---
language: hif
language_name: Fiji Hindi
language_family: indoaryan_fiji
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-indoaryan_fiji
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: 4.228
  - name: best_isotropy
    type: isotropy
    value: 0.8158
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-10
---

# Fiji Hindi - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Fiji Hindi** 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** | 3.785x | 3.79 | 0.0809% | 234,998 |
| **16k** | 4.011x | 4.02 | 0.0857% | 221,746 |
| **32k** | 4.156x | 4.16 | 0.0888% | 214,028 |
| **64k** | 4.228x 🏆 | 4.23 | 0.0903% | 210,369 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Khandeshi bhasa ek Indo-European bhasa hae jisme India ke Maharashtra state ke 1...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁k hand es hi ▁bhasa ▁ek ▁indo - european ▁bhasa ... (+32 more)` | 42 |
| 16k | `▁khand es hi ▁bhasa ▁ek ▁indo - european ▁bhasa ▁hae ... (+27 more)` | 37 |
| 32k | `▁khand eshi ▁bhasa ▁ek ▁indo - european ▁bhasa ▁hae ▁jisme ... (+25 more)` | 35 |
| 64k | `▁khand eshi ▁bhasa ▁ek ▁indo - european ▁bhasa ▁hae ▁jisme ... (+23 more)` | 33 |

**Sample 2:** `Elören ek gaon hae jon Turkey ke Bolu praant ke Gerede district me hae. Elören k...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁el ören ▁ek ▁gaon ▁hae ▁jon ▁turkey ▁ke ▁bolu ▁praant ... (+22 more)` | 32 |
| 16k | `▁el ören ▁ek ▁gaon ▁hae ▁jon ▁turkey ▁ke ▁bolu ▁praant ... (+22 more)` | 32 |
| 32k | `▁el ören ▁ek ▁gaon ▁hae ▁jon ▁turkey ▁ke ▁bolu ▁praant ... (+22 more)` | 32 |
| 64k | `▁elören ▁ek ▁gaon ▁hae ▁jon ▁turkey ▁ke ▁bolu ▁praant ▁ke ... (+20 more)` | 30 |

**Sample 3:** `Palia Kalan bhaarat mein Uttar Pradesh ke Municipal board hain. References Prade...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁pal ia ▁kal an ▁bhaarat ▁mein ▁uttar ▁pradesh ▁ke ▁municipal ... (+6 more)` | 16 |
| 16k | `▁pal ia ▁kal an ▁bhaarat ▁mein ▁uttar ▁pradesh ▁ke ▁municipal ... (+6 more)` | 16 |
| 32k | `▁pal ia ▁kalan ▁bhaarat ▁mein ▁uttar ▁pradesh ▁ke ▁municipal ▁board ... (+5 more)` | 15 |
| 64k | `▁pal ia ▁kalan ▁bhaarat ▁mein ▁uttar ▁pradesh ▁ke ▁municipal ▁board ... (+5 more)` | 15 |


