---
language: diq
language_name: Dimli (individual language)
language_family: iranian_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-iranian_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: 3.946
  - name: best_isotropy
    type: isotropy
    value: 0.8232
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

# Dimli (individual language) - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Dimli (individual language)** 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** | 3.111x | 3.11 | 0.0973% | 324,747 |
| **16k** | 3.420x | 3.42 | 0.1070% | 295,419 |
| **32k** | 3.692x | 3.70 | 0.1155% | 273,644 |
| **64k** | 3.946x 🏆 | 3.95 | 0.1234% | 256,028 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `.weir, nameyê bandıra sewiyaya serêna jeneriko (be İngılızki: Generic top-level ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁. we ir , ▁nameyê ▁bandıra ▁sewiyaya ▁serêna ▁jeneriko ▁( ... (+19 more)` | 29 |
| 16k | `▁. we ir , ▁nameyê ▁bandıra ▁sewiyaya ▁serêna ▁jeneriko ▁( ... (+19 more)` | 29 |
| 32k | `▁. we ir , ▁nameyê ▁bandıra ▁sewiyaya ▁serêna ▁jeneriko ▁( ... (+19 more)` | 29 |
| 64k | `▁. we ir , ▁nameyê ▁bandıra ▁sewiyaya ▁serêna ▁jeneriko ▁( ... (+19 more)` | 29 |

**Sample 2:** `Bègues, dewleta Fransa de, mıntıqaya Auvergne-Rhône-Alpes miyan de yew komuna wı...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁b è gues , ▁dewleta ▁fransa ▁de , ▁mıntıqaya ▁auvergne ... (+15 more)` | 25 |
| 16k | `▁b è gues , ▁dewleta ▁fransa ▁de , ▁mıntıqaya ▁auvergne ... (+15 more)` | 25 |
| 32k | `▁b è gues , ▁dewleta ▁fransa ▁de , ▁mıntıqaya ▁auvergne ... (+15 more)` | 25 |
| 64k | `▁bè gues , ▁dewleta ▁fransa ▁de , ▁mıntıqaya ▁auvergne - ... (+14 more)` | 24 |

