---
language: gd
language_name: Scottish Gaelic
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: 4.255
  - name: best_isotropy
    type: isotropy
    value: 0.8836
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

# Scottish Gaelic - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Scottish Gaelic** 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** | 3.505x | 3.51 | 0.1554% | 361,085 |
| **16k** | 3.790x | 3.79 | 0.1680% | 333,933 |
| **32k** | 4.047x | 4.05 | 0.1794% | 312,732 |
| **64k** | 4.255x 🏆 | 4.26 | 0.1886% | 297,465 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Cleachdaidhean eile aig Cuach (soilleireachadh) 'S e baile ann an Contae Dhoire ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cleachdaidhean ▁eile ▁aig ▁cu ach ▁( s oilleir eachadh ) ... (+20 more)` | 30 |
| 16k | `▁cleachdaidhean ▁eile ▁aig ▁cuach ▁( soilleireachadh ) ▁' s ▁e ... (+16 more)` | 26 |
| 32k | `▁cleachdaidhean ▁eile ▁aig ▁cuach ▁( soilleireachadh ) ▁' s ▁e ... (+16 more)` | 26 |
| 64k | `▁cleachdaidhean ▁eile ▁aig ▁cuach ▁( soilleireachadh ) ▁' s ▁e ... (+16 more)` | 26 |

**Sample 2:** `Fang, feichid, preachan: eun a tha ag ithe beathaichean marbh. Tha sgòrnan fada ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁f ang , ▁fe ich id , ▁pr eachan : ... (+16 more)` | 26 |
| 16k | `▁f ang , ▁fe ich id , ▁pr eachan : ... (+15 more)` | 25 |
| 32k | `▁fang , ▁fe ich id , ▁pr eachan : ▁eun ... (+13 more)` | 23 |
| 64k | `▁fang , ▁fe ichid , ▁preachan : ▁eun ▁a ▁tha ... (+11 more)` | 21 |

**Sample 3:** `'S e bliadhna-leum a bha ann an (MLXXVI). Tachartasan Breithean Bàsan`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+8 more)` | 18 |
| 16k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+8 more)` | 18 |
| 32k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+7 more)` | 17 |
| 64k | `▁' s ▁e ▁bliadhna - leum ▁a ▁bha ▁ann ▁an ... (+7 more)` | 17 |


### Key Findings

- **Best Compression:** 64k achieves 4.255x compression
- **Lowest UNK Rate:** 8k with 0.1554% 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 | 7,513 | 12.88 | 45,521 | 23.1% | 48.4% |
| **2-gram** | Subword | 241 🏆 | 7.91 | 4,942 | 71.6% | 98.7% |
| **3-gram** | Word | 22,207 | 14.44 | 79,383 | 11.8% | 32.1% |
| **3-gram** | Subword | 1,855 | 10.86 | 33,559 | 33.3% | 74.9% |
| **4-gram** | Word | 49,301 | 15.59 | 146,615 | 8.5% | 23.6% |
| **4-gram** | Subword | 9,340 | 13.19 | 158,296 | 18.3% | 46.8% |
| **5-gram** | Word | 45,346 | 15.47 | 116,302 | 7.6% | 22.5% |
| **5-gram** | Subword | 29,576 | 14.85 | 374,322 | 11.3% | 32.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ann an` | 44,901 |
| 2 | `s e` | 15,127 |
| 3 | `na h` | 12,468 |
| 4 | `an t` | 11,551 |
| 5 | `a tha` | 10,609 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `na h alba` | 6,088 |
| 2 | `a th ann` | 4,967 |
| 3 | `a tha ann` | 4,917 |
| 4 | `ceanglaichean a mach` | 3,964 |
| 5 | `tha ann an` | 3,533 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a tha ann an` | 3,497 |
| 2 | `a th ann an` | 2,302 |
| 3 | `iomraidhean ceanglaichean a mach` | 2,128 |
| 4 | `a tha ann am` | 1,042 |
| 5 | `os cionn ìre na` | 1,011 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `os cionn ìre na mara` | 957 |
| 2 | `a rèir a chunntais shluaigh` | 730 |
| 3 | `an duais nobel ann an` | 688 |
| 4 | `a chunntais shluaigh ann an` | 668 |
| 5 | `rèir a chunntais shluaigh ann` | 667 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a` | 512,441 |
| 2 | `a n` | 416,454 |
| 3 | `n _` | 394,988 |
| 4 | `a i` | 315,323 |
| 5 | `c h` | 267,240 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n _` | 225,121 |
| 2 | `_ a n` | 207,360 |
| 3 | `a c h` | 122,355 |
| 4 | `n _ a` | 119,942 |
| 5 | `a n n` | 106,926 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a n _` | 121,672 |
| 2 | `_ a n n` | 77,613 |
| 3 | `a n n _` | 71,439 |
| 4 | `n n _ a` | 66,595 |
| 5 | `n _ a n` | 59,630 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n n _ a` | 59,213 |
| 2 | `_ a n n _` | 58,945 |
| 3 | `n _ a n _` | 50,924 |
| 4 | `n n _ a n` | 48,309 |
| 5 | `_ a g u s` | 39,355 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 241
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~32% 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 | 0.8527 | 1.806 | 5.97 | 117,662 | 14.7% |
| **1** | Subword | 0.8777 | 1.837 | 6.88 | 2,032 | 12.2% |
| **2** | Word | 0.2808 | 1.215 | 1.75 | 699,420 | 71.9% |
| **2** | Subword | 0.8889 | 1.852 | 5.20 | 13,963 | 11.1% |
| **3** | Word | 0.1273 | 1.092 | 1.27 | 1,221,448 | 87.3% |
| **3** | Subword | 0.7487 | 1.680 | 3.81 | 72,603 | 25.1% |
| **4** | Word | 0.0625 🏆 | 1.044 | 1.11 | 1,546,357 | 93.7% |
| **4** | Subword | 0.6229 | 1.540 | 2.73 | 276,636 | 37.7% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `an aghaidh poileasaidh airson na h uile dùinte a th ann an old man wins nobel`
2. `a tha denver na gàidhealtachd agus thogadh e dìreach ri bràthair agus tha co chruthachd còmhla`
3. `ann an t ainm oifigeil na h alba pàrlamaid à alba chlach ghràin a mhoncaidh lùchairt`