### Key Findings

- **Best Compression:** 64k achieves 4.228x compression
- **Lowest UNK Rate:** 8k with 0.0809% 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 | 6,213 | 12.60 | 22,149 | 21.0% | 50.1% |
| **2-gram** | Subword | 263 🏆 | 8.04 | 3,336 | 67.9% | 99.2% |
| **3-gram** | Word | 10,451 | 13.35 | 32,506 | 17.2% | 41.0% |
| **3-gram** | Subword | 2,210 | 11.11 | 22,191 | 26.4% | 71.8% |
| **4-gram** | Word | 18,375 | 14.17 | 56,140 | 15.8% | 34.2% |
| **4-gram** | Subword | 11,729 | 13.52 | 106,944 | 14.3% | 40.3% |
| **5-gram** | Word | 14,491 | 13.82 | 42,977 | 17.8% | 36.0% |
| **5-gram** | Subword | 36,295 | 15.15 | 256,262 | 9.3% | 28.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ke gaon` | 3,298 |
| 2 | `hae ii` | 3,135 |
| 3 | `me banaa` | 2,853 |
| 4 | `ii film` | 2,821 |
| 5 | `ke ek` | 2,370 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ke gaon ke` | 1,619 |
| 2 | `gaon ke gaon` | 1,618 |
| 3 | `ek me banaa` | 1,425 |
| 4 | `banaa rahaa ii` | 1,402 |
| 5 | `rahaa ii film` | 1,398 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ke gaon ke gaon` | 1,618 |
| 2 | `banaa rahaa ii film` | 1,394 |
| 3 | `rahaa ii film me` | 1,380 |
| 4 | `ke direction me banaa` | 1,378 |
| 5 | `direction me banaa rahaa` | 1,377 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `banaa rahaa ii film me` | 1,377 |
| 2 | `ke direction me banaa rahaa` | 1,377 |
| 3 | `me banaa rahaa ii film` | 1,364 |
| 4 | `direction me banaa rahaa ii` | 1,363 |
| 5 | `acting kare rahin external link` | 968 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 215,179 |
| 2 | `_ k` | 118,527 |
| 3 | `h a` | 109,485 |
| 4 | `a n` | 94,117 |
| 5 | `a _` | 90,974 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `k e _` | 78,323 |
| 2 | `_ k e` | 70,674 |
| 3 | `_ m e` | 42,082 |
| 4 | `_ h a` | 35,377 |
| 5 | `m e _` | 31,901 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ k e _` | 66,724 |
| 2 | `_ m e _` | 27,033 |
| 3 | `_ h a e` | 24,843 |
| 4 | `_ r a h` | 20,874 |
| 5 | `_ a u r` | 19,225 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a u r _` | 18,842 |
| 2 | `_ r a h a` | 16,026 |
| 3 | `r a h a a` | 15,421 |
| 4 | `_ h a e .` | 15,329 |
| 5 | `h a e . _` | 14,766 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 263
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~28% 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 | 0.7772 | 1.714 | 4.95 | 83,282 | 22.3% |
| **1** | Subword | 0.8893 | 1.852 | 5.71 | 2,227 | 11.1% |
| **2** | Word | 0.2435 | 1.184 | 1.59 | 410,746 | 75.7% |
| **2** | Subword | 0.6909 | 1.614 | 4.11 | 12,721 | 30.9% |
| **3** | Word | 0.0951 | 1.068 | 1.18 | 650,872 | 90.5% |
| **3** | Subword | 0.7145 | 1.641 | 3.67 | 52,201 | 28.5% |
| **4** | Word | 0.0428 🏆 | 1.030 | 1.07 | 760,827 | 95.7% |
| **4** | Subword | 0.6343 | 1.552 | 2.75 | 191,335 | 36.6% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `ke border kare rahin kuchh sau sau isse barra chaand pe dher town nagar palika hain`
2. `me bharti hoe gais rahaa uu philosophiae naturalis principia mathematica likhis rahaa ghatna guadelo...`
3. `hae ocean aur minister hae jiske rewa suva ke kendr ke american actress ke direction me`

**Context Size 2:**

1. `hae ii film usa me khela gais rahaa iske jaada kar ke hatais rahaa apartheid ek afrikaans`
2. `me banaa english film hae ii sab county heritage me lia rahaa ii film germany me bhais`
3. `ii film india me karaa jaawe hae duusra websites cia world factbook central intelligence agency foru...`

**Context Size 3:**

1. `ke gaon ke gaon bihar ke gaon bahaari jorr references ke gaon ke gaon ke gaon bihar ke`
2. `ek me banaa english film hae ii film canada me michel jetté ke direction me banaa rahaa ii`
3. `banaa rahaa ii film me sam worthington liam neeson ralph fiennes edgar ramírez acting kare the sandh...`

**Context Size 4:**

1. `banaa rahaa ii film me jonathan daniel brown kenny wormald aaron yoo ron perlman acting kare rahin e...`
2. `rahaa ii film me larry rahin cable guy owen wilson michael caine emily mortimer acting kare rahin sa...`
3. `ke direction me banaa rahaa ii film me jill clayburgh amelia heinle adam kaufman austin lysy acting ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_kilaeet,_bhanti`
2. `ae)_l_tn,_tevadi`
3. `eoe_(r_con_otenc`

