---
language: nrm
language_name: Narom
language_family: romance_galloitalic
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_galloitalic
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: 4.079
  - name: best_isotropy
    type: isotropy
    value: 0.5294
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

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

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Narom** 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** | 3.473x | 3.48 | 0.1334% | 248,823 |
| **16k** | 3.710x | 3.71 | 0.1425% | 232,959 |
| **32k** | 3.901x | 3.91 | 0.1499% | 221,528 |
| **64k** | 4.079x 🏆 | 4.08 | 0.1567% | 211,880 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Vienna Allobrogum 'tait le nom de la ville de Vienne en Isère oû temps qu'alle é...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁vi en na ▁all ob ro g um ▁' tait ... (+19 more)` | 29 |
| 16k | `▁vi enna ▁allobro g um ▁' tait ▁le ▁nom ▁de ... (+16 more)` | 26 |
| 32k | `▁vienna ▁allobro g um ▁' tait ▁le ▁nom ▁de ▁la ... (+14 more)` | 24 |
| 64k | `▁vienna ▁allobrogum ▁' tait ▁le ▁nom ▁de ▁la ▁ville ▁de ... (+12 more)` | 22 |

**Sample 2:** `Préfailles est eune ceutie de Fraunce, dain lé départament de Loire-Atlantique. ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pré f ailles ▁est ▁eune ▁ceutie ▁de ▁fraunce , ▁dain ... (+17 more)` | 27 |
| 16k | `▁pré f ailles ▁est ▁eune ▁ceutie ▁de ▁fraunce , ▁dain ... (+17 more)` | 27 |
| 32k | `▁préf ailles ▁est ▁eune ▁ceutie ▁de ▁fraunce , ▁dain ▁lé ... (+16 more)` | 26 |
| 64k | `▁préfailles ▁est ▁eune ▁ceutie ▁de ▁fraunce , ▁dain ▁lé ▁départament ... (+15 more)` | 25 |

**Sample 3:** `Le câtel des Mesnières est un câtel-maneir du coumenchement du XVIe siècle qui s...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁le ▁câtel ▁des ▁mes ni ères ▁est ▁un ▁câtel - ... (+23 more)` | 33 |
| 16k | `▁le ▁câtel ▁des ▁mes nières ▁est ▁un ▁câtel - maneir ... (+20 more)` | 30 |
| 32k | `▁le ▁câtel ▁des ▁mesnières ▁est ▁un ▁câtel - maneir ▁du ... (+18 more)` | 28 |
| 64k | `▁le ▁câtel ▁des ▁mesnières ▁est ▁un ▁câtel - maneir ▁du ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 4.079x compression
- **Lowest UNK Rate:** 8k with 0.1334% 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 | 2,347 | 11.20 | 9,731 | 34.1% | 64.7% |
| **2-gram** | Subword | 284 🏆 | 8.15 | 2,061 | 65.9% | 99.3% |
| **3-gram** | Word | 1,892 | 10.89 | 11,749 | 41.6% | 68.1% |
| **3-gram** | Subword | 1,967 | 10.94 | 15,580 | 29.3% | 74.2% |
| **4-gram** | Word | 2,087 | 11.03 | 18,947 | 43.7% | 67.7% |
| **4-gram** | Subword | 8,299 | 13.02 | 65,567 | 15.6% | 47.9% |
| **5-gram** | Word | 1,247 | 10.28 | 13,026 | 49.6% | 75.7% |
| **5-gram** | Subword | 20,942 | 14.35 | 136,123 | 11.0% | 35.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `annaées annaées` | 4,163 |
| 2 | `l annaée` | 2,810 |
| 3 | `ch est` | 2,005 |
| 4 | `bailliage dé` | 1,933 |
| 5 | `à l` | 1,828 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `annaées annaées annaées` | 3,121 |
| 2 | `rapporte à l` | 1,384 |
| 3 | `du calendri grégorian` | 1,384 |
| 4 | `chute page sé` | 1,383 |
| 5 | `page sé rapporte` | 1,383 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `annaées annaées annaées annaées` | 2,089 |
| 2 | `sé rapporte à l` | 1,383 |
| 3 | `page sé rapporte à` | 1,383 |
| 4 | `chute page sé rapporte` | 1,383 |
| 5 | `rapporte à l annaée` | 1,382 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `chute page sé rapporte à` | 1,383 |
| 2 | `page sé rapporte à l` | 1,383 |
| 3 | `sé rapporte à l annaée` | 1,382 |
| 4 | `histouère dé l annaée mounde` | 1,382 |
| 5 | `calendri grégorian histouère dé l` | 1,376 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 91,818 |
| 2 | `s _` | 79,349 |
| 3 | `e s` | 59,284 |
| 4 | `_ d` | 57,856 |
| 5 | `t _` | 48,802 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e s _` | 41,563 |
| 2 | `_ | _` | 19,643 |
| 3 | `e _ d` | 18,209 |
| 4 | `_ d e` | 16,600 |
| 5 | `a n n` | 13,717 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l e s _` | 10,545 |
| 2 | `a n n a` | 10,406 |
| 3 | `n a é e` | 10,398 |
| 4 | `_ l a _` | 10,338 |
| 5 | `n n a é` | 10,314 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n n a é` | 10,298 |
| 2 | `n n a é e` | 10,297 |
| 3 | `_ | _ | _` | 9,219 |
| 4 | `a é e s _` | 8,489 |
| 5 | `| _ | _ |` | 8,166 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 284
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~36% 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 | 0.7190 | 1.646 | 4.14 | 47,048 | 28.1% |
| **1** | Subword | 1.1642 | 2.241 | 9.24 | 480 | 0.0% |
| **2** | Word | 0.2570 | 1.195 | 1.57 | 193,346 | 74.3% |
| **2** | Subword | 1.0306 | 2.043 | 6.31 | 4,431 | 0.0% |
| **3** | Word | 0.0875 | 1.063 | 1.14 | 300,997 | 91.3% |
| **3** | Subword | 0.8372 | 1.787 | 3.95 | 27,927 | 16.3% |
| **4** | Word | 0.0312 🏆 | 1.022 | 1.05 | 341,376 | 96.9% |
| **4** | Subword | 0.5961 | 1.512 | 2.50 | 110,055 | 40.4% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `la porte du hoummet au père ampraésm veuvyire sauns perde les fêtes les valeurs républlicannes par`
2. `l équielle des calenges ès syins qùi s lon l jour d oui de l progrès`
3. `d la bouone cadenche le remerchier swinburne posseyeit chûte forme géométrique tch est eune campâne ...`