**Context Size 2:**

1. `ann an sealtainn eadar unst agus fetlar a tha ealantach cruthachail air cuan dubh drilseach bho n`
2. `s e 0 5 km 0 3 km 1 7 ha 4 7 acair s e am`
3. `na h alba a stiuireadh rugbaidh ann an altaibh air teicneòlasaibh mar eisimpleir theirear gun robh c...`

**Context Size 3:**

1. `na h alba a tha ann an càrn deas tha e ainmeil gus ar làithean lunds universitetchaochail an`
2. `a th ann an ainmean àite cuideachd mar eispimpleir sgùrr alasdair a bheinn as àirde ann an agri`
3. `a tha ann an sgoil air a bheil shambellie house trust iomraidhean na h eilbheise suidhichte ri taobh`

**Context Size 4:**

1. `a tha ann an diospròsium le samhla dy agus àireamh atamach 66 s e meatailt bog agus lantanach a`
2. `a th ann an chernihivska oblast ucràinis черні́гівська о́бласть ainm neo fhoirmeil khmelnychchyna s ...`
3. `iomraidhean ceanglaichean a mach dealbhan aig geograph org na h alba ann an arcaibh`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_botile_lbr.omin`
2. `achnnnnomzogheat`
3. `nnbhchùtiaseir_m`

**Context Size 2:**

1. `_an_logha_ghearai`
2. `an_na_daidhe_fhom`
3. `n_bh_a_'s_jonzoli`

**Context Size 3:**

1. `an_nan_breithrìomh`
2. `_an-riagh_sìos_(ga`
3. `ach_(pàrt_aireadh_`

**Context Size 4:**

1. `_an_àitean_cervus_e`
2. `_ann_an_ierus_cionn`
3. `ann_an_na_phàrtaidh`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (276,636 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 | 52,313 |
| Total Tokens | 2,168,944 |
| Mean Frequency | 41.46 |
| Median Frequency | 4 |
| Frequency Std Dev | 965.84 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | an | 124,281 |
| 2 | a | 122,798 |
| 3 | ann | 64,022 |
| 4 | na | 56,811 |
| 5 | e | 46,001 |
| 6 | tha | 39,597 |
| 7 | agus | 39,434 |
| 8 | air | 34,639 |
| 9 | s | 20,787 |
| 10 | am | 19,741 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | według | 2 |
| 2 | kodu | 2 |
| 3 | grup | 2 |
| 4 | zawodowych | 2 |
| 5 | sztuka | 2 |
| 6 | muzea | 2 |
| 7 | britishpedia | 2 |
| 8 | osobistości | 2 |
| 9 | bph | 2 |
| 10 | frightened | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1387 |
| R² (Goodness of Fit) | 0.997741 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 47.5% |
| Top 1,000 | 72.9% |
| Top 5,000 | 86.6% |
| Top 10,000 | 91.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9977 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 47.5% of corpus
- **Long Tail:** 42,313 words needed for remaining 8.6% 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 | 0.8836 | 0.3460 | N/A | N/A |
| **mono_64d** | 64 | 0.8732 | 0.2710 | N/A | N/A |
| **mono_128d** | 128 | 0.8209 | 0.2012 | N/A | N/A |
| **aligned_32d** | 32 | 0.8836 🏆 | 0.3541 | 0.0940 | 0.4500 |
| **aligned_64d** | 64 | 0.8732 | 0.2677 | 0.1360 | 0.4920 |
| **aligned_128d** | 128 | 0.8209 | 0.2012 | 0.2460 | 0.6360 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8836 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2735. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 24.6% 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 | **-0.299** | 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` | chlabhier, chraobh, chleachdaidhean |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | elfyn, newton, pàisdean |
| `-h` | dhiadhaidh, dhùnleibh, uralach |
| `-an` | pàisdean, seaghan, bliadhaichean |
| `-ch` | uralach, catailiseach, shealbhach |
| `-dh` | dhiadhaidh, tràghaidh, bhrathadh |
| `-ach` | uralach, catailiseach, shealbhach |
| `-ean` | pàisdean, bliadhaichean, bawean |
| `-adh` | bhrathadh, fòrladh, caochladh |

