RESEARCH_REPORT.md

# French — Full Ablation Study & Research Report

Detailed evaluation of all model variants trained on **French** 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** | 3.723x | 3.72 | 0.0810% | 7,061,086 |
| **16k** | 4.078x | 4.08 | 0.0887% | 6,446,468 |
| **32k** | 4.368x | 4.37 | 0.0950% | 6,018,653 |
| **64k** | 4.573x 🏆 | 4.57 | 0.0994% | 5,748,614 |

### Tokenization Examples

Below are sample sentences tokenized with each vocabulary size:

**Sample 1:** `Lapon peut désigner : les Samis ; les langues sames ; Lapon, une ville du Soudan...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+27 more)` | 37 |
| 16k | `▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+27 more)` | 37 |
| 32k | `▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+26 more)` | 36 |
| 64k | `▁lap on ▁peut ▁désigner ▁: ▁les ▁sam is ▁; ▁les ... (+25 more)` | 35 |

**Sample 2:** `Le pentadécane est un alcane linéaire de formule brute . Il possède 4 347 isomèr...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁le ▁pent ad éc ane ▁est ▁un ▁al c ane ... (+27 more)` | 37 |
| 16k | `▁le ▁pent ad éc ane ▁est ▁un ▁alc ane ▁linéaire ... (+22 more)` | 32 |
| 32k | `▁le ▁pent ad éc ane ▁est ▁un ▁alc ane ▁linéaire ... (+20 more)` | 30 |
| 64k | `▁le ▁pent ad éc ane ▁est ▁un ▁alcane ▁linéaire ▁de ... (+18 more)` | 28 |

**Sample 3:** `L'eicosane est un alcane linéaire de formule brute . Il possède isomères structu...`

| Vocab | Tokens | Count |
|-------|--------|-------|
| 8k | `▁l ' e ic os ane ▁est ▁un ▁al c ... (+22 more)` | 32 |
| 16k | `▁l ' e icos ane ▁est ▁un ▁alc ane ▁linéaire ... (+16 more)` | 26 |
| 32k | `▁l ' e icos ane ▁est ▁un ▁alc ane ▁linéaire ... (+14 more)` | 24 |
| 64k | `▁l ' e icos ane ▁est ▁un ▁alcane ▁linéaire ▁de ... (+12 more)` | 22 |


### Key Findings

- **Best Compression:** 64k achieves 4.573x compression
- **Lowest UNK Rate:** 8k with 0.0810% 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 | 197,170 | 17.59 | 5,674,755 | 9.3% | 21.3% |
| **2-gram** | Subword | 251 🏆 | 7.97 | 40,333 | 68.1% | 99.4% |
| **3-gram** | Word | 1,815,223 | 20.79 | 18,029,220 | 2.4% | 9.5% |
| **3-gram** | Subword | 1,988 | 10.96 | 269,239 | 30.3% | 73.7% |
| **4-gram** | Word | 5,518,864 | 22.40 | 36,868,834 | 1.8% | 8.6% |
| **4-gram** | Subword | 11,120 | 13.44 | 1,563,238 | 15.8% | 42.2% |
| **5-gram** | Word | 4,103,331 | 21.97 | 28,227,926 | 2.4% | 11.6% |
| **5-gram** | Subword | 46,850 | 15.52 | 5,742,636 | 8.7% | 25.7% |

### Top 5 N-grams by Size

**2-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la` | 5,296,650 |
| 2 | `de l` | 3,236,403 |
| 3 | `à la` | 1,514,334 |
| 4 | `à l` | 1,261,623 |
| 5 | `dans le` | 992,683 |

**3-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `de la commune` | 330,769 |
| 2 | `notes et références` | 310,459 |
| 3 | `occupation des sols` | 189,915 |
| 4 | `et de la` | 154,877 |
| 5 | `le nom de` | 144,766 |

