# Italian — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **Italian** 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** | 3.856x | 3.86 | 0.1569% | 3,369,266 |
| **16k** | 4.248x | 4.25 | 0.1729% | 3,057,865 |
| **32k** | 4.578x | 4.58 | 0.1863% | 2,837,619 |
| **64k** | 4.817x 🏆 | 4.82 | 0.1960% | 2,696,638 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Eventi, invenzioni e scoperte Viene inventato il Lapis Benjamin Franklin inventa...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁viene ▁inv entato ▁il ▁la ... (+29 more)` | 39 |
| 16k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁viene ▁inventato ▁il ▁la pis ... (+21 more)` | 31 |
| 32k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁viene ▁inventato ▁il ▁la pis ... (+17 more)` | 27 |
| 64k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁viene ▁inventato ▁il ▁la pis ... (+17 more)` | 27 |

**Sample 2:** `Eventi, invenzioni e scoperte Roma - Inaugurazione del Colosseo Personaggi 81 Ro...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁roma ▁- ▁inaugu razione ▁del ... (+19 more)` | 29 |
| 16k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁roma ▁- ▁inaugu razione ▁del ... (+19 more)` | 29 |
| 32k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁roma ▁- ▁inaugurazione ▁del ▁colo ... (+18 more)` | 28 |
| 64k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁roma ▁- ▁inaugurazione ▁del ▁colosseo ... (+16 more)` | 26 |

**Sample 3:** `Eventi, invenzioni e scoperte Fine della cattività avignonese A Vicenza venne sp...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁fine ▁della ▁ca tti vità ... (+23 more)` | 33 |
| 16k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁fine ▁della ▁ca ttività ▁avi ... (+22 more)` | 32 |
| 32k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁fine ▁della ▁ca ttività ▁avi ... (+22 more)` | 32 |
| 64k | `▁eventi , ▁invenzioni ▁e ▁scoperte ▁fine ▁della ▁cattività ▁avignon ese ... (+18 more)` | 28 |


### Key Findings

- **Best Compression:** 64k achieves 4.817x compression
- **Lowest UNK Rate:** 8k with 0.1569% 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 | 204,245 | 17.64 | 1,475,040 | 6.1% | 16.8% |
| **2-gram** | Subword | 214 🏆 | 7.74 | 16,385 | 74.4% | 99.4% |
| **3-gram** | Word | 980,193 | 19.90 | 3,253,104 | 3.2% | 7.9% |
| **3-gram** | Subword | 1,722 | 10.75 | 125,759 | 29.1% | 78.9% |
| **4-gram** | Word | 1,937,953 | 20.89 | 4,769,877 | 3.5% | 7.0% |
| **4-gram** | Subword | 10,064 | 13.30 | 693,084 | 14.1% | 42.3% |
| **5-gram** | Word | 1,090,157 | 20.06 | 2,714,110 | 5.0% | 9.7% |
| **5-gram** | Subword | 43,596 | 15.41 | 2,255,172 | 7.7% | 24.4% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `per la` | 97,286 |
| 2 | `è un` | 96,027 |
| 3 | `di un` | 94,634 |
| 4 | `e il` | 87,633 |
| 5 | `altri progetti` | 84,533 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `altri progetti collegamenti` | 60,396 |
| 2 | `progetti collegamenti esterni` | 60,395 |
| 3 | `è un comune` | 49,422 |
| 4 | `note altri progetti` | 43,464 |
| 5 | `società evoluzione demografica` | 42,434 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `altri progetti collegamenti esterni` | 60,395 |
| 2 | `è un comune francese` | 33,569 |
| 3 | `abitanti situato nel dipartimento` | 33,506 |
| 4 | `un comune francese di` | 33,266 |
| 5 | `società evoluzione demografica note` | 32,814 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `è un comune francese di` | 33,067 |
| 2 | `evoluzione demografica note altri progetti` | 32,558 |
| 3 | `società evoluzione demografica note altri` | 32,545 |
| 4 | `note altri progetti collegamenti esterni` | 27,862 |
| 5 | `demografica note altri progetti collegamenti` | 18,549 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 14,124,940 |
| 2 | `a _` | 13,040,624 |
| 3 | `i _` | 10,977,304 |
| 4 | `o _` | 10,608,684 |
| 5 | `_ d` | 9,830,426 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i` | 3,986,152 |
| 2 | `_ d e` | 3,607,817 |
| 3 | `l a _` | 3,337,560 |
| 4 | `d i _` | 3,263,476 |
| 5 | `_ c o` | 3,099,394 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d i _` | 3,072,491 |
| 2 | `_ d e l` | 2,506,551 |
| 3 | `l l a _` | 1,668,082 |
| 4 | `_ i l _` | 1,519,530 |
| 5 | `d e l l` | 1,488,470 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e l l` | 1,459,429 |
| 2 | `e l l a _` | 1,154,387 |
| 3 | `i o n e _` | 1,144,610 |
| 4 | `_ d e l _` | 1,020,510 |
| 5 | `z i o n e` | 936,001 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 214
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~24% 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 | 1.1017 | 2.146 | 14.31 | 1,066,977 | 0.0% |
| **1** | Subword | 1.1777 | 2.262 | 7.67 | 8,745 | 0.0% |
| **2** | Word | 0.4680 | 1.383 | 2.78 | 15,250,485 | 53.2% |
| **2** | Subword | 0.6777 | 1.600 | 4.48 | 67,098 | 32.2% |
| **3** | Word | 0.2017 | 1.150 | 1.44 | 42,356,757 | 79.8% |
| **3** | Subword | 0.7209 | 1.648 | 4.10 | 300,612 | 27.9% |
| **4** | Word | 0.0737 🏆 | 1.052 | 1.12 | 61,123,669 | 92.6% |
| **4** | Subword | 0.6799 | 1.602 | 3.41 | 1,231,483 | 32.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `di assessore regionale del manto di pilotaggio e la frase di classificazione i dimostranti scendono ...`
2. `e della borgogna franca contea società evoluzione demografica note book apogeo del jkd è inoltre l`
3. `il numero di sacco viene riportato che all inizio con le descrizioni matematicamente da cui le`

