README.md

---
language: la
language_name: Latin
language_family: romance_other
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-romance_other
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: 4.603
  - name: best_isotropy
    type: isotropy
    value: 0.7724
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-14
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Latin** 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** | 3.558x | 3.56 | 0.2329% | 1,084,571 |
| **16k** | 3.943x | 3.94 | 0.2582% | 978,495 |
| **32k** | 4.295x | 4.30 | 0.2812% | 898,287 |
| **64k** | 4.603x 🏆 | 4.60 | 0.3013% | 838,317 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Organum est: Organum, membrum corporis Organum, instrumentum musicum`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁org anum ▁est : ▁org anum , ▁memb rum ▁corporis ... (+6 more)` | 16 |
| 16k | `▁organum ▁est : ▁organum , ▁membrum ▁corporis ▁organum , ▁instrumentum ... (+1 more)` | 11 |
| 32k | `▁organum ▁est : ▁organum , ▁membrum ▁corporis ▁organum , ▁instrumentum ... (+1 more)` | 11 |
| 64k | `▁organum ▁est : ▁organum , ▁membrum ▁corporis ▁organum , ▁instrumentum ... (+1 more)` | 11 |

**Sample 2:** `Fanum Sancti Boni potest esse: Fanum Sancti Boni (Francia): oppidum et municipiu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁fanum ▁sancti ▁boni ▁potest ▁esse : ▁fanum ▁sancti ▁boni ▁( ... (+19 more)` | 29 |
| 16k | `▁fanum ▁sancti ▁boni ▁potest ▁esse : ▁fanum ▁sancti ▁boni ▁( ... (+18 more)` | 28 |
| 32k | `▁fanum ▁sancti ▁boni ▁potest ▁esse : ▁fanum ▁sancti ▁boni ▁( ... (+18 more)` | 28 |
| 64k | `▁fanum ▁sancti ▁boni ▁potest ▁esse : ▁fanum ▁sancti ▁boni ▁( ... (+18 more)` | 28 |

**Sample 3:** `Strata potest esse: Strata (via), via saxis strata Strata imperialis Toponyma St...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁str ata ▁potest ▁esse : ▁str ata ▁( via ), ... (+15 more)` | 25 |
| 16k | `▁str ata ▁potest ▁esse : ▁str ata ▁( via ), ... (+14 more)` | 24 |
| 32k | `▁strata ▁potest ▁esse : ▁strata ▁( via ), ▁via ▁saxis ... (+8 more)` | 18 |
| 64k | `▁strata ▁potest ▁esse : ▁strata ▁( via ), ▁via ▁saxis ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 4.603x compression
- **Lowest UNK Rate:** 8k with 0.2329% 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 | 51,862 | 15.66 | 360,878 | 13.4% | 29.8% |
| **2-gram** | Subword | 286 🏆 | 8.16 | 14,118 | 66.8% | 98.7% |
| **3-gram** | Word | 59,359 | 15.86 | 463,584 | 15.1% | 30.5% |
| **3-gram** | Subword | 2,613 | 11.35 | 108,871 | 22.0% | 70.4% |
| **4-gram** | Word | 112,438 | 16.78 | 863,879 | 13.1% | 26.4% |
| **4-gram** | Subword | 16,071 | 13.97 | 574,779 | 10.3% | 36.1% |
| **5-gram** | Word | 81,026 | 16.31 | 688,820 | 14.8% | 29.0% |
| **5-gram** | Subword | 66,945 | 16.03 | 1,725,435 | 6.4% | 22.2% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nexus externi` | 101,763 |
| 2 | `incolarum anno` | 39,735 |
| 3 | `est commune` | 35,756 |
| 4 | `communium praefecturae` | 35,448 |
| 5 | `habitati praefecturae` | 34,882 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `incolarum anno praefecturae` | 33,086 |
| 2 | `est commune francicum` | 24,941 |
| 3 | `indicem communium praefecturae` | 19,628 |
| 4 | `notae nexus externi` | 18,914 |
| 5 | `a c n` | 18,718 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nexus externi de hoc` | 9,195 |
| 2 | `inclinatio orbitalis reperiebatur anomalia` | 8,417 |
| 3 | `dies circa solem movebatur` | 8,417 |
| 4 | `per dies circa solem` | 8,417 |
| 5 | `epochae constitit qua epocha` | 8,417 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `orbitalium ratio epochae constitit qua` | 8,417 |
| 2 | `ratio epochae constitit qua epocha` | 8,417 |
| 3 | `inclinatio orbitalis reperiebatur anomalia media` | 8,417 |
| 4 | `rerum orbitalium ratio epochae constitit` | 8,417 |
| 5 | `per dies circa solem movebatur` | 8,417 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `s _` | 2,715,430 |
| 2 | `e _` | 2,239,521 |
| 3 | `i n` | 1,851,567 |
| 4 | `e r` | 1,823,230 |
| 5 | `_ a` | 1,796,413 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `u s _` | 1,100,792 |
| 2 | `u m _` | 1,077,693 |
| 3 | `a e _` | 827,009 |
| 4 | `i s _` | 820,960 |
| 5 | `_ i n` | 801,099 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ e t _` | 408,282 |
| 2 | `_ i n _` | 398,812 |
| 3 | `r u m _` | 331,124 |
| 4 | `_ e s t` | 292,802 |
| 5 | `u s _ e` | 249,383 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ p r a e` | 213,345 |
| 2 | `_ e s t _` | 189,487 |
| 3 | `a n n o _` | 184,906 |
| 4 | `u r a e _` | 155,417 |
| 5 | `_ a n n o` | 154,528 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 286
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~22% 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 | 0.9373 | 1.915 | 7.67 | 1,035,027 | 6.3% |
| **1** | Subword | 1.1119 | 2.161 | 6.89 | 7,646 | 0.0% |
| **2** | Word | 0.2344 | 1.176 | 1.60 | 7,913,093 | 76.6% |
| **2** | Subword | 0.7310 | 1.660 | 4.62 | 52,645 | 26.9% |
| **3** | Word | 0.0703 | 1.050 | 1.13 | 12,599,276 | 93.0% |
| **3** | Subword | 0.7788 | 1.716 | 4.08 | 243,139 | 22.1% |
| **4** | Word | 0.0305 🏆 | 1.021 | 1.05 | 14,149,041 | 96.9% |
| **4** | Subword | 0.6656 | 1.586 | 3.20 | 991,440 | 33.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `et ef49 3 haud anglice charles w charny le maisnil est asteroides systematis solaris nostri asteroid...`
2. `in dictionario musicae choralis canonici anni site in laborinto dicit presbyter titulo mr 18 dec xj8...`
3. `est oppidum 2 dictionnaire topographique du gandhara étude sur cartografía y gasset ra 2 vol 9`