**4-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `l occupation des sols` | 124,755 |
| 2 | `occupation des sols de` | 93,658 |
| 3 | `des sols de la` | 93,553 |
| 4 | `sols de la commune` | 93,442 |
| 5 | `notes et références voir` | 79,475 |

**5-grams (Word):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `occupation des sols de la` | 93,478 |
| 2 | `des sols de la commune` | 93,402 |
| 3 | `l occupation des sols de` | 93,364 |
| 4 | `notes et références voir aussi` | 79,373 |
| 5 | `notes et références liens externes` | 68,549 |

**2-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `e _` | 125,785,698 |
| 2 | `s _` | 74,291,364 |
| 3 | `_ d` | 73,439,085 |
| 4 | `_ l` | 55,706,551 |
| 5 | `e s` | 54,301,349 |

**3-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e` | 41,554,921 |
| 2 | `e s _` | 37,119,081 |
| 3 | `d e _` | 32,944,492 |
| 4 | `e _ d` | 22,149,546 |
| 5 | `l e _` | 20,731,208 |

**4-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _` | 30,047,475 |
| 2 | `_ l a _` | 16,205,522 |
| 3 | `e _ d e` | 12,867,124 |
| 4 | `_ l e _` | 11,621,670 |
| 5 | `_ e t _` | 11,489,728 |

**5-grams (Subword):**

| Rank | N-gram | Count |
|------|--------|-------|
| 1 | `_ d e _ l` | 9,678,287 |
| 2 | `e _ d e _` | 9,546,481 |
| 3 | `_ d e s _` | 7,709,198 |
| 4 | `_ l e s _` | 7,167,363 |
| 5 | `e _ l a _` | 6,536,044 |


### Key Findings

- **Best Perplexity:** 2-gram (subword) with 251
- **Entropy Trend:** Decreases with larger n-grams (more predictable)
- **Coverage:** Top-1000 patterns cover ~26% 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 | 0.9052 | 1.873 | 14.72 | 3,729,596 | 9.5% |
| **1** | Subword | 1.2049 | 2.305 | 9.45 | 20,472 | 0.0% |
| **2** | Word | 0.4648 | 1.380 | 3.15 | 54,852,526 | 53.5% |
| **2** | Subword | 0.6045 | 1.520 | 3.87 | 193,340 | 39.6% |
| **3** | Word | 0.2551 | 1.193 | 1.71 | 172,431,097 | 74.5% |
| **3** | Subword | 0.6357 | 1.554 | 3.88 | 747,541 | 36.4% |
| **4** | Word | 0.1275 🏆 | 1.092 | 1.26 | 294,675,620 | 87.3% |
| **4** | Subword | 0.6602 | 1.580 | 3.61 | 2,901,861 | 34.0% |

### Generated Text Samples (Word-based)

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

**Context Size 1:**

1. `de titan éditions plon 424 p haffner inventaire de paris occupation des modèles différents les début...`
2. `la haine féroce le bon pasteur afro américaine par la saison régulière se basent sur le`
3. `le sprinteur britannique de l insigne homologué au rat dû à l ambitieux antipater d apel`

**Context Size 2:**

1. `de la légion d honneur fleurs chapelle de la mer alt gauche vignette cimetière protestant de maulbro...`
2. `de l œuvre est un dessinateur et peintre ses tableaux de derain h 10 min 50 s`
3. `à la fin du la classe 1 avec un chevalet en butée dans ces moments là le`

**Context Size 3:**

1. `de la commune est de 325 soit un indicateur de concentration d emploi de 85 2 la répartition`
2. `notes et références liens externes sud coréen sorti en d aventure américain d aventure américain met...`
3. `occupation des sols center carte des infrastructures et de l électromagnétisme universel de vitalité...`

**Context Size 4:**

1. `l occupation des sols carte des infrastructures et de l occupation des sols de la commune telle qu e...`
2. `occupation des sols de la commune telle qu elle ressort de la base de données européenne d occupatio...`
3. `des sols de la commune en clc risques majeurs le territoire de la commune durant quinze ans christop...`


