit nunaanni namminersorlutik oqartussat pigisaat kni a s imut grønlandsfly...`
2. `nunat avannarliit naalakkersuisuini siunnersuisoqatigiit tassaasoq nunani avannarlerni oqaatsinut is...`
3. `kalaallit nunaat savalimmiut og åland ilu nunat avannarliit suleqatigiinneranni nunat avannarliit si...`

**Context Size 3:**

1. `nunat avannarliit siunnersuisoqatigiit ukiut tamaasa nersornaasiuttagai nunat avannarliit siunnersui...`
2. `kommunerigaluani ilaasoq ullumikkut kommuneqarfik sermersuumiittoq nunaat`
3. `chordata inuiaqatigiinni inissisimanerit mammalia tullerit perissodactyla ilatutariit equidae hiisti...`

**Context Size 4:**

1. `250px kunngeqarfik animalia siuleriit chordata inuiaqatigiinni inissisimanerit mammalia miluumasut t...`
2. `siuleriit chordata inuiaqatigiinni inissisimanerit aves tullerit anseriformes ilatutariit anatidae k...`
3. `animalia siuleriit chordata inuiaqatigiinni inissisimanerit mammalia tullerit perissodactyla ilatuta...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `arsisssernnsi_sa`
2. `inusit_atilaatiu`
3. `_ik_i_sartiga_is`

**Context Size 2:**

1. `aanngraellimaqisa`
2. `arsineaullut_taa.`
3. `t_elfebriarissitt`

**Context Size 3:**

1. `ut_tulu_ilimaffiga`
2. `qartoq_-_thagnhein`
3. `nermattoq._efrosma`

**Context Size 4:**

1. `eqarsimavoq_atorlu_`
2. `neqarluni._ilaq_nun`
3. `nunaanerpaat_"qitar`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (28,935 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 | 3,095 |
| Total Tokens | 15,574 |
| Mean Frequency | 5.03 |
| Median Frequency | 3 |
| Frequency Std Dev | 9.84 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | aamma | 346 |
| 2 | kalaallit | 170 |
| 3 | nunaat | 138 |
| 4 | 1 | 91 |
| 5 | soorlu | 84 |
| 6 | tassaavoq | 79 |
| 7 | nunaanni | 73 |
| 8 | nunat | 72 |
| 9 | the | 72 |
| 10 | aammalu | 71 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | triumph | 2 |
| 2 | shall | 2 |
| 3 | iluartut | 2 |
| 4 | ulluat | 2 |
| 5 | osmanniske | 2 |
| 6 | rige | 2 |
| 7 | annertusarsimavaa | 2 |
| 8 | anginersaq | 2 |
| 9 | hendrik | 2 |
| 10 | suersaq | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.7052 |
| R² (Goodness of Fit) | 0.973400 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.2% |
| Top 1,000 | 68.5% |
| Top 5,000 | 0.0% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9734 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.2% of corpus
- **Long Tail:** -6,905 words needed for remaining 100.0% 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 | 0.1725 | 0.4560 | N/A | N/A |
| **mono_64d** | 64 | 0.0238 | 0.4660 | N/A | N/A |
| **mono_128d** | 128 | 0.0021 | 0.4747 | N/A | N/A |
| **aligned_32d** | 32 | 0.1725 🏆 | 0.4619 | 0.0884 | 0.3946 |
| **aligned_64d** | 64 | 0.0238 | 0.4695 | 0.1224 | 0.4354 |
| **aligned_128d** | 128 | 0.0021 | 0.4829 | 0.1429 | 0.4422 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.1725 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4685. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 14.3% 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 | **1.639** | 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 |
|--------|----------|
| `-a` | attuumassuteqarput, annersaraat, atmosfære |
| `-i` | inganermi, ineriartortitsineq, inneruulaaraq |
| `-s` | siammasinnerusumik, seqernup, star |
| `-in` | inganermi, ineriartortitsineq, inneruulaaraq |
| `-si` | siammasinnerusumik, siulleq, sisimiunut |
| `-ta` | tassaneereerluni, tamaasa, taasarpaat |
| `-il` | illorsuit, ilusilersuisup, ilaanni |
| `-na` | naak, namminiinnarsortumik, nammineq |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-t` | qaammatit, attuumassuteqarput, annersaraat |
| `-ut` | attuumassuteqarput, meeqqanut, sakkut |
| `-q` | uumasoq, ineriartortitsineq, terianniaasaq |
| `-ik` | siammasinnerusumik, annertuumik, pissusaanik |
| `-i` | juuli, inganermi, qeqertarsuarmi |
| `-it` | qaammatit, sumiluunniit, illorsuit |
| `-k` | siammasinnerusumik, annertuumik, pissusaanik |
| `-oq` | uumasoq, nimeruaartoq, atorneqarpoq |

