---
language: smn
language_name: Inari 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: 4.507
  - name: best_isotropy
    type: isotropy
    value: 0.8392
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Inari 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** | 3.409x | 3.41 | 0.2072% | 253,414 |
| **16k** | 3.817x | 3.82 | 0.2320% | 226,314 |
| **32k** | 4.186x | 4.19 | 0.2544% | 206,349 |
| **64k** | 4.507x 🏆 | 4.51 | 0.2739% | 191,652 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `(MCCCXC) lâi normaalihe, mii aalgij já nuuvâi juliaanlâš kalender mield lávurduv...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁( mccc xc ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 16k | `▁( mccc xc ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 32k | `▁( mccc xc ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 64k | `▁( mccc xc ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |

**Sample 2:** `(MDXLIII) lâi normaalihe, mii aalgij já nuuvâi juliaanlâš kalender mield vuossaa...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁( md x lii i ) ▁lâi ▁normaalihe , ▁mii ... (+18 more)` | 28 |
| 16k | `▁( mdx liii ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 32k | `▁( mdx liii ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 64k | `▁( mdx liii ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |

**Sample 3:** `(MCCL) lâi normaalihe, mii aalgij já nuuvâi juliaanlâš kalender mield lávurduv. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁( mcc l ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 16k | `▁( mcc l ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 32k | `▁( mcc l ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |
| 64k | `▁( mcc l ) ▁lâi ▁normaalihe , ▁mii ▁aalgij ▁já ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 64k achieves 4.507x compression
- **Lowest UNK Rate:** 8k with 0.2072% 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 | 7,928 | 12.95 | 21,306 | 16.4% | 40.6% |
| **2-gram** | Subword | 438 🏆 | 8.78 | 3,597 | 52.7% | 98.5% |
| **3-gram** | Word | 12,010 | 13.55 | 31,830 | 14.7% | 35.6% |
| **3-gram** | Subword | 4,149 | 12.02 | 29,729 | 16.8% | 56.6% |
| **4-gram** | Word | 25,724 | 14.65 | 62,360 | 10.1% | 27.6% |
| **4-gram** | Subword | 21,915 | 14.42 | 158,183 | 9.5% | 30.7% |
| **5-gram** | Word | 22,379 | 14.45 | 49,308 | 9.2% | 27.8% |
| **5-gram** | Subword | 62,537 | 15.93 | 398,267 | 7.2% | 23.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `c g` | 5,252 |
| 2 | `eres soojijn` | 3,088 |
| 3 | `fáádást eres` | 3,076 |
| 4 | `soojijn käldeeh` | 2,451 |
| 5 | `kalender mield` | 1,682 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `fáádást eres soojijn` | 3,076 |
| 2 | `eres soojijn käldeeh` | 2,451 |
| 3 | `ton vijđodâh lii` | 890 |
| 4 | `juliaanlâš kalender mield` | 860 |
| 5 | `peivimeeri ij tiäđust` | 853 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `fáádást eres soojijn käldeeh` | 2,449 |
| 2 | `tärhis peivimeeri ij tiäđust` | 852 |
| 3 | `normaalihe mii aalgij já` | 638 |
| 4 | `aalgij já nuuvâi juliaanlâš` | 638 |
| 5 | `lâi normaalihe mii aalgij` | 638 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `já nuuvâi juliaanlâš kalender mield` | 638 |
| 2 | `lâi normaalihe mii aalgij já` | 638 |
| 3 | `mii aalgij já nuuvâi juliaanlâš` | 638 |
| 4 | `aalgij já nuuvâi juliaanlâš kalender` | 638 |
| 5 | `normaalihe mii aalgij já nuuvâi` | 638 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `i _` | 96,176 |
| 2 | `. _` | 92,482 |
| 3 | `s t` | 89,805 |
| 4 | `_ k` | 87,039 |
| 5 | `, _` | 79,601 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `m á á` | 37,873 |
| 2 | `á n u` | 37,015 |
| 3 | `á á n` | 36,800 |
| 4 | `n u _` | 33,090 |
| 5 | `j á _` | 29,034 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `m á á n` | 36,631 |
| 2 | `á á n u` | 36,485 |
| 3 | `á n u _` | 32,803 |
| 4 | `_ j á _` | 27,818 |
| 5 | `l i i _` | 17,588 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `m á á n u` | 36,472 |
| 2 | `á á n u _` | 32,800 |
| 3 | `_ l i i _` | 16,341 |
| 4 | `â m á á n` | 14,304 |
| 5 | `i m á á n` | 12,187 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 438
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~23% 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 | 0.6940 | 1.618 | 4.01 | 131,617 | 30.6% |
| **1** | Subword | 0.7277 | 1.656 | 5.59 | 1,828 | 27.2% |
| **2** | Word | 0.1805 | 1.133 | 1.39 | 526,458 | 82.0% |
| **2** | Subword | 0.8394 | 1.789 | 5.35 | 10,216 | 16.1% |
| **3** | Word | 0.0654 | 1.046 | 1.12 | 728,322 | 93.5% |
| **3** | Subword | 0.8706 | 1.828 | 4.46 | 54,674 | 12.9% |
| **4** | Word | 0.0361 🏆 | 1.025 | 1.06 | 814,752 | 96.4% |
| **4** | Subword | 0.7207 | 1.648 | 2.98 | 243,936 | 27.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `já suu käälis mikko manner petteri niva škovlâ lâi 1 2 ella kesimáánu kesimáánu 12 peivi`
2. `lii šoddâm syemmilâš musikkár jämimeh njuhčâmáánu 25 peeivi guo wei kiinalaš kiäisár iivij čyeđeh ha...`
3. `ive rääjist fáádást eres soojijn the colour inside daisy strand stubböle torbacka tvära vormö väster...`

