RESEARCH_REPORT.md

# Cebuano — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **Cebuano** Wikipedia data by [Wikilangs](https://wikilangs.org).

👈 [Back to README](README.md)

## 📋 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** | 3.198x | 3.20 | 0.4957% | 265,676 |
| **16k** | 3.587x | 3.59 | 0.5559% | 236,895 |
| **32k** | 3.895x | 3.90 | 0.6036% | 218,173 |
| **64k** | 4.164x 🏆 | 4.17 | 0.6455% | 204,032 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Ang (MDCCL) mao ang usa ka tuig sa kalendaryong Gregoryano. Ang maoy usa ka tuig...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ang ▁( m d c cl ) ▁mao ▁ang ▁usa ... (+27 more)` | 37 |
| 16k | `▁ang ▁( m d c cl ) ▁mao ▁ang ▁usa ... (+24 more)` | 34 |
| 32k | `▁ang ▁( m d c cl ) ▁mao ▁ang ▁usa ... (+22 more)` | 32 |
| 64k | `▁ang ▁( md c cl ) ▁mao ▁ang ▁usa ▁ka ... (+21 more)` | 31 |

**Sample 2:** `Vilnius - Ulohan, Lyetuwanya. lungsod ug dakbayan sa Uropa`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁v il n ius ▁- ▁ulo han , ▁ly et ... (+9 more)` | 19 |
| 16k | `▁vil n ius ▁- ▁ulohan , ▁ly et uw an ... (+7 more)` | 17 |
| 32k | `▁vil n ius ▁- ▁ulohan , ▁ly et uw an ... (+7 more)` | 17 |
| 64k | `▁vil n ius ▁- ▁ulohan , ▁lyetuwanya . ▁lungsod ▁ug ... (+3 more)` | 13 |

**Sample 3:** `Ang manunuwat usa ka tawo nga naay propesyon sa pagsulat.`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ang ▁man un u wat ▁usa ▁ka ▁tawo ▁nga ▁na ... (+9 more)` | 19 |
| 16k | `▁ang ▁man un u wat ▁usa ▁ka ▁tawo ▁nga ▁na ... (+8 more)` | 18 |
| 32k | `▁ang ▁man un u wat ▁usa ▁ka ▁tawo ▁nga ▁naay ... (+6 more)` | 16 |
| 64k | `▁ang ▁man un uwat ▁usa ▁ka ▁tawo ▁nga ▁naay ▁propes ... (+4 more)` | 14 |


### Key Findings

- **Best Compression:** 64k achieves 4.164x compression
- **Lowest UNK Rate:** 8k with 0.4957% 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 | 1,490 | 10.54 | 185,133 | 57.1% | 77.3% |
| **2-gram** | Subword | 244 🏆 | 7.93 | 4,031 | 67.3% | 99.8% |
| **3-gram** | Word | 2,538 | 11.31 | 375,720 | 52.5% | 71.1% |
| **3-gram** | Subword | 1,343 | 10.39 | 30,833 | 30.7% | 83.1% |
| **4-gram** | Word | 4,059 | 11.99 | 640,004 | 49.1% | 65.5% |
| **4-gram** | Subword | 3,750 | 11.87 | 184,896 | 19.6% | 67.9% |
| **5-gram** | Word | 5,049 | 12.30 | 714,886 | 47.5% | 62.8% |
| **5-gram** | Subword | 6,751 | 12.72 | 629,698 | 15.6% | 62.9% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `nga matang` | 332,031 |
| 2 | `ang mga` | 257,884 |
| 3 | `sakop sa` | 255,886 |
| 4 | `catalogue of` | 255,734 |
| 5 | `mga gi` | 255,465 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ang mga gi` | 255,464 |
| 2 | `mga gi basihan` | 255,464 |
| 3 | `gi basihan niini` | 255,464 |
| 4 | `catalogue of life` | 247,130 |
| 5 | `sakop sa kahenera` | 225,289 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `mga gi basihan niini` | 255,464 |
| 2 | `ang mga gi basihan` | 255,464 |
| 3 | `sakop sa kahenera nga` | 225,289 |
| 4 | `una ning gihulagway ni` | 221,595 |
| 5 | `leiden the netherlands issn` | 218,326 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `ang mga gi basihan niini` | 255,464 |
| 2 | `annual checklist roskov y ower` | 218,326 |
| 3 | `of life annual checklist roskov` | 218,326 |
| 4 | `y ower g orrell t` | 218,326 |
| 5 | `roskov y ower g orrell` | 218,326 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a _` | 5,047,183 |
| 2 | `, _` | 4,781,955 |
| 3 | `a n` | 4,335,344 |
| 4 | `_ n` | 4,282,281 |
| 5 | `n g` | 3,457,212 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `. , _` | 2,839,080 |
| 2 | `_ s a` | 2,121,271 |
| 3 | `n g _` | 2,068,103 |
| 4 | `_ n i` | 1,666,672 |
| 5 | `a n g` | 1,567,452 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `a n g _` | 1,504,868 |
| 2 | `_ s a _` | 1,342,701 |
| 3 | `_ n g a` | 1,178,364 |
| 4 | `n g a _` | 1,167,784 |
| 5 | `_ a n g` | 872,500 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ n g a _` | 1,165,749 |
| 2 | `_ a n g _` | 865,643 |
| 3 | `n _ s a _` | 599,691 |
| 4 | `t a n g _` | 499,600 |
| 5 | `s p e c i` | 496,776 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 244
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~63% 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 | 1.1540 | 2.225 | 5.53 | 285,670 | 0.0% |
| **1** | Subword | 0.8701 | 1.828 | 5.60 | 2,205 | 13.0% |
| **2** | Word | 0.3400 | 1.266 | 1.77 | 1,571,794 | 66.0% |
| **2** | Subword | 0.6716 | 1.593 | 4.58 | 12,300 | 32.8% |
| **3** | Word | 0.1703 | 1.125 | 1.39 | 2,770,828 | 83.0% |
| **3** | Subword | 0.7154 | 1.642 | 4.50 | 56,330 | 28.5% |
| **4** | Word | 0.0559 🏆 | 1.040 | 1.22 | 3,842,457 | 94.4% |
| **4** | Subword | 0.6886 | 1.612 | 3.49 | 253,091 | 31.1% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `sa turkeya aserbaiyan iran and speciation the world spider catalog version in species naturalis leid...`
2. `nga sama niini nga onychogomphus maculivertex sakop sa java pulo sa mont saint franchy usa ka`
3. `ang mga gi basihan niini gordon d bailly n kirk p m bourgoin t custodian nicolson`