**Sample 3:** `Cosne-d'Allier, dewleta Fransa de, mıntıqaya Overn-Ron-Alpan miyan de yew komuna...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁cos ne - d ' allier , ▁dewleta ▁fransa ▁de ... (+21 more)` | 31 |
| 16k | `▁cos ne - d ' allier , ▁dewleta ▁fransa ▁de ... (+19 more)` | 29 |
| 32k | `▁cos ne - d ' allier , ▁dewleta ▁fransa ▁de ... (+18 more)` | 28 |
| 64k | `▁cos ne - d ' allier , ▁dewleta ▁fransa ▁de ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 3.946x compression
- **Lowest UNK Rate:** 8k with 0.0973% 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 | 2,900 | 11.50 | 32,472 | 37.7% | 66.7% |
| **2-gram** | Subword | 361 🏆 | 8.50 | 6,487 | 60.7% | 98.0% |
| **3-gram** | Word | 2,363 | 11.21 | 37,780 | 38.7% | 72.4% |
| **3-gram** | Subword | 3,111 | 11.60 | 45,197 | 22.3% | 67.0% |
| **4-gram** | Word | 3,683 | 11.85 | 77,102 | 34.1% | 68.2% |
| **4-gram** | Subword | 15,466 | 13.92 | 232,167 | 13.2% | 42.0% |
| **5-gram** | Word | 3,179 | 11.63 | 61,892 | 33.7% | 70.0% |
| **5-gram** | Subword | 42,786 | 15.38 | 597,917 | 10.1% | 34.5% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de ca` | 13,749 |
| 2 | `de mıntıqaya` | 12,351 |
| 3 | `ca gêno` | 11,945 |
| 4 | `fransa de` | 11,892 |
| 5 | `de yew` | 11,359 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `fransa de mıntıqaya` | 11,768 |
| 2 | `dewleta fransa de` | 11,147 |
| 3 | `de ca gêno` | 10,321 |
| 4 | `bıvênên lista komunanê` | 8,041 |
| 5 | `katalogê neweyê pêroyi` | 7,026 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `dewleta fransa de mıntıqaya` | 11,101 |
| 2 | `katalogê neweyê pêroyi de` | 7,025 |
| 3 | `cısım katalogê neweyê pêroyi` | 7,025 |
| 4 | `no cısım katalogê neweyê` | 6,678 |
| 5 | `lista cısmanê ngc gıreyê` | 6,644 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `cısım katalogê neweyê pêroyi de` | 7,024 |
| 2 | `no cısım katalogê neweyê pêroyi` | 6,678 |
| 3 | `lista cısmanê ngc gıreyê teberi` | 6,644 |
| 4 | `de ca gêno de terefê` | 5,997 |
| 5 | `asmêniyo no cısım katalogê neweyê` | 5,870 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 300,863 |
| 2 | `e _` | 289,730 |
| 3 | `a n` | 274,481 |
| 4 | `ê _` | 267,322 |
| 5 | `_ d` | 217,060 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 157,628 |
| 2 | `d e _` | 100,392 |
| 3 | `o . _` | 73,592 |
| 4 | `n ê _` | 68,515 |
| 5 | `i y a` | 67,461 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 94,419 |
| 2 | `a n ê _` | 43,769 |
| 3 | `_ y e w` | 40,703 |
| 4 | `_ k o m` | 40,690 |
| 5 | `_ r a _` | 38,802 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ y e w _` | 36,954 |
| 2 | `_ k o m u` | 34,451 |
| 3 | `k o m u n` | 34,446 |
| 4 | `_ b ı v ê` | 23,569 |
| 5 | `b ı v ê n` | 23,557 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 361
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~35% 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 | 0.7487 | 1.680 | 4.43 | 220,418 | 25.1% |
| **1** | Subword | 0.9728 | 1.963 | 6.81 | 2,853 | 2.7% |
| **2** | Word | 0.1773 | 1.131 | 1.38 | 970,777 | 82.3% |
| **2** | Subword | 0.8745 | 1.833 | 5.24 | 19,403 | 12.6% |
| **3** | Word | 0.0542 | 1.038 | 1.10 | 1,326,261 | 94.6% |
| **3** | Subword | 0.7728 | 1.709 | 4.01 | 101,524 | 22.7% |
| **4** | Word | 0.0216 🏆 | 1.015 | 1.04 | 1,442,368 | 97.8% |
| **4** | Subword | 0.6913 | 1.615 | 2.98 | 406,622 | 30.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de biyê ke yew belediyaya sûkê wayiye nıfus grafikê diagrami sero gorey serran ra nıfusê vilasantar`
2. `ra nıfusê anouldi website resayış 14 807 windsor ontario kanada yew qezay lalapaşaya ekonomiye be ro...`
3. `yew komunê aulnois beaufremont de anciyao embıryani nıfus bıvênên qam hewahebur kelek u nameyê bandı...`

**Context Size 2:**

1. `de ca gêno schleswig holsteini de wılayetê ardennesi de yew serra teqwimiya seramey biyayış gaius pl...`
2. `de mıntıqaya normandiya de ca gêno xızmete gesnes en argonne ca gênê xızmete rozerotte de şebekey aw...`
3. `ca gêno bıvênên lista komunanê loire atlantique pays de la loire de ca gêna xızmete escouloubre de`

**Context Size 3:**

1. `fransa de mıntıqaya occitanie de ca gêna xızmete trausse de şebekey awe esto û sistemê kanalizasyoni...`
2. `dewleta fransa de mıntıqaya auvergne rhône alpesi miyan de yew komuna bıvênên lista komunanê seine e...`
3. `de ca gêno embıryani nıfus grafikê diagrami sero gorey seran ra nıfusê sandiás bıvênên belediyey our...`

**Context Size 4:**

1. `dewleta fransa de mıntıqaya grand esti de wılayetê vosgesi dero komuni 31 87 km2 ca gêno dormey herb...`
2. `katalogê neweyê pêroyi de komê estareyanê miyan de ca gêno de terefê i ra keşıf biyo bıvênên asmên g...`
3. `cısım katalogê neweyê pêroyi de komê estareyanê miyan de ca gêno de terefê astronom i ra keşıf biyo ...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_6_gaus-seyan_zı`
2. `eyirdê_ardullale`
3. `anên_d_usi_n-cet`