**Context Size 2:**

1. `c g mycetophila illita freeman c g leptochilus fuscipes gusenleitner c g polypedilum luteum forsyth ...`
2. `eres soojijn käldeeh 3`
3. `fáádást eres soojijn nevala puoh kištoh käldeeh šoddâmeh nisonij jyelgipállueennâmjuávkku táppái taa...`

**Context Size 3:**

1. `fáádást eres soojijn käldeeh šoddâmeh olmoošvuoigâdvuotâpiälušteijeeh vyeitteeh vyeitteeh`
2. `eres soojijn käldeeh ovdiih kieldah siijdah`
3. `ton vijđodâh lii 76 66 km já alodâh 777 m arquata del tronto naaburkieldah láá accumoli acquasanta t...`

**Context Size 4:**

1. `fáádást eres soojijn käldeeh 7`
2. `tärhis peivimeeri ij tiäđust eennâm tuárgistij korrâsávt erzincanist tuurkist eennâmtuárgástâs inten...`
3. `nuuvâi juliaanlâš kalender mield lávurduv tot lâi kuuđâd ihe tábáhtusah kuovâmáánu kuovâmáánu 5 peei...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pypovâlimivuonâ`
2. `iiastrerooráávej`
3. `enussazd_m_airir`

**Context Size 2:**

1. `i_19_58_ivi).saal`
2. `._kij_yorsimáid._`
3. `stiláástaal,_kuov`

**Context Size 3:**

1. `máánu_7._skylä_jam`
2. `ánu_vuotâ_reenny_v`
3. `áánu_9._peeicinen,`

**Context Size 4:**

1. `máánu_22._čohčâmáán`
2. `áánu_25._vyesimáánu`
3. `ánu_52_säänis_njälm`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (243,936 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 | 56,543 |
| Total Tokens | 980,163 |
| Mean Frequency | 17.33 |
| Median Frequency | 3 |
| Frequency Std Dev | 192.38 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | já | 27,834 |
| 2 | lii | 16,486 |
| 3 | ive | 10,270 |
| 4 | peeivi | 7,716 |
| 5 | the | 7,233 |
| 6 | lâi | 7,177 |
| 7 | láá | 6,710 |
| 8 | käldeeh | 6,475 |
| 9 | g | 5,865 |
| 10 | c | 5,828 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | kelemeny | 2 |
| 2 | animaatiorááiđuh | 2 |
| 3 | ámátteh | 2 |
| 4 | geävrrie | 2 |
| 5 | smiths | 2 |
| 6 | ringettest | 2 |
| 7 | moolâvaavtâin | 2 |
| 8 | gloucester | 2 |
| 9 | nuorttâjuávkku | 2 |
| 10 | lovoiguin | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9814 |
| R² (Goodness of Fit) | 0.998205 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 30.6% |
| Top 1,000 | 56.7% |
| Top 5,000 | 74.6% |
| Top 10,000 | 82.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9982 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 30.6% of corpus
- **Long Tail:** 46,543 words needed for remaining 17.5% 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 | 0.8392 | 0.3414 | N/A | N/A |
| **mono_64d** | 64 | 0.6621 | 0.2951 | N/A | N/A |
| **mono_128d** | 128 | 0.2154 | 0.2973 | N/A | N/A |
| **aligned_32d** | 32 | 0.8392 🏆 | 0.3374 | 0.0360 | 0.2520 |
| **aligned_64d** | 64 | 0.6621 | 0.3047 | 0.0580 | 0.3280 |
| **aligned_128d** | 128 | 0.2154 | 0.2807 | 0.0940 | 0.3760 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8392 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3094. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 9.4% 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 | **0.195** | 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` | saksofonist, soldiers, studente |
| `-k` | kajanân, kirjetárukielân, kirvesmies |
| `-t` | tac, treat, tena |
| `-p` | persialuovtâ, petri, puovttijn |
| `-m` | myeongjong, máinusist, manchester |
| `-a` | attenuata, argonaut, acme |
| `-l` | longobardlâš, luándutile, lista |
| `-r` | roovvâdmáánu, ruttâdemeennâm, ruttâdmist |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | kajanân, puovttijn, kirjetárukielân |
| `-i` | petri, peltoinlahti, ozi |
| `-t` | saksofonist, máinusist, ruttâdmist |
| `-st` | saksofonist, máinusist, ruttâdmist |
| `-a` | nabda, båtsmora, guerra |
| `-s` | soldiers, neomys, ils |
| `-e` | studente, courte, oovce |
| `-h` | äddejeh, väärialodâh, underneath |