### Generated Text Samples (Subword-based)

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

**Context Size 1:**

1. `_partene_doy_e_s`
2. `e_larit_dus_iome`
3. `avide_cèsouéoù_c`

**Context Size 2:**

1. `e_jam_à_les_du_de`
2. `s_thé_ilite_la_wa`
3. `_de_sa_comist_est`

**Context Size 3:**

1. `_de_prementrest_un`
2. `es_non_de_balling_`
3. `de_canadieurs_la_p`

**Context Size 4:**

1. `_de_saxe,_le_cumulu`
2. `_la_capitalie._8_si`
3. `e_de_de_fumer_l'éco`


### Key Findings

- **Best Predictability:** Context-4 (word) with 87.3% predictability
- **Branching Factor:** Decreases with context size (more deterministic)
- **Memory Trade-off:** Larger contexts require more storage (2,901,861 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 | 1,519,124 |
| Total Tokens | 496,742,137 |
| Mean Frequency | 326.99 |
| Median Frequency | 4 |
| Frequency Std Dev | 37954.61 |

### Most Common Words

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | de | 30,301,637 |
| 2 | la | 16,417,649 |
| 3 | le | 11,875,190 |
| 4 | et | 11,702,997 |
| 5 | l | 10,150,468 |
| 6 | en | 9,437,564 |
| 7 | à | 9,348,887 |
| 8 | des | 7,741,717 |
| 9 | d | 7,508,960 |
| 10 | les | 7,283,372 |

### Least Common Words (from vocabulary)

| Rank | Word | Frequency |
|------|------|-----------|
| 1 | caracallæ | 2 |
| 2 | santapaulina | 2 |
| 3 | publinf | 2 |
| 4 | vijñānabhairava | 2 |
| 5 | benbor | 2 |
| 6 | kunpan | 2 |
| 7 | moderndrawings | 2 |
| 8 | jexiste | 2 |
| 9 | ⴰⵣⵎⵎⵓⵔ | 2 |
| 10 | pseudocarcinus | 2 |

### Zipf's Law Analysis

| Metric | Value |
|--------|-------|
| Zipf Coefficient | 1.0347 |
| R² (Goodness of Fit) | 0.992664 |
| Adherence Quality | **excellent** |

### Coverage Analysis

| Top N Words | Coverage |
|-------------|----------|
| Top 100 | 44.8% |
| Top 1,000 | 63.9% |
| Top 5,000 | 79.7% |
| Top 10,000 | 85.5% |

### Key Findings

- **Zipf Compliance:** R²=0.9927 indicates excellent adherence to Zipf's law
- **High Frequency Dominance:** Top 100 words cover 44.8% of corpus
- **Long Tail:** 1,509,124 words needed for remaining 14.5% 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 | 0.7808 🏆 | 0.3764 | N/A | N/A |
| **mono_64d** | 64 | 0.7574 | 0.3033 | N/A | N/A |
| **mono_128d** | 128 | 0.6995 | 0.2569 | N/A | N/A |
| **aligned_32d** | 32 | 0.7808 | 0.3878 | 0.4820 | 0.8240 |
| **aligned_64d** | 64 | 0.7574 | 0.3079 | 0.7080 | 0.9420 |
| **aligned_128d** | 128 | 0.6995 | 0.2657 | 0.8120 | 0.9680 |

### Key Findings

- **Best Isotropy:** mono_32d with 0.7808 (more uniform distribution)
- **Semantic Density:** Average pairwise similarity of 0.3163. Lower values indicate better semantic separation.
- **Alignment Quality:** Aligned models achieve up to 81.2% 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 | **-0.550** | 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` | altschloss, aën, alfège |
| `-s` | similairesselon, shochugeiko, sodapop |
| `-c` | cugn, crocefisso, colomer |
| `-m` | maracanaú, mandriole, morzine |
| `-ma` | maracanaú, mandriole, mastaï |
| `-d` | drăculeștibasarab, déchirent, durégnatons |
| `-p` | pame, pichery, pleased |
| `-b` | bingoto, blennies, brusuglio |