**Context Size 2:**

1. `e_me_shaad,_al_sh`
2. `_ke_dvincenve_ban`
3. `haagence_ginv_bar`

**Context Size 3:**

1. `ke_bakhstandhmada_`
2. `_ke_nource)_sive_p`
3. `_me_hasanga_iske_j`

**Context Size 4:**

1. `_ke_logan_ke_ki_uu_`
2. `_me_lautoka_0-0_0-0`
3. `_hae._āndhra_projec`


### Key Findings

- **Best Predictability:** Context-4 (word) with 95.7% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (191,335 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 | 36,370 |
| Total Tokens | 971,297 |
| Mean Frequency | 26.71 |
| Median Frequency | 4 |
| Frequency Std Dev | 466.12 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | ke | 67,375 |
| 2 | me | 28,710 |
| 3 | hae | 24,635 |
| 4 | aur | 18,902 |
| 5 | rahaa | 15,337 |
| 6 | ek | 13,483 |
| 7 | se | 11,961 |
| 8 | the | 10,559 |
| 9 | ii | 10,014 |
| 10 | of | 9,683 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | mahajanapadas | 2 |
| 2 | kikatas | 2 |
| 3 | brihadratha | 2 |
| 4 | gangaridae | 2 |
| 5 | prasioi | 2 |
| 6 | asokas | 2 |
| 7 | excavations | 2 |
| 8 | pāṭali | 2 |
| 9 | sutta | 2 |
| 10 | chhetraphal | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0911 |
| R² (Goodness of Fit) | 0.997141 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 42.5% |
| Top 1,000 | 69.1% |
| Top 5,000 | 85.2% |
| Top 10,000 | 91.1% |

### Key Findings

- **Zipf Compliance:** R²=0.9971 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 42.5% of corpus
- **Long Tail:** 26,370 words needed for remaining 8.9% 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 | 0.8158 | 0.3455 | N/A | N/A |
| **mono_64d** | 64 | 0.6008 | 0.3053 | N/A | N/A |
| **mono_128d** | 128 | 0.1730 | 0.2933 | N/A | N/A |
| **aligned_32d** | 32 | 0.8158 🏆 | 0.3433 | 0.0800 | 0.3760 |
| **aligned_64d** | 64 | 0.6008 | 0.2939 | 0.1640 | 0.5060 |
| **aligned_128d** | 128 | 0.1730 | 0.3011 | 0.2060 | 0.5720 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8158 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3137. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 20.6% 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 | **0.267** | 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` | sampati, satha, scheer |
| `-a` | airspeed, administrators, avery |
| `-b` | balavu, bright, bonaire |
| `-ma` | mace, mahmoud, mayawati |
| `-m` | mère, munia, mace |
| `-sa` | sampati, satha, sanvaadadaata |
| `-p` | patakatha, parrii, prasith |
| `-ba` | balavu, balcılar, barisan |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-n` | jawaan, haddiyaan, bunun |
| `-s` | galaxies, nepals, administrators |
| `-e` | shakeshafte, mère, karke |
| `-a` | patakatha, virendra, tuva |
| `-r` | scheer, oper, rahikpur |
| `-on` | lebanon, davaon, definition |
| `-an` | jawaan, haddiyaan, lillian |
| `-t` | bright, environment, piedmont |

### 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 |
|------|----------|------------------|----------|
| `aara` | 2.02x | 49 contexts | taara, saara, maara |
| `tion` | 1.92x | 39 contexts | action, motion, option |
| `anaa` | 1.84x | 40 contexts | ganaa, manaa, hanaa |
| `atio` | 1.96x | 29 contexts | patio, ratio, nation |
| `ctio` | 1.93x | 21 contexts | action, actions, faction |
| `arat` | 1.44x | 50 contexts | marat, parat, carat |
| `ecti` | 1.86x | 18 contexts | section, lection, election |
| `indi` | 1.74x | 19 contexts | bindi, hindi, indic |
| `ence` | 1.87x | 15 contexts | fence, pence, hence |
| `mber` | 1.77x | 16 contexts | amber, ember, timber |
| `nati` | 1.80x | 15 contexts | unnati, banati, nation |
| `renc` | 1.82x | 14 contexts | french, trench, örencik |