**Context Size 2:**

1. `nexus externi de hoc communi apud cassini ehess fr praefecturae garumnae superioris habitati praefec...`
2. `incolarum anno praefecturae calvorum dorsorum nexus externi rerum novarum socius circuli musici bala...`
3. `est commune 192 incolarum anno praefecturae sarthae habitati praefecturae septentrionis habitati pra...`

**Context Size 3:**

1. `incolarum anno praefecturae mariculi in franciae occidentalis regione aquitania index communium prae...`
2. `est commune francicum 1 608 incolarum anno praefecturae mosellae in regione orientali rhodano et alp...`
3. `indicem communium praefecturae araris superioris fr saulx`

**Context Size 4:**

1. `nexus externi de hoc comitatu in censu anno texiae`
2. `inclinatio orbitalis reperiebatur anomalia media notae nexus externi anno reperti cinguli principali...`
3. `per dies circa solem movebatur axem orbitalem habebat unitatum astronomicarum et eccentricitatem dis...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_πόντω)_imoraber`
2. `ibs_t._us_ctitex`
3. `elpprtucunus_nib`

**Context Size 2:**

1. `s_ded_arpost._lib`
2. `e_ionscrenhus_tun`
3. `in_a,_anno_subuto`

**Context Size 3:**

1. `us_theologustratom`
2. `um_orioris_and”_“i`
3. `ae_caland_aris_ext`

**Context Size 4:**

1. `_et_latins"_apud_co`
2. `_in_partii_adiectac`
3. `rum_insulae_praefec`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.9% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (991,440 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 | 492,328 |
| Total Tokens | 18,420,286 |
| Mean Frequency | 37.41 |
| Median Frequency | 4 |
| Frequency Std Dev | 1191.66 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | et | 411,432 |
| 2 | in | 406,796 |
| 3 | est | 288,280 |
| 4 | anno | 185,522 |
| 5 | de | 154,355 |
| 6 | a | 152,727 |
| 7 | praefecturae | 141,766 |
| 8 | nexus | 111,685 |
| 9 | the | 102,127 |
| 10 | externi | 102,027 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | abgad | 2 |
| 2 | segmentally | 2 |
| 3 | consonantary | 2 |
| 4 | consonantal | 2 |
| 5 | ideoneum | 2 |
| 6 | levantinensis | 2 |
| 7 | versimillimum | 2 |
| 8 | propono | 2 |
| 9 | pahlavium | 2 |
| 10 | ʾí | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0085 |
| R² (Goodness of Fit) | 0.997131 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 26.3% |
| Top 1,000 | 50.8% |
| Top 5,000 | 67.1% |
| Top 10,000 | 73.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9971 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 26.3% of corpus
- **Long Tail:** 482,328 words needed for remaining 26.1% 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 | 0.7724 | 0.3497 | N/A | N/A |
| **mono_64d** | 64 | 0.7621 | 0.2810 | N/A | N/A |
| **mono_128d** | 128 | 0.7157 | 0.2133 | N/A | N/A |
| **aligned_32d** | 32 | 0.7724 🏆 | 0.3645 | 0.2620 | 0.6320 |
| **aligned_64d** | 64 | 0.7621 | 0.2846 | 0.3840 | 0.7980 |
| **aligned_128d** | 128 | 0.7157 | 0.2144 | 0.5300 | 0.8760 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7724 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2846. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 53.0% 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 | **0.308** | High formulaic/idiomatic 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` | sanationes, sawlôn, sigenburgum |
| `-a` | av16, alternately, almanaque |
| `-c` | capetian, conlectionis, cramesnil |
| `-r` | roiano, rimetti, restaurationes |
| `-t` | turuf, transgenerae, termite |
| `-e` | ectodermatis, europaeorum, euphratem |
| `-b` | bm33, biotechnologica, bourzeis |
| `-g` | guralnick, gratien, gribbin |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | ectodermatis, conlectionis, lockius |
| `-e` | phoenice, ulixeae, jonvelle |
| `-m` | islamum, mosam, obitum |
| `-um` | islamum, obitum, europaeorum |
| `-a` | lombardia, biotechnologica, vergiliusgeorgica |
| `-is` | ectodermatis, conlectionis, organismis |
| `-us` | lockius, verlus, pretiosissimus |
| `-i` | zulawski, leniniani, rimetti |

