# Hungarian — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **Hungarian** 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** | 3.505x | 3.51 | 0.1725% | 3,328,421 |
| **16k** | 3.921x | 3.92 | 0.1930% | 2,974,904 |
| **32k** | 4.311x | 4.31 | 0.2122% | 2,705,982 |
| **64k** | 4.661x 🏆 | 4.66 | 0.2295% | 2,502,482 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Elvonás, addiktológia Elvonás, a szóalkotás egy módja`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁elv on ás , ▁ad d ikt ológia ▁elv on ... (+9 more)` | 19 |
| 16k | `▁elv on ás , ▁add ikt ológia ▁elv on ás ... (+8 more)` | 18 |
| 32k | `▁elvon ás , ▁add ikt ológia ▁elvon ás , ▁a ... (+5 more)` | 15 |
| 64k | `▁elvon ás , ▁add ikt ológia ▁elvon ás , ▁a ... (+4 more)` | 14 |

**Sample 2:** `Memória (biológia) Memória (számítástechnika): Számítástechnikában használják Me...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁mem ória ▁( bi ológia ) ▁mem ória ▁( szám ... (+23 more)` | 33 |
| 16k | `▁mem ória ▁( bi ológia ) ▁mem ória ▁( számítás ... (+19 more)` | 29 |
| 32k | `▁memória ▁( bi ológia ) ▁memória ▁( számítás technika ): ... (+12 more)` | 22 |
| 64k | `▁memória ▁( biológia ) ▁memória ▁( számítás technika ): ▁számítástechn ... (+10 more)` | 20 |

**Sample 3:** `Óe, japán családnév Óe, kisváros Japánban, Jamagata prefektúrában ÓE, az Óbudai ...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁ó e , ▁japán ▁család név ▁ó e , ▁kis ... (+21 more)` | 31 |
| 16k | `▁ó e , ▁japán ▁családnév ▁ó e , ▁kisváros ▁japánban ... (+16 more)` | 26 |
| 32k | `▁ó e , ▁japán ▁családnév ▁ó e , ▁kisváros ▁japánban ... (+13 more)` | 23 |
| 64k | `▁ó e , ▁japán ▁családnév ▁ó e , ▁kisváros ▁japánban ... (+11 more)` | 21 |


### Key Findings

- **Best Compression:** 64k achieves 4.661x compression
- **Lowest UNK Rate:** 8k with 0.1725% 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 | 362,917 | 18.47 | 2,207,301 | 5.4% | 14.2% |
| **2-gram** | Subword | 429 🏆 | 8.74 | 22,141 | 54.6% | 98.3% |
| **3-gram** | Word | 1,261,909 | 20.27 | 3,510,384 | 2.1% | 6.2% |
| **3-gram** | Subword | 4,501 | 12.14 | 188,349 | 17.4% | 56.2% |
| **4-gram** | Word | 2,487,801 | 21.25 | 5,404,855 | 2.0% | 5.1% |
| **4-gram** | Subword | 29,749 | 14.86 | 1,214,042 | 7.6% | 26.9% |
| **5-gram** | Word | 1,806,602 | 20.78 | 3,707,959 | 2.3% | 5.8% |
| **5-gram** | Subword | 135,455 | 17.05 | 4,635,566 | 3.7% | 15.6% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `és a` | 381,304 |
| 2 | `hogy a` | 127,431 |
| 3 | `és az` | 111,129 |
| 4 | `a magyar` | 107,955 |
| 5 | `volt a` | 102,268 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `személyek elhunyt személyek` | 25,908 |
| 2 | `született személyek elhunyt` | 25,567 |
| 3 | `madarai madarai madarai` | 21,522 |
| 4 | `jegyzetek további információk` | 19,348 |
| 5 | `kisbolygók listája jegyzetek` | 13,405 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `született személyek elhunyt személyek` | 25,567 |
| 2 | `madarai madarai madarai madarai` | 17,618 |
| 3 | `listája jegyzetek naprendszer kisbolygói` | 13,129 |
| 4 | `kisbolygók listája jegyzetek naprendszer` | 13,128 |
| 5 | `kapcsolódó szócikkek kisbolygók listája` | 13,112 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `madarai madarai madarai madarai madarai` | 14,553 |
| 2 | `kisbolygók listája jegyzetek naprendszer kisbolygói` | 13,128 |
| 3 | `kapcsolódó szócikkek kisbolygók listája jegyzetek` | 13,034 |
| 4 | `szócikkek kisbolygók listája jegyzetek naprendszer` | 12,763 |
| 5 | `a naprendszer kisbolygóövében található aszteroida` | 12,084 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a` | 14,447,157 |
| 2 | `a _` | 13,088,817 |
| 3 | `s z` | 10,335,605 |
| 4 | `t _` | 8,923,690 |
| 5 | `e l` | 8,560,877 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a _` | 7,569,874 |
| 2 | `_ s z` | 3,684,895 |
| 3 | `_ a z` | 2,740,812 |
| 4 | `é s _` | 2,565,914 |
| 5 | `s z e` | 2,500,891 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a z _` | 2,372,557 |
| 2 | `_ é s _` | 2,184,467 |
| 3 | `_ e g y` | 1,442,169 |
| 4 | `_ m e g` | 1,293,813 |
| 5 | `. _ a _` | 1,289,446 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ a z _ e` | 641,291 |
| 2 | `_ s z e r` | 617,289 |
| 3 | `_ é s _ a` | 566,317 |
| 4 | `_ e g y _` | 545,352 |
| 5 | `_ v o l t` | 535,186 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 429
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~16% 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 | 0.9424 | 1.922 | 10.97 | 3,256,935 | 5.8% |
| **1** | Subword | 1.1652 | 2.243 | 8.26 | 11,176 | 0.0% |
| **2** | Word | 0.3123 | 1.242 | 2.03 | 35,712,539 | 68.8% |
| **2** | Subword | 0.6772 | 1.599 | 4.69 | 92,249 | 32.3% |
| **3** | Word | 0.1163 | 1.084 | 1.24 | 72,420,142 | 88.4% |
| **3** | Subword | 0.7664 | 1.701 | 4.71 | 432,153 | 23.4% |
| **4** | Word | 0.0401 🏆 | 1.028 | 1.06 | 89,534,275 | 96.0% |
| **4** | Subword | 0.7484 | 1.680 | 3.95 | 2,032,871 | 25.2% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `a filozófiában jeleskedők élete vácon igazgatótanár aszalón bőcsön borsod abaúj zemplén vármegye hon...`
2. `az elfelejtett kísérlet singer berta fia némó elbűvölő szörnyeteg régebben megszűnt a európa bajnoki...`
3. `és dániai roskilde dánia szoroson át kellett találni a királyi engedélyt egy bizonyos ágakra elosztó...`

