---
language: ga
language_name: Irish
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: 4.595
  - name: best_isotropy
    type: isotropy
    value: 0.8459
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-09
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Irish** 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** | 3.807x | 3.81 | 0.1479% | 836,105 |
| **16k** | 4.135x | 4.14 | 0.1607% | 769,705 |
| **32k** | 4.402x | 4.40 | 0.1711% | 723,137 |
| **64k** | 4.595x 🏆 | 4.60 | 0.1786% | 692,774 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Is baile suite i gContae an Longfoirt é Caonach. Tagairtí i gContae an Longfoirt`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁is ▁baile ▁suite ▁i ▁gcontae ▁an ▁longfoirt ▁é ▁cao nach ... (+6 more)` | 16 |
| 16k | `▁is ▁baile ▁suite ▁i ▁gcontae ▁an ▁longfoirt ▁é ▁cao nach ... (+6 more)` | 16 |
| 32k | `▁is ▁baile ▁suite ▁i ▁gcontae ▁an ▁longfoirt ▁é ▁caonach . ... (+5 more)` | 15 |
| 64k | `▁is ▁baile ▁suite ▁i ▁gcontae ▁an ▁longfoirt ▁é ▁caonach . ... (+5 more)` | 15 |

**Sample 2:** `Sráidbhaile beag i gContae Ros Comáin is ea An Seanbhaile (Old Town as Béarla). ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁sráidbhaile ▁beag ▁i ▁gcontae ▁ros ▁comáin ▁is ▁ea ▁an ▁sean ... (+10 more)` | 20 |
| 16k | `▁sráidbhaile ▁beag ▁i ▁gcontae ▁ros ▁comáin ▁is ▁ea ▁an ▁sean ... (+10 more)` | 20 |
| 32k | `▁sráidbhaile ▁beag ▁i ▁gcontae ▁ros ▁comáin ▁is ▁ea ▁an ▁seanbhaile ... (+8 more)` | 18 |
| 64k | `▁sráidbhaile ▁beag ▁i ▁gcontae ▁ros ▁comáin ▁is ▁ea ▁an ▁seanbhaile ... (+8 more)` | 18 |

**Sample 3:** `Is imreoir leadóige as An tSeapáin í Misaki Doi. Rugadh í ar an 29 Aibreán leadó...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁is ▁imreoir ▁leadóige ▁as ▁an ▁tseapáin ▁í ▁m isa ki ... (+17 more)` | 27 |
| 16k | `▁is ▁imreoir ▁leadóige ▁as ▁an ▁tseapáin ▁í ▁m isa ki ... (+17 more)` | 27 |
| 32k | `▁is ▁imreoir ▁leadóige ▁as ▁an ▁tseapáin ▁í ▁m isa ki ... (+16 more)` | 26 |
| 64k | `▁is ▁imreoir ▁leadóige ▁as ▁an ▁tseapáin ▁í ▁m isa ki ... (+16 more)` | 26 |


