README.md

---
language: gv
language_name: Manx
language_family: celtic_goidelic
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-celtic_goidelic
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: 4.366
  - name: best_isotropy
    type: isotropy
    value: 0.8673
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Manx** 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** | 3.783x | 3.79 | 0.1096% | 245,339 |
| **16k** | 4.045x | 4.05 | 0.1173% | 229,410 |
| **32k** | 4.238x | 4.24 | 0.1229% | 218,965 |
| **64k** | 4.366x 🏆 | 4.37 | 0.1266% | 212,544 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `She nane jeh rheynnyn y Rank ee Mor-Bihan (). Ta'n rheynn soit 'sy Vritaan. y Ra...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁she ▁nane ▁jeh ▁rheynnyn ▁y ▁rank ▁ee ▁mor - bihan ... (+12 more)` | 22 |
| 16k | `▁she ▁nane ▁jeh ▁rheynnyn ▁y ▁rank ▁ee ▁mor - bihan ... (+12 more)` | 22 |
| 32k | `▁she ▁nane ▁jeh ▁rheynnyn ▁y ▁rank ▁ee ▁mor - bihan ... (+12 more)` | 22 |
| 64k | `▁she ▁nane ▁jeh ▁rheynnyn ▁y ▁rank ▁ee ▁mor - bihan ... (+12 more)` | 22 |

**Sample 2:** `Blein: - (MDCCCLVII) - Taghyrtyn Ruggyryn 15 Mean Fouyir - William H. Taft, 27oo...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁blein : ▁- ▁( mdcc cl vii ) ▁- ▁taghyrtyn ... (+25 more)` | 35 |
| 16k | `▁blein : ▁- ▁( mdcccl vii ) ▁- ▁taghyrtyn ▁ruggyryn ... (+24 more)` | 34 |
| 32k | `▁blein : ▁- ▁( mdcccl vii ) ▁- ▁taghyrtyn ▁ruggyryn ... (+23 more)` | 33 |
| 64k | `▁blein : ▁- ▁( mdccclvii ) ▁- ▁taghyrtyn ▁ruggyryn ▁ ... (+22 more)` | 32 |

**Sample 3:** `Feaillaghyn Taghyrtyn Ruggyryn Baaseyn Jerrey Geuree, 30 30`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁feaillaghyn ▁taghyrtyn ▁ruggyryn ▁baaseyn ▁jerrey ▁geuree , ▁ 3 0 ... (+3 more)` | 13 |
| 16k | `▁feaillaghyn ▁taghyrtyn ▁ruggyryn ▁baaseyn ▁jerrey ▁geuree , ▁ 3 0 ... (+3 more)` | 13 |
| 32k | `▁feaillaghyn ▁taghyrtyn ▁ruggyryn ▁baaseyn ▁jerrey ▁geuree , ▁ 3 0 ... (+3 more)` | 13 |
| 64k | `▁feaillaghyn ▁taghyrtyn ▁ruggyryn ▁baaseyn ▁jerrey ▁geuree , ▁ 3 0 ... (+3 more)` | 13 |


