Refactor: Simplify PCA implementation and improve visualization

[leonvanbokhorst]

• Simplified PCA implementation by initializing and fitting PCA for each number of components within the loop.
• Removed redundant transformations and reconstruction steps, enhancing code clarity.
• Updated comments for better understanding of the PCA process and its visualization.
• Improved the display of reconstructed images and compression ratios.

Summary by Sourcery

Simplify the PCA implementation by initializing and fitting PCA for each number of components within the loop, removing redundant steps. Update comments for clarity. Add a new transformer-based addition learning model as an educational example, demonstrating the application of attention mechanisms to arithmetic operations.

Enhancements:

• Simplified the PCA implementation by initializing and fitting PCA for each number of components within the loop, removing redundant transformations and reconstruction steps.

Documentation:

• Updated comments for better understanding of the PCA process and its visualization.

[sourcery-ai]

Reviewer's Guide by Sourcery

The PR introduces two main changes: a simplification of the PCA implementation in the MNIST example and the addition of a new transformer-based model for learning arithmetic operations. The PCA changes focus on code clarity and efficiency by removing redundant steps, while the new transformer implementation provides a comprehensive example of using attention mechanisms for mathematical operations.

Sequence diagram for PCA compression process

sequenceDiagram
    participant User
    participant PCA
    User->>PCA: Initialize PCA with n_components
    User->>PCA: Fit and transform data
    PCA-->>User: Transformed data
    User->>PCA: Inverse transform data
    PCA-->>User: Reconstructed image
    Note right of User: Repeats for each n_components in list

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Class diagram for the AdditionTransformer and PositionalEncoding

classDiagram
    class PositionalEncoding {
        +PositionalEncoding(int d_model, int max_len=1000)
        +forward(Tensor x) Tensor
        pe: Tensor
    }
    class AdditionTransformer {
        +AdditionTransformer(int vocab_size=12, int d_model=128, int nhead=8, int num_layers=4, int max_len=20, float dropout=0.1)
        +forward(Tensor src) Tensor
        embedding: nn.Embedding
        pos_encoder: PositionalEncoding
        dropout: nn.Dropout
        transformer_encoder: nn.TransformerEncoder
        decoder: nn.Sequential
    }
    PositionalEncoding --> AdditionTransformer

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File-Level Changes

Change	Details	Files
Simplified PCA implementation for MNIST digit compression	Removed pre-initialization of PCA with maximum components Eliminated redundant data transformation steps Simplified image reconstruction process using inverse_transform Updated comments for better clarity	pocs/pca_minst.py
Added new transformer-based model for learning addition operations	Implemented PositionalEncoding class for sequence position information Created AdditionTransformer class with multi-head attention mechanism Added data generation utilities for addition problems Implemented training and testing functions with example usage Added comprehensive documentation and historical context	pocs/transf.py

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[sourcery-ai]

Hey @leonvanbokhorst - I've reviewed your changes - here's some feedback:

Overall Comments:

• Please update the PR title to be more descriptive of the changes (e.g., 'Simplify PCA implementation and add transformer-based addition learning model')

Here's what I looked at during the review

• 🟡 General issues: 1 issue found
• 🟢 Security: all looks good
• 🟢 Testing: all looks good
• 🟢 Complexity: all looks good
• 🟢 Documentation: all looks good

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