**Context Size 2:**

1. `per la stirpe più distante e poi per varie statue a delfi in grecia per la prima`
2. `è un genere teatrale di rendere il suo simbolo è appunto quello di stern gerlach numero quantico`
3. `di un giovane nero floyd patterson mettendolo anche in alcuni casi come trimble contro gordon brown ...`

**Context Size 3:**

1. `altri progetti collegamenti esterni white teeth a conversation with cary grant che lo portò in testa...`
2. `è un comune francese di abitanti situato nel dipartimento della valle della politica di per il migli...`
3. `progetti collegamenti esterni t dell oceano pacifico meridionale polinesia con una superficie per co...`

**Context Size 4:**

1. `altri progetti collegamenti esterni topo gigio all ed sullivan show di elvis presley scatenò i teena...`
2. `è un comune francese di 75 abitanti situato nella comunità autonoma della navarra altri progetti del...`
3. `abitanti situato nel dipartimento dell eure nella regione della normandia società evoluzione demogra...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_ri_fi_ami_l'agi`
2. `i_po_mpr_pri_mpa`
3. `eo_ia,_ltavinafa`

**Context Size 2:**

1. `e_diatuas,_of_spe`
2. `a_inasa_quo_ca_ar`
3. `i_nal_re_e_ne_pie`

**Context Size 3:**

1. `_di_anni_di_gioria`
2. `_della_galle._mali`
3. `la_perfalcune_pelt`

**Context Size 4:**

1. `_di_fontempi_livini`
2. `_del_romanzo_è_anch`
3. `lla_classi_e_l'inse`


### Key Findings

- **Best Predictability:** Context-4 (word) with 92.6% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (1,231,483 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 | 511,837 |
| Total Tokens | 75,575,358 |
| Mean Frequency | 147.66 |
| Median Frequency | 4 |
| Frequency Std Dev | 7438.35 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | di | 3,083,677 |
| 2 | e | 1,824,641 |
| 3 | il | 1,551,962 |
| 4 | la | 1,467,509 |
| 5 | in | 1,133,909 |
| 6 | a | 1,025,836 |
| 7 | del | 1,022,058 |
| 8 | che | 801,243 |
| 9 | un | 799,178 |
| 10 | della | 790,420 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | strensall | 2 |
| 2 | towthorpe | 2 |
| 3 | flamininus | 2 |
| 4 | etolici | 2 |
| 5 | riveros | 2 |
| 6 | kuntur | 2 |
| 7 | wachana | 2 |
| 8 | queñua | 2 |
| 9 | karabotas | 2 |
| 10 | tveitite | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0088 |
| R² (Goodness of Fit) | 0.996765 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 39.3% |
| Top 1,000 | 60.2% |
| Top 5,000 | 76.8% |
| Top 10,000 | 83.4% |