**Context Size 2:**

1. `és a helybeli hazafiak köztük władysław gomułka lett akkor több fellépést is a neve és a razorblade`
2. `hogy a gerjesztést követően 0 0 0 0 0 0 0 fe7 lépéssorozatból áll a leendő űrkísérletekhez`
3. `és az egy évvel korábban halt meg csak hallomásból ismerik a kantonmozdony mivel az ember annak érde...`

**Context Size 3:**

1. `született személyek elhunyt személyek drámaírók novogyevicsi temetőben eltemetett személyek erdélyi ...`
2. `madarai madarai madarai északi mariana szigetek madarai madarai madarai madarai amerikai egyesült ál...`
3. `jegyzetek további információk labdarúgók river plate labdarúgói cruz azul labdarúgói atlas labdarúgó...`

**Context Size 4:**

1. `madarai madarai madarai madarai madarai madarai tomé és príncipe madarai madarai madarai seychelle s...`
2. `született személyek elhunyt személyek úszók olimpiai ezüstérmesek nők`
3. `kisbolygók listája jegyzetek naprendszer kisbolygói vec lista de aënna`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_tén.krermi_k_ho`
2. `emi_ra_vaiszegyő`
3. `ajat_(gola,_jena`

**Context Size 2:**

1. `_a_törül_ingmukiv`
2. `a_katt,_fő_sztünc`
3. `szvetibelyek_mika`

**Context Size 3:**

1. `_a_„tusábang_napil`
2. `_szócikkel_a_bolyg`
3. `_az_a4_március_211`

**Context Size 4:**

1. `_az_eszit_lasszultá`
2. `_és_galéria_szereti`
3. `_egyik_mária_foglal`


### Key Findings

- **Best Predictability:** Context-4 (word) with 96.0% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,032,871 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 | 1,458,224 |
| Total Tokens | 103,537,627 |
| Mean Frequency | 71.00 |
| Median Frequency | 4 |
| Frequency Std Dev | 7231.61 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | a | 7,834,400 |
| 2 | az | 2,443,698 |
| 3 | és | 2,194,407 |
| 4 | is | 733,028 |
| 5 | egy | 579,913 |
| 6 | hogy | 494,341 |
| 7 | volt | 474,789 |
| 8 | nem | 446,048 |
| 9 | 1 | 405,757 |
| 10 | magyar | 343,055 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | léggömbzár | 2 |
| 2 | elterelővel | 2 |
| 3 | hajófelderítő | 2 |
| 4 | szűrőrendszerrel | 2 |
| 5 | 801ml | 2 |
| 6 | 801tp | 2 |
| 7 | sorosmotort | 2 |
| 8 | stammkennzeichen | 2 |
| 9 | schindleréről | 2 |
| 10 | kapraraszműlesiklásnem | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 0.9296 |
| R² (Goodness of Fit) | 0.996343 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 25.8% |
| Top 1,000 | 45.6% |
| Top 5,000 | 61.9% |
| Top 10,000 | 69.2% |