### Key Findings

- **Best Compression:** 64k achieves 4.595x compression
- **Lowest UNK Rate:** 8k with 0.1479% 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 | 41,051 | 15.33 | 224,402 | 11.6% | 28.8% |
| **2-gram** | Subword | 260 🏆 | 8.02 | 7,311 | 69.6% | 99.2% |
| **3-gram** | Word | 129,955 | 16.99 | 394,113 | 5.2% | 15.9% |
| **3-gram** | Subword | 2,220 | 11.12 | 56,094 | 27.5% | 72.9% |
| **4-gram** | Word | 328,612 | 18.33 | 698,569 | 3.1% | 9.7% |
| **4-gram** | Subword | 13,083 | 13.68 | 311,374 | 13.3% | 40.0% |
| **5-gram** | Word | 276,286 | 18.08 | 496,389 | 2.8% | 9.5% |
| **5-gram** | Subword | 52,276 | 15.67 | 940,984 | 7.3% | 24.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ar an` | 55,595 |
| 2 | `sa bhliain` | 34,147 |
| 3 | `a bhí` | 24,293 |
| 4 | `leis an` | 21,408 |
| 5 | `a rugadh` | 15,751 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a rugadh i` | 11,250 |
| 2 | `baile átha cliath` | 4,993 |
| 3 | `ina dhiaidh sin` | 4,414 |
| 4 | `is é an` | 4,339 |
| 5 | `go dtí an` | 3,964 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a rugadh i i` | 3,258 |
| 2 | `a rugadh i beo` | 3,011 |
| 3 | `tagairtí a rugadh i` | 2,902 |
| 4 | `i mbaile átha cliath` | 2,279 |
| 5 | `baile fearainn i gcontae` | 2,227 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `tagairtí a rugadh i i` | 1,261 |
| 2 | `milliún duine ar an eipeasóid` | 1,003 |
| 3 | `an eipeasóid seo d fhéach` | 997 |
| 4 | `breitheanna básanna ceannairí domhanda tagairtí` | 817 |
| 5 | `eachtraí breitheanna básanna ceannairí domhanda` | 812 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a` | 1,728,019 |
| 2 | `a _` | 1,304,438 |
| 3 | `n _` | 1,293,557 |
| 4 | `c h` | 1,096,662 |
| 5 | `a n` | 1,083,880 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a c h` | 528,297 |
| 2 | `a n _` | 512,170 |
| 3 | `_ a n` | 478,331 |
| 4 | `a r _` | 407,037 |
| 5 | `n a _` | 405,810 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a n _` | 398,568 |
| 2 | `_ n a _` | 252,847 |
| 3 | `a c h _` | 239,043 |
| 4 | `a g u s` | 237,745 |
| 5 | `g u s _` | 237,257 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a g u s` | 236,766 |
| 2 | `a g u s _` | 236,632 |
| 3 | `r _ a n _` | 82,111 |
| 4 | `_ a r _ a` | 75,982 |
| 5 | `_ b h í _` | 72,519 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 260
- **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 | 0.9964 | 1.995 | 8.63 | 343,683 | 0.4% |
| **1** | Subword | 0.9582 | 1.943 | 6.76 | 3,318 | 4.2% |
| **2** | Word | 0.3580 | 1.282 | 2.08 | 2,957,508 | 64.2% |
| **2** | Subword | 0.8596 | 1.815 | 5.42 | 22,430 | 14.0% |
| **3** | Word | 0.1474 | 1.108 | 1.31 | 6,125,828 | 85.3% |
| **3** | Subword | 0.7941 | 1.734 | 4.34 | 121,437 | 20.6% |
| **4** | Word | 0.0625 🏆 | 1.044 | 1.11 | 7,985,903 | 93.8% |
| **4** | Subword | 0.7210 | 1.648 | 3.32 | 527,224 | 27.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `an tarbh cogaidh ar eolas digiteal i siam agus don 19ú haois bhunaigh sé go raibh`
2. `a bhíonn faoi dhó é turas eitilt seo tagairtí nuachta le dobharmharc e restrictor chun cinn`
3. `na mbráthar bán is mó ná neart ceoil de chuid iarnród éireann athrú mór an tslóvaicis`

**Context Size 2:**

1. `ar an toirt agus méid ceimeacháin atá i gceist a éilíonn is a thiocfaidh an galar seo`
2. `sa bhliain chuir eorpaigh fúthu san india ó bombay thaistil siad ar an gcuid is mó sna`
3. `a bhí dílis d údarás na gaeltachta taibhdhearc na gaillimhe an ros contae na gaillimhe naisc sheacht...`

**Context Size 3:**

1. `a rugadh i as londain sasanacha sasanacha sasanacha a rugadh i meiriceánacha meiriceánacha meiriceán...`
2. `baile átha cliath tomás ó laidhin céimí de chuid ollscoil missouri kansas city agus scoil dlí na nig...`
3. `ina dhiaidh sin agus dúirt sé go raibh galar intinne uirthi agus go leor úsáidí ann mar dhíolacháin`

**Context Size 4:**

1. `tagairtí a rugadh i i moslamacha otamánacha ioslamach`
2. `baile fearainn i gcontae an chabháin tuaim contae an chláir baile fearainn i gcontae chiarraí an cil...`
3. `is baile suite i gcontae aontroma é tagairtí in albain dhùn phris is ghall ghàidhealaibh in iardheis...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_tíoleánaiteaiob`
2. `ach,_achagh_liru`
3. `iachtaspáinns_gu`

