---
language: sco
language_name: Scots
language_family: germanic_west_anglofrisian
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-germanic_west_anglofrisian
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: 4.412
  - name: best_isotropy
    type: isotropy
    value: 0.8628
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Scots** 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** | 3.617x | 3.62 | 0.0092% | 577,294 |
| **16k** | 3.956x | 3.96 | 0.0100% | 527,731 |
| **32k** | 4.216x | 4.22 | 0.0107% | 495,233 |
| **64k** | 4.412x 🏆 | 4.41 | 0.0112% | 473,222 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `La Cruz is a smaw ceety in the Mexican state o Sinaloa. The ceety reportit 15,65...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁la ▁cruz ▁is ▁a ▁smaw ▁ceety ▁in ▁the ▁mexican ▁state ... (+26 more)` | 36 |
| 16k | `▁la ▁cruz ▁is ▁a ▁smaw ▁ceety ▁in ▁the ▁mexican ▁state ... (+22 more)` | 32 |
| 32k | `▁la ▁cruz ▁is ▁a ▁smaw ▁ceety ▁in ▁the ▁mexican ▁state ... (+22 more)` | 32 |
| 64k | `▁la ▁cruz ▁is ▁a ▁smaw ▁ceety ▁in ▁the ▁mexican ▁state ... (+22 more)` | 32 |

**Sample 2:** `Navalafuente is a municipality o the Commonty o Madrid, Spain. Freemit airtins i...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁naval af u ente ▁is ▁a ▁municipality ▁o ▁the ▁commonty ... (+18 more)` | 28 |
| 16k | `▁naval af u ente ▁is ▁a ▁municipality ▁o ▁the ▁commonty ... (+18 more)` | 28 |
| 32k | `▁naval af u ente ▁is ▁a ▁municipality ▁o ▁the ▁commonty ... (+18 more)` | 28 |
| 64k | `▁naval afu ente ▁is ▁a ▁municipality ▁o ▁the ▁commonty ▁o ... (+17 more)` | 27 |

**Sample 3:** `Magnetite is a rock mineral an ane o the main airn ures. References minerals gro...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁magn et ite ▁is ▁a ▁rock ▁mineral ▁an ▁ane ▁o ... (+24 more)` | 34 |
| 16k | `▁magnet ite ▁is ▁a ▁rock ▁mineral ▁an ▁ane ▁o ▁the ... (+20 more)` | 30 |
| 32k | `▁magnet ite ▁is ▁a ▁rock ▁mineral ▁an ▁ane ▁o ▁the ... (+18 more)` | 28 |
| 64k | `▁magnetite ▁is ▁a ▁rock ▁mineral ▁an ▁ane ▁o ▁the ▁main ... (+14 more)` | 24 |


