---
language: gan
language_name: Gan Chinese
language_family: sinitic_mandarin
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-sinitic_mandarin
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: 2.135
  - name: best_isotropy
    type: isotropy
    value: 0.2986
  - name: vocabulary_size
    type: vocab
    value: 0
generated: 2026-01-04
---

# Gan Chinese - Wikilangs Models
## Comprehensive Research Report & Full Ablation Study

This repository contains NLP models trained and evaluated by Wikilangs, specifically on **Gan Chinese** 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** | 1.275x | 1.28 | 0.8628% | 165,035 |
| **16k** | 1.622x | 1.63 | 1.0979% | 129,708 |
| **32k** | 1.835x | 1.84 | 1.2420% | 114,654 |
| **64k** | 2.135x 🏆 | 2.15 | 1.4446% | 98,572 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `區劃 隆共管到八隻鎮同到兩隻鄉： 鎮：湘東鎮、荷堯鎮、老關鎮、下埠鎮、臘市鎮、麻山鎮、排上鎮、東橋鎮。 鄉：廣寒寨鄉、白竺鄉。 外部連接 湘東區政府網站`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁區劃 ▁ 隆 共 管到 八 隻 鎮 同到 兩隻 ... (+52 more)` | 62 |
| 16k | `▁區劃 ▁隆 共 管到 八 隻鎮 同到 兩隻 鄉 : ... (+41 more)` | 51 |
| 32k | `▁區劃 ▁隆 共 管到 八 隻鎮 同到 兩隻鄉 : ▁鎮 ... (+36 more)` | 46 |
| 64k | `▁區劃 ▁隆 共 管到八隻鎮同到 兩隻鄉 : ▁鎮 : 湘東鎮 、 ... (+30 more)` | 40 |

**Sample 2:** `崇義係贛州管到嗰一隻縣。 行政區劃 鎮：橫水鎮、揚眉鎮、過埠鎮、鉛廠鎮、長龍鎮、關田鎮 鄉：龍勾鄉、杰壩鄉、金坑鄉、思順鄉、麟潭鄉、上堡鄉、聶都鄉、文英鄉、樂洞...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 崇 義 係 贛州 管到嗰一隻縣 。 ▁行政區劃 ▁鎮 : ... (+68 more)` | 78 |
| 16k | `▁崇 義 係贛州管到嗰一隻縣 。 ▁行政區劃 ▁鎮 : 橫 水鎮 、 ... (+57 more)` | 67 |
| 32k | `▁崇義 係贛州管到嗰一隻縣 。 ▁行政區劃 ▁鎮 : 橫水鎮 、 揚 眉 ... (+49 more)` | 59 |
| 64k | `▁崇義 係贛州管到嗰一隻縣 。 ▁行政區劃 ▁鎮 : 橫水鎮 、 揚 眉 ... (+45 more)` | 55 |

**Sample 3:** `文身一般係話一隻人完身嗰器官組織，好似由上到下嗰頭、頸、胸、肚、腳箇滴子身體部件。 別嗰條目 文身最大嗰器官`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ 文 身 一般 係話 一隻 人 完 身 嗰 ... (+33 more)` | 43 |
| 16k | `▁文 身 一般 係話一隻人 完 身 嗰 器官 組織 , ... (+25 more)` | 35 |
| 32k | `▁文身 一般 係話一隻人 完 身 嗰器官 組織 , 好似 由 ... (+20 more)` | 30 |
| 64k | `▁文身一般 係話一隻人完身 嗰器官組織 , 好似 由上到下嗰頭 、 頸 、 胸 ... (+8 more)` | 18 |