**Context Size 2:**

1. `annaées annaées chute page sé rapporte à l êvêque prenge compte dé la seine entre paris et`
2. `l annaée du calendri grégorian histouère dé l églyise dé saint vi lé pont d sexe i`
3. `ch est quand ch t apport des normaunds en 911 le roué de neustrieroué des frauncs y`

**Context Size 3:**

1. `annaées annaées annaées chute page sé rapporte à l annaée 831 du calendri grégorian histouère dé l a...`
2. `rapporte à l annaée du calendri grégorian histouère dé l annaée mounde ûrope normaundie duchie de no...`
3. `du calendri grégorian histouère dé l annaée mounde ûrope pais de neûtrie biâos arts tchulteure scien...`

**Context Size 4:**

1. `annaées annaées annaées annaées chute page sé rapporte à l annaée 943 du calendri grégorian histouèr...`
2. `page sé rapporte à l annaée du calendri grégorian histouère dé l annaée mounde chrêtchiannetaé pais ...`
3. `sé rapporte à l annaée 938 du calendri grégorian histouère dé l annaée mounde ûrope pais de neûtrie ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_l_altischnderbi`
2. `eanerouniz_ciméc`
3. `ni)_cona_jonds_e`

**Context Size 2:**

1. `e_pre_?_31les_vie`
2. `s_vuû_d'té._les_&`
3. `es_bêtch'es_page_`

**Context Size 3:**

1. `es_;_il_espéciale_`
2. `_|_|_|_|_|_|_|_ann`
3. `e_dé_de_ceut,_poti`

**Context Size 4:**

1. `les_goût_–_22_23_24`
2. `annaées_|_annaées_|`
3. `naées_|_annaées_bêt`


### 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 (110,055 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 | 20,102 |
| Total Tokens | 457,971 |
| Mean Frequency | 22.78 |
| Median Frequency | 3 |
| Frequency Std Dev | 254.98 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | la | 12,492 |
| 2 | l | 12,475 |
| 3 | d | 12,289 |
| 4 | de | 9,606 |
| 5 | dé | 9,602 |
| 6 | et | 9,132 |
| 7 | les | 8,078 |
| 8 | est | 7,697 |
| 9 | annaées | 7,446 |
| 10 | en | 7,063 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | domfront | 2 |
| 2 | jarcieu | 2 |
| 3 | schientifike | 2 |
| 4 | mélisse | 2 |
| 5 | italiàn | 2 |
| 6 | présidant | 2 |
| 7 | tribunal | 2 |
| 8 | pénal | 2 |
| 9 | cassation | 2 |
| 10 | feltrinelli | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.1086 |
| R² (Goodness of Fit) | 0.996123 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 51.0% |
| Top 1,000 | 76.4% |
| Top 5,000 | 89.8% |
| Top 10,000 | 95.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9961 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 51.0% of corpus
- **Long Tail:** 10,102 words needed for remaining 5.0% 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 | 0.5294 🏆 | 0.3720 | N/A | N/A |
| **mono_64d** | 64 | 0.1646 | 0.3967 | N/A | N/A |
| **mono_128d** | 128 | 0.0234 | 0.3639 | N/A | N/A |
| **aligned_32d** | 32 | 0.5294 | 0.3660 | 0.0280 | 0.1720 |
| **aligned_64d** | 64 | 0.1646 | 0.3815 | 0.0400 | 0.1980 |
| **aligned_128d** | 128 | 0.0234 | 0.3681 | 0.0500 | 0.2520 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.5294 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3747. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 5.0% 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 | **1.128** | 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 |