### Key Findings

- **Zipf Compliance:** R²=0.9968 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 39.3% of corpus
- **Long Tail:** 501,837 words needed for remaining 16.6% 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 | 0.7834 | 0.3810 | N/A | N/A |
| **mono_64d** | 64 | 0.7465 | 0.3030 | N/A | N/A |
| **mono_128d** | 128 | 0.6690 | 0.2585 | N/A | N/A |
| **aligned_32d** | 32 | 0.7834 🏆 | 0.3788 | 0.3920 | 0.7480 |
| **aligned_64d** | 64 | 0.7465 | 0.3134 | 0.6060 | 0.8580 |
| **aligned_128d** | 128 | 0.6690 | 0.2626 | 0.6780 | 0.9340 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7834 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3162. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 67.8% 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 | **-0.603** | 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 |
|--------|----------|
| `-s` | sansavi, sfocianti, santegidiese |
| `-a` | astrolabes, applicheremo, ancia |
| `-ma` | madonne, marclay, mastrantuono |
| `-m` | mistruzzi, medioriente, madonne |
| `-c` | camminerò, ceraio, coltellacci |
| `-p` | primaibidem, pohliana, poschiavini |
| `-b` | brozzo, berlette, bucherer |
| `-t` | tigerdirect, takahito, tintry |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | medioriente, madonne, lasiocampidae |
| `-o` | takahito, ceraio, brozzo |
| `-a` | gialloviola, pohliana, dawa |
| `-i` | mistruzzi, coltellacci, creatrici |
| `-s` | astrolabes, glîrs, canids |
| `-no` | mastrantuono, corrispondano, leprino |
| `-n` | guédelon, esametilen, cupidon |
| `-te` | medioriente, berlette, supercorazzate |

### 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 |
|------|----------|------------------|----------|
| `rono` | 2.58x | 96 contexts | grono, crono, ronon |
| `nche` | 1.63x | 202 contexts | anche, nchev, ponche |
| `ogra` | 1.55x | 226 contexts | fogra, sogra, dogra |
| `nter` | 1.48x | 287 contexts | enter, inter, nterr |
| `lmen` | 1.98x | 62 contexts | almen, ulmen, ilmen |
| `izza` | 1.47x | 191 contexts | vizza, mizza, nizza |
| `stru` | 1.49x | 158 contexts | strub, strup, strum |
| `ostr` | 1.37x | 174 contexts | costr, ostro, nostr |
| `uest` | 1.64x | 65 contexts | quest, fuest, guest |
| `ntro` | 1.50x | 94 contexts | antro, intro, entro |
| `ontr` | 1.42x | 115 contexts | contr, contrò, hontra |
| `ggio` | 1.33x | 157 contexts | iggio, aggio, eggio |

### 6.4 Affix Compatibility (Co-occurrence)

This table shows which prefixes and suffixes most frequently co-occur on the same stems, revealing the 'stacking' rules of the language's morphology.

| Prefix | Suffix | Frequency | Examples |
|--------|--------|-----------|----------|
| `-c` | `-o` | 141 words | collalto, connettivo |
| `-c` | `-e` | 139 words | cappelline, clorotiche |
| `-s` | `-a` | 138 words | stäfa, serratissima |
| `-s` | `-e` | 136 words | shilke, sommette |
| `-a` | `-e` | 132 words | acquaforte, accreditabile |
| `-s` | `-o` | 128 words | sperandiofrancesco, sfido |
| `-c` | `-i` | 116 words | caseifici, consistenticittadini |
| `-c` | `-a` | 114 words | cabarga, carapinheira |
| `-a` | `-o` | 111 words | arcagato, ammandorlato |
| `-a` | `-i` | 110 words | appaltatrici, angiulli |

### 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 |
|------|-----------------|------------|------|
| iannacone | **`ianna-co-ne`** | 7.5 | `co` |
| frantumata | **`frantum-a-ta`** | 7.5 | `a` |
| strigosus | **`strigo-s-us`** | 7.5 | `s` |
| roccatani | **`rocca-ta-ni`** | 7.5 | `ta` |
| scoppiato | **`scoppi-a-to`** | 7.5 | `a` |
| archedemo | **`arched-e-mo`** | 7.5 | `e` |
| pontificem | **`pontific-e-m`** | 7.5 | `e` |
| approvarono | **`approvar-o-no`** | 7.5 | `o` |
| millières | **`milliè-re-s`** | 7.5 | `re` |
| cercheremo | **`cercher-e-mo`** | 7.5 | `e` |
| sintaxina | **`sintax-i-na`** | 7.5 | `i` |
| ancorarono | **`ancora-ro-no`** | 7.5 | `ro` |
| contesero | **`conte-se-ro`** | 7.5 | `se` |
| wirelessman | **`wirelessm-a-n`** | 7.5 | `a` |
| granadini | **`granad-i-ni`** | 7.5 | `i` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Italian 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 (4.82x) |
| N-gram | **2-gram** | Lowest perplexity (214) |
| Markov | **Context-4** | Highest predictability (92.6%) |
| 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 · 2026-03-03 12:12:25*