### Key Findings

- **Best Compression:** 64k achieves 2.135x compression
- **Lowest UNK Rate:** 8k with 0.8628% 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 | 312 🏆 | 8.28 | 618 | 60.9% | 100.0% |
| **2-gram** | Subword | 3,099 | 11.60 | 11,007 | 25.5% | 62.5% |
| **3-gram** | Word | 398 | 8.64 | 933 | 54.5% | 100.0% |
| **3-gram** | Subword | 8,755 | 13.10 | 21,630 | 12.5% | 40.1% |
| **4-gram** | Word | 964 | 9.91 | 2,558 | 41.1% | 72.4% |
| **4-gram** | Subword | 18,991 | 14.21 | 42,273 | 10.4% | 28.5% |
| **5-gram** | Word | 867 | 9.76 | 2,341 | 41.7% | 72.6% |
| **5-gram** | Subword | 17,229 | 14.07 | 37,732 | 12.0% | 30.1% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `td valign` | 209 |
| 2 | `valign top` | 209 |
| 3 | `1 2` | 192 |
| 4 | `五月 六月` | 169 |
| 5 | `四月 五月` | 167 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `td valign top` | 209 |
| 2 | `四月 五月 六月` | 167 |
| 3 | `五月 六月 七月` | 167 |
| 4 | `六月 七月 八月` | 165 |
| 5 | `七月 八月 九月` | 165 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `四月 五月 六月 七月` | 166 |
| 2 | `三月 四月 五月 六月` | 165 |
| 3 | `五月 六月 七月 八月` | 165 |
| 4 | `六月 七月 八月 九月` | 164 |
| 5 | `二月 三月 四月 五月` | 163 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `四月 五月 六月 七月 八月` | 165 |
| 2 | `三月 四月 五月 六月 七月` | 165 |
| 3 | `五月 六月 七月 八月 九月` | 164 |
| 4 | `二月 三月 四月 五月 六月` | 163 |
| 5 | `六月 七月 八月 九月 十月` | 162 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `— _` | 2,866 |
| 2 | `_ —` | 2,861 |
| 3 | `。 _` | 2,279 |
| 4 | `_ 1` | 2,238 |
| 5 | `月 _` | 2,024 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ — _` | 2,857 |
| 2 | `— _ —` | 2,223 |
| 3 | `_ t h` | 701 |
| 4 | `_ 1 _` | 674 |
| 5 | `t h e` | 669 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `— _ — _` | 2,223 |
| 2 | `_ — _ —` | 2,221 |
| 3 | `_ t h e` | 494 |
| 4 | `t h e _` | 487 |
| 5 | `嗰 一 隻 縣` | 349 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ — _ — _` | 2,221 |
| 2 | `— _ — _ —` | 1,789 |
| 3 | `_ t h e _` | 408 |
| 4 | `嗰 一 隻 縣 。` | 309 |
| 5 | `_ < t d _` | 260 |


### Key Findings

- **Best Perplexity:** 2-gram (word) with 312
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~30% 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 | 0.2249 | 1.169 | 1.51 | 40,478 | 77.5% |
| **1** | Subword | 1.3854 | 2.612 | 10.78 | 8,730 | 0.0% |
| **2** | Word | 0.0458 | 1.032 | 1.08 | 59,809 | 95.4% |
| **2** | Subword | 0.4003 | 1.320 | 2.03 | 93,900 | 60.0% |
| **3** | Word | 0.0197 | 1.014 | 1.03 | 62,884 | 98.0% |
| **3** | Subword | 0.1871 | 1.138 | 1.37 | 189,773 | 81.3% |
| **4** | Word | 0.0095 🏆 | 1.007 | 1.01 | 63,294 | 99.1% |
| **4** | Subword | 0.1108 | 1.080 | 1.18 | 258,581 | 88.9% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `1 韓 紅 譚傑希 往事隨風 齊 秦 1 2 李 健 沈夢辰 一起搖擺 汪 網枉 王黃璜簧蟥磺皇隍蝗煌`
2. `2 3 d 7 6 7 4 4 8 徐佳瑩 1 2 5 13 55 164`
3. `5 彭佳慧 196 185 190 5 2 5 font size 5 2 張信哲 陳家麗 薛忠銘 james`

**Context Size 2:**

1. `td valign top aegyptus td td valign top 英格兰 td valign top galatia td td valign top`
2. `valign top 元首行省 td valign top 元首行省 td valign top 吕基亚行省 td valign top 小亚细亚中东部 td valign`
3. `1 2 諧歌劇 未完成 k 430 3 4 4 3 5 孫 楠 李 銳 三月的一整月 武滿徹`