### 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 |
|--------|--------|-----------|----------|
| `-p` | `-n` | 77 words | puraanan, penelitian |
| `-s` | `-n` | 69 words | sampann, shailiyon |
| `-p` | `-s` | 68 words | primates, planets |
| `-s` | `-a` | 66 words | sarma, sakata |
| `-s` | `-r` | 56 words | shoemaker, screenwriter |
| `-p` | `-a` | 55 words | pandya, pratibaddhata |
| `-a` | `-s` | 52 words | aras, anegnos |
| `-s` | `-s` | 49 words | status, strauss |
| `-s` | `-e` | 48 words | seville, sale |
| `-a` | `-a` | 47 words | ashéninka, aba |

### 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 |
|------|-----------------|------------|------|
| chitrkalaa | **`chitrka-la-a`** | 7.5 | `la` |
| prateekon | **`pratee-k-on`** | 7.5 | `k` |
| developing | **`develop-i-ng`** | 7.5 | `i` |
| oxidizing | **`oxidiz-i-ng`** | 7.5 | `i` |
| gyllenhaal | **`gyllenh-a-al`** | 7.5 | `a` |
| zonguldak | **`zonguld-a-k`** | 7.5 | `a` |
| constance | **`const-an-ce`** | 7.5 | `an` |
| reactants | **`react-an-ts`** | 7.5 | `an` |
| lagaataar | **`lagaa-ta-ar`** | 7.5 | `ta` |
| boliviano | **`bolivi-an-o`** | 7.5 | `an` |
| americans | **`americ-an-s`** | 7.5 | `an` |
| metaphysical | **`me-ta-physical`** | 7.5 | `physical` |
| sukumaran | **`su-kumar-an`** | 6.0 | `kumar` |
| javascript | **`ja-va-script`** | 6.0 | `script` |
| krishneel | **`krishn-ee-l`** | 6.0 | `krishn` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Fiji Hindi 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 (4.23x) |
| N-gram | **2-gram** | Lowest perplexity (263) |
| Markov | **Context-4** | Highest predictability (95.7%) |
| Embeddings | **100d** | Balanced semantic capture and isotropy |


---
## Appendix: Metrics Glossary & Interpretation Guide

This section provides definitions, intuitions, and guidance for interpreting the metrics used throughout this report.

### Tokenizer Metrics

**Compression Ratio**
> *Definition:* The ratio of characters to tokens (chars/token). Measures how efficiently the tokenizer represents text.
>
> *Intuition:* Higher compression means fewer tokens needed to represent the same text, reducing sequence lengths for downstream models. A 3x compression means ~3 characters per token on average.
>
> *What to seek:* Higher is generally better for efficiency, but extremely high compression may indicate overly aggressive merging that loses morphological information.

**Average Token Length (Fertility)**
> *Definition:* Mean number of characters per token produced by the tokenizer.
>
> *Intuition:* Reflects the granularity of tokenization. Longer tokens capture more context but may struggle with rare words; shorter tokens are more flexible but increase sequence length.
>
> *What to seek:* Balance between 2-5 characters for most languages. Arabic/morphologically-rich languages may benefit from slightly longer tokens.

**Unknown Token Rate (OOV Rate)**
> *Definition:* Percentage of tokens that map to the unknown/UNK token, indicating words the tokenizer cannot represent.
>
> *Intuition:* Lower OOV means better vocabulary coverage. High OOV indicates the tokenizer encounters many unseen character sequences.
>
> *What to seek:* Below 1% is excellent; below 5% is acceptable. BPE tokenizers typically achieve very low OOV due to subword fallback.

### N-gram Model Metrics

**Perplexity**
> *Definition:* Measures how "surprised" the model is by test data. Mathematically: 2^(cross-entropy). Lower values indicate better prediction.
>
> *Intuition:* If perplexity is 100, the model is as uncertain as if choosing uniformly among 100 options at each step. A perplexity of 10 means effectively choosing among 10 equally likely options.
>
> *What to seek:* Lower is better. Perplexity decreases with larger n-grams (more context). Values vary widely by language and corpus size.