### Key Findings

- **Best Compression:** 64k achieves 4.412x compression
- **Lowest UNK Rate:** 8k with 0.0092% 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 | 26,453 | 14.69 | 140,557 | 16.0% | 32.2% |
| **2-gram** | Subword | 271 🏆 | 8.08 | 7,416 | 67.7% | 99.0% |
| **3-gram** | Word | 72,001 | 16.14 | 210,013 | 7.3% | 19.9% |
| **3-gram** | Subword | 2,416 | 11.24 | 51,687 | 25.6% | 69.9% |
| **4-gram** | Word | 131,079 | 17.00 | 309,274 | 5.1% | 14.5% |
| **4-gram** | Subword | 14,275 | 13.80 | 273,093 | 12.8% | 37.3% |
| **5-gram** | Word | 95,213 | 16.54 | 199,412 | 4.7% | 15.0% |
| **5-gram** | Subword | 54,670 | 15.74 | 795,931 | 8.2% | 24.3% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `o the` | 83,237 |
| 2 | `in the` | 58,596 |
| 3 | `is a` | 24,631 |
| 4 | `tae the` | 17,805 |
| 5 | `an the` | 13,525 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ane o the` | 5,732 |
| 2 | `references freemit airtins` | 4,456 |
| 3 | `the unitit states` | 4,149 |
| 4 | `pairt o the` | 4,120 |
| 5 | `the province o` | 3,589 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `in the province o` | 2,669 |
| 2 | `o the order o` | 2,501 |
| 3 | `is ane o the` | 2,083 |
| 4 | `is a toun an` | 1,707 |
| 5 | `o the unitit states` | 1,656 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `is a toun an municipality` | 1,214 |
| 2 | `o the order o the` | 1,192 |
| 3 | `a toun an municipality in` | 966 |
| 4 | `as o the municipality haed` | 846 |
| 5 | `o the municipality haed a` | 784 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 1,050,184 |
| 2 | `n _` | 810,931 |
| 3 | `s _` | 775,649 |
| 4 | `_ t` | 732,959 |
| 5 | `_ a` | 719,183 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t h` | 504,310 |
| 2 | `t h e` | 474,947 |
| 3 | `h e _` | 449,929 |
| 4 | `i n _` | 295,599 |
| 5 | `_ o _` | 271,843 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t h e` | 434,137 |
| 2 | `t h e _` | 428,262 |
| 3 | `_ i n _` | 189,422 |
| 4 | `_ a n _` | 173,723 |
| 5 | `n _ t h` | 114,460 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ t h e _` | 418,560 |
| 2 | `n _ t h e` | 105,154 |
| 3 | `_ o _ t h` | 87,165 |
| 4 | `o _ t h e` | 85,549 |
| 5 | `i n _ t h` | 75,907 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 271
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 0.9277 | 1.902 | 8.10 | 272,309 | 7.2% |
| **1** | Subword | 1.0662 | 2.094 | 6.39 | 4,231 | 0.0% |
| **2** | Word | 0.3124 | 1.242 | 1.88 | 2,201,132 | 68.8% |
| **2** | Subword | 0.7253 | 1.653 | 4.46 | 27,028 | 27.5% |
| **3** | Word | 0.1197 | 1.086 | 1.24 | 4,131,130 | 88.0% |
| **3** | Subword | 0.7329 | 1.662 | 3.98 | 120,570 | 26.7% |
| **4** | Word | 0.0487 🏆 | 1.034 | 1.08 | 5,105,427 | 95.1% |
| **4** | Subword | 0.6942 | 1.618 | 3.19 | 479,292 | 30.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `the order of seduction dos veadeirosalto paraíso borbotón la revolucion in the distance rinners male...`
2. `o san juan mixtepec mixteca region in bages on the horizontal cross o the various schuils`
3. `in coonty yintian toun the aurie which led mission in australie seestem in its headquarters head`

**Context Size 2:**

1. `o the ceety o madrid an the van province is subdividit intae cantons municipality inhabitants seat l...`
2. `in the places mentionit in the savinja statistical region name the divide atween the an gan yavne`
3. `is a roushie mid size hatchback caur frae components made frae its oreeginal name o an alternate`

**Context Size 3:**

1. `ane o the maist strangest player frae osaka in the throu efter the incorporation o ford saf intae`
2. `references freemit airtins honda warldwide steid honda press library japanese but wi graphical timel...`
3. `pairt o the province o cuenca cuenca spaingie congress electoral destrict the commune is still no re...`

**Context Size 4:**

1. `in the province o tarragona vilanova de sau toun in the province o enna references`
2. `o the order o the aztec eagle o the order o meerit o the federal republic o germany o`
3. `is ane o the original thirteen states the caipital o massachusetts is boston that is an aw the tradi...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_an's_sir_r_cs-g`
2. `ee_t_te_tenti_in`
3. `aprenrothsicanin`