**Context Size 2:**

1. `nga matang nga sama niini ang mga gi basihan niini pycnobase bamber r n lea and j`
2. `ang mga gi basihan niini boyko c b taiti s schotte m wilson g d f d`
3. `sakop sa kahenera nga episinus ug kabanay nga sisoridae giklaseklase sa iucn ang kaliwatan sa manana...`

**Context Size 3:**

1. `mga gi basihan niini millard n a h monograph on the hydroida dredged by h m s challenger`
2. `ang mga gi basihan niini jeekel c a w nomenclator generum et familiarum diplopodorum a list of the`
3. `catalogue of life annual checklist roskov y ower g orrell t nicolson d bailly n kirk p m`

**Context Size 4:**

1. `ang mga gi basihan niini bock p gordon d worms bryozoa world list of bryozoa version in species itis`
2. `mga gi basihan niini frank norman ramus erica a complete guide to scientific and common names of rep...`
3. `sakop sa kahenera nga rhyacodrilis ug kabanay nga almidae walay nalista nga matang nga sama niini an...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_pemahi_tit._he.`
2. `al_sopol_i_ong_h`
3. `n_chewal:_ahydsa`

**Context Size 2:**

1. `a_ni._&_ficoce_ws`
2. `,_e.,_ta_decologu`
3. `anal_c.,_dus_&_it`

**Context Size 3:**

1. `.,_data_nuzelatta_`
2. `_sa_hason_fromallo`
3. `ng_mga_tural_check`

**Context Size 4:**

1. `ang_kadagatang_kaba`
2. `_sa_hulagway_ni_wil`
3. `_nga_matang_hayop_n`


### Key Findings

- **Best Predictability:** Context-4 (word) with 94.4% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (253,091 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 | 208,251 |
| Total Tokens | 32,410,695 |
| Mean Frequency | 155.63 |
| Median Frequency | 4 |
| Frequency Std Dev | 6860.23 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | sa | 1,466,791 |
| 2 | nga | 1,165,822 |
| 3 | ang | 906,355 |
| 4 | of | 522,496 |
| 5 | t | 521,002 |
| 6 | species | 490,688 |
| 7 | e | 486,096 |
| 8 | niini | 478,412 |
| 9 | ni | 451,703 |
| 10 | the | 433,952 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | parvanalis | 2 |
| 2 | micronemus | 2 |
| 3 | distolothrix | 2 |
| 4 | dolicholophia | 2 |
| 5 | brachypopterus | 2 |
| 6 | moolenburghae | 2 |
| 7 | debauwi | 2 |
| 8 | buffei | 2 |
| 9 | longibarbis | 2 |
| 10 | durinii | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.2679 |
| R² (Goodness of Fit) | 0.993803 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 72.0% |
| Top 1,000 | 87.3% |
| Top 5,000 | 93.0% |
| Top 10,000 | 94.9% |

### Key Findings

- **Zipf Compliance:** R²=0.9938 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 72.0% of corpus
- **Long Tail:** 198,251 words needed for remaining 5.1% coverage

---
## 5. Word Embeddings Evaluation

![Embedding Isotropy](visualizations/embedding_isotropy.png)

![Similarity Matrix](visualizations/embedding_similarity.png)

![t-SNE Words](visualizations/tsne_words.png)

![t-SNE Sentences](visualizations/tsne_sentences.png)


### 5.1 Cross-Lingual Alignment

![Alignment Quality](visualizations/embedding_alignment_quality.png)

![Multilingual t-SNE](visualizations/embedding_tsne_multilingual.png)