### Key Findings

- **Zipf Compliance:** R²=0.9963 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 25.8% of corpus
- **Long Tail:** 1,448,224 words needed for remaining 30.8% 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 | 0.7886 | 0.3560 | N/A | N/A |
| **mono_64d** | 64 | 0.7831 | 0.2846 | N/A | N/A |
| **mono_128d** | 128 | 0.7114 | 0.2337 | N/A | N/A |
| **aligned_32d** | 32 | 0.7886 🏆 | 0.3516 | 0.3600 | 0.7520 |
| **aligned_64d** | 64 | 0.7831 | 0.2765 | 0.5320 | 0.8560 |
| **aligned_128d** | 128 | 0.7114 | 0.2243 | 0.6300 | 0.9180 |

### Key Findings

- **Best Isotropy:** aligned_32d with 0.7886 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.2878. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 63.0% 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 | **-0.625** | 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` | schmör, szabadítására, szertárai |
| `-k` | kelvinator, kürtszavára, keselyűféléket |
| `-a` | arkopharma, adequate, akszukhosz |
| `-m` | megyéjébe, mongu, mozilátogatók |
| `-t` | tlp, terheltségének, tanulhatóak |
| `-b` | balszárnyának, bhov, beszédfejlődési |
| `-ma` | mainstoneky, margati, mayrnak |
| `-e` | elektronszerkezetével, egységnyiek, esztyemirova |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-k` | mozilátogatók, balszárnyának, kóruspadok |
| `-t` | használókat, felvevőpiacot, keselyűféléket |
| `-n` | végezetlen, érinthetetlen, állatkertjeiben |
| `-a` | arkopharma, kürtszavára, vaskarika |
| `-l` | elektronszerkezetével, versenyeitől, pálinkafőzéssel |
| `-s` | rombouts, ikszes, gibbins |
| `-i` | lxviii, desai, vibrálni |
| `-e` | megyéjébe, jugoslovenske, adequate |

### 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 |
|------|----------|------------------|----------|
| `váro` | 2.03x | 219 contexts | város, váron, várod |
| `embe` | 1.60x | 288 contexts | ember, embed, bembe |
| `llen` | 1.53x | 361 contexts | llena, illen, lleno |
| `atás` | 1.48x | 365 contexts | patás, hatás, avatás |
| `llet` | 1.60x | 226 contexts | allet, ellet, illet |
| `ítás` | 1.43x | 316 contexts | újítás, ásítás, ámítás |
| `ítot` | 1.65x | 136 contexts | ított, vított, osított |
| `erül` | 1.43x | 288 contexts | kerül, terül, derül |
| `mber` | 1.33x | 400 contexts | ember, imber, amber |
| `ület` | 1.38x | 311 contexts | fület, szület, őrület |
| `rtén` | 2.09x | 42 contexts | örtény, értény, kurtén |
| `örté` | 1.85x | 64 contexts | törté, örtény, körték |

### 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 |
|--------|--------|-----------|----------|
| `-k` | `-t` | 115 words | közéletét, kansast |
| `-k` | `-k` | 112 words | kreatívnak, kiújulnak |
| `-s` | `-l` | 101 words | szúfizmussal, szinkronstábbal |
| `-s` | `-k` | 99 words | sírkamrájuk, szülővárosnak |
| `-s` | `-t` | 95 words | szakmáikat, shiflett |
| `-m` | `-k` | 86 words | mellékérték, maffiacsoportok |
| `-k` | `-l` | 83 words | középjel, krízisekkel |
| `-s` | `-n` | 81 words | szövegírásban, spalatóban |
| `-k` | `-n` | 76 words | kihalásában, konstruktiven |
| `-k` | `-a` | 72 words | korongcsiga, kaparinthatja |

### 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 |
|------|-----------------|------------|------|
| vercruysse | **`vercruys-s-e`** | 7.5 | `s` |
| szocialta | **`szoci-al-ta`** | 7.5 | `al` |
| stílusbanaz | **`stílusban-a-z`** | 7.5 | `a` |
| részvényeiket | **`részvényei-k-et`** | 7.5 | `k` |
| hátoldalra | **`hátold-al-ra`** | 7.5 | `al` |
| fullernek | **`fuller-n-ek`** | 7.5 | `n` |
| nézhetőnek | **`nézhető-n-ek`** | 7.5 | `n` |
| napjainkbeli | **`napjainkb-el-i`** | 7.5 | `el` |
| gyarmataikra | **`gyarmatai-k-ra`** | 7.5 | `k` |
| mandülion | **`mandül-i-on`** | 7.5 | `i` |
| robotterheit | **`robotterhe-i-t`** | 7.5 | `i` |
| albuginea | **`albugin-e-a`** | 7.5 | `e` |
| elnagyoltak | **`elnagyol-t-ak`** | 7.5 | `t` |
| minőségileg | **`minőségil-e-g`** | 7.5 | `e` |
| szárnyacskák | **`szárnyacs-k-ák`** | 7.5 | `k` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language Hungarian 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 (4.66x) |
| N-gram | **2-gram** | Lowest perplexity (429) |
| Markov | **Context-4** | Highest predictability (96.0%) |
| 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 21:45:03*