### 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 |
|------|----------|------------------|----------|
| `ielâ` | 1.89x | 19 contexts | šielâ, kielâ, mielâ |
| `ield` | 1.75x | 22 contexts | field, mield, mielde |
| `kiel` | 1.63x | 27 contexts | kielâ, kiela, kieli |
| `kirj` | 1.80x | 17 contexts | kirja, kirje, kirjed |
| `kuáv` | 2.00x | 12 contexts | kuávlu, kuávžur, kuávsui |
| `miel` | 1.82x | 12 contexts | mieli, mield, mielâ |
| `kaav` | 1.81x | 11 contexts | kaavi, kaava, kaavio |
| `staa` | 1.70x | 13 contexts | gstaad, staalu, staađâ |
| `llee` | 1.53x | 16 contexts | ellee, elleeh, lällee |
| `vtâs` | 1.65x | 11 contexts | laavtâs, piivtâs, oovtâst |
| `ijee` | 1.71x | 9 contexts | räijee, leijee, saijeed |
| `ovtâ` | 1.71x | 9 contexts | ovtâi, oovtâ, moovtâ |

### 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` | `-i` | 99 words | kođoääigi, kuorgâi |
| `-k` | `-a` | 85 words | klaipėda, kerola |
| `-s` | `-n` | 80 words | söderudden, superman |
| `-p` | `-n` | 76 words | pin, palestiin |
| `-k` | `-n` | 74 words | kaandâin, kotimaisten |
| `-m` | `-i` | 69 words | majniemi, muusiksyergi |
| `-s` | `-a` | 65 words | selänoja, sigādtsiga |
| `-m` | `-n` | 63 words | moiguin, mcpherson |
| `-t` | `-n` | 61 words | torjuin, tiipšon |
| `-k` | `-t` | 60 words | kertomukset, koirat |

### 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 |
|------|-----------------|------------|------|
| kunâgâliih | **`kunâgâl-i-ih`** | 7.5 | `i` |
| sisašijminister | **`sisašijmini-st-er`** | 7.5 | `st` |
| anthomyia | **`anthomy-i-a`** | 7.5 | `i` |
| historjáliih | **`historjál-i-ih`** | 7.5 | `i` |
| miänástus | **`miäná-st-us`** | 7.5 | `st` |
| kieldâlisto | **`kieldâli-st-o`** | 7.5 | `st` |
| tuulosist | **`tuulos-i-st`** | 7.5 | `i` |
| spiekâsteh | **`spiekâ-st-eh`** | 7.5 | `st` |
| uđđâivemáánuio | **`uđđâivemáánu-i-o`** | 7.5 | `i` |
| čuávumist | **`čuávu-mi-st`** | 7.5 | `mi` |
| uásálisteh | **`uásáli-st-eh`** | 7.5 | `st` |
| journalists | **`journali-st-s`** | 7.5 | `st` |
| faithless | **`faithle-s-s`** | 7.5 | `s` |
| leppäranta | **`leppära-n-ta`** | 7.5 | `n` |
| silbâmitalistân | **`silbâmitali-st-ân`** | 7.5 | `st` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Inari Sami 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 (4.51x) |
| N-gram | **2-gram** | Lowest perplexity (438) |
| Markov | **Context-4** | Highest predictability (96.4%) |
| 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 21:29:57*