**Context Size 2:**

1. `e_licturichypence`
2. `n_the_uniage_spe_`
3. `s_st_rompion_kerm`

**Context Size 3:**

1. `_the_samate_voyar,`
2. `the_umwhilocht-sou`
3. `he_cries_airty_o_r`

**Context Size 4:**

1. `_the_elemen_wumman_`
2. `the_elemen's_pols_p`
3. `_in_as_the_municipa`


### 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 (479,292 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 | 123,249 |
| Total Tokens | 6,164,921 |
| Mean Frequency | 50.02 |
| Median Frequency | 4 |
| Frequency Std Dev | 1749.35 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | the | 427,737 |
| 2 | o | 273,854 |
| 3 | in | 193,597 |
| 4 | an | 176,125 |
| 5 | a | 119,842 |
| 6 | is | 93,570 |
| 7 | tae | 70,765 |
| 8 | wis | 49,082 |
| 9 | as | 41,842 |
| 10 | frae | 34,119 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | erlier | 2 |
| 2 | margules | 2 |
| 3 | lifshitz | 2 |
| 4 | lakeith | 2 |
| 5 | exploder | 2 |
| 6 | fipresci | 2 |
| 7 | zubeen | 2 |
| 8 | beutel | 2 |
| 9 | badmen | 2 |
| 10 | taggert | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0502 |
| R² (Goodness of Fit) | 0.993417 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.5% |
| Top 1,000 | 63.1% |
| Top 5,000 | 80.2% |
| Top 10,000 | 86.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9934 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.5% of corpus
- **Long Tail:** 113,249 words needed for remaining 13.5% 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 | 0.8628 | 0.3487 | N/A | N/A |
| **mono_64d** | 64 | 0.8453 | 0.2622 | N/A | N/A |
| **mono_128d** | 128 | 0.8330 | 0.1921 | N/A | N/A |
| **aligned_32d** | 32 | 0.8628 🏆 | 0.3373 | 0.4500 | 0.8320 |
| **aligned_64d** | 64 | 0.8453 | 0.2597 | 0.6080 | 0.8960 |
| **aligned_128d** | 128 | 0.8330 | 0.1921 | 0.7060 | 0.9300 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8628 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2653. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 70.6% 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 | **-0.383** | 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` | sts, sables, safar |
| `-a` | armature, abkhazians, ald |
| `-ma` | mazīnān, manar, materazzi |
| `-b` | breid, blume, birnie |
| `-m` | mazīnān, michelangelos, mcqueers |
| `-t` | tu, tsugaru, tezuka |
| `-c` | cuiverin, coontin, ceasefire |
| `-p` | phrase, padmore, polje |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | sts, michelangelos, mcqueers |
| `-n` | cuiverin, mazīnān, focusin |
| `-e` | phrase, padmore, neale |
| `-a` | donnacona, tezuka, camara |
| `-t` | hjärtat, insicht, 145t |
| `-y` | validity, climatology, horthy |
| `-d` | ootsauld, breid, liquidated |
| `-es` | sables, straddles, charlottes |

### 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 |
|------|----------|------------------|----------|
| `eren` | 2.02x | 57 contexts | keren, ferenc, kerend |
| `ment` | 1.63x | 93 contexts | menta, ament, amenta |
| `stri` | 1.63x | 89 contexts | strid, strix, strip |
| `tric` | 1.59x | 71 contexts | trick, nitric, strict |
| `atio` | 1.62x | 56 contexts | patio, ratio, cation |
| `atit` | 1.67x | 45 contexts | datit, fatit, matit |
| `tion` | 1.45x | 78 contexts | cation, nation, action |
| `estr` | 1.56x | 56 contexts | bestry, vestry, sestra |
| `alit` | 1.61x | 40 contexts | alita, balita, kalita |
| `ence` | 1.64x | 37 contexts | fence, pence, dence |
| `renc` | 1.73x | 27 contexts | renca, ferenc, french |
| `dest` | 1.66x | 27 contexts | modest, oldest, widest |

### 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 |
|--------|--------|-----------|----------|
| `-c` | `-s` | 129 words | cuevas, colorless |
| `-a` | `-s` | 95 words | awaurness, aigeiroúses |
| `-s` | `-s` | 94 words | sanctions, skippers |
| `-p` | `-s` | 89 words | prowess, pairtisans |
| `-s` | `-n` | 89 words | samson, sudan |
| `-c` | `-n` | 64 words | copulation, caryn |
| `-s` | `-e` | 61 words | sparse, suerte |
| `-a` | `-e` | 60 words | airsie, australie |
| `-t` | `-s` | 55 words | termales, trumpeters |
| `-m` | `-s` | 54 words | makarios, montañas |

### 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 |
|------|-----------------|------------|------|
| freistaat | **`freista-a-t`** | 7.5 | `a` |
| ovulators | **`ovulat-o-rs`** | 7.5 | `o` |
| cardenden | **`carden-d-en`** | 7.5 | `d` |
| auldgirth | **`auldgir-t-h`** | 7.5 | `t` |
| islamists | **`islami-s-ts`** | 7.5 | `s` |
| steamboats | **`steambo-a-ts`** | 7.5 | `a` |
| spulyiein | **`spulyi-e-in`** | 7.5 | `e` |
| carrascosa | **`carrasco-s-a`** | 7.5 | `s` |
| armizonsky | **`armizon-s-ky`** | 7.5 | `s` |
| wiktionary | **`wiktion-ar-y`** | 7.5 | `ar` |
| sundsvall | **`sundsv-al-l`** | 7.5 | `al` |
| eventually | **`eventu-al-ly`** | 7.5 | `al` |
| montesson | **`montes-s-on`** | 7.5 | `s` |
| lifeboats | **`lifebo-a-ts`** | 7.5 | `a` |
| kindersley | **`kinders-le-y`** | 7.5 | `le` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Scots 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 (4.41x) |
| N-gram | **2-gram** | Lowest perplexity (271) |
| 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 20:17:20*