**Context Size 2:**

1. `_ad_lon_áfaon_agu`
2. `a_gintaeipearna_r`
3. `n_thaobedate_clek`

**Context Size 3:**

1. `ach,_geolas_sé_phy`
2. `an_tar_come)"._ar_`
3. `_an_ar_féach_ar_ús`

**Context Size 4:**

1. `_an_téadach_stuaist`
2. `_na_héireann_5_de_t`
3. `ach_na_thábháil._ma`


### Key Findings

- **Best Predictability:** Context-4 (word) with 93.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (527,224 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 | 161,708 |
| Total Tokens | 10,057,096 |
| Mean Frequency | 62.19 |
| Median Frequency | 4 |
| Frequency Std Dev | 1917.88 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | an | 411,365 |
| 2 | a | 299,072 |
| 3 | na | 254,180 |
| 4 | agus | 237,584 |
| 5 | ar | 204,783 |
| 6 | i | 198,698 |
| 7 | is | 131,814 |
| 8 | le | 97,770 |
| 9 | sa | 94,976 |
| 10 | go | 90,513 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | múcapholaisiúicrídí | 2 |
| 2 | slock | 2 |
| 3 | oinonen | 2 |
| 4 | frithsciúradh | 2 |
| 5 | varoufakis | 2 |
| 6 | wordnet | 2 |
| 7 | babelnet | 2 |
| 8 | cdle | 2 |
| 9 | malavoglia | 2 |
| 10 | btv | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0687 |
| R² (Goodness of Fit) | 0.997049 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 41.5% |
| Top 1,000 | 64.7% |
| Top 5,000 | 80.4% |
| Top 10,000 | 86.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9970 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 41.5% of corpus
- **Long Tail:** 151,708 words needed for remaining 13.8% 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 | 0.8458 | 0.3686 | N/A | N/A |
| **mono_64d** | 64 | 0.8459 🏆 | 0.2792 | N/A | N/A |
| **mono_128d** | 128 | 0.8282 | 0.2131 | N/A | N/A |
| **aligned_32d** | 32 | 0.8458 | 0.3623 | 0.1860 | 0.5460 |
| **aligned_64d** | 64 | 0.8459 | 0.2830 | 0.2320 | 0.6040 |
| **aligned_128d** | 128 | 0.8282 | 0.2127 | 0.3460 | 0.6980 |

### Key Findings

- **Best Isotropy:** mono_64d with 0.8459 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2865. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 34.6% 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 | **-0.611** | 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` | chillán, chomhlachtaí, choimeádacha |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-a` | vieja, jedna, zha |
| `-ch` | achtanóideach, mhuraenach, chlochach |
| `-ach` | achtanóideach, mhuraenach, chlochach |
| `-in` | rodin, coimisiúin, arcáin |
| `-ha` | zha, choimeádacha, sheandálaíocha |
| `-ir` | reachtair, dóttir, stóir |

### 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 |
|------|----------|------------------|----------|
| `rach` | 1.68x | 258 contexts | brach, trach, àrach |
| `agai` | 1.83x | 98 contexts | nagai, agaid, agair |
| `mhai` | 1.47x | 225 contexts | mhair, mhail, mhais |
| `chta` | 1.45x | 238 contexts | achta, échta, uchta |
| `aíoc` | 1.72x | 89 contexts | aíoch, aíocht, aíochta |
| `reac` | 1.59x | 128 contexts | reach, preac, breac |
| `aith` | 1.40x | 224 contexts | maith, raith, daith |
| `eith` | 1.59x | 116 contexts | beith, reith, feith |
| `irea` | 1.40x | 194 contexts | pirea, éirean, oirear |
| `bhai` | 1.39x | 175 contexts | bhais, bhain, bhaic |
| `omha` | 1.43x | 140 contexts | domha, íomha, comha |
| `onta` | 1.39x | 151 contexts | ponta, gonta, konta |

### 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` | `-a` | 31 words | chreata, chongócha |
| `-ch` | `-ch` | 25 words | chích, charbocsaileach |
| `-ch` | `-ach` | 22 words | charbocsaileach, chumasach |
| `-ch` | `-in` | 16 words | choimeádáin, chíomháin |
| `-ch` | `-ir` | 16 words | choisir, chreachadóir |
| `-ch` | `-ha` | 10 words | chongócha, chriméacha |

### 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 |
|------|-----------------|------------|------|
| chruthach | **`ch-ruth-ach`** | 6.0 | `ruth` |
| cheannach | **`ch-eann-ach`** | 6.0 | `eann` |
| gcruithneach | **`gcruithne-ach`** | 4.5 | `gcruithne` |
| éireanach | **`éirean-ach`** | 4.5 | `éirean` |
| uathbhásach | **`uathbhás-ach`** | 4.5 | `uathbhás` |
| reitineach | **`reitine-ach`** | 4.5 | `reitine` |
| chaithreachas | **`ch-aithreachas`** | 4.5 | `aithreachas` |
| chomhfhachtóir | **`ch-omhfhachtó-ir`** | 3.0 | `omhfhachtó` |
| cellachain | **`cellac-ha-in`** | 3.0 | `cellac` |
| mhórchathair | **`mhórchat-ha-ir`** | 3.0 | `mhórchat` |
| phartaláin | **`phartalá-in`** | 1.5 | `phartalá` |
| motherfoclóir | **`motherfocló-ir`** | 1.5 | `motherfocló` |
| bhaictéaracha | **`bhaictéarac-ha`** | 1.5 | `bhaictéarac` |
| mheasartha | **`mheasart-ha`** | 1.5 | `mheasart` |
| annalacha | **`annalac-ha`** | 1.5 | `annalac` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Irish 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 (4.59x) |
| N-gram | **2-gram** | Lowest perplexity (260) |
| Markov | **Context-4** | Highest predictability (93.8%) |
| 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: 2026-01-09 22:37:05*