**Entropy**
> *Definition:* Average information content (in bits) needed to encode the next token given the context. Related to perplexity: perplexity = 2^entropy.
>
> *Intuition:* High entropy means high uncertainty/randomness; low entropy means predictable patterns. Natural language typically has entropy between 1-4 bits per character.
>
> *What to seek:* Lower entropy indicates more predictable text patterns. Entropy should decrease as n-gram size increases.

**Coverage (Top-K)**
> *Definition:* Percentage of corpus occurrences explained by the top K most frequent n-grams.
>
> *Intuition:* High coverage with few patterns indicates repetitive/formulaic text; low coverage suggests diverse vocabulary usage.
>
> *What to seek:* Depends on use case. For language modeling, moderate coverage (40-60% with top-1000) is typical for natural text.

### Markov Chain Metrics

**Average Entropy**
> *Definition:* Mean entropy across all contexts, measuring average uncertainty in next-word prediction.
>
> *Intuition:* Lower entropy means the model is more confident about what comes next. Context-1 has high entropy (many possible next words); Context-4 has low entropy (few likely continuations).
>
> *What to seek:* Decreasing entropy with larger context sizes. Very low entropy (<0.1) indicates highly deterministic transitions.

**Branching Factor**
> *Definition:* Average number of unique next tokens observed for each context.
>
> *Intuition:* High branching = many possible continuations (flexible but uncertain); low branching = few options (predictable but potentially repetitive).
>
> *What to seek:* Branching factor should decrease with context size. Values near 1.0 indicate nearly deterministic chains.

**Predictability**
> *Definition:* Derived metric: (1 - normalized_entropy) × 100%. Indicates how deterministic the model's predictions are.
>
> *Intuition:* 100% predictability means the next word is always certain; 0% means completely random. Real text falls between these extremes.
>
> *What to seek:* Higher predictability for text generation quality, but too high (>98%) may produce repetitive output.

### Vocabulary & Zipf's Law Metrics

**Zipf's Coefficient**
> *Definition:* The slope of the log-log plot of word frequency vs. rank. Zipf's law predicts this should be approximately -1.
>
> *Intuition:* A coefficient near -1 indicates the corpus follows natural language patterns where a few words are very common and most words are rare.
>
> *What to seek:* Values between -0.8 and -1.2 indicate healthy natural language distribution. Deviations may suggest domain-specific or artificial text.

**R² (Coefficient of Determination)**
> *Definition:* Measures how well the linear fit explains the frequency-rank relationship. Ranges from 0 to 1.
>
> *Intuition:* R² near 1.0 means the data closely follows Zipf's law; lower values indicate deviation from expected word frequency patterns.
>
> *What to seek:* R² > 0.95 is excellent; > 0.99 indicates near-perfect Zipf adherence typical of large natural corpora.

**Vocabulary Coverage**
> *Definition:* Cumulative percentage of corpus tokens accounted for by the top N words.
>
> *Intuition:* Shows how concentrated word usage is. If top-100 words cover 50% of text, the corpus relies heavily on common words.
>
> *What to seek:* Top-100 covering 30-50% is typical. Higher coverage indicates more repetitive text; lower suggests richer vocabulary.

### Word Embedding Metrics

**Isotropy**
> *Definition:* Measures how uniformly distributed vectors are in the embedding space. Computed as the ratio of minimum to maximum singular values.
>
> *Intuition:* High isotropy (near 1.0) means vectors spread evenly in all directions; low isotropy means vectors cluster in certain directions, reducing expressiveness.
>
> *What to seek:* Higher isotropy generally indicates better-quality embeddings. Values > 0.1 are reasonable; > 0.3 is good. Lower-dimensional embeddings tend to have higher isotropy.

**Average Norm**
> *Definition:* Mean magnitude (L2 norm) of word vectors in the embedding space.
>
> *Intuition:* Indicates the typical "length" of vectors. Consistent norms suggest stable training; high variance may indicate some words are undertrained.
>
> *What to seek:* Relatively consistent norms across models. The absolute value matters less than consistency (low std deviation).