### 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 |
|------|----------|------------------|----------|
| `nsis` | 2.76x | 56 contexts | ensis, ansis, censis |
| `atio` | 1.69x | 419 contexts | datio, fatio, satio |
| `ranc` | 1.88x | 174 contexts | rance, ranco, ranci |
| `fect` | 1.74x | 183 contexts | affect, effect, defect |
| `urae` | 2.12x | 53 contexts | nurae, purae, aurae |
| `bita` | 1.72x | 113 contexts | bitam, bitat, obita |
| `inco` | 1.85x | 75 contexts | incol, zinco, sinco |
| `inci` | 1.67x | 119 contexts | incis, vinci, zinci |
| `xter` | 1.87x | 55 contexts | exter, hexter, dexter |
| `exte` | 1.88x | 53 contexts | extet, exter, texte |
| `efec` | 1.88x | 51 contexts | defect, efecto, defecit |
| `ctur` | 1.53x | 123 contexts | acturi, actura, dictur |

### 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` | 196 words | consortionis, confidens |
| `-s` | `-s` | 170 words | siccarius, securius |
| `-a` | `-s` | 152 words | angustissimus, aesacus |
| `-p` | `-s` | 149 words | petillius, pecudis |
| `-c` | `-m` | 109 words | centaurorum, clausurarum |
| `-c` | `-e` | 106 words | coëgisse, corsice |
| `-c` | `-a` | 93 words | compsa, competenza |
| `-d` | `-s` | 92 words | derriopes, diplomatiques |
| `-a` | `-m` | 91 words | amylum, acroasim |
| `-a` | `-a` | 87 words | affiliata, anegia |

### 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 |
|------|-----------------|------------|------|
| aragoniensia | **`aragonien-s-ia`** | 7.5 | `s` |
| cruciensis | **`crucien-s-is`** | 7.5 | `s` |
| cantonensis | **`cantonen-s-is`** | 7.5 | `s` |
| lipetzkensis | **`lipetzken-s-is`** | 7.5 | `s` |
| circensis | **`circen-s-is`** | 7.5 | `s` |
| statoniensis | **`statonien-s-is`** | 7.5 | `s` |
| virodunum | **`virodu-n-um`** | 7.5 | `n` |
| yérasimos | **`yérasi-m-os`** | 7.5 | `m` |
| dispendiosa | **`dispendio-s-a`** | 7.5 | `s` |
| castamonitissa | **`castamonitis-s-a`** | 7.5 | `s` |
| sulavesiensia | **`sulavesien-s-ia`** | 7.5 | `s` |
| ferrariensis | **`ferrarien-s-is`** | 7.5 | `s` |
| strahoviensis | **`strahovien-s-is`** | 7.5 | `s` |
| salfeldensi | **`salfelden-s-i`** | 7.5 | `s` |
| bulgarenses | **`bulgaren-s-es`** | 7.5 | `s` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Latin shows high morphological productivity. The subword models are significantly more efficient than word models, suggesting a rich system of affixation or compounding.

> **Note on Idiomaticity:** The high Idiomaticity Gap suggests a large number of frequent multi-word expressions or formulaic sequences that are statistically distinct from their component parts.

---
## 7. Summary & Recommendations

![Performance Dashboard](visualizations/performance_dashboard.png)

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.60x) |
| N-gram | **2-gram** | Lowest perplexity (286) |
| Markov | **Context-4** | Highest predictability (96.9%) |
| 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: 2026-01-14 21:17:28*