### Key Findings

- **Best Compression:** 64k achieves 4.366x compression
- **Lowest UNK Rate:** 8k with 0.1096% 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 | 8,764 | 13.10 | 27,165 | 17.3% | 42.4% |
| **2-gram** | Subword | 267 🏆 | 8.06 | 3,213 | 67.9% | 99.3% |
| **3-gram** | Word | 18,876 | 14.20 | 39,871 | 9.1% | 28.2% |
| **3-gram** | Subword | 2,139 | 11.06 | 23,013 | 26.3% | 72.8% |
| **4-gram** | Word | 32,610 | 14.99 | 58,839 | 6.7% | 21.0% |
| **4-gram** | Subword | 10,768 | 13.39 | 112,078 | 13.7% | 41.9% |
| **5-gram** | Word | 22,648 | 14.47 | 37,341 | 7.2% | 23.3% |
| **5-gram** | Subword | 32,659 | 15.00 | 257,320 | 8.0% | 28.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sy vlein` | 5,442 |
| 2 | `ta n` | 4,504 |
| 3 | `ny h` | 3,395 |
| 4 | `t eh` | 3,265 |
| 5 | `er y` | 2,744 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ny steatyn unnaneysit` | 1,092 |
| 2 | `imraaghyn kianglaghyn magh` | 1,051 |
| 3 | `sy vlein vio` | 912 |
| 4 | `y chooid smoo` | 815 |
| 5 | `sy vlein sy` | 753 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `sy vlein sy vlein` | 663 |
| 2 | `kianglaghyn magh sy vlein` | 600 |
| 3 | `magh sy vlein vio` | 492 |
| 4 | `son y chooid smoo` | 460 |
| 5 | `imraaghyn kianglaghyn magh sy` | 359 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `kianglaghyn magh sy vlein vio` | 489 |
| 2 | `imraaghyn kianglaghyn magh sy vlein` | 340 |
| 3 | `as thallooyn bunnit sy vlein` | 330 |
| 4 | `currit er cummaltee yn valley` | 210 |
| 5 | `ayns sheear hwoaie ny frank` | 191 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `n _` | 162,079 |
| 2 | `y _` | 140,625 |
| 3 | `g h` | 135,289 |
| 4 | `a g` | 129,114 |
| 5 | `y n` | 125,587 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a g h` | 115,774 |
| 2 | `y n _` | 80,040 |
| 3 | `g h _` | 63,973 |
| 4 | `e y _` | 47,584 |
| 5 | `_ a s` | 40,866 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a g h _` | 62,613 |
| 2 | `_ a s _` | 33,690 |
| 3 | `_ n y _` | 30,730 |
| 4 | `n a g h` | 26,067 |
| 5 | `_ a y n` | 22,053 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a y n s _` | 20,378 |
| 2 | `_ a y n s` | 20,257 |
| 3 | `n a g h _` | 19,764 |
| 4 | `_ ' s y _` | 13,703 |
| 5 | `a g h y n` | 11,504 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 267
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.9102 | 1.879 | 6.06 | 78,553 | 9.0% |
| **1** | Subword | 1.0148 | 2.021 | 7.60 | 1,229 | 0.0% |
| **2** | Word | 0.2842 | 1.218 | 1.71 | 474,494 | 71.6% |
| **2** | Subword | 0.8801 | 1.840 | 5.16 | 9,341 | 12.0% |
| **3** | Word | 0.1148 | 1.083 | 1.21 | 805,921 | 88.5% |
| **3** | Subword | 0.7972 | 1.738 | 4.02 | 48,186 | 20.3% |
| **4** | Word | 0.0492 🏆 | 1.035 | 1.08 | 971,794 | 95.1% |
| **4** | Subword | 0.6574 | 1.577 | 2.76 | 193,482 | 34.3% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `as chur undinyssyn argidoil ta n abbyrlhit romanagh çhengaghyn elley ayns pobblaght hoveidjagh va ca...`
2. `ny henn wheiggaghyn gorzów wielkopolski as y theihll slane ayns fockleyr aahoilshit ayns wilmington ...`
3. `y gogledd ny caslys syn ookraan saint cyndeyrn ap gwilym jenkins john hewlett packard johnny morris`

**Context Size 2:**

1. `sy vlein y reeriaght stiagh ayns e ynnyd fea jerrinagh ayns karacteyr aghteyr yn shayll ray kelly`
2. `ta n ennym eck ayns soilsheenyn çhellveeish as scannane yernagh lunnin as barrantee aachaptanys eche...`
3. `ny h ellanyn phillippeenagh maputo yn preeu valley tradishoonagh imraaghyn jesh chliaghtagh hostyn h...`

**Context Size 3:**

1. `ny steatyn unnaneysit lesh y talvador lesh y teer lesh y terb lesh yn ungaar caggee lesh y`
2. `imraaghyn kianglaghyn magh the deep photographic guide to the butterflies of britain and europe harp...`
3. `sy vlein vio firryn faaroagh`

**Context Size 4:**

1. `sy vlein sy vlein bentyn rish y chapitlaghys bentyn rish rheynn verçhys lesh adam smith classicagh t...`
2. `kianglaghyn magh sy vlein vio soccer firryn bretnagh wigan athletic f c bradford city a f c as wrexh...`
3. `magh sy vlein vio ass los angeles ass california fillym bwoirrin americaanagh fillym bwoirrin americ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_d-ots_c_l_sh_eb`
2. `ahlee)_bhtoiodas`
3. `eamh_y_owat_meee`