### 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 |
|------|----------|------------------|----------|
| `ilea` | 1.69x | 137 contexts | eilean, àilean, bileag |
| `irea` | 1.60x | 117 contexts | coirea, èireas, uiread |
| `aidh` | 1.48x | 165 contexts | taidh, uaidh, faidh |
| `raid` | 1.74x | 75 contexts | òraid, àraid, braid |
| `inne` | 1.47x | 158 contexts | rinne, tinne, inner |
| `reac` | 1.87x | 51 contexts | reach, breac, creach |
| `isea` | 1.53x | 112 contexts | isean, lùisea, misean |
| `ainn` | 1.61x | 81 contexts | uainn, rainn, lainn |
| `hean` | 1.74x | 56 contexts | bhean, shean, mhean |
| `bhai` | 1.45x | 112 contexts | bhain, bhail, ubhail |
| `hadh` | 2.17x | 20 contexts | achadh, chadha, iadhadh |
| `chai` | 1.45x | 89 contexts | chain, chaid, chair |

### 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` | `-h` | 75 words | choltach, chraoibh |
| `-ch` | `-n` | 62 words | chomharran, christiaan |
| `-ch` | `-ch` | 35 words | choltach, chòigeach |
| `-ch` | `-an` | 29 words | chomharran, christiaan |
| `-ch` | `-dh` | 29 words | chòmhradh, cheasnachadh |
| `-ch` | `-ach` | 23 words | choltach, chòigeach |
| `-ch` | `-ean` | 17 words | chomharraidhean, chlachairean |
| `-ch` | `-adh` | 17 words | chòmhradh, cheasnachadh |
| `-ch` | `-in` | 12 words | chruinnein, chaocháin |
| `-ch` | `-idh` | 12 words | chàraidh, chnagaidh |

### 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 |
|------|-----------------|------------|------|
| cruthachadh | **`cruth-ach-adh`** | 6.0 | `cruth` |
| teasachadh | **`teas-ach-adh`** | 6.0 | `teas` |
| blàthachadh | **`blàth-ach-adh`** | 6.0 | `blàth` |
| adhartachadh | **`adhart-ach-adh`** | 6.0 | `adhart` |
| srònachadh | **`sròn-ach-adh`** | 6.0 | `sròn` |
| ceàrnaidhean | **`ceàrna-idh-ean`** | 6.0 | `ceàrna` |
| ràitheachan | **`ràithe-ach-an`** | 6.0 | `ràithe` |
| itealachadh | **`iteal-ach-adh`** | 6.0 | `iteal` |
| ealainean | **`eala-in-ean`** | 6.0 | `eala` |
| chliathach | **`ch-liath-ach`** | 6.0 | `liath` |
| sinnsirean | **`sinnsir-ean`** | 4.5 | `sinnsir` |
| prionnsabalan | **`prionnsabal-an`** | 4.5 | `prionnsabal` |
| feumalachdan | **`feumalachd-an`** | 4.5 | `feumalachd` |
| sheinneadairean | **`sheinneadair-ean`** | 4.5 | `sheinneadair` |
| breitheamhan | **`breitheamh-an`** | 4.5 | `breitheamh` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Scottish Gaelic 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 (4.25x) |
| N-gram | **2-gram** | Lowest perplexity (241) |
| Markov | **Context-4** | Highest predictability (93.7%) |
| 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: 2026-01-04 15:23:34*