### 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 |
|------|----------|------------------|----------|
| `alla` | 1.56x | 18 contexts | allat, allaq, allani |
| `aani` | 1.56x | 13 contexts | maani, qaani, imaani |
| `ssaa` | 1.58x | 12 contexts | ssaat, assaat, missaa |
| `anna` | 1.53x | 12 contexts | manna, maanna, sannaa |
| `aann` | 1.39x | 15 contexts | maanna, taanna, ilaanni |
| `ullu` | 1.56x | 9 contexts | ullut, ullup, imullu |
| `atsi` | 1.40x | 12 contexts | tatsip, oqaatsit, aatsitaq |
| `nner` | 1.60x | 8 contexts | banner, sinneri, sinnera |
| `issa` | 1.56x | 8 contexts | missaa, missaat, timissat |
| `assa` | 1.63x | 7 contexts | tassa, assaat, nassaat |
| `oqar` | 1.88x | 5 contexts | inoqartoq, inoqarpoq, illoqarfia |
| `aqar` | 1.64x | 5 contexts | imaqarpoq, imaqartoq, nunaqarfii |

### 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 |
|--------|--------|-----------|----------|
| `-a` | `-t` | 137 words | attuumassuteqarput, annersaraat |
| `-i` | `-t` | 121 words | illorsuit, imit |
| `-a` | `-ut` | 70 words | attuumassuteqarput, atortut |
| `-i` | `-q` | 66 words | ineriartortitsineq, inneruulaaraq |
| `-i` | `-ut` | 66 words | inuutissarsiutitut, immikkoortut |
| `-s` | `-t` | 64 words | sumiluunniit, sakkut |
| `-a` | `-q` | 63 words | atorneqarpoq, aalisarneq |
| `-a` | `-k` | 54 words | annertuumik, aapasunik |
| `-a` | `-ik` | 52 words | annertuumik, aapasunik |
| `-i` | `-i` | 50 words | inganermi, ilaanni |

### 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 |
|------|-----------------|------------|------|
| pukkitsormiut | **`pukkitsor-mi-ut`** | 7.5 | `mi` |
| nunataata | **`nunata-at-a`** | 7.5 | `at` |
| kujataata | **`kujata-at-a`** | 7.5 | `at` |
| immikkoortuini | **`immikkoortu-i-ni`** | 7.5 | `i` |
| nutaarmiut | **`nutaar-mi-ut`** | 7.5 | `mi` |
| danmarkimilu | **`danmarki-mi-lu`** | 7.5 | `mi` |
| pingaarnersaata | **`pingaarnersa-at-a`** | 7.5 | `at` |
| piumasaqaatit | **`piumasaqa-at-it`** | 7.5 | `at` |
| avannarliit | **`avannarl-i-it`** | 7.5 | `i` |
| ikuallatat | **`ikuall-at-at`** | 7.5 | `at` |
| naalernerata | **`naalerner-at-a`** | 7.5 | `at` |
| qalipaataa | **`qalipa-at-aa`** | 7.5 | `at` |
| demokraatit | **`demokra-at-it`** | 7.5 | `at` |
| danmarkimit | **`danmarki-mi-t`** | 7.5 | `mi` |
| sananeranilu | **`sananera-ni-lu`** | 6.0 | `sananera` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Kalaallisut 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 | **32k BPE** | Best compression (6.10x) |
| N-gram | **2-gram** | Lowest perplexity (93) |
| Markov | **Context-4** | Highest predictability (99.6%) |
| 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 07:49:12*