**Context Size 2:**

1. `a_fra_hun_no_û_ho`
2. `e_letektempar_–_d`
3. `anê_man_lolynsall`

**Context Size 3:**

1. `_de_temê_ki_sec,_y`
2. `de_verneyo_ra_nows`
3. `o._telebebat_yılbı`

**Context Size 4:**

1. `_de_komunê_wılayetê`
2. `anê_muzisyeno,_ber_`
3. `_yew_film_rol_çakal`


### Key Findings

- **Best Predictability:** Context-4 (word) with 97.8% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (406,622 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 | 92,779 |
| Total Tokens | 2,332,304 |
| Mean Frequency | 25.14 |
| Median Frequency | 3 |
| Frequency Std Dev | 515.39 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 115,037 |
| 2 | ra | 40,569 |
| 3 | yew | 37,084 |
| 4 | u | 26,509 |
| 5 | bıvênên | 23,466 |
| 6 | û | 21,932 |
| 7 | lista | 20,682 |
| 8 | ca | 17,900 |
| 9 | dewleta | 17,340 |
| 10 | ke | 16,742 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | aksiyongerilim | 2 |
| 2 | vizyonkewtış | 2 |
| 3 | sude | 2 |
| 4 | alınca | 2 |
| 5 | vurmaz | 2 |
| 6 | dramgerilim | 2 |
| 7 | gülsoy | 2 |
| 8 | sarsu | 2 |
| 9 | toktamışoğlu | 2 |
| 10 | öğden | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0696 |
| R² (Goodness of Fit) | 0.997357 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.8% |
| Top 1,000 | 65.1% |
| Top 5,000 | 78.5% |
| Top 10,000 | 84.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9974 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.8% of corpus
- **Long Tail:** 82,779 words needed for remaining 16.0% 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 | 0.8232 | 0.3686 | N/A | N/A |
| **mono_64d** | 64 | 0.7882 | 0.3130 | N/A | N/A |
| **mono_128d** | 128 | 0.5576 | 0.2631 | N/A | N/A |
| **aligned_32d** | 32 | 0.8232 🏆 | 0.3734 | 0.0360 | 0.2220 |
| **aligned_64d** | 64 | 0.7882 | 0.3026 | 0.0680 | 0.3100 |
| **aligned_128d** | 128 | 0.5576 | 0.2680 | 0.1060 | 0.4260 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8232 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3148. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 10.6% 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 | **1.030** | 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 |
|--------|----------|

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-an` | ban, yewbiyayiyan, algan |

### 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 |
|------|----------|------------------|----------|
| `iyay` | 1.76x | 207 contexts | niyay, siyay, şiyay |
| `iyan` | 1.73x | 143 contexts | biyan, niyan, ziyan |
| `ista` | 1.71x | 64 contexts | kista, lista, vista |
| `eber` | 1.92x | 37 contexts | teber, zeber, xeber |
| `wlet` | 2.29x | 20 contexts | dewlet, dewletu, dewleto |
| `ewle` | 2.23x | 20 contexts | dewle, sewle, hewle |
| `leta` | 1.95x | 30 contexts | letan, aleta, ğeleta |
| `nter` | 1.78x | 41 contexts | enter, inter, anter |
| `rans` | 1.84x | 35 contexts | crans, frans, trans |
| `laye` | 2.00x | 23 contexts | claye, layer, alaye |
| `ıntı` | 2.38x | 12 contexts | alıntı, saçıntı, çalıntı |
| `ntıq` | 1.93x | 18 contexts | mantıq, mentıq, mentıqi |

### 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.

*No significant affix co-occurrences detected.*


### 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 |
|------|-----------------|------------|------|
| vınderdışan | **`vınderdış-an`** | 4.5 | `vınderdış` |
| hıkumetan | **`hıkumet-an`** | 4.5 | `hıkumet` |
| pêxamberan | **`pêxamber-an`** | 4.5 | `pêxamber` |
| destnuşteyan | **`destnuştey-an`** | 4.5 | `destnuştey` |
| sekuleran | **`sekuler-an`** | 4.5 | `sekuler` |
| beynelmılelan | **`beynelmılel-an`** | 4.5 | `beynelmılel` |
| karxaneyan | **`karxaney-an`** | 4.5 | `karxaney` |
| meqaleyan | **`meqaley-an`** | 4.5 | `meqaley` |
| qerebegan | **`qerebeg-an`** | 1.5 | `qerebeg` |
| boğazlıyan | **`boğazlıy-an`** | 1.5 | `boğazlıy` |
| çıldirtan | **`çıldirt-an`** | 1.5 | `çıldirt` |
| meheliyan | **`meheliy-an`** | 1.5 | `meheliy` |
| saskatchewan | **`saskatchew-an`** | 1.5 | `saskatchew` |
| kalimantan | **`kalimant-an`** | 1.5 | `kalimant` |
| gentleman | **`gentlem-an`** | 1.5 | `gentlem` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Dimli (individual language) 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 (3.95x) |
| N-gram | **2-gram** | Lowest perplexity (361) |
| Markov | **Context-4** | Highest predictability (97.8%) |
| 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: 2026-01-04 02:29:30*