#### Productive Suffixes
| Suffix | Examples |
|--------|----------|
| `-e` | pame, mandriole, morzine |
| `-s` | altschloss, blennies, durégnatons |
| `-es` | blennies, moyensles, fraternelles |
| `-n` | cugn, similairesselon, fransson |
| `-a` | occasionna, exea, paçoca |
| `-t` | déchirent, lovefist, crabbet |
| `-r` | colomer, elvir, eckersbacher |
| `-i` | wubi, idiomorphini, oroi |

### 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 |
|------|----------|------------------|----------|
| `ient` | 2.44x | 382 contexts | nient, fient, rient |
| `aphi` | 2.02x | 140 contexts | aphis, aphia, aphid |
| `ienn` | 1.59x | 391 contexts | ienne, vienn, fienne |
| `ogra` | 1.62x | 276 contexts | logra, bogra, fogra |
| `éren` | 1.81x | 150 contexts | héren, kéren, érenn |
| `ontr` | 1.59x | 266 contexts | montr, ontra, kontr |
| `tiqu` | 1.49x | 318 contexts | tiqui, tique, tiqué |
| `aiso` | 1.66x | 172 contexts | baiso, gaiso, daiso |
| `utre` | 1.56x | 215 contexts | butre, outre, autre |
| `niqu` | 1.42x | 248 contexts | nique, niqué, niqua |
| `rtic` | 1.44x | 179 contexts | artic, hrtica, artici |
| `onal` | 1.50x | 136 contexts | conal, monal, sonal |

### 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` | `-s` | 143 words | couleuses, cammaerts |
| `-m` | `-s` | 137 words | morians, merckens |
| `-c` | `-e` | 121 words | clémentine, classessite |
| `-p` | `-s` | 115 words | pétards, psylles |
| `-a` | `-s` | 114 words | alvaros, aldrinus |
| `-s` | `-s` | 107 words | sportpaleis, shaggys |
| `-p` | `-e` | 105 words | pédagogique, poursuiveuse |
| `-m` | `-e` | 102 words | maastrichtle, martinofiministre |
| `-a` | `-e` | 95 words | alboize, autoparodie |
| `-s` | `-e` | 92 words | salicyline, studiesthe |

### 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 |
|------|-----------------|------------|------|
| sarrabeyrouse | **`sarrabeyrou-s-e`** | 7.5 | `s` |
| grippement | **`grippem-e-nt`** | 7.5 | `e` |
| égalementsite | **`égalements-i-te`** | 7.5 | `i` |
| rediviser | **`redivi-s-er`** | 7.5 | `s` |
| ambrosini | **`ambrosi-n-i`** | 7.5 | `n` |
| rencontrerai | **`rencontrer-a-i`** | 7.5 | `a` |
| détroitsaison | **`détroitsai-s-on`** | 7.5 | `s` |
| monpalais | **`monpal-a-is`** | 7.5 | `a` |
| vieumaison | **`vieumai-s-on`** | 7.5 | `s` |
| caractéristise | **`caractéristi-s-e`** | 7.5 | `s` |
| circonvient | **`circonvi-e-nt`** | 7.5 | `e` |
| tilehurst | **`tilehur-s-t`** | 7.5 | `s` |
| chongsheng | **`chongsh-e-ng`** | 7.5 | `e` |
| bloemfontein | **`bloemfont-e-in`** | 7.5 | `e` |
| voorspoel | **`voorspo-e-l`** | 7.5 | `e` |

### 6.6 Linguistic Interpretation

> **Automated Insight:**
The language French 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 (4.57x) |
| N-gram | **2-gram** | Lowest perplexity (251) |
| Markov | **Context-4** | Highest predictability (87.3%) |
| 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 09:31:27*