|--------|----------|
| `-c` | couochon, carraée, cardinâos |
| `-a` | alicante, atôme, aicme |
| `-p` | protégie, poussit, pleuvent |
| `-s` | sitôt, sainte, seyaz |
| `-m` | mînt, man, méthe |
| `-b` | bouorguingnoun, barbade, bernadotte |
| `-d` | des, dépendance, dinners |
| `-co` | couochon, couorse, continnentale |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | révolutionnaithe, dépendance, alicante |
| `-s` | des, longtemps, veireis |
| `-es` | des, êtatcharles, libres |
| `-t` | mînt, poussit, pleuvent |
| `-nt` | mînt, pleuvent, remplléchement |
| `-n` | couochon, bouorguingnoun, man |
| `-r` | touor, doumer, quar |
| `-le` | continnentale, avuule, îndustrielle |

### 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 |
|------|----------|------------------|----------|
| `ouor` | 1.74x | 56 contexts | touor, jouor, fouor |
| `tent` | 1.77x | 37 contexts | datent, dîtent, fûtent |
| `oune` | 1.70x | 33 contexts | boune, doune, toune |
| `ique` | 1.63x | 38 contexts | wique, sique, pique |
| `raun` | 1.72x | 27 contexts | raung, fraun, iraun |
| `aund` | 1.69x | 27 contexts | quaund, graund, aundré |
| `tion` | 1.67x | 24 contexts | notion, nation, action |
| `maun` | 1.71x | 22 contexts | maunde, romaun, mauntes |
| `orma` | 1.70x | 21 contexts | norma, norman, normal |
| `unde` | 1.74x | 19 contexts | ounde, rounde, mounde |
| `ques` | 1.57x | 25 contexts | vaques, pâques, luques |
| `itaé` | 2.00x | 9 contexts | citaé, naitaé, naitaée |

### 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` | `-e` | 211 words | cite, cyrille |
| `-c` | `-s` | 193 words | costeunmes, cousioums |
| `-p` | `-s` | 155 words | peis, patrons |
| `-a` | `-e` | 153 words | accounaître, aĥoque |
| `-p` | `-e` | 153 words | préchaine, présidenciêle |
| `-m` | `-e` | 123 words | muée, ministe |
| `-a` | `-s` | 122 words | ais, associatiouns |
| `-m` | `-s` | 100 words | métriques, martchis |
| `-d` | `-e` | 98 words | doctrène, dualême |
| `-s` | `-s` | 89 words | sèrcquiais, scots |

### 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 |
|------|-----------------|------------|------|
| soulaient | **`soulai-e-nt`** | 7.5 | `e` |
| demeuraient | **`demeurai-e-nt`** | 7.5 | `e` |
| précieuse | **`précieu-s-e`** | 7.5 | `s` |
| cosséquent | **`cosséqu-e-nt`** | 7.5 | `e` |
| religieuse | **`religieu-s-e`** | 7.5 | `s` |
| assiègement | **`assiègem-e-nt`** | 7.5 | `e` |
| décheûtrent | **`décheûtr-e-nt`** | 7.5 | `e` |
| devintent | **`devint-e-nt`** | 7.5 | `e` |
| rétablîment | **`rétablîm-e-nt`** | 7.5 | `e` |
| acatîtrent | **`acatîtr-e-nt`** | 7.5 | `e` |
| independent | **`independ-e-nt`** | 7.5 | `e` |
| assembliaient | **`assembliai-e-nt`** | 7.5 | `e` |
| développement | **`développem-e-nt`** | 7.5 | `e` |
| firmament | **`firmam-e-nt`** | 7.5 | `e` |
| mèrveilleux | **`mèrveill-e-ux`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Narom 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 (4.08x) |
| N-gram | **2-gram** | Lowest perplexity (284) |
| 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: 2026-01-10 16:08:44*