### 5.2 Model Comparison

| Model | Dimension | Isotropy | Semantic Density | Alignment R@1 | Alignment R@10 |
|-------|-----------|----------|------------------|---------------|----------------|
| **mono_32d** | 32 | 0.8551 | 0.3308 | N/A | N/A |
| **mono_64d** | 64 | 0.8254 | 0.2774 | N/A | N/A |
| **mono_128d** | 128 | 0.7631 | 0.2408 | N/A | N/A |
| **aligned_32d** | 32 | 0.8551 🏆 | 0.3257 | 0.0580 | 0.3140 |
| **aligned_64d** | 64 | 0.8254 | 0.2774 | 0.1120 | 0.4640 |
| **aligned_128d** | 128 | 0.7631 | 0.2443 | 0.2380 | 0.5920 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.8551 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2827. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 23.8% 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 | **-0.003** | Low formulaic 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 |
|--------|----------|
| `-a` | amotus, aethes, appolinard |
| `-ma` | macrura, maigné, magpapatik |
| `-s` | stieren, solasteridae, spermophilopsis |
| `-b` | bahit, baod, berchtold |
| `-p` | pseudocollinus, pseudoannulata, pseudocompressa |
| `-m` | macrura, moscu, maigné |
| `-pa` | panomya, pagkaayo, pagkapagka |
| `-ca` | carteroniella, caudaornata, catmon |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-s` | amotus, turdinus, pseudocollinus |
| `-a` | elucubata, macrura, coccopoma |
| `-us` | amotus, turdinus, pseudocollinus |
| `-is` | dactylis, yambaensis, tenuis |
| `-e` | hyèvre, ogyridione, raspailiidae |
| `-ae` | raspailiidae, solasteridae, mitwabae |
| `-i` | heurni, gaskelli, ogdeni |
| `-es` | corneilles, récoltes, fragilipes |

### 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 |
|------|----------|------------------|----------|
| `aban` | 2.82x | 102 contexts | abang, gaban, daban |
| `icol` | 2.34x | 196 contexts | nicol, bicol, vicola |
| `lson` | 2.80x | 38 contexts | olson, nelson, bulson |
| `kaba` | 2.65x | 43 contexts | kabay, kabat, kabag |
| `ihan` | 2.85x | 27 contexts | gihan, atihan, dihang |
| `rell` | 1.89x | 103 contexts | torell, trelly, crella |
| `orre` | 2.07x | 56 contexts | yorre, orret, orres |
| `ener` | 1.96x | 61 contexts | enero, tener, eener |
| `atal` | 1.89x | 56 contexts | datal, batal, natal |
| `sako` | 2.86x | 12 contexts | sakop, masako, masakop |
| `akop` | 2.88x | 10 contexts | sakop, panakop, sinakop |
| `nera` | 1.77x | 41 contexts | minera, cinera, ponera |

### 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` | `-s` | 290 words | pteroctopus, purpurescens |
| `-a` | `-s` | 246 words | apopkensis, albicaudatus |
| `-p` | `-a` | 218 words | pontoparta, paiwa |
| `-s` | `-s` | 207 words | suctotegeus, stavropoulos |
| `-c` | `-s` | 207 words | camelopardalis, conjugalis |
| `-p` | `-us` | 155 words | pteroctopus, piliocolobus |
| `-s` | `-a` | 153 words | siqueira, sexmacula |
| `-a` | `-a` | 151 words | alaria, arafoera |
| `-t` | `-s` | 134 words | thyroidus, trapelus |
| `-b` | `-s` | 132 words | billings, bourdeilles |

### 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 |
|------|-----------------|------------|------|
| bruneitarsis | **`bruneitar-s-is`** | 7.5 | `s` |
| validentata | **`valident-a-ta`** | 7.5 | `a` |
| pretoriaensis | **`pretoriaen-s-is`** | 7.5 | `s` |
| geograpsus | **`geograp-s-us`** | 7.5 | `s` |
| gimatangmatang | **`gimatangmat-a-ng`** | 7.5 | `a` |
| labropsis | **`labrop-s-is`** | 7.5 | `s` |
| chihuahuaensis | **`chihuahuaen-s-is`** | 7.5 | `s` |
| chevannay | **`chevann-a-y`** | 7.5 | `a` |
| ovosetosa | **`ovoseto-s-a`** | 7.5 | `s` |
| leporosum | **`leporo-s-um`** | 7.5 | `s` |
| schistosum | **`schisto-s-um`** | 7.5 | `s` |
| antromysis | **`antromy-s-is`** | 7.5 | `s` |
| chalonnes | **`chalon-n-es`** | 7.5 | `n` |
| strongyloxea | **`strongylox-e-a`** | 7.5 | `e` |
| paragaveae | **`paragav-e-ae`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

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

---
## 7. Summary & Recommendations

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

### Production Recommendations

| Component | Recommended | Rationale |
|-----------|-------------|-----------|
| Tokenizer | **64k BPE** | Best compression (4.16x) |
| N-gram | **2-gram** | Lowest perplexity (244) |
| Markov | **Context-4** | Highest predictability (94.4%) |
| 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 |

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*Generated by Wikilangs Pipeline · 2026-03-04 08:50:39*