**Cosine Similarity**
> *Definition:* Measures angular similarity between vectors, ranging from -1 (opposite) to 1 (identical direction).
>
> *Intuition:* Words with similar meanings should have high cosine similarity. This is the standard metric for semantic relatedness in embeddings.
>
> *What to seek:* Semantically related words should score > 0.5; unrelated words should be near 0. Synonyms often score > 0.7.

**t-SNE Visualization**
> *Definition:* t-Distributed Stochastic Neighbor Embedding - a dimensionality reduction technique that preserves local structure for visualization.
>
> *Intuition:* Clusters in t-SNE plots indicate groups of semantically related words. Spread indicates vocabulary diversity; tight clusters suggest semantic coherence.
>
> *What to seek:* Meaningful clusters (e.g., numbers together, verbs together). Avoid over-interpreting distances - t-SNE preserves local, not global, structure.

### General Interpretation Guidelines

1. **Compare within model families:** Metrics are most meaningful when comparing models of the same type (e.g., 8k vs 64k tokenizer).
2. **Consider trade-offs:** Better performance on one metric often comes at the cost of another (e.g., compression vs. OOV rate).
3. **Context matters:** Optimal values depend on downstream tasks. Text generation may prioritize different metrics than classification.
4. **Corpus influence:** All metrics are influenced by corpus characteristics. Wikipedia text differs from social media or literature.
5. **Language-specific patterns:** Morphologically rich languages (like Arabic) may show different optimal ranges than analytic languages.


### Visualizations Index

| Visualization | Description |
|---------------|-------------|
| Tokenizer Compression | Compression ratios by vocabulary size |
| Tokenizer Fertility | Average token length by vocabulary |
| Tokenizer OOV | Unknown token rates |
| Tokenizer Total Tokens | Total tokens by vocabulary |
| N-gram Perplexity | Perplexity by n-gram size |
| N-gram Entropy | Entropy by n-gram size |
| N-gram Coverage | Top pattern coverage |
| N-gram Unique | Unique n-gram counts |
| Markov Entropy | Entropy by context size |
| Markov Branching | Branching factor by context |
| Markov Contexts | Unique context counts |
| Zipf's Law | Frequency-rank distribution with fit |
| Vocab Frequency | Word frequency distribution |
| Top 20 Words | Most frequent words |
| Vocab Coverage | Cumulative coverage curve |
| Embedding Isotropy | Vector space uniformity |
| Embedding Norms | Vector magnitude distribution |
| Embedding Similarity | Word similarity heatmap |
| Nearest Neighbors | Similar words for key terms |
| t-SNE Words | 2D word embedding visualization |
| t-SNE Sentences | 2D sentence embedding visualization |
| Position Encoding | Encoding method comparison |
| Model Sizes | Storage requirements |
| Performance Dashboard | Comprehensive performance overview |

---
## About This Project

### Data Source

Models trained on [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly) - a monthly snapshot of Wikipedia articles across 300+ languages.

### Project

A project by **[Wikilangs](https://wikilangs.org)** - Open-source NLP models for every Wikipedia language.

### Maintainer

[Omar Kamali](https://omarkamali.com) - [Omneity Labs](https://omneitylabs.com)

### Citation

If you use these models in your research, please cite:

```bibtex
@misc{wikilangs2025,
  author = {Kamali, Omar},
  title = {Wikilangs: Open NLP Models for Wikipedia Languages},
  year = {2025},
  doi = {10.5281/zenodo.18073153},
  publisher = {Zenodo},
  url = {https://huggingface.co/wikilangs}
  institution = {Omneity Labs}
}
```

### License

MIT License - Free for academic and commercial use.

### Links

- 🌐 Website: [wikilangs.org](https://wikilangs.org)
- 🤗 Models: [huggingface.co/wikilangs](https://huggingface.co/wikilangs)
- 📊 Data: [wikipedia-monthly](https://huggingface.co/datasets/omarkamali/wikipedia-monthly)
- 👤 Author: [Omar Kamali](https://huggingface.co/omarkamali)
- 🤝 Sponsor: [Featherless AI](https://featherless.ai)
---
*Generated by Wikilangs Models Pipeline*

*Report Date: 2026-01-10 02:32:56*