**Context Size 2:**

1. `n_huleanco-hagh_e`
2. `y_as_rush_veeal_a`
3. `ghticadjeant_momb`

**Context Size 3:**

1. `agh_drey-lettys_dy`
2. `yn_ec_y_romwelyn_e`
3. `gh_yn_eh_myr_ger_e`

**Context Size 4:**

1. `agh_treeockleyn_spo`
2. `_as_ontae_ghow_ee_s`
3. `_ny_griff_john_fock`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (193,482 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 | 35,254 |
| Total Tokens | 1,132,292 |
| Mean Frequency | 32.12 |
| Median Frequency | 4 |
| Frequency Std Dev | 426.46 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | as | 34,141 |
| 2 | ny | 31,248 |
| 3 | y | 29,520 |
| 4 | er | 22,963 |
| 5 | ayns | 20,469 |
| 6 | ta | 20,110 |
| 7 | yn | 17,952 |
| 8 | sy | 13,978 |
| 9 | n | 13,453 |
| 10 | eh | 12,232 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | alnair | 2 |
| 2 | rollageydyr | 2 |
| 3 | mirfak | 2 |
| 4 | notations | 2 |
| 5 | assembly | 2 |
| 6 | equulei | 2 |
| 7 | doradus | 2 |
| 8 | reticuli | 2 |
| 9 | sextantis | 2 |
| 10 | asteraghtyn | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1436 |
| R² (Goodness of Fit) | 0.995856 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 42.2% |
| Top 1,000 | 71.1% |
| Top 5,000 | 87.0% |
| Top 10,000 | 92.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9959 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 42.2% of corpus
- **Long Tail:** 25,254 words needed for remaining 7.6% 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 | 0.8673 | 0.3548 | N/A | N/A |
| **mono_64d** | 64 | 0.8292 | 0.2688 | N/A | N/A |
| **mono_128d** | 128 | 0.6512 | 0.2218 | N/A | N/A |
| **aligned_32d** | 32 | 0.8673 🏆 | 0.3561 | 0.0820 | 0.3820 |
| **aligned_64d** | 64 | 0.8292 | 0.2710 | 0.1420 | 0.4640 |
| **aligned_128d** | 128 | 0.6512 | 0.2269 | 0.1940 | 0.5460 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8673 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2832. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 19.4% 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 | **-0.175** | 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 |
|--------|----------|
| `-ch` | children, choontys, chartvelagh |
| `-co` | colleishyn, cooidjagh, conmhaícne |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | keirdlannyn, cullen, carradjeyn |
| `-yn` | keirdlannyn, carradjeyn, cluicyn |
| `-gh` | ennaghtagh, cooidjagh, frangagh |
| `-agh` | ennaghtagh, cooidjagh, frangagh |
| `-ey` | morrey, gerrey, unnaneyssey |
| `-er` | better, xavier, challenger |
| `-ys` | ghooghys, vraaraghys, choontys |

### 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 |
|------|----------|------------------|----------|
| `aghe` | 2.02x | 61 contexts | baghey, magher, baghee |
| `aghy` | 1.87x | 76 contexts | aghyn, baghyl, daghyr |
| `lley` | 1.88x | 72 contexts | ulley, olley, alley |
| `ghey` | 1.92x | 42 contexts | gheyr, baghey, gheyre |
| `llag` | 1.57x | 90 contexts | ollagh, kallag, mollag |
| `anag` | 1.78x | 47 contexts | anagh, ganagh, managh |
| `eeag` | 1.76x | 46 contexts | eeagh, veeagh, keeagh |
| `eagh` | 1.49x | 89 contexts | reagh, leagh, eaght |
| `lagh` | 1.48x | 90 contexts | clagh, glagh, aalagh |
| `rrey` | 1.75x | 41 contexts | arrey, murrey, girrey |
| `aagh` | 1.58x | 55 contexts | saagh, haagh, aaght |
| `erre` | 1.83x | 24 contexts | erree, merre, terre |

### 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 |
|--------|--------|-----------|----------|
| `-ch` | `-n` | 49 words | chragheyderyn, chapman |
| `-ch` | `-gh` | 40 words | chlogh, chollaigh |
| `-co` | `-n` | 38 words | coloin, collooghyn |
| `-ch` | `-agh` | 36 words | charolingagh, chondaigagh |
| `-co` | `-gh` | 30 words | cosmaidagh, corralagh |
| `-co` | `-yn` | 28 words | collooghyn, cocoonyn |
| `-co` | `-agh` | 26 words | cosmaidagh, corralagh |
| `-ch` | `-yn` | 23 words | chragheyderyn, cheirdyn |
| `-ch` | `-ey` | 15 words | chohirrey, chiangley |
| `-ch` | `-er` | 11 words | chooidjeyder, character |

### 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 |
|------|-----------------|------------|------|
| shennaghyn | **`shenn-agh-yn`** | 6.0 | `shenn` |
| mishaghey | **`mish-agh-ey`** | 6.0 | `mish` |
| nieuaghey | **`nieu-agh-ey`** | 6.0 | `nieu` |
| strooghyn | **`stroo-gh-yn`** | 6.0 | `stroo` |
| buighaghey | **`buigh-agh-ey`** | 6.0 | `buigh` |
| çhynskylaghey | **`çhynskyl-agh-ey`** | 6.0 | `çhynskyl` |
| troailtaghey | **`troailt-agh-ey`** | 6.0 | `troailt` |
| cruinnaghyn | **`cruinn-agh-yn`** | 6.0 | `cruinn` |
| skeayllaghyn | **`skeayll-agh-yn`** | 6.0 | `skeayll` |
| obbyraghyn | **`obbyr-agh-yn`** | 6.0 | `obbyr` |
| cohoyrtagh | **`co-hoyrt-agh`** | 6.0 | `hoyrt` |
| coheshaghtys | **`co-heshaght-ys`** | 6.0 | `heshaght` |
| sheelaghey | **`sheel-agh-ey`** | 6.0 | `sheel` |
| moanaghey | **`moan-agh-ey`** | 6.0 | `moan` |
| skynnaghyn | **`skynn-agh-yn`** | 6.0 | `skynn` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Manx 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 (4.37x) |
| N-gram | **2-gram** | Lowest perplexity (267) |
| Markov | **Context-4** | Highest predictability (95.1%) |
| 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 00:44:21*