**Context Size 3:**

1. `td valign top 埃及行省 td valign top 里昂高卢行省 td valign top 默西亚行省 td valign top 希腊西部 td valign`
2. `五月 六月 七月 八月 九月 十月 十一月 十二月 出世 過世 諾貝爾獎 參考 注釋 外部鏈接 年楔`
3. `四月 五月 六月 七月 八月 九月 十月 十一月 十二月 出世 過世 諾貝爾獎 參考 注釋 外部鏈接 佢啵吥睺礹吖`

**Context Size 4:**

1. `四月 五月 六月 七月 八月 九月 十月 十一月 十二月 出世 過世 諾貝爾獎 參考 注釋 外部鏈接 佢啵吥睺礹吖`
2. `五月 六月 七月 八月 九月 十月 十一月 十二月 出世 過世 諾貝爾獎 參考 注釋 外部鏈接 佢啵吥睺礹吖`
3. `三月 四月 五月 六月 七月 八月 九月 十月 十一月 十二月 出世 過世 諾貝爾獎 參考 注釋 外部鏈接 佢啵吥睺礹吖`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_勒安嗰一隻成嗰位。rendil`
2. `ethemt_展怎样，係鐘呂桶環`
3. `ai)_陶臻四十月_—_5_6_`

**Context Size 2:**

1. `—_—_—_—_—_—_7_10_`
2. `_—_—_—_7_6_黃象熙臨川係`
3. `。_話[],[]_二月_五月_六月`

**Context Size 3:**

1. `_—_—_—_—_—_—_—_／_1`
2. `—_—_—_—_—_—_—_—_7_`
3. `_the_polarge_up_ef`

**Context Size 4:**

1. `—_—_—_—_—_—_—_3.75_`
2. `_—_—_—_—_1_6_4_6_6_`
3. `_the_murmurous_hast`


### Key Findings

- **Best Predictability:** Context-4 (word) with 99.1% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (258,581 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 | 6,911 |
| Total Tokens | 44,860 |
| Mean Frequency | 6.49 |
| Median Frequency | 2 |
| Frequency Std Dev | 25.37 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | 1 | 844 |
| 2 | 2 | 664 |
| 3 | 5 | 645 |
| 4 | 4 | 574 |
| 5 | 3 | 522 |
| 6 | 6 | 483 |
| 7 | the | 474 |
| 8 | 7 | 468 |
| 9 | of | 336 |
| 10 | td | 262 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | t͡ɕʰi | 2 |
| 2 | ɕiɛu | 2 |
| 3 | ɕiuŋ | 2 |
| 4 | 睏 | 2 |
| 5 | kʰun | 2 |
| 6 | 㩳 | 2 |
| 7 | suŋ | 2 |
| 8 | 係情緒嗰一隻狀態 | 2 |
| 9 | 年至 | 2 |
| 10 | creative | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.7745 |
| R² (Goodness of Fit) | 0.971706 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 34.3% |
| Top 1,000 | 63.4% |
| Top 5,000 | 91.5% |
| Top 10,000 | 0.0% |

### Key Findings

- **Zipf Compliance:** R²=0.9717 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 34.3% of corpus
- **Long Tail:** -3,089 words needed for remaining 100.0% 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 | 0.2986 | 0.4633 | N/A | N/A |
| **mono_64d** | 64 | 0.0919 | 0.3715 | N/A | N/A |
| **mono_128d** | 128 | 0.0250 | 0.4261 | N/A | N/A |
| **aligned_32d** | 32 | 0.2986 🏆 | 0.4632 | 0.0089 | 0.1782 |
| **aligned_64d** | 64 | 0.0919 | 0.3612 | 0.0379 | 0.2316 |
| **aligned_128d** | 128 | 0.0250 | 0.4243 | 0.0846 | 0.3029 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.2986 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.4183. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 8.5% 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 | **1.417** | 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.

*No productive affixes detected.*


### 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.

*No significant bound stems detected.*


### 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`).

*Insufficient data for recursive segmentation.*


### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Gan Chinese 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 (2.13x) |
| N-gram | **2-gram** | Lowest perplexity (312) |
| Markov | **Context-4** | Highest predictability (99.